HABQTlib.Data.Particle

Data structures and functions that deal with storing and processing particle hierarchies.

Warning: functions in this module assume that the ptsParticles is non-empty and NumberOfParticles, Dim, and Rank are positive, no validation is performed. If you use them directly, instead of employing API from HABQTlib, you must ensure those assumptions hold.

Documentation

data Particles

A vector of weighed density matrices is stored along with their rank and number. ptsWeight corresponds to the collective weight of particles of rank ptsRank in the hierarchical model, it is not the sum of individual weights of particles (that is normalised to unity after every update).

Constructors

Particles

Fields

• ptsRank :: Rank
• ptsWeight :: Weight
• ptsNumber :: NumberOfParticles
• ptsParticles :: Vector WeighedDensityMatrix

Instances

Show Particles

Methods

showsPrec :: Int -> Particles -> ShowS

show :: Particles -> String

showList :: [Particles] -> ShowS

genParticles :: Dim -> Rank -> NumberOfParticles -> IO Particles

Generates random particles (according to induced measure).

updateParticles :: PureStateVector -> Particles -> Particles

Given a measurement result, perform a Bayesian update over the particles.

type ParticleHierarchy = Vector Particles

Particle hierarchy is described by a vector of Particles.

initialiseParticleHierarchy :: Dim -> NumberOfParticles -> IO ParticleHierarchy

Helper function that generates random particles of each applicable rank.

updateParticleHierarchy :: PureStateVector -> ParticleHierarchy -> ParticleHierarchy

Given a measurement result, update all particles, then normalise resulting hierarchical weights to sum to unity.

getMixedEstimate :: ParticleHierarchy -> DensityMatrix

Summarise the whole particle hierarchy into one mean Bayesian estimate.

foldOverPts

Arguments

:: (DensityMatrix -> a)

function to map over density matrices

-> (Weight -> a -> b)

function to combine weights with results of mapping

-> (c -> b -> c)

fold funciton

-> c

seed value for folding

-> Particles

-> c

Map density matrices, combine them with their weights, and then perform a (strict left) fold of results.

reduceParticlesToMean :: Particles -> WeighedDensityMatrix

Summarise particles to a mean estimate (weighed by the corresponding hierarchical weight of the rank).

effectiveSize :: Particles -> Double

Calculate the effective sample size of particles (weights don’t necessarily have to be normalised).

data ResampleArgs

Arguments for the resampling function.

Constructors

ResampleArgs

Fields

• argOut :: OutputVerb
• argGen :: GenIO
• argDim :: Dim
• argMinIter :: MHMCiter

resampleMultinom :: GenIO -> Particles -> IO Particles

Multinomial resampling of particle vector, which equalises weights of particles.

resample :: ResampleArgs -> [PureStateVector] -> Particles -> IO Particles

Resample particles. First does one multinomial step that equalises the weights, then performs MHMC iterations adaptively refining the proposal distribution based on acceptance rate. argMinIter iterations are performed for proposal distributions with significant acceptance rates.

ecdf :: Vector WeighedDensityMatrix -> Vector Double

Calculates values of empirical distribution function at data points.

icdf :: Vector Double -> Double -> Int

O(log n) Given a non-empty sorted vector (typically an empirical cdf evaluated at data points returned by ecdf) and a real number return the (0-based) index of the least element of vector which is greater or equal to the given real number (or the index of the last element, in case there is no element smaller than the argument).

nudgeParticle

Arguments

:: Dim

-> Weight

Relative weight (from 0 to 1) of random component

-> WeighedDensityMatrix

-> IO WeighedDensityMatrix

Nudges a particle by mixing the state together with some randomly generated pure state. Relative weight of the random component determines how “close” a nudged particle is to the original one.