dynax.evolution

Classes for simulating the evolution of dynamical systems over time.

Classes

`AbstractEvolution`(system)	Abstract base-class for evolutions.
`Flow`(system[, solver, stepsize_controller])	Evolution for continous-time dynamical systems.
`Map`(system)	Evolution for discrete-time dynamical systems.

class dynax.evolution.AbstractEvolution(system)[source]

Bases: Module

Abstract base-class for evolutions.

Evolutions combine dynamical systems with a solver. They simulate the evolution of the system state and output over time given an initial and, possibly, an input sequence.

abstractmethod __call__(t, u, initial_state)[source]

Evolve an initial state along the vector field and compute output.

Parameters:

t (Array) – Times at which to evaluate the evolution.
u (Array | None) – Optional input sequence of same length.
initial_state (Array | None) – Optional, fixed initial state used instead of AbstractSystem.initial_state.

Returns:

tuple[Array, Array] – Tuple (x, y) of state and output sequences.

class dynax.evolution.Flow(system, solver=<factory>, stepsize_controller=<factory>)[source]

Bases: AbstractEvolution

Evolution for continous-time dynamical systems.

Parameters:

system (AbstractSystem) – Dynamical system.
solver (AbstractAdaptiveSolver) – Differential equation solver. Defaults to diffrax.Dopri5.
stepsize_controller (AbstractStepSizeController) – Stepsize controller. Defaults to diffrax.ConstantStepSize.

__call__(t, u=None, initial_state=None, *, ufun=None, ucoeffs=None, **diffeqsolve_kwargs)[source]

Evolve an initial state along the vector field and compute output.

Parameters:

t (ArrayLike) – Times at which to evaluate the evolution.
u (ArrayLike | None) – Optional input sequence of same length.
initial_state (ArrayLike | None) – Optional, fixed initial state used instead of AbstractSystem.initial_state.
ufun (Callable[[float], Array] | None) – A function \(t \mapsto u\). Can be used instead of u or ucoeffs.
ucoeffs (tuple[PyTree, PyTree, PyTree, PyTree] | None) – Precomputed spline coefficients of the input passed to diffrax.CubicInterpolation. Can be used instead of u or ufun.
**diffeqsolve_kwargs – Additional arguments passed to diffrax.diffeqsolve().

Returns:

tuple[Array, Array] – Tuple (x, y) of state and output sequences.

class dynax.evolution.Map(system)[source]

Bases: AbstractEvolution

Evolution for discrete-time dynamical systems.

Parameters:: system (AbstractSystem) – Dynamical system.

__call__(t=None, u=None, initial_state=None, *, num_steps=None)[source]

Evolve an initial state along the vector field and compute output.

Parameters:

t (ArrayLike | None) – Times at which to evaluate the evolution.
u (ArrayLike | None) – Optional input sequence of same length.
initial_state (ArrayLike | None) – Optional, fixed initial state used instead of AbstractSystem.initial_state.
num_steps (int | None) – Number of steps to compute if t and u are not specified.

Returns:

tuple[Array, Array] – Tuple (x, y) of state and output sequences.