MultinormalGen Class Reference

Extends RandomMultivariateGen for a multivariate normal (or multinormal) distribution [98] . More...

Inheritance diagram for MultinormalGen:

Collaboration diagram for MultinormalGen:

Public Member Functions
	MultinormalGen (NormalGen gen1, int d)
	Constructs a generator with the standard multinormal distribution (with \(\boldsymbol{\mu}=\boldsymbol{0}\) and \(\boldsymbol{\Sigma}= \mathbf{I}\)) in \(d\) dimensions. More...
double []	getMu ()
	Returns the mean vector used by this generator. More...
double	getMu (int i)
	Returns the \(i\)-th component of the mean vector for this generator. More...
void	setMu (double[] mu)
	Sets the mean vector to mu. More...
void	setMu (int i, double mui)
	Sets the \(i\)-th component of the mean vector to mui. More...
DoubleMatrix2D	getSigma ()
	Returns the covariance matrix \(\boldsymbol{\Sigma}\) used by this generator. More...
void	nextPoint (double[] p)
	Generates a point from this multinormal distribution. More...
Public Member Functions inherited from RandomMultivariateGen
abstract void	nextPoint (double[] p)
	Generates a random point \(p\) using the the stream contained in this object.
void	nextArrayOfPoints (double[][] v, int start, int n)
	Generates \(n\) random points. More...
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. More...
void	setStream (RandomStream stream)
	Sets the umontreal.ssj.rng.RandomStream used by this object to stream.

Protected Member Functions
	MultinormalGen (NormalGen gen1, double[] mu, DoubleMatrix2D sigma)
	Constructs a multinormal generator with mean vector mu and covariance matrix sigma. More...
	MultinormalGen (NormalGen gen1, double[] mu, double[][] sigma)
	Equivalent to MultinormalGen(gen1, mu, new DenseDoubleMatrix2D (sigma)).

Protected Attributes
double []	mu
DoubleMatrix2D	sigma
DoubleMatrix2D	sqrtSigma
double []	temp
Protected Attributes inherited from RandomMultivariateGen
int	dimension
RandomStream	stream
RandomVariateGen	gen1

Static Protected Attributes
static final double	MYINF = 37.54

Detailed Description

Extends RandomMultivariateGen for a multivariate normal (or multinormal) distribution [98] .

The \(d\)-dimensional multivariate normal distribution with mean vector \(\boldsymbol{\mu}\in\mathbb{R}^d\) and (symmetric positive-definite) covariance matrix \(\boldsymbol{\Sigma}\), denoted \(N(\boldsymbol{\mu}, \boldsymbol{\Sigma})\), has density

\[ f(\mathbf{X})=\frac{1}{\sqrt{(2\pi)^d\det(\boldsymbol{\Sigma})}} \exp\left(-(\mathbf{X}- \boldsymbol{\mu})^{\!\mathsf{t}}\boldsymbol{\Sigma}^{-1}(\mathbf{X}- \boldsymbol{\mu})/2\right), \]

for all \(\mathbf{X}\in\mathbb{R}^d\), and \(\mathbf{X}^{\mathsf{t}}\) is the transpose vector of \(\mathbf{X}\). If \(\mathbf{Z}\sim N(\boldsymbol{0}, \mathbf{I})\) where \(\mathbf{I}\) is the identity matrix, \(\mathbf{Z}\) is said to have the standard multinormal distribution.

For the special case \(d=2\), if the random vector \(\mathbf{X}= (X_1, X_2)^{\mathsf{t}}\) has a bivariate normal distribution, then it has mean \(\boldsymbol{\mu}= (\mu_1, \mu_2)^{\mathsf{t}}\), and covariance matrix

\[ \boldsymbol{\Sigma}= \left[\begin{array}{cc} \sigma_1^2 & \rho\sigma_1\sigma_2 \\ \rho\sigma_1\sigma_2 & \sigma_2^2 \end{array}\right] \]

if and only if \(\mathrm{Var}[X_1] = \sigma_1^2\), \(\mathrm{Var}[X_2] = \sigma_2^2\), and the linear correlation between \(X_1\) and \(X_2\) is \(\rho\), where \(\sigma_1 > 0\), \(\sigma_2 > 0\), and \(-1 \le\rho\le1\).

Constructor & Destructor Documentation

MultinormalGen() [1/2]

MultinormalGen	(	NormalGen	gen1,
		int	d
	)

Constructs a generator with the standard multinormal distribution (with \(\boldsymbol{\mu}=\boldsymbol{0}\) and \(\boldsymbol{\Sigma}= \mathbf{I}\)) in \(d\) dimensions.

Each vector \(\mathbf{Z}\) will be generated via \(d\) successive calls to gen1, which must be a standard normal generator.

Parameters

gen1	the one-dimensional generator
d	the dimension of the generated vectors

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 d is negative.
NullPointerException	if gen1 is null.

MultinormalGen() [2/2]

MultinormalGen ( NormalGen  gen1, double []  mu, DoubleMatrix2D  sigma  )

protected

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 standard normal.

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.

Member Function Documentation

getMu() [1/2]

double [] getMu

(

)

Returns the mean vector used by this generator.

Returns

the current mean vector.

getMu() [2/2]

double getMu

(

int

i

)

Returns the \(i\)-th component of the mean vector for this generator.

Parameters

i	the index of the required component.

Returns

the value of \(\mu_i\).

Exceptions

ArrayIndexOutOfBoundsException

if i is negative or greater than or equal to getDimension.

getSigma()

DoubleMatrix2D getSigma

(

)

Returns the covariance matrix \(\boldsymbol{\Sigma}\) used by this generator.

Returns

the used covariance matrix.

nextPoint()

void nextPoint

(

double []

p

)

Generates a point from this multinormal distribution.

Parameters

p	the array to be filled with the generated point

setMu() [1/2]

void setMu

(

double []

mu

)

Sets the mean vector to mu.

Parameters

mu	the new mean vector.

Exceptions

NullPointerException	if mu is null.
IllegalArgumentException	if the length of mu does not correspond to getDimension.

setMu() [2/2]

void setMu	(	int	i,
		double	mui
	)

Sets the \(i\)-th component of the mean vector to mui.

Parameters

i	the index of the modified component.
mui	the new value of \(\mu_i\).

Exceptions

ArrayIndexOutOfBoundsException

if i is negative or greater than or equal to getDimension.

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

• MultinormalGen.java