org.apache.commons.math3.distribution
Class MultivariateNormalDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution
      org.apache.commons.math3.distribution.MultivariateNormalDistribution

All Implemented Interfaces:

MultivariateRealDistribution

public class MultivariateNormalDistribution
extends AbstractMultivariateRealDistribution

Implementation of the multivariate normal (Gaussian) distribution.

Since:

3.1

Version:

$Id: MultivariateNormalDistribution.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Multivariate normal distribution (Wikipedia), Multivariate normal distribution (MathWorld)

Field Summary

Fields inherited from class org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution

random

Constructor Summary

MultivariateNormalDistribution(double[] means, double[][] covariances)
Creates a multivariate normal distribution with the given mean vector and covariance matrix.

MultivariateNormalDistribution(RandomGenerator rng, double[] means, double[][] covariances)
Creates a multivariate normal distribution with the given mean vector and covariance matrix.

Method Summary

double	density(double[] vals) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
RealMatrix	getCovariances() Gets the covariance matrix.
double[]	getMeans() Gets the mean vector.
double[]	getStandardDeviations() Gets the square root of each element on the diagonal of the covariance matrix.
double[]	sample() Generates a random value vector sampled from this distribution.

Methods inherited from class org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution

getDimension, reseedRandomGenerator, sample

Methods inherited from class java.lang.Object

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

Constructor Detail

MultivariateNormalDistribution

public MultivariateNormalDistribution(double[] means,
                                      double[][] covariances)
                               throws SingularMatrixException,
                                      DimensionMismatchException,
                                      NonPositiveDefiniteMatrixException

Creates a multivariate normal distribution with the given mean vector and covariance matrix.
The number of dimensions is equal to the length of the mean vector and to the number of rows and columns of the covariance matrix. It is frequently written as "p" in formulae.

Parameters:

means - Vector of means.

covariances - Covariance matrix.

Throws:

DimensionMismatchException - if the arrays length are inconsistent.

SingularMatrixException - if the eigenvalue decomposition cannot be performed on the provided covariance matrix.

NonPositiveDefiniteMatrixException - if any of the eigenvalues is negative.

MultivariateNormalDistribution

public MultivariateNormalDistribution(RandomGenerator rng,
                                      double[] means,
                                      double[][] covariances)
                               throws SingularMatrixException,
                                      DimensionMismatchException,
                                      NonPositiveDefiniteMatrixException

Creates a multivariate normal distribution with the given mean vector and covariance matrix.
The number of dimensions is equal to the length of the mean vector and to the number of rows and columns of the covariance matrix. It is frequently written as "p" in formulae.

Parameters:

rng - Random Number Generator.

means - Vector of means.

covariances - Covariance matrix.

Throws:

DimensionMismatchException - if the arrays length are inconsistent.

SingularMatrixException - if the eigenvalue decomposition cannot be performed on the provided covariance matrix.

NonPositiveDefiniteMatrixException - if any of the eigenvalues is negative.

Method Detail

getMeans

public double[] getMeans()

Gets the mean vector.

Returns:

the mean vector.

getCovariances

public RealMatrix getCovariances()

Gets the covariance matrix.

Returns:

the covariance matrix.

density

public double density(double[] vals)
               throws DimensionMismatchException

Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the cumulative distribution function. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.

Parameters:

vals - Point at which the PDF is evaluated.

Returns:

the value of the probability density function at point x.

Throws:

DimensionMismatchException

getStandardDeviations

public double[] getStandardDeviations()

Gets the square root of each element on the diagonal of the covariance matrix.

Returns:

the standard deviations.

sample

public double[] sample()

Generates a random value vector sampled from this distribution.

Specified by:

sample in interface MultivariateRealDistribution

Specified by:

sample in class AbstractMultivariateRealDistribution

Returns:

a random value vector.