IBM¶
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class
probnum.filtsmooth.statespace.
IBM
(ordint, spatialdim, diffconst)[source]¶ Bases:
probnum.filtsmooth.statespace.integrator.Integrator
,probnum.filtsmooth.statespace.sde.LTISDE
Integrated Brownian motion in \(d\) dimensions.
Attributes Summary
Spatial dimension (utility attribute).
Discretised IN THE PRECONDITIONED SPACE.
Methods Summary
discretise
(step)Equivalent discretisation of the process.
proj2coord
(coord)Projection matrix to \(i\) th coordinates.
transition_realization
(real, start, stop, …)Transition a realization of a random variable from time \(t\) to time \(t+\Delta t\).
Applies the transition, assuming that the state is already preconditioned.
transition_rv
(rv, start, stop, **kwargs)Transition a random variable from time \(t\) to time \(t+\Delta t\).
transition_rv_preconditioned
(rv, start, **kwargs)Applies the transition, assuming that the state is already preconditioned.
Attributes Documentation
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dimension
¶ Spatial dimension (utility attribute).
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equivalent_discretisation_preconditioned
¶ Discretised IN THE PRECONDITIONED SPACE.
Methods Documentation
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discretise
(step)[source]¶ Equivalent discretisation of the process.
Overwrites matrix-fraction decomposition in the super-class. Only present for user’s convenience and to maintain a clean interface. Not used for transition_rv, etc..
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proj2coord
(coord)¶ 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))
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transition_realization
(real, start, stop, **kwargs)[source]¶ Transition a realization of a random variable from time \(t\) to time \(t+\Delta t\).
For random variable \(x_t\), it returns the random variable defined by
\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t = r) .\]This is different to
transition_rv()
which computes the parametrization of \(x_{t + \Delta t}\) based on the parametrization of \(x_t\).Nb: Think of transition as a verb, i.e. this method “transitions” a realization of a random variable.
- Parameters
real – Realization of the random variable.
start – Starting point \(t\).
stop – End point \(t + \Delta t\).
step – Intermediate step-size. Optional, default is None.
linearise_at – For approximate transitions , for instance ContinuousEKFComponent, this argument overloads the state at which the Jacobian is computed.
- Returns
RandomVariable – Random variable, describing the state at time \(t + \Delta t\) based on realization at time \(t\).
dict – Additional information in form of a dictionary, for instance the cross-covariance in the prediction step, access to which is useful in smoothing.
See also
transition_rv()
Apply transition to a random variable.
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transition_realization_preconditioned
(real, start, **kwargs)[source]¶ Applies the transition, assuming that the state is already preconditioned.
This is useful for numerically stable implementation of Kalman smoothing steps and Kalman updates.
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transition_rv
(rv, start, stop, **kwargs)[source]¶ Transition a random variable from time \(t\) to time \(t+\Delta t\).
For random variable \(x_t\), it returns the random variable defined by
\[x_{t + \Delta t} \sim p(x_{t + \Delta t} | x_t) .\]This returns a random variable where the parametrization depends on the paramtrization of \(x_t\). This is different to
transition_rv()
which computes the parametrization of \(x_{t + \Delta t}\) based on a realization of \(x_t\).Nb: Think of transition as a verb, i.e. this method “transitions” a random variable.
- Parameters
rv – Realization of the random variable.
start – Starting point \(t\).
stop – End point \(t + \Delta t\).
step – Intermediate step-size. Optional, default is None.
linearise_at – For approximate transitions , for instance ContinuousEKFComponent, this argument overloads the state at which the Jacobian is computed.
- Returns
RandomVariable – Random variable, describing the state at time \(t + \Delta t\) based on realization at time \(t\).
dict – Additional information in form of a dictionary, for instance the cross-covariance in the prediction step, access to which is useful in smoothing.
See also
transition_realization()
Apply transition to a realization of a random variable.
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