ParticleSystem
A Particle system is a mixture of Dirac distributions.
\[P(x) = \sum_{i= 1}^n w_i \delta(x - μ^{(i)})\]
It can also be used to represent a mixture of trajectories.
\[P(x) = \sum_{i= 1}^n w_i \delta(x_{1:T} - μ^{(i)}_{1:T})\]
Types
MarkovKernels.AbstractParticleSystem — TypeAbstractParticleSystem{T} <: AbstractDistribution{T}abstract type for representing systems of particles.
MarkovKernels.ParticleSystem — TypeParticleSystem{T,A,B} <: AbstractParticleSystem{T}type for representing a standard particle system.
Constructors
MarkovKernels.ParticleSystem — MethodParticleSystem(logws::AbstractVector{<:Real}, X::AbstractArray{<:AbstractVector{T}})Creates a ParticleSystem with logarithm of the mixture weights given by logws and location parameters in X. If X is an AbstractVector the resulting object represents a classical Dirac mixtrue. Whereas if X is an AbstractMatrix, the resulting object represents a Dirac mixture over trajectories, where the row dimension represents time and the column dimension enumerates the particles.
Basics
MarkovKernels.dim — Methoddim(P::AbstractParticleSystem)Returns the dimension of the particle system distribution P.
MarkovKernels.logweights — Methodlogweights(P::AbstractParticleSystem)Returns the logarithms of the mixture weights of the particle system P.
MarkovKernels.weights — Methodweights(P::AbstractParticleSystem)Returns the mixture weights of the particle system P.
MarkovKernels.nparticles — Methodnparticles(P::AbstractParticleSystem)Computes the number of particles in the particle system P.
MarkovKernels.particles — Methodparticles(P::AbstractParticleSystem)Returns the particle locations of the particle system P.
Statistics.mean — Methodmean(P::AbstractParticleSystem)Computes the mean of the particle system distribution P.