# Class MultivariateNormalDistribution

java.lang.Object
org.hipparchus.distribution.multivariate.AbstractMultivariateRealDistribution
org.hipparchus.distribution.multivariate.MultivariateNormalDistribution
All Implemented Interfaces:
MultivariateRealDistribution

public class MultivariateNormalDistribution
Implementation of the multivariate normal (Gaussian) distribution.
• ## Field Summary

### Fields inherited from class org.hipparchus.distribution.multivariate.AbstractMultivariateRealDistribution

random
• ## Constructor Summary

Constructors
Constructor
Description
MultivariateNormalDistribution(double[] means, double[][] covariances)
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.
MultivariateNormalDistribution(double[] means, double[][] covariances, double singularMatrixCheckTolerance)
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.
MultivariateNormalDistribution(RandomGenerator rng, double[] means, double[][] covariances)
Creates a multivariate normal distribution with the given mean vector and covariance matrix.
MultivariateNormalDistribution(RandomGenerator rng, double[] means, double[][] covariances, double singularMatrixCheckTolerance)
Creates a multivariate normal distribution with the given mean vector and covariance matrix.
• ## Method Summary

Modifier and Type
Method
Description
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
getSingularMatrixCheckTolerance()
Gets the current setting for the tolerance check used during singular checks before inversion
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.hipparchus.distribution.multivariate.AbstractMultivariateRealDistribution

getDimension, reseedRandomGenerator, 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 MathIllegalArgumentException
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 AbstractMultivariateRealDistribution.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 - Vector of means.
covariances - Covariance matrix.
Throws:
MathIllegalArgumentException - if the arrays length are inconsistent.
MathIllegalArgumentException - if the eigenvalue decomposition cannot be performed on the provided covariance matrix.
MathIllegalArgumentException - if any of the eigenvalues is negative.
• ### MultivariateNormalDistribution

public MultivariateNormalDistribution(double[] means, double[][] covariances, double singularMatrixCheckTolerance) throws MathIllegalArgumentException
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 AbstractMultivariateRealDistribution.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 - Vector of means.
covariances - Covariance matrix.
singularMatrixCheckTolerance - Tolerance used during the singular matrix check before inversion
Throws:
MathIllegalArgumentException - if the arrays length are inconsistent.
MathIllegalArgumentException - if the eigenvalue decomposition cannot be performed on the provided covariance matrix.
MathIllegalArgumentException - if any of the eigenvalues is negative.
• ### MultivariateNormalDistribution

public MultivariateNormalDistribution(RandomGenerator rng, double[] means, double[][] covariances)
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:
MathIllegalArgumentException - if the arrays length are inconsistent.
MathIllegalArgumentException - if the eigenvalue decomposition cannot be performed on the provided covariance matrix.
MathIllegalArgumentException - if any of the eigenvalues is negative.
• ### MultivariateNormalDistribution

public MultivariateNormalDistribution(RandomGenerator rng, double[] means, double[][] covariances, double singularMatrixCheckTolerance) throws MathIllegalArgumentException
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.
singularMatrixCheckTolerance - Tolerance used during the singular matrix check before inversion
Throws:
MathIllegalArgumentException - if the arrays length are inconsistent.
MathIllegalArgumentException - if the eigenvalue decomposition cannot be performed on the provided covariance matrix.
MathIllegalArgumentException - 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.
• ### getSingularMatrixCheckTolerance

public double getSingularMatrixCheckTolerance()
Gets the current setting for the tolerance check used during singular checks before inversion
Returns:
tolerance
• ### density

public double density(double[] vals) throws MathIllegalArgumentException
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:
MathIllegalArgumentException
• ### 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.