Extends MultinormalGen for a multivariate normal distribution [98] , generated via the method of principal components analysis (PCA) of the covariance matrix. More...

Inheritance diagram for MultinormalPCAGen:

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Collaboration diagram for MultinormalPCAGen:

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Public Member Functions
	MultinormalPCAGen (NormalGen gen1, double[] mu, double[][] sigma)
	Equivalent to MultinormalPCAGen(gen1, mu, new DenseDoubleMatrix2D(sigma)).

	MultinormalPCAGen (NormalGen gen1, double[] mu, DoubleMatrix2D sigma)
	Constructs a multinormal generator with mean vector `mu` and covariance matrix `sigma`. More...

DoubleMatrix2D	getPCADecompSigma ()
	Returns the matrix \(\mathbf{A}= \mathbf{V}\sqrt{\boldsymbol{\Lambda}}\) of this object. More...

double []	getLambda ()
	Returns the eigenvalues of \(\boldsymbol{\Sigma}\) in decreasing order.

void	setSigma (DoubleMatrix2D sigma)
	Sets the covariance matrix \(\boldsymbol{\Sigma}\) of this multinormal generator to `sigma` (and recomputes \(\mathbf{A}\)). More...

void	nextPoint (double[] p)
	Generates a point from this multinormal distribution. More...

Public Member Functions inherited from MultinormalGen
	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`.

Static Public Member Functions
static DoubleMatrix2D	decompPCA (double[][] sigma)
	Computes the decomposition `sigma` = \(\boldsymbol{\Sigma}= \mathbf{V}\boldsymbol{\Lambda}\mathbf{V}^{\mathsf{t}}\). More...

static DoubleMatrix2D	decompPCA (DoubleMatrix2D sigma)
	Computes the decomposition `sigma` = \(\boldsymbol{\Sigma}= \mathbf{V}\boldsymbol{\Lambda}\mathbf{V}^{\mathsf{t}}\). More...

static double []	getLambda (DoubleMatrix2D sigma)
	Computes and returns the eigenvalues of `sigma` in decreasing order.

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 PCA decomposition of \(\boldsymbol{\Sigma}\). More...

static void	nextPoint (NormalGen gen1, double[] mu, double[][] sigma, double[] p)
	Equivalent to nextPoint(gen1, mu, new DenseDoubleMatrix2D(sigma), p).

Additional Inherited Members
Protected Member Functions inherited from MultinormalGen
	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 inherited from MultinormalGen
double []	mu

DoubleMatrix2D	sigma

DoubleMatrix2D	sqrtSigma

double []	temp

Protected Attributes inherited from RandomMultivariateGen
int	dimension

RandomStream	stream

RandomVariateGen	gen1

Static Protected Attributes inherited from MultinormalGen
static final double	MYINF = 37.54

Detailed Description

Extends MultinormalGen for a multivariate normal distribution [98] , generated via the method of principal components analysis (PCA) of the covariance matrix.

The covariance matrix \(\boldsymbol{\Sigma}\) is decomposed (by the constructor) as \(\boldsymbol{\Sigma}= \mathbf{V}\boldsymbol{\Lambda}\mathbf{V}^{\mathsf{t}}\) where \(\mathbf{V}\) is an orthogonal matrix and \(\boldsymbol{\Lambda}\) is the diagonal matrix made up of the eigenvalues of \(\boldsymbol{\Sigma}\). \(\mathbf{V}^{\mathsf{t}}\) is the transpose matrix of \(\mathbf{V}\). The eigenvalues are ordered from the largest ( \(\lambda_1\)) to the smallest ( \(\lambda_d\)). The random multinormal vector \(\mathbf{X}\) is generated via

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

where \(\mathbf{A}= \mathbf{V}\sqrt{\boldsymbol{\Lambda}}\), and \(\mathbf{Z}\) is a \(d\)-dimensional vector of independent standard normal random variates. The decomposition method uses the SingularValueDecomposition class in colt.

Constructor & Destructor Documentation

◆ MultinormalPCAGen()

MultinormalPCAGen	(	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 semi-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.

Member Function Documentation

◆ decompPCA() [1/2]

static DoubleMatrix2D decompPCA ( double sigma[][] )

static

Computes the decomposition sigma = \(\boldsymbol{\Sigma}= \mathbf{V}\boldsymbol{\Lambda}\mathbf{V}^{\mathsf{t}}\).

Returns \(\mathbf{A}= \mathbf{V}\sqrt{\boldsymbol{\Lambda}}\).

◆ decompPCA() [2/2]

static DoubleMatrix2D decompPCA ( DoubleMatrix2D sigma )

static

Computes the decomposition sigma = \(\boldsymbol{\Sigma}= \mathbf{V}\boldsymbol{\Lambda}\mathbf{V}^{\mathsf{t}}\).

Returns \(\mathbf{A}= \mathbf{V}\sqrt{\boldsymbol{\Lambda}}\).

◆ getPCADecompSigma()

DoubleMatrix2D getPCADecompSigma ( )

Returns the matrix \(\mathbf{A}= \mathbf{V}\sqrt{\boldsymbol{\Lambda}}\) of this object.

Returns: the PCA square root of the covariance matrix

◆ nextPoint() [1/2]

static void 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 PCA decomposition of \(\boldsymbol{\Sigma}\).

The resulting vector is put into p. Note that this static method will be very slow for large dimensions, because it recomputes the singular value decomposition at every call. It is therefore recommended to use a MultinormalPCAGen 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`.

◆ nextPoint() [2/2]

void 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

◆ setSigma()

void 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.

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

MultinormalPCAGen.java

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MultinormalPCAGen()

Member Function Documentation

◆ decompPCA() [1/2]

◆ decompPCA() [2/2]

◆ getPCADecompSigma()

◆ nextPoint() [1/2]

◆ nextPoint() [2/2]

◆ setSigma()