Facemorph
Class Gaussian

java.lang.Object
  Facemorph.BigMat
      Facemorph.Gaussian

All Implemented Interfaces:

java.io.Serializable

public class Gaussian
extends BigMat

A Gaussian distribution class

See Also:

Serialized Form

Constructor Summary

Gaussian()
Constructor for an empty Gaussian

Gaussian(double[] mean, BigMat covar, boolean invert)
Construct a Gaussian using the data given

Gaussian(int dim)
Constructs a Gaussian for the dimensions specified

Method Summary

boolean	build(java.util.Vector samples) Builds a Gaussian from a set of arrays
boolean	build(java.util.Vector samples, BigMat dist) Build a Gaussian from the supplied samples
double	build(java.util.Vector samples, java.util.Vector sampleWeights, int index) Builds the mean and covariance matrix from the samples given
void	display(java.lang.String label) DIsplay the eigenvector matrix, the eigenvalue array and the mean
double[]	eigenAnalysis(double[] sample) Analyse the sample into its principal components
double[]	eigenSynthesis(double[] sample) Synthesise a sample with the given principal component weights
BigMat	getCovar(boolean invert) Uses the eigenvalues and eigenvectors to reconstruct the covariance matrix or it inverse
double[]	getDiag() gets the variances of this Gaussian
double[]	getMean() Get the mean of this Gaussian
double[]	getRandomSample(java.util.Random rand) Gets a random vector sampled from this Gaussian distribution
static void	main(java.lang.String[] args) Used for testing
double	probability(double[] sample) Calculates the probability of a sample vector
boolean	read(java.io.InputStream in) Read this Gaussian from the given InputStream
boolean	read(java.io.StreamTokenizer st) Read from the given StreamTokenizer
void	setSize(int dim) Sets the size of this Gaussian
Gaussian	slice(double[] sample, double[] weight) Takes a slice through the Gaussian, to produce a new Gaussian first "fixed" elements are fixed remaining elements of the Gaussian are used in the new Gaussian
double[]	slice1d(double[] start, double[] direction) Takes a 1D slice through the Gaussian along the line through start pointing in direction the output Gaussian is centred on start and the units are 1 equals the length of direction
double	squaredMeanDistance(double[] sample) Get the squared distance of the mean from the sample
double	T_squared(Gaussian g, double weight1, double weight2) Hotelling's T^2 statistic (the N-D t-test equivalent)
boolean	write(java.io.PrintStream out) Writes this to the given PrintStream

Methods inherited from class Facemorph.BigMat

add, add, copy, copy, dotProduct, equals, equals, get, getColumn, getColumnCopy, getHeight, getRowCopy, getWidth, invertSVD, jacobi, magnitude, multiply, multiply, multiply, multiplyOtherTranspose, multiplySelfTranspose, multiplyTranspose, multiplyTranspose, normaliseColumns, normaliseRows, put, qrdcmp, qrdcmp, qrsolv, read, read, readBinary, readBinary, reconstructQR, removeNaNRecords, rsolv, setColumn, setRow, setSize, SIGN, sort, subMat, subMat, subMat, subMatCols, subMatRows, subtract, sumSquares, svbksb, svbksb, svbksbt, svbksbt, svdcmp, svdcmpt, transposeCopy, upperTriangularBacksub, upperTriangularInverseMultiply, vectorise, write, writeBinary, writeBinary

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Gaussian

public Gaussian()

Constructor for an empty Gaussian

Gaussian

public Gaussian(int dim)

Constructs a Gaussian for the dimensions specified

Parameters:

dim - the required dimensionality of this Gaussian

Gaussian

public Gaussian(double[] mean,
                BigMat covar,
                boolean invert)

Construct a Gaussian using the data given

Parameters:

mean - The mean vector

covar - The covariance matrix

invert - specifies if the covariane matrix should be inverted

Method Detail

setSize

public void setSize(int dim)
             throws BigMatException

Sets the size of this Gaussian

Parameters:

dim - The number of dimensions

Throws:

BigMatException - thrown if problems setting the matrix size

build

public boolean build(java.util.Vector samples)

Builds a Gaussian from a set of arrays

Parameters:

samples - The vector of sample arrays

Returns:

true if built OK, false otherwise

build

public boolean build(java.util.Vector samples,
                     BigMat dist)

Build a Gaussian from the supplied samples

Parameters:

samples - the data samples

dist - The a priri distribution

Returns:

returns true if built OK, false otherwise

build

public double build(java.util.Vector samples,
                    java.util.Vector sampleWeights,
                    int index)

Builds the mean and covariance matrix from the samples given

Parameters:

samples - the Vector of double[] samples

sampleWeights - the Vector of double[] sample weights

index - the index in each sampleWeight array of this Gaussian

Returns:

returns the sum of weights

getCovar

public BigMat getCovar(boolean invert)
                throws BigMatException

Uses the eigenvalues and eigenvectors to reconstruct the covariance matrix or it inverse

Parameters:

invert - flag indicating if the inverse covariance matrix is required

Returns:

returns the covariance matrix or its inverse

Throws:

BigMatException

getMean

public double[] getMean()

Get the mean of this Gaussian

Returns:

the mean vector

getDiag

public double[] getDiag()

gets the variances of this Gaussian

Returns:

the variances

eigenAnalysis

public double[] eigenAnalysis(double[] sample)

Analyse the sample into its principal components

Parameters:

sample - the sample to analyse

Returns:

the sample weights

eigenSynthesis

public double[] eigenSynthesis(double[] sample)

Synthesise a sample with the given principal component weights

Parameters:

sample - the weights

Returns:

the reconstructed sample

squaredMeanDistance

public double squaredMeanDistance(double[] sample)

Get the squared distance of the mean from the sample

Parameters:

sample - the sample to test

Returns:

the squared distance from sample to the mean

probability

public double probability(double[] sample)
                   throws BigMatException

Calculates the probability of a sample vector

Parameters:

sample - The sample to test

Returns:

the probability of the sample in this Gaussian

Throws:

BigMatException

T_squared

public double T_squared(Gaussian g,
                        double weight1,
                        double weight2)
                 throws BigMatException

Hotelling's T^2 statistic (the N-D t-test equivalent)

Parameters:

g - The Gaussian to compare with

weight1 - the weight of this Gaussian

weight2 - the weight of g

Returns:

the T^2 statistic

Throws:

BigMatException

getRandomSample

public double[] getRandomSample(java.util.Random rand)

Gets a random vector sampled from this Gaussian distribution

Parameters:

rand - A random number generating object

Returns:

Returns a random sample from this distribution

slice

public Gaussian slice(double[] sample,
                      double[] weight)
               throws BigMatException

Takes a slice through the Gaussian, to produce a new Gaussian first "fixed" elements are fixed remaining elements of the Gaussian are used in the new Gaussian

Parameters:

sample - the fixed values of the first n dimensions

weight - an optional array of size 1 used to store the slice probability, can be null if not needed

Returns:

The Gaussian slice through this Gaussian

Throws:

BigMatException

slice1d

public double[] slice1d(double[] start,
                        double[] direction)

Takes a 1D slice through the Gaussian along the line through start pointing in direction the output Gaussian is centred on start and the units are 1 equals the length of direction

Parameters:

start - the starting point

direction - the direction the line is going in

Returns:

returns a the mean and standard deviation centred on start in the direction given

display

public void display(java.lang.String label)

DIsplay the eigenvector matrix, the eigenvalue array and the mean

Overrides:

display in class BigMat

Parameters:

label - The label to display with this Gaussian

write

public boolean write(java.io.PrintStream out)

Writes this to the given PrintStream

Overrides:

write in class BigMat

Parameters:

out - the PrintStream to write to

Returns:

return's true if written OK

read

public boolean read(java.io.InputStream in)

Read this Gaussian from the given InputStream

Parameters:

in - the InputStream to read from

Returns:

return true if read OK

read

public boolean read(java.io.StreamTokenizer st)

Read from the given StreamTokenizer

Overrides:

read in class BigMat

Parameters:

st - the StreamTokenizer to read from

Returns:

return true if all OK

main

public static void main(java.lang.String[] args)
                 throws BigMatException

Used for testing

Parameters:

args - the command line arguments

Throws:

BigMatException