# bdmtoolbox - List of available basic objects

Basic objects of BDM are:**RV**decriptor of data vectors and random variables**fnc**functions of vector arguments**pdf**pdf with non-empty conditioning part**epdf**pdf with empty conditioning part**BM**Bayesian model - (approximate) calculation of specific type of the Bayes rule,**DS**Data Sources - recursive sources of data**logger**object storing results of all experiments

See, BDM Use - Probability density functions and BDM Use - System, Data, Simulation for their introduction.

## Working with RV

In bdmtoolbox, RV is represented by a matlab structure. It is recommended to use the following function to work with it:

**RV**,**rva=RV('a',1)**,**rvab=RV({'b','c'},[1,2])**create empty RV, RV named "a" of size 1, and vector of RV "b" and "c" of sizes 1 and 2, respectively.**RVtimes(rva,-1)**set time (delay) of rva to -1 from current time.**RVjoin([rva,rvb])**joins rva and rvb into a vector

## Basic functions

Predefined functions are:**constfn**Class representing function , here rv is empty**linfn**Class representing function**mexFnc**Matlab extension of a function, calling predefined matlab functions**grid_fnc**Function defined by values on a fixed grid and interpolated inbetween them

## Square root decompositions of symetric matrices

For information purpose, these matrices are used in epdfs:**chmat**Symmetric matrix stored in square root decomposition using upper cholesky**fsqmat**Fake sqmat. This class maps sqmat operations to operations on full matrix**ldmat**Matrix stored in LD form, (commonly known as UD)

## Basic epdfs accessible from matlab are:

**dirac**Dirac delta function distribution**eDirich**Dirichlet posterior density**eEF**General conjugate exponential family posterior density**eEmp**Weighted empirical density**egamma**Gamma posterior density**egiw**Gauss-inverse-Wishart density stored in LD form**egrid**Discrete density defined on a continuous grid**eigamma**Inverse-Gamma posterior density**eiWishartCh**Inverse Wishart on Choleski decomposition**enorm<ldmat>**Gaussian density with positive definite (decomposed) covariance matrix**enorm<chmat>**Gaussian density with positive definite (decomposed) covariance matrix**enorm<fsqmat>**Gaussian density with positive definite (decomposed) covariance matrix**elognorm**LogNormal density**emix**Mixture of epdfs**eprod**Product of densities, elements may be unconditional, however, the result should be unconditioned pdf.**estudent< ldmat>**Student-t density**estudent< ldmat>**Student-t density**estudent< ldmat>**Student-t density**euni**Uniform density on rectangular support**eWishartCh**Wishart in choleski decomposition

## Basic (conditioned) pdfs accessible from matlab are:

**mDirich**Dirichlet random walk**mexBM**BM with functions implemented in matlab**mexEpdf**Epdf with functions implemented in matlab**mgamma**Gamma random walk**mgamma_fix**Gamma random walk around a fixed point**mgdirac**Dirac delta pdf with geenral function of the support point**mgnorm< ldmat >**Gaussian Pdf with general function for mean value**mgnorm< chmat >**Gaussian Pdf with general function for mean value**mgnorm< fsqmat >**Gaussian Pdf with general function for mean value**mguni**Uniform density with geenral function of mean value**migamma**Inverse-Gamma random walk**migamma_ref**Inverse-Gamma random walk around a fixed point**mlnorm< ldmat>**Normal distribution with linear function with linear function of mean value;**mlnorm< chmat>**Normal distribution with linear function with linear function of mean value;**mlnorm< fsqmat>**Normal distribution with linear function with linear function of mean value;**mlognorm**Log-Normal random walk**mlstudent**Student distributed linear function with linear function of mean value;**mmix**Mixture of pdfs with constant weights, all pdfs are of equal RV and RVC**mprod**Chain rule decomposition of epdf**mratio**Class representing ratio of two densities which arise e.g. by applying the Bayes rule.**rwiWishartCh**Random Walk on inverse Wishart

## DataSources

**MemDS**Memory storage of off-line data column-wise**CsvFileDS**CSV file data storage The constructor creates Data matrix from the records in a CSV file fname. The orientation can be of two types: 1. BY_COL which is default - the data are stored in columns; one column per time , one row per data item. 2. BY_ROW if the data are stored the classical CSV style. Then each column stores the values for data item, for ex. , one row for each discrete time instant**EpdfDS**Simulate data from a static pdf (epdf)**PdfDS**Simulate data from conditional density Still having only one density but allowing conditioning on either input or delayed values

## Loggers - storage of results

**mexlog**Logger storing results into an mxArray**dirfilelog**Logging into dirfile with buffer in memory**stdlog**Simple logger used for debugging All data records are written out to std from where they could be send to file**ITppFileDS**Read Data Matrix from an IT file

## Mergers

**merger_base**Base class for general combination of pdfs on discrete support**merger_mix**Merger using importance sampling with mixture proposal density

## Bayesian Models

Basic filters:

**ARX**Linear Autoregressive model with Gaussian noise**ARXfrg**ARX with conditioned on forgetting factor**ARXg**ARX with Non-linear transformation + Gaussian noise**EKFCh**Extended Kalman Filter in Square root**EKFfull**Extended Kalman Filter in full matrices**KalmanCh**Kalman filter in square root form**KalmanFull**Basic Kalman filter with full matrices**MixEF**Estimator of Mixtures of Exponential Family Densities**multiBM**Estimator for Multinomial density**MultiModel**(Switching) Multiple Models. The model runs several BMs in parallel and evaluates thier weights (fittness)**PF**Particle filtering: Wrapper for particles**BootstrapParticle**Class used in PF**MarginalizedParticle**Class used in PF

## Controllers (and related classes)

**LQG**Basic class computing LQG control**LQG_ARX**Controller using ARX model for estimation and LQG designer for control**StateFromARX**conversion function**StateSpace< ldmat>**Basic elements of linear state-space model**StateSpace< chmat>**Basic elements of linear state-space model

## Multiple Patricipant Decision Makers

**ARXAgent**ARX agent

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