IntegratorTransition¶

class probnum.randprocs.markov.integrator.IntegratorTransition(num_derivatives, wiener_process_dimension)¶

Bases: object

Transitions for integrator processes.

An integrator is a special kind of random process that models a stack of a state and its first \(\nu\) time-derivatives. For instances, this includes integrated Wiener processes or Matern processes.

In ProbNum, integrators are always driven by \(d\) dimensional Wiener processes. We compute the transitions usually in a preconditioned state (Nordsieck-like coordinates).

Attributes Summary

`num_derivatives`
`precon`
`wiener_process_dimension`

Methods Summary

proj2coord(coord)

Projection matrix to \(i\) th coordinates.

Attributes Documentation

num_derivatives¶

precon¶

wiener_process_dimension¶

Methods Documentation

proj2coord(coord)[source]¶

Projection matrix to \(i\) th coordinates.

Computes the matrix

\[H_i = \left[ I_d \otimes e_i \right] P^{-1},\]

where \(e_i\) is the \(i\) th unit vector, that projects to the \(i\) th coordinate of a vector. If the ODE is multidimensional, it projects to each of the \(i\) th coordinates of each ODE dimension.

Parameters: coord (int) – Coordinate index \(i\) which to project to. Expected to be in range \(0 \leq i \leq q + 1\).
Returns: Projection matrix \(H_i\).
Return type: np.ndarray, shape=(d, d*(q+1))