PerturbedStepSolution¶

class probnum.diffeq.perturbed.step.PerturbedStepSolution(scales, locations, states, interpolants)[source]¶

Bases: ODESolution

Probabilistic ODE solution corresponding to the PerturbedStepSolver.

Attributes Summary

`frozen`	Whether the posterior is frozen.
`locations`	Locations of the states of the posterior.
`states`	States of the posterior.

Methods Summary

`__call__`(t)	Evaluate the time-continuous posterior at location t
`append`(location, state)	Append a state to the posterior.
`freeze`()	Freeze the posterior.
`interpolate`(t[, previous_index, next_index])	Evaluate the posterior at a measurement-free point.
`sample`(rng[, t, size])	Sample from the ODE solution.
`transform_base_measure_realizations`(...)	Transform base-measure-realizations into posteriors samples.

Attributes Documentation

Parameters:

scales (List[float]) –
locations (ndarray) –
states (_RandomVariableList) –
interpolants (List[DenseOutput]) –

frozen¶: Whether the posterior is frozen.

locations¶: Locations of the states of the posterior.

states¶: States of the posterior.

Methods Documentation

__call__(t)¶

Evaluate the time-continuous posterior at location t

Algorithm: 1. Find closest t_prev and t_next, with t_prev < t < t_next 2. Predict from t_prev to t 3. (if self._with_smoothing=True) Predict from t to t_next 4. (if self._with_smoothing=True) Smooth from t_next to t 5. Return random variable for time t

Parameters:: t (ArrayLike) – Location, or time, at which to evaluate the posterior.
Raises:: ValueError – If time-points are not strictly increasing.
Returns:: Estimate of the states at time t.
Return type:: randvars.RandomVariable or randvars._RandomVariableList

append(location, state)¶

Append a state to the posterior.

Parameters:

location (FloatLike) –
state (RandomVariable) –

Return type:

None

freeze()¶

Freeze the posterior.

Return type:: None

interpolate(t, previous_index=None, next_index=None)[source]¶

Evaluate the posterior at a measurement-free point.

Returns:

Dense evaluation.

Return type:

randvars.RandomVariable or randvars._RandomVariableList

Parameters:

t (float | Real | floating) –
previous_index (float | Real | floating | None) –
next_index (float | Real | floating | None) –

sample(rng, t=None, size=())¶

Sample from the ODE solution.

Parameters:

rng (Generator) – Random number generator.
t (_SupportsArray[dtype] | _NestedSequence[_SupportsArray[dtype]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None) – Location / time at which to sample. If nothing is specified, samples at the ODE-solver grid points are computed. If it is a float, a sample of the ODE-solution at this time point is computed. Similarly, if it is a list of floats (or an array), samples at the specified grid-points are returned. This is not the same as computing i.i.d samples at the respective locations.
size (int | Integral | integer | Iterable[int | Integral | integer] | None) – Number of samples.

Return type:

ndarray

transform_base_measure_realizations(base_measure_realizations, t)¶

Transform base-measure-realizations into posteriors samples.

Parameters:

base_measure_realizations (ndarray) – Base measure realizations.
t (_SupportsArray[dtype] | _NestedSequence[_SupportsArray[dtype]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Locations on which the transformed realizations shall represent realizations from the posterior.

Returns:

Transformed realizations.

Return type:

np.ndarray