Package org.apache.commons.math4.distribution

Class MultivariateNormalDistribution

java.lang.Object

org.apache.commons.math4.distribution.AbstractMultivariateRealDistribution

org.apache.commons.math4.distribution.MultivariateNormalDistribution

All Implemented Interfaces:

MultivariateRealDistribution

public class MultivariateNormalDistribution
extends AbstractMultivariateRealDistribution

Implementation of the multivariate normal (Gaussian) distribution.

Since:

3.1

See Also:

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

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.math4.distribution.MultivariateRealDistribution

MultivariateRealDistribution.Sampler

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
MultivariateRealDistribution.Sampler	createSampler(UniformRandomProvider rng)	Creates a sampler.
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.

Methods inherited from class org.apache.commons.math4.distribution.AbstractMultivariateRealDistribution

getDimension, sample

Methods inherited from class java.lang.Object

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

Constructor Details

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.

Method Details

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.

createSampler

public MultivariateRealDistribution.Sampler createSampler(UniformRandomProvider rng)

Creates a sampler.

Specified by:

createSampler in interface MultivariateRealDistribution

Specified by:

createSampler in class AbstractMultivariateRealDistribution

Parameters:

rng - Generator of uniformly distributed numbers.

Returns:

a sampler that produces random numbers according this distribution.