Apache Commons Math 3.6.1 · org.apache.commons.math3.distribution.MultivariateNormalDistribution

Field Summary

Modifier and Type	Field and Description
private final RealMatrix	covarianceMatrix Covariance matrix.
private final double	covarianceMatrixDeterminant The determinant of the covariance matrix.
private final RealMatrix	covarianceMatrixInverse The matrix inverse of the covariance matrix.
private final double[]	means Vector of means.
private final RealMatrix	samplingMatrix Matrix used in computation of samples.

Inherited from org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution:: random

Constructor Summary

Access	Constructor and Description
public	MultivariateNormalDistribution(final double[] Vector of means. means, final double[][] Covariance matrix. covariances) Creates a multivariate normal distribution with the given mean vector and covariance matrix.
public	MultivariateNormalDistribution(RandomGenerator Random Number Generator. rng, final double[] Vector of means. means, final double[][] Covariance matrix. covariances) Creates a multivariate normal distribution with the given mean vector and covariance matrix.

Method Summary

Modifier and Type	Method and Description
public double	density(final double[] Point at which the PDF is evaluated. vals) Implements org.apache.commons.math3.distribution.MultivariateRealDistribution.density. Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
public RealMatrix	Returns: the covariance matrix. getCovariances() Gets the covariance matrix.
private double	Returns: the multiplication factor of density calculations. getExponentTerm(final double[] Values at which to compute density. values) Computes the term used in the exponent (see definition of the distribution).
public double[]	Returns: the mean vector. getMeans() Gets the mean vector.
public double[]	Returns: the standard deviations. getStandardDeviations() Gets the square root of each element on the diagonal of the covariance matrix.
public double[]	sample() Implements abstract org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution.sample. Implements org.apache.commons.math3.distribution.MultivariateRealDistribution.sample. Generates a random value vector sampled from this distribution.

Inherited from org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution:: getDimension reseedRandomGenerator sample

Field Detail

covarianceMatrix	back to summary
private final RealMatrix covarianceMatrix Covariance matrix.

covarianceMatrixDeterminant	back to summary
private final double covarianceMatrixDeterminant The determinant of the covariance matrix.

covarianceMatrixInverse	back to summary
private final RealMatrix covarianceMatrixInverse The matrix inverse of the covariance matrix.

means	back to summary
private final double[] means Vector of means.

samplingMatrix	back to summary
private final RealMatrix samplingMatrix Matrix used in computation of samples.

Constructor Detail

MultivariateNormalDistribution back to summary

MultivariateNormalDistribution	back to summary
public MultivariateNormalDistribution(final double[] means, final 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. Note this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `sample(int)`). In case no sampling is needed for the created distribution, it is advised to pass `null` as random generator via the appropriate constructors to avoid the additional initialisation overhead. Parameters means:double[] Vector of means. covariances:double[][] Covariance matrix. Exceptions SingularMatrixException: if the eigenvalue decomposition cannot be performed on the provided covariance matrix. DimensionMismatchException: if the arrays length are inconsistent. NonPositiveDefiniteMatrixException: if any of the eigenvalues is negative.

public MultivariateNormalDistribution(final double[] means, final 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.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

Parameters

means:double[]: Vector of means.
covariances:double[][]: Covariance matrix.

Exceptions

SingularMatrixException:: if the eigenvalue decomposition cannot be performed on the provided covariance matrix.
DimensionMismatchException:: if the arrays length are inconsistent.
NonPositiveDefiniteMatrixException:: if any of the eigenvalues is negative.

MultivariateNormalDistribution	back to summary
public MultivariateNormalDistribution(RandomGenerator rng, final double[] means, final 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:RandomGenerator Random Number Generator. means:double[] Vector of means. covariances:double[][] Covariance matrix. Exceptions SingularMatrixException: if the eigenvalue decomposition cannot be performed on the provided covariance matrix. DimensionMismatchException: if the arrays length are inconsistent. NonPositiveDefiniteMatrixException: if any of the eigenvalues is negative.

MultivariateNormalDistribution

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

Parameters

rng:RandomGenerator: Random Number Generator.
means:double[]: Vector of means.
covariances:double[][]: Covariance matrix.

Exceptions

SingularMatrixException:: if the eigenvalue decomposition cannot be performed on the provided covariance matrix.
DimensionMismatchException:: if the arrays length are inconsistent.
NonPositiveDefiniteMatrixException:: if any of the eigenvalues is negative.

Method Detail

density back to summary

density	back to summary
public double density(final double[] vals) throws DimensionMismatchException Implements org.apache.commons.math3.distribution.MultivariateRealDistribution.density. Doc from org.apache.commons.math3.distribution.MultivariateRealDistribution.density. 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:double[] Point at which the PDF is evaluated. Returns:double the value of the probability density function at point `x`.

public double density(final double[] vals) throws DimensionMismatchException

Implements org.apache.commons.math3.distribution.MultivariateRealDistribution.density.

Doc from org.apache.commons.math3.distribution.MultivariateRealDistribution.density.

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:double[]: Point at which the PDF is evaluated.

Returns:double

the value of the probability density function at point x.

getCovariances	back to summary
public RealMatrix getCovariances() Gets the covariance matrix. Returns:RealMatrix the covariance matrix.

getCovariances

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public RealMatrix getCovariances()

Gets the covariance matrix.

Returns:RealMatrix: the covariance matrix.

getExponentTerm	back to summary
private double getExponentTerm(final double[] values) Computes the term used in the exponent (see definition of the distribution). Parameters values:double[] Values at which to compute density. Returns:double the multiplication factor of density calculations.

getExponentTerm

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private double getExponentTerm(final double[] values)

Computes the term used in the exponent (see definition of the distribution).

Parameters

values:double[]: Values at which to compute density.

Returns:double

the multiplication factor of density calculations.

getMeans	back to summary
public double[] getMeans() Gets the mean vector. Returns:double[] the mean vector.

getMeans

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public double[] getMeans()

Gets the mean vector.

Returns:double[]: the mean vector.

getStandardDeviations	back to summary
public double[] getStandardDeviations() Gets the square root of each element on the diagonal of the covariance matrix. Returns:double[] the standard deviations.

getStandardDeviations

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public double[] getStandardDeviations()

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

Returns:double[]: the standard deviations.

sample	back to summary
public double[] sample() Implements abstract org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution.sample. Implements org.apache.commons.math3.distribution.MultivariateRealDistribution.sample. Doc from org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution.sample. Generates a random value vector sampled from this distribution. Returns:double[] Doc from org.apache.commons.math3.distribution.MultivariateRealDistribution.sample. a random value vector. Annotations @Override

sample

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public double[] sample()

Implements abstract org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution.sample.

Implements org.apache.commons.math3.distribution.MultivariateRealDistribution.sample.

Doc from org.apache.commons.math3.distribution.AbstractMultivariateRealDistribution.sample.

Generates a random value vector sampled from this distribution.

Returns:double[]

Doc from org.apache.commons.math3.distribution.MultivariateRealDistribution.sample.

a random value vector.

Annotations

@Override

public Class MultivariateNormalDistribution

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