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

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))