mappy_ds.Map.image_detail

abstractmethod Map.image_detail(y0, params=None, n=1, *, jacobian=True, hessian=False, trajectory=False, parameter_jacobian=False, parameter_hessian=False)

Compute the n-th image of y0 with derivatives.

Parameters:

y0array_like

Initial state.

paramsmapping, optional

Parameters of the system.

nint, optional

Number of iterations of the map, by default 1.

jacobianbool, optional

Compute the Jacobian matrix, by default True.

hessianbool, optional

Compute the Hessian tensor (implies jacobian), by default False.

trajectorybool, optional

Record the trajectory, by default False.

parameter_jacobianbool, optional

Compute the derivative with respect to every parameter in param_keys (implies jacobian), by default False.

parameter_hessianbool, optional

Compute the mixed second derivative hes_p (implies hessian and parameter_jacobian), by default False.

Returns:

MapResult

Notes

Requesting derivatives integrates the variational equations together with the state, which changes the adaptive step sizes of the ODE solver. The image therefore differs slightly (on the order of the solver tolerance) from the one obtained with jacobian=False.