MultivarGaussian.html

MultivarGaussian.java

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package blog.distrib;

import blog.*;
import java.util.*;
import Jama.*;

Gaussian (normal) distribution over real vectors of some fixed dimensionality d. This CPD can be initialized with one, two, or three parameters. If three parameters are given, then they are the dimension, mean, and covariance matrix. If two parameters are given, they are interpreted as the dimension and covariance matrix; in this case the mean must be passed as an argument to the getProb and sampleVal methods. If only one parameter is given, it is the dimension, and the mean and covariance matrix must both be given as arguments.


public class MultivarGaussian extends AbstractCondProbDistrib {

Creates a new MultivarGaussian distribution with the given mean vector and covariance matrix. The dimension is inferred from the length of the mean vector.

Parameters:

mean - 1-by-d mean vector

covariance - d-by-d covariance matrix


    public MultivarGaussian(Matrix mean, Matrix covariance) {
	setDimension(mean.getRowDimension());
	fixedMean = true;
	setMean(mean);
	fixedCovariance = true;
	setCovariance(covariance);
    }

Sets mean and covariance and ensures that their dimensions match.


    public MultivarGaussian(List params){
	if (params.size() == 0) {
	    throw new IllegalArgumentException
		("Dimension of MultivarGaussian distribution must be "
		 + "specified as parameter.");
	} 
	if (!(params.get(0) instanceof Integer)) {
		throw new IllegalArgumentException
		    ("Dimension of MultivarGaussian distribution must be an "
		     + "integer, not " + params.get(0) + " of " 
		     + params.get(0).getClass());
	}
	setDimension(((Integer) params.get(0)).intValue());

	if (params.size() == 1) {
	    fixedMean = false;
	    fixedCovariance = false;
	} else if (params.size() == 2) {
	    fixedMean = false;
	    fixedCovariance = true;
	    setCovariance(params.get(1));
	} else if (params.size() == 3) {
	    fixedMean = true;
	    setMean(params.get(1));
	    fixedCovariance = true;
	    setCovariance(params.get(2));
	} else {
	    throw new IllegalArgumentException
		("MultivarGaussian CPD expects at most 3 parameters, not " 
		 + params.size());
	}
    }

Ensures that x = value is a column matrix of appropriate dimension d and returns the density of this Gaussian distribution at x.

 
    public double getProb(List args, Object value){
	initParams(args);

	if (!((value instanceof Matrix) 
	     && (((Matrix)value).getRowDimension() == d) 
	     && (((Matrix)value).getColumnDimension() == 1)))
	    throw new IllegalArgumentException
		("The value passed to the " + d + "-dimensional "
		 + "multivariate Gaussian distribution's getProb "
		 + "method must be a column vector of length " + d
		 + ", not " + value);

	return getProbInternal((Matrix) value);
    }

Given a d-dimensional column vector x, returns the density value p = 1/sqrt((2pi)^d|sigma|)exp{-0.5(x-mean)'inverse(sigma)(x-mean)} mean and covariance

Throws: IllegalStateException if this distribution does not have fixed


    public double getProb(Matrix x) {
	if (!fixedMean || !fixedCovariance) {
	    throw new IllegalStateException
		("Mean and covariance are not fixed.");
	}
	return getProbInternal(x);
    }

Returns the natural log of the probability returned by getProb.


    public double getLogProb(Matrix x) {
	if (!fixedMean || !fixedCovariance) {
	    throw new IllegalStateException
		("Mean and covariance are not fixed.");
	}
	return getLogProbInternal(x);
    }

Samples a value from this multivariate Gaussian by generating d independent samples from univariate Gaussians with unit variance, one for each dimension, and multiplying the obtained vector on the left by the square root of sigma (Cholesky decomposition of sigma). This method should only be called if this distribution was constructed with a fixed mean and covariance matrix (internal calls are ok if the private method initParams is called first).


    public Object sampleVal(List args, Type childType){
	initParams(args);
	return sampleVal();
    }

Samples a value from this multivariate Gaussian by generating d independent samples from univariate Gaussians with unit variance, one for each mean in the mean vector, and multiplying the obtained vector on the left by the square root of sigma (Cholesky decomposition of sigma). This method should only be called if this distribution was constructed with a fixed mean and covariance matrix (internal calls are ok if the private method initParams is called first).


    public Matrix sampleVal() {
	Matrix temp = new Matrix(d, 1);
	for (int i = 0; i < d; i++){
	    temp.set(i,0, UnivarGaussian.STANDARD.sampleVal());
	}
	return mu.plus(sqrtSigma.times(temp));
    }

Returns the mean of this distribution, or null if the mean is not fixed.


    public Matrix getMean() {
	if (fixedMean) {
	    return mu;
	}
	return null;
    }

Returns the covariance matrix of this distribution, or null if the covariance is not fixed.


    public Matrix getCovar() {
	if (fixedCovariance) {
	    return sigma;
	}
	return null;
    }

Given a d-dimensional column vector x, returns the density value p = 1/sqrt((2pi)^d|sigma|)exp{-0.5(x-mean)'inverse(sigma)(x-mean)}


    private double getProbInternal(Matrix x) {
	return Math.exp(-0.5*x.minus(mu).transpose().times
		  (sigmaInverse).times(x.minus(mu)).get(0,0)) / normConst;
    }

    private double getLogProbInternal(Matrix x) {
	return ((-0.5 * x.minus(mu).transpose().times(sigmaInverse)
		 .times(x.minus(mu)).get(0,0)) 
		- Math.log(normConst));
    }

    private void initParams(List args) {
	if (fixedMean) {
	    if (args.size() > 0) {
		throw new IllegalArgumentException
		    ("MultivarGaussian CPD with fixed mean expects no "
		     + "arguments.");
	    }
	} else {
	    if (args.size() < 1) {
		throw new IllegalArgumentException
		    ("MultivarGaussian CPD created without a fixed mean; "
		     + "requires mean as an argument.");
	    }
	    setMean(args.get(0));

	    if (fixedCovariance) {
		if (args.size() > 1) {
		    throw new IllegalArgumentException
			("MultivarGaussian CPD with fixed covariance matrix "
			 + "expects only one argument.");
		}
	    } else {
		if (args.size() < 2) {
		    throw new IllegalArgumentException
			("MultivarGaussian CPD created without a fixed "
			 + "covariance matrix; requires covariance matrix "
			 + "as argument.");
		}
		setCovariance(args.get(1));
	    }
	}
    }

    private void setDimension(int dim) {
	if (dim <= 0) {
	    throw new IllegalArgumentException
		("Dimension of MultivarGaussian distribution must be "
		 + "positive, not " + dim);
	}

	d = dim;
	dimFactor = Math.pow(2 * Math.PI, d / 2.0);
    }

    private void setMean(Object mean) {
	if (!((mean instanceof Matrix) 
	      && (((Matrix) mean).getColumnDimension() == 1))){
	    throw new IllegalArgumentException 
		("The mean of a MultivarGaussian distribution must be a "
		 + "column vector, not " + mean + " of " + mean.getClass());
	}
	
	mu = (Matrix) mean;

	if (mu.getRowDimension() != d) {
	    throw new IllegalArgumentException
		("Mean of " + d + "-dimensional Gaussian distribution must "
		 + "be column vector of length " + d);
	}
    }

    private void setCovariance(Object cov) {
	if (!((cov instanceof Matrix)
	      && (((Matrix) cov).getColumnDimension() == d)
	      && (((Matrix) cov).getColumnDimension() == d))) {
	    throw new IllegalArgumentException 
		("The covariance matrix of a " + d + "-dimensional Gaussian "
		 + "distribution must be a " + d + "-by-" + d + " Matrix, "
		 + "not " + cov + " of " + cov.getClass());
	}

	sigma = (Matrix) cov;

	for (int i = 0; i < sigma.getRowDimension(); i++){
	    for (int j = 0; j < sigma.getColumnDimension(); j++){
		double ratio = sigma.get(i, j) / sigma.get(j, i);
		if (Math.abs(ratio - 1) > 1e-6)
		    throw new IllegalArgumentException
			("Invalid covariance matrix (not symmetric): " 
			 + sigma);
	    }
	}

	normConst = Math.sqrt(sigma.det()) * dimFactor;
	sigmaInverse = sigma.inverse();
	sqrtSigma = sigma.chol().getL();
    }

    private boolean fixedMean;
    private boolean fixedCovariance;

    private int d;
    private Matrix mu;
    private Matrix sigma;

    private double dimFactor;
    private double normConst;
    private Matrix sigmaInverse;
    private Matrix sqrtSigma;
}

This file was generated on Tue Jun 08 17:53:47 PDT 2010 from file MultivarGaussian.java
by the ilog.language.tools.Hilite Java tool written by Hassan Aït-Kaci