# probnum.statespace¶

Probabilistic State Space Models.

This package implements components of continuous-discrete and discrete-discrete state space models, which are the basis for Bayesian filtering and smoothing, but also for probabilistic ODE solvers.

## Functions¶

 matrix_fraction_decomposition(driftmat, …) Matrix fraction decomposition (assuming no force). generate_samples(dynmod, measmod, initrv, times) Samples true states and observations at pre-determined timesteps “times” for a state space model. condition_state_on_measurement(measurement, …) condition_state_on_rv(attained_rv, …)

## Classes¶

 Transition(input_dim, output_dim) Interface for Markov transitions in discrete and continuous time. SDE(dimension, driftfun, dispmatfun, jacobfun) Stochastic differential equation. LinearSDE(dimension, driftmatfun, …[, …]) Linear stochastic differential equation (SDE), LTISDE(driftmat, forcevec, dispmat[, …]) Linear time-invariant continuous Markov models of the form. Integrator(ordint, spatialdim) An integrator is a special kind of SDE, where the $$i$$ th coordinate models the $$i$$ th derivative. IBM(ordint, spatialdim[, …]) Integrated Brownian motion in $$d$$ dimensions. IOUP(ordint, spatialdim, driftspeed[, …]) Integrated Ornstein-Uhlenbeck process in $$d$$ dimensions. Matern(ordint, spatialdim, lengthscale[, …]) Matern process in $$d$$ dimensions. DiscreteGaussian(input_dim, output_dim, …) Discrete transitions with additive Gaussian noise. DiscreteLinearGaussian(input_dim, …[, …]) Discrete, linear Gaussian transition models of the form. DiscreteLTIGaussian(state_trans_mat, …[, …]) Discrete, linear, time-invariant Gaussian transition models of the form. Coordinate change transformations as preconditioners in state space models. NordsieckLikeCoordinates(powers, scales, …) Nordsieck-like coordinates.