Extends MultinormalGen for a multivariate normal distribution. More...

Inheritance diagram for umontreal.ssj.randvarmulti.MultinormalCholeskyGen:

Public Member Functions
	MultinormalCholeskyGen (NormalGen gen1, double[] mu, double[][] sigma)
	Equivalent to `MultinormalCholeskyGen(gen1, mu, new DenseDoubleMatrix2D(sigma))`.
	MultinormalCholeskyGen (NormalGen gen1, double[] mu, DoubleMatrix2D sigma)
	Constructs a multinormal generator with mean vector mu and covariance matrix sigma.
DoubleMatrix2D	getCholeskyDecompSigma ()
	Returns the lower-triangular matrix \(\mathbf{A}\) in the Cholesky decomposition of \(\boldsymbol{\Sigma}\).
void	setSigma (DoubleMatrix2D sigma)
	Sets the covariance matrix \(\boldsymbol{\Sigma}\) of this multinormal generator to sigma (and recomputes \(\mathbf{A}\)).
void	nextPoint (double[] p)
	Generates a point from this multinormal distribution.
Public Member Functions inherited from umontreal.ssj.randvarmulti.MultinormalGen
	MultinormalGen (NormalGen gen1, int d)
	Constructs a generator with the standard multinormal distribution (with \(\boldsymbol{\mu}=\boldsymbol{0}\) and.
double[]	getMu ()
	Returns the mean vector used by this generator.
double	getMu (int i)
	Returns the \(i\)-th component of the mean vector for this generator.
void	setMu (double[] mu)
	Sets the mean vector to mu.
void	setMu (int i, double mui)
	Sets the \(i\)-th component of the mean vector to mui.
DoubleMatrix2D	getSigma ()
	Returns the covariance matrix \(\boldsymbol{\Sigma}\) used by this generator.
Public Member Functions inherited from umontreal.ssj.randvarmulti.RandomMultivariateGen
void	nextArrayOfPoints (double[][] v, int start, int n)
	Generates \(n\) random points.
int	getDimension ()
	Returns the dimension of this multivariate generator (the dimension of the random points).
RandomStream	getStream ()
	Returns the umontreal.ssj.rng.RandomStream used by this object.
void	setStream (RandomStream stream)
	Sets the umontreal.ssj.rng.RandomStream used by this object to stream.

Static Public Member Functions
static void	nextPoint (NormalGen gen1, double[] mu, double[][] sigma, double[] p)
	Equivalent to `nextPoint(gen1, mu, new DenseDoubleMatrix2D(sigma), p)`.
static void	nextPoint (NormalGen gen1, double[] mu, DoubleMatrix2D sigma, double[] p)
	Generates a \(d\)-dimensional vector from the multinormal distribution with mean vector mu and covariance matrix sigma, using the one-dimensional normal generator gen1 to generate the coordinates of \(\mathbf{Z}\), and using the Cholesky decomposition of \(\boldsymbol{\Sigma}\).

Additional Inherited Members
Protected Member Functions inherited from umontreal.ssj.randvarmulti.MultinormalGen
	MultinormalGen (NormalGen gen1, double[] mu, DoubleMatrix2D sigma)
	Constructs a multinormal generator with mean vector mu and covariance matrix sigma.
	MultinormalGen (NormalGen gen1, double[] mu, double[][] sigma)
	Equivalent to `MultinormalGen(gen1, mu, new DenseDoubleMatrix2D (sigma))`.

Detailed Description

Extends MultinormalGen for a multivariate normal distribution.

[94] , generated via a Cholesky decomposition of the covariance matrix. The covariance matrix \(\boldsymbol{\Sigma}\) is decomposed (by the constructor) as \(\boldsymbol{\Sigma}= \mathbf{A}\mathbf{A}^{\!\mathsf{t}}\) where \(\mathbf{A}\) is a lower-triangular matrix (this is the Cholesky decomposition), and \(\mathbf{X}\) is generated via

\[ \mathbf{X}= \boldsymbol{\mu}+ \mathbf{A}\mathbf{Z}, \]

where \(\mathbf{Z}\) is a \(d\)-dimensional vector of independent standard normal random variates, and \(\mathbf{A}^{\!\mathsf{t}}\) is the transpose of \(\mathbf{A}\). The covariance matrix \(\boldsymbol{\Sigma}\) must be positive-definite, otherwise the Cholesky decomposition will fail. The decomposition method uses the CholeskyDecomposition class in colt.

Definition at line 54 of file MultinormalCholeskyGen.java.

Constructor & Destructor Documentation

◆ MultinormalCholeskyGen() [1/2]

umontreal.ssj.randvarmulti.MultinormalCholeskyGen.MultinormalCholeskyGen	(	NormalGen	gen1,
		double[]	mu,
		double	sigma[][] )

Equivalent to MultinormalCholeskyGen(gen1, mu, new DenseDoubleMatrix2D(sigma)).

Parameters

gen1	the one-dimensional generator
mu	the mean vector.
sigma	the covariance matrix.

Exceptions

NullPointerException	if any argument is `null`.
IllegalArgumentException	if the length of the mean vector is incompatible with the dimensions of the covariance matrix.

Definition at line 79 of file MultinormalCholeskyGen.java.

◆ MultinormalCholeskyGen() [2/2]

umontreal.ssj.randvarmulti.MultinormalCholeskyGen.MultinormalCholeskyGen	(	NormalGen	gen1,
		double[]	mu,
		DoubleMatrix2D	sigma )

Constructs a multinormal generator with mean vector mu and covariance matrix sigma.

The mean vector must have the same length as the dimensions of the covariance matrix, which must be symmetric and positive-definite. If any of the above conditions is violated, an exception is thrown. The vector \(\mathbf{Z}\) is generated by calling \(d\) times the generator gen1, which must be a standard normal 1-dimensional generator.

Parameters

gen1	the one-dimensional generator
mu	the mean vector.
sigma	the covariance matrix.

Exceptions

NullPointerException	if any argument is `null`.
IllegalArgumentException	if the length of the mean vector is incompatible with the dimensions of the covariance matrix.

Definition at line 100 of file MultinormalCholeskyGen.java.

Member Function Documentation

◆ getCholeskyDecompSigma()

DoubleMatrix2D umontreal.ssj.randvarmulti.MultinormalCholeskyGen.getCholeskyDecompSigma ( )

Returns the lower-triangular matrix \(\mathbf{A}\) in the Cholesky decomposition of \(\boldsymbol{\Sigma}\).

Returns: the Cholesky decomposition of the covariance matrix.

Definition at line 111 of file MultinormalCholeskyGen.java.

◆ nextPoint() [1/3]

void umontreal.ssj.randvarmulti.MultinormalCholeskyGen.nextPoint ( double[] p )

Generates a point from this multinormal distribution.

This is much faster than the static method as it computes the singular value decomposition matrix only once in the constructor.

Parameters

p	the array to be filled with the generated point

Reimplemented from umontreal.ssj.randvarmulti.MultinormalGen.

Definition at line 200 of file MultinormalCholeskyGen.java.

◆ nextPoint() [2/3]

void umontreal.ssj.randvarmulti.MultinormalCholeskyGen.nextPoint	(	NormalGen	gen1,
		double[]	mu,
		double	sigma[][],
		double[]	p )

static

Equivalent to nextPoint(gen1, mu, new DenseDoubleMatrix2D(sigma), p).

Definition at line 137 of file MultinormalCholeskyGen.java.

◆ nextPoint() [3/3]

void umontreal.ssj.randvarmulti.MultinormalCholeskyGen.nextPoint	(	NormalGen	gen1,
		double[]	mu,
		DoubleMatrix2D	sigma,
		double[]	p )

static

Generates a \(d\)-dimensional vector from the multinormal distribution with mean vector mu and covariance matrix sigma, using the one-dimensional normal generator gen1 to generate the coordinates of \(\mathbf{Z}\), and using the Cholesky decomposition of \(\boldsymbol{\Sigma}\).

The resulting vector is put into p. Note that this static method will be very slow for large dimensions, since it computes the Cholesky decomposition at every call. It is therefore recommended to use a MultinormalCholeskyGen object instead, if the method is to be called more than once.

Parameters

p	the array to be filled with the generated point.

Exceptions

IllegalArgumentException	if the one-dimensional normal generator uses a normal distribution with \(\mu\) not equal to 0, or \(\sigma\) not equal to 1.
IllegalArgumentException	if the length of the mean vector is different from the dimensions of the covariance matrix, or if the covariance matrix is not symmetric and positive-definite.
NullPointerException	if any argument is `null`.

Definition at line 163 of file MultinormalCholeskyGen.java.

◆ setSigma()

void umontreal.ssj.randvarmulti.MultinormalCholeskyGen.setSigma ( DoubleMatrix2D sigma )

Sets the covariance matrix \(\boldsymbol{\Sigma}\) of this multinormal generator to sigma (and recomputes \(\mathbf{A}\)).

Parameters

sigma the new covariance matrix.

Exceptions

IllegalArgumentException if `sigma` has incorrect dimensions.

Definition at line 122 of file MultinormalCholeskyGen.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/randvarmulti/MultinormalCholeskyGen.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MultinormalCholeskyGen() [1/2]

◆ MultinormalCholeskyGen() [2/2]

Member Function Documentation

◆ getCholeskyDecompSigma()

◆ nextPoint() [1/3]

◆ nextPoint() [2/3]

◆ nextPoint() [3/3]

◆ setSigma()