choreo.segm.ODE.ImplicitSymplecticIVP#
- ImplicitSymplecticIVP()#
Implicit symplectic integration of a partitionned initial value problem.
Follows closely the implementation tips detailled in chapter VIII of [1]
- Cited:
- Parameters:
fun (
callable
orscipy.LowLevelCallable
) – Function defining the IVP.gun (
callable
orscipy.LowLevelCallable
) – Function defining the IVP.t_span (
tuple
(numpy.float64
,numpy.float64
)) – Initial and final time of integration.xo (
numpy.ndarray
(shape = (n), dtype = np.float64)
, optional) – Initial value for x. Overriden by reg_xo if provided. By default,None
.vo (
numpy.ndarray
(shape = (n), dtype = np.float64)
, optional) – Initial value for v. Overriden by reg_xo if provided. By default,None
.rk_x (
ImplicitRKTable
, optional) – Runge-Kutta tables for the integration of the IVP. By default,choreo.segm.multiprec_tables.ComputeImplicitRKTable()
.rk_v (
ImplicitRKTable
, optional) – Runge-Kutta tables for the integration of the IVP. By default,choreo.segm.multiprec_tables.ComputeImplicitRKTable()
.vector_calls (
bool
, optional) – Whether to call functions on multiple inputs at once or not, by defaultFalse
.grad_fun (
callable
orscipy.LowLevelCallable
, optional) – Gradient of the function defining the IVP, by defaultNone
.grad_gun (
callable
orscipy.LowLevelCallable
, optional) – Gradient of the function defining the IVP, by defaultNone
.nint (
int
, optional) – Number of integration steps, by default1
.keep_freq (
int
, optional) – Number of integration steps to be taken before saving output, by default-1
.reg_xo (
numpy.ndarray
(shape = (nreg, n), dtype = np.float64)
) – Array of initial values for x for regular reset.reg_vo (
numpy.ndarray
(shape = (nreg, n), dtype = np.float64)
) – Array of initial values for v for regular reset.reg_init_freq (
int
, optional) – Number of timesteps before resetting initial values for x and v. Non-positive values disable the reset, by default-1
.keep_init (
bool
, optional) – Whether to save the initial values, by defaultFalse
.DoEFT (
bool
, optional) – Whether to use an error-free transformation for summation, by defaultTrue
.eps (
numpy:numpy.float64
, optional) – Tolerence on the error of each implicit problem, by defaultnp.finfo(np.float64).eps
.maxiter (
int
, optional) – Maximum number of iterations to solve each implicit problem, by default50
.
- Returns:
Arrays containing the computed approximation of the solution to the IVP at evaluation points.
- Return type:
tuple
ofnumpy.ndarray
.