DiscreteGaussianModel

class probnum.filtsmooth.DiscreteGaussianModel(dynafct, diffmatfct, jacfct=None)

Bases: probnum.filtsmooth.DiscreteModel

Discrete Gauss-Markov models of the form x_{i+1} = N(g(t_i, x_i), S(t_i)),

Notes

g : dynamics x : state S : diffusion matrix

Attributes Summary

ndim

Methods Summary

diffusionmatrix(time, **kwargs) Evaluate S(t_i)
dynamics(time, state, **kwargs) Evaluate g(t_i, x_i).
jacobian(time, state, **kwargs) Evaluate Jacobian, d_x g(t_i, x_i), of g(t_i, x_i) w.r.t.
pdf(loc, time, state, **kwargs) Evaluates “future” pdf p(x_t | x_s) at loc.
sample(time, state, **kwargs) Samples x_{t} ~ p(x_{t} | x_{s}) as a function of t and x_s (plus additional parameters).

Attributes Documentation

ndim

Methods Documentation

diffusionmatrix(time, **kwargs)[source]

Evaluate S(t_i)

dynamics(time, state, **kwargs)[source]

Evaluate g(t_i, x_i).

jacobian(time, state, **kwargs)[source]

Evaluate Jacobian, d_x g(t_i, x_i), of g(t_i, x_i) w.r.t. x_i.

pdf(loc, time, state, **kwargs)[source]

Evaluates “future” pdf p(x_t | x_s) at loc.

sample(time, state, **kwargs)[source]

Samples x_{t} ~ p(x_{t} | x_{s}) as a function of t and x_s (plus additional parameters).

In a discrete system, i.e. t = s + 1, s in mathbb{N}

In an ODE solver setting, one of the additional parameters would be the step size.