# jMEF.MultivariateGaussian Class Reference

List of all members.

## Public Member Functions

double F (PVectorMatrix T)
Computes the log normalizer .
Computes .
double G (PVectorMatrix H)
Computes .
Computes .
PVectorMatrix t (PVector x)
Computes the sufficient statistic .
double k (PVector x)
Computes the carrier measure .
PVectorMatrix Lambda2Theta (PVectorMatrix L)
Converts source parameters to natural parameters.
PVectorMatrix Theta2Lambda (PVectorMatrix T)
Converts natural parameters to source parameters.
PVectorMatrix Lambda2Eta (PVectorMatrix L)
Converts source parameters to expectation parameters.
PVectorMatrix Eta2Lambda (PVectorMatrix H)
Converts expectation parameters to source parameters.
double density (PVector x, PVectorMatrix param)
Computes the density value .
PVector drawRandomPoint (PVectorMatrix L)
Draws a point from the considered distribution.
double KLD (PVectorMatrix LP, PVectorMatrix LQ)
Computes the Kullback-Leibler divergence between two multivariate Gaussian distributions.

Version:
1.0

## Description

The multivariate Gaussian distribution is an exponential family and, as a consequence, the probability density function is given by

where are the natural parameters. This class implements the different functions allowing to express a multivariate Gaussian distribution as a member of an exponential family.

## Parameters

The parameters of a given distribution are:
• Source parameters
• Natural parameters
• Expectation parameters

## Member Function Documentation

 double jMEF.MultivariateGaussian.density ( PVector x, PVectorMatrix param )

Computes the density value .

Parameters:
 x point param parameters (source, natural, or expectation)
Returns:

 PVector jMEF.MultivariateGaussian.drawRandomPoint ( PVectorMatrix L )

Draws a point from the considered distribution.

Parameters:
 L source parameters
Returns:
a point.

 PVectorMatrix jMEF.MultivariateGaussian.Eta2Lambda ( PVectorMatrix H )

Converts expectation parameters to source parameters.

Parameters:
 H expectation parameters
Returns:
source parameters

 double jMEF.MultivariateGaussian.F ( PVectorMatrix T )

Computes the log normalizer .

Parameters:
 T natural parameters
Returns:

 double jMEF.MultivariateGaussian.G ( PVectorMatrix H )

Computes .

Parameters:
 H expectation parameters
Returns:

 PVectorMatrix jMEF.MultivariateGaussian.gradF ( PVectorMatrix T )

Computes .

Parameters:
 T natural
Returns:

 PVectorMatrix jMEF.MultivariateGaussian.gradG ( PVectorMatrix H )

Computes .

Parameters:
 H expectation parameters
Returns:

 double jMEF.MultivariateGaussian.k ( PVector x )

Computes the carrier measure .

Parameters:
 x a point
Returns:

 double jMEF.MultivariateGaussian.KLD ( PVectorMatrix LP, PVectorMatrix LQ )

Computes the Kullback-Leibler divergence between two multivariate Gaussian distributions.

Parameters:
 LP source parameters LQ source parameters
Returns:

 PVectorMatrix jMEF.MultivariateGaussian.Lambda2Eta ( PVectorMatrix L )

Converts source parameters to expectation parameters.

Parameters:
 L source parameters
Returns:
expectation parameters

 PVectorMatrix jMEF.MultivariateGaussian.Lambda2Theta ( PVectorMatrix L )

Converts source parameters to natural parameters.

Parameters:
 L source parameters
Returns:
natural parameters

 PVectorMatrix jMEF.MultivariateGaussian.t ( PVector x )

Computes the sufficient statistic .

Parameters:
 x a point
Returns:

 PVectorMatrix jMEF.MultivariateGaussian.Theta2Lambda ( PVectorMatrix T )

Converts natural parameters to source parameters.

Parameters:
 T natural parameters
Returns:
source parameters

The documentation for this class was generated from the following file:

Generated on Mon Nov 23 15:46:26 2009 for jMEF by  1.5.9