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DP54 Integrator

Dormand-Prince 5(4) adaptive integrator with FSAL optimization.

DP54Integrator 

DP54Integrator(dimension: int, dynamics_fn: callable, jacobian: Union[DAnalyticJacobian, DNumericalJacobian] = None, sensitivity: Any = None, control_fn: Any = None, config: IntegratorConfig = None)

Dormand-Prince 5(4) adaptive integrator (MATLAB's ode45).

More efficient than RKF45 due to FSAL (First Same As Last) property. This is the industry-standard general-purpose adaptive integrator.

Parameters:

Name Type Description Default
dimension int

State vector dimension

 required
dynamics_fn callable

Dynamics function with signature (t: float, state: ndarray) -> ndarray

 required
jacobian DAnalyticJacobian or DNumericalJacobian

Jacobian provider for variational matrix propagation

 None
config IntegratorConfig

Integration configuration

 None
Example 
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import brahe as bh
import numpy as np

def dynamics(t, state):
    return -state

config = bh.IntegratorConfig.adaptive(abs_tol=1e-9, rel_tol=1e-6)
integrator = bh.DP54Integrator(dimension=1, dynamics_fn=dynamics, config=config)

# Adaptive step (tolerances from config)
result = integrator.step(0.0, np.array([1.0]), 0.1)

Initialize instance.

dimension property 

dimension: Any

step method descriptor 

step(t: float, state: ndarray, dt: float) -> AdaptiveStepResult

Perform one adaptive integration step.

Tolerances are read from the integrator's configuration.

Parameters:

Name Type Description Default
t float

Current time

 required
state ndarray

State vector at time t

 required
dt float

Requested timestep

 required

Returns:

Name Type Description
AdaptiveStepResult AdaptiveStepResult

Result containing new state, actual dt used, error estimate, and suggested next dt

step_with_sensmat method descriptor 

step_with_sensmat(t: float, state: ndarray, sens: ndarray, params: ndarray, dt: float) -> Tuple

Advance state and sensitivity matrix with adaptive step control.

Propagates the sensitivity matrix S that maps parameter uncertainties to state uncertainties. The sensitivity evolves according to dS/dt = A*S + B.

Parameters:

Name Type Description Default
t float

Current time

 required
state ndarray

State vector at time t

 required
sens ndarray

Sensitivity matrix at time t (state_dim x param_dim)

 required
params ndarray

Parameter vector

 required
dt float

Requested timestep

 required

Returns:

Name Type Description
tuple Tuple

(new_state, new_sensitivity, dt_used, error_estimate, dt_next)
Example 
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import brahe as bh
import numpy as np

# Setup integrator with Jacobian and sensitivity providers
config = bh.IntegratorConfig.adaptive(abs_tol=1e-9, rel_tol=1e-6)
integrator = bh.DP54Integrator(6, dynamics, jacobian, sensitivity, config)
state = np.array([...])
sens = np.zeros((6, 2))  # 6 state dims, 2 params
params = np.array([1.0, 2.0])

new_state, new_sens, dt_used, error, dt_next = integrator.step_with_sensmat(
    0.0, state, sens, params, 1.0
)

step_with_varmat method descriptor 

step_with_varmat(t: float, state: ndarray, phi: ndarray, dt: float) -> Tuple

Perform one adaptive integration step with variational matrix.

Tolerances are read from the integrator's configuration.

Parameters:

Name Type Description Default
t float

Current time

 required
state ndarray

State vector at time t

 required
phi ndarray

State transition matrix (dimension x dimension)

 required
dt float

Requested timestep

 required

Returns:

Name Type Description
tuple Tuple

(new_state, new_phi, dt_used, error_estimate, dt_next)

step_with_varmat_sensmat method descriptor 

step_with_varmat_sensmat(t: float, state: ndarray, phi: ndarray, sens: ndarray, params: ndarray, dt: float) -> Tuple

Advance state, variational matrix (STM), and sensitivity matrix with adaptive step control.

Propagates both matrices simultaneously for complete uncertainty quantification: - STM (Phi): Maps initial state uncertainties to current state uncertainties - Sensitivity (S): Maps parameter uncertainties to state uncertainties

Parameters:

Name Type Description Default
t float

Current time

 required
state ndarray

State vector at time t

 required
phi ndarray

State transition matrix at time t (state_dim x state_dim)

 required
sens ndarray

Sensitivity matrix at time t (state_dim x param_dim)

 required
params ndarray

Parameter vector

 required
dt float

Requested timestep

 required

Returns:

Name Type Description
tuple Tuple

(new_state, new_phi, new_sensitivity, dt_used, error_estimate, dt_next)
Example 
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import brahe as bh
import numpy as np

# Setup integrator with Jacobian and sensitivity providers
config = bh.IntegratorConfig.adaptive(abs_tol=1e-9, rel_tol=1e-6)
integrator = bh.DP54Integrator(6, dynamics, jacobian, sensitivity, config)
state = np.array([...])
phi = np.eye(6)
sens = np.zeros((6, 2))  # 6 state dims, 2 params
params = np.array([1.0, 2.0])

new_state, new_phi, new_sens, dt_used, error, dt_next = integrator.step_with_varmat_sensmat(
    0.0, state, phi, sens, params, 1.0
)

See Also