Return a vectorised numerically-integrated function.

Decorator that will numerically integrate an ODE and return a callable that is vectorised. The integration will start from t=0. You must specify the y-value at that starting point. You may optionally specify additional “fixed points” which should fall along the curve at chosen t-values. If someone requests a result at this position, the fixed-point will be returned instead. This can be useful if you need to enforce the end-point of a curve to within a very high level of precision.

Parameters:¶

start: numpy.typing.ArrayLike¶

The starting point for the integration

scale: float = 1.0¶

By default the integration will be performed between 0 and 1, but you can increase or decrease it by a factor of scale

fixed_points: dict[float, numpy.typing.ArrayLike] = {}¶

Keys are values of the integration variable at which the solution is assumed to be the corresponding value in the dictionary. Useful to make sure end-points are respected exactly.

rtol: float = 1e-12¶

Relative tolerance to use for the integration.

atol: float = 1e-14¶

Absolute tolerance to use for hte integration.

vectorize_integrand_calls: bool = True¶

Whether calls to the integrand can be done in a vectorised manner.

event_generator: Callable[[float], Callable[[float, numpy.typing.NDArray], float]] | None = None¶

If present, will use this function to create events that indicate when the integration has reached one of the t_eval points.

Returns:¶

A decorator that will take an integrand a return a function that is the solution of the ODE.

Return type:¶

Callable[[Integrand], IntegratedFunction]