#include <GaussianSumUtilities.h>

Public Types
typedef ROOT::Math::SMatrix < double, N, N, ROOT::Math::MatRepStd< double, N > >	GenMatrix
typedef SingleState::Matrix	Matrix
typedef MultiGaussianState< N >	MultiState
typedef SingleGaussianState< N >	SingleState
typedef MultiState::SingleStateContainer	SingleStateContainer
typedef MultiState::SingleStatePtr	SingleStatePtr
typedef SingleState::Vector	Vector
Public Member Functions
const SingleStateContainer &	components () const
	components
const Matrix &	covariance (unsigned int i) const
	covariance matrix of a component
const Matrix &	covariance () const
	combined covariance
Vector	d1LnPdf (const Vector &) const
	gradient of ln(pdf)
Vector	d1Pdf (const Vector &) const
	gradient
Matrix	d2LnPdf (const Vector &) const
	Hessian of ln(pdf)
Matrix	d2Pdf (const Vector &) const
	Hessian.
	GaussianSumUtilities (const MultiState &state)
double	lnPdf (const Vector &) const
	value of ln(pdf)
const Vector &	mean () const
	combined mean
const Vector &	mean (unsigned int i) const
	mean value of a component
const SingleGaussianState< N > &	mode () const
bool	modeIsValid () const
	mode status
double	pdf (const Vector &) const
	value of the p.d.f.
unsigned int	size () const
	number of components
const MultiState &	state () const
	multi-state
double	weight () const
	combined weight
double	weight (unsigned int i) const
	weight of a component
	~GaussianSumUtilities ()
Protected Member Functions
Vector	computeModeWithoutTransform () const
	calculation of mode
Private Types
enum	ModeStatus { Valid, NotValid, NotComputed }
Private Member Functions
void	computeMode () const
	calculation of mode with transformation of pdf
MultiGaussianState1D	constrainedState (const Vector &d, const Vector &x0) const
	state constrained to a line x = s*d+x0
Vector	d1LnPdf (const Vector &, const std::vector< double > &) const
	gradient of ln(pdf) using the pdf components at the evaluation point
Vector	d1Pdf (const Vector &, const std::vector< double > &) const
	gradient using the pdf components at the evaluation point
Matrix	d2LnPdf (const Vector &, const std::vector< double > &) const
	Hessian of ln(pdf) using the pdf components at the evaluation point.
Matrix	d2Pdf (const Vector &, const std::vector< double > &) const
	Hessian using the pdf components at the evaluation point.
bool	findMode (Vector &mode, double &pdfAtMode, const Vector &xStart) const
	mode from starting value in ln(pdf); returns true on success
double	gauss (const double &, const double &, const double &) const
	value of gaussian distribution
double	gauss (const Vector &, const Vector &, const Matrix &) const
	value of multidimensional gaussian distribution
double	lnPdf (const Vector &, const std::vector< double > &) const
	value of ln(pdf) using the pdf components at the evaluation point
Matrix	localCovariance (const Vector &x) const
double	pdf (const Vector &, const std::vector< double > &) const
	value of the p.d.f. using the pdf components at the evaluation point
std::vector< double >	pdfComponents (const Vector &) const
	pdf components
void	setInvalidMode () const
	set mode "state" in case of failure
void	setMode (const Vector &mode) const
	set mode "state" from solution of mode finding
Matrix	tensorProduct (const Vector &) const
	Symmetric Tensor Product (not recognized by standard ROOT Math)
Private Attributes
SingleGaussianState< N >	theMode
ModeStatus	theModeStatus
const MultiState &	theState

Detailed Description

template<unsigned int N>
class GaussianSumUtilities< N >

Utility class for the analysis of multi-dimensional Gaussian mixtures. The input state is assumed to exist for the lifetime of this object.

Definition at line 15 of file GaussianSumUtilities.h.

Member Typedef Documentation

template<unsigned int N>

typedef ROOT::Math::SMatrix<double,N,N,ROOT::Math::MatRepStd<double,N> > GaussianSumUtilities< N >::GenMatrix

Definition at line 20 of file GaussianSumUtilities.h.

template<unsigned int N>

typedef SingleState::Matrix GaussianSumUtilities< N >::Matrix

Definition at line 23 of file GaussianSumUtilities.h.

template<unsigned int N>

typedef MultiGaussianState<N> GaussianSumUtilities< N >::MultiState

Definition at line 18 of file GaussianSumUtilities.h.

template<unsigned int N>

typedef SingleGaussianState<N> GaussianSumUtilities< N >::SingleState

Definition at line 17 of file GaussianSumUtilities.h.

template<unsigned int N>

typedef MultiState::SingleStateContainer GaussianSumUtilities< N >::SingleStateContainer

Definition at line 25 of file GaussianSumUtilities.h.

template<unsigned int N>

typedef MultiState::SingleStatePtr GaussianSumUtilities< N >::SingleStatePtr

Definition at line 24 of file GaussianSumUtilities.h.

template<unsigned int N>

typedef SingleState::Vector GaussianSumUtilities< N >::Vector

Definition at line 22 of file GaussianSumUtilities.h.

Member Enumeration Documentation

template<unsigned int N>

enum GaussianSumUtilities::ModeStatus [private]

Enumerator:

Valid
NotValid
NotComputed

Definition at line 28 of file GaussianSumUtilities.h.

{ Valid, NotValid, NotComputed };

Constructor & Destructor Documentation

template<unsigned int N>

GaussianSumUtilities< N >::GaussianSumUtilities ( const MultiState & state ) [inline]

Definition at line 31 of file GaussianSumUtilities.h.

                                                 :
    theState(state), 
    theModeStatus(NotComputed) {
  }

template<unsigned int N>

GaussianSumUtilities< N >::~GaussianSumUtilities ( ) [inline]

Definition at line 35 of file GaussianSumUtilities.h.

                           {
  }

Member Function Documentation

template<unsigned int N>

const SingleStateContainer& GaussianSumUtilities< N >::components ( ) const [inline]

components

Definition at line 43 of file GaussianSumUtilities.h.

References MultiGaussianState< N >::components(), and GaussianSumUtilities< N >::theState.

Referenced by GaussianSumUtilities< N >::covariance(), GaussianSumUtilities< N >::mean(), GaussianSumUtilities< N >::size(), and GaussianSumUtilities< N >::weight().

                                                  {
    return theState.components();
  }

template<unsigned int N>

void GaussianSumUtilities< N >::computeMode ( ) const [private]

calculation of mode with transformation of pdf

template<unsigned int N>

Vector GaussianSumUtilities< N >::computeModeWithoutTransform ( ) const [protected]

calculation of mode

template<unsigned int N>

MultiGaussianState1D GaussianSumUtilities< N >::constrainedState	(	const Vector &	d,
		const Vector &	x0
	)		const `[private]`

state constrained to a line x = s*d+x0

template<unsigned int N>

const Matrix& GaussianSumUtilities< N >::covariance ( void ) const [inline]

combined covariance

Definition at line 89 of file GaussianSumUtilities.h.

References MultiGaussianState< N >::covariance(), and GaussianSumUtilities< N >::theState.

                                    {
    return theState.covariance();
  }

template<unsigned int N>

const Matrix& GaussianSumUtilities< N >::covariance ( unsigned int i ) const [inline]

covariance matrix of a component

Definition at line 59 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::components(), and i.

                                                         {
    return components()[i]->covariance();
  }

template<unsigned int N>

Vector GaussianSumUtilities< N >::d1LnPdf	(	const Vector &	,
		const std::vector< double > &
	)		const `[private]`

gradient of ln(pdf) using the pdf components at the evaluation point

template<unsigned int N>

Vector GaussianSumUtilities< N >::d1LnPdf ( const Vector & ) const

gradient of ln(pdf)

template<unsigned int N>

Vector GaussianSumUtilities< N >::d1Pdf ( const Vector & ) const

gradient

template<unsigned int N>

Vector GaussianSumUtilities< N >::d1Pdf	(	const Vector &	,
		const std::vector< double > &
	)		const `[private]`

gradient using the pdf components at the evaluation point

template<unsigned int N>

Matrix GaussianSumUtilities< N >::d2LnPdf	(	const Vector &	,
		const std::vector< double > &
	)		const `[private]`

Hessian of ln(pdf) using the pdf components at the evaluation point.

template<unsigned int N>

Matrix GaussianSumUtilities< N >::d2LnPdf ( const Vector & ) const

Hessian of ln(pdf)

template<unsigned int N>

Matrix GaussianSumUtilities< N >::d2Pdf	(	const Vector &	,
		const std::vector< double > &
	)		const `[private]`

Hessian using the pdf components at the evaluation point.

template<unsigned int N>

Matrix GaussianSumUtilities< N >::d2Pdf ( const Vector & ) const

Hessian.

template<unsigned int N>

bool GaussianSumUtilities< N >::findMode	(	Vector &	mode,
		double &	pdfAtMode,
		const Vector &	xStart
	)		const `[private]`

mode from starting value in ln(pdf); returns true on success

template<unsigned int N>

double GaussianSumUtilities< N >::gauss	(	const double &	,
		const double &	,
		const double &
	)		const `[private]`

value of gaussian distribution

template<unsigned int N>

double GaussianSumUtilities< N >::gauss	(	const Vector &	,
		const Vector &	,
		const Matrix &
	)		const `[private]`

value of multidimensional gaussian distribution

template<unsigned int N>

double GaussianSumUtilities< N >::lnPdf	(	const Vector &	,
		const std::vector< double > &
	)		const `[private]`

value of ln(pdf) using the pdf components at the evaluation point

template<unsigned int N>

double GaussianSumUtilities< N >::lnPdf ( const Vector & ) const

value of ln(pdf)

template<unsigned int N>

Matrix GaussianSumUtilities< N >::localCovariance ( const Vector & x ) const [private]

Local variance from Hessian matrix. Only valid if x corresponds to a (local) maximum!

template<unsigned int N>

const Vector& GaussianSumUtilities< N >::mean ( ) const [inline]

combined mean

Definition at line 85 of file GaussianSumUtilities.h.

References MultiGaussianState< N >::mean(), and GaussianSumUtilities< N >::theState.

                              {
    return theState.mean();
  }

template<unsigned int N>

const Vector& GaussianSumUtilities< N >::mean ( unsigned int i ) const [inline]

mean value of a component

Definition at line 55 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::components(), and i.

                                                   {
    return components()[i]->mean();
  }

template<unsigned int N>

const SingleGaussianState<N>& GaussianSumUtilities< N >::mode ( ) const

Mode "state": mean = mode, covariance = local covariance at mode, weight chosen to have pdf(mode) equal to the one of the mixture

template<unsigned int N>

bool GaussianSumUtilities< N >::modeIsValid ( ) const

mode status

template<unsigned int N>

double GaussianSumUtilities< N >::pdf	(	const Vector &	,
		const std::vector< double > &
	)		const `[private]`

value of the p.d.f. using the pdf components at the evaluation point

template<unsigned int N>

double GaussianSumUtilities< N >::pdf ( const Vector & ) const

value of the p.d.f.

template<unsigned int N>

std::vector<double> GaussianSumUtilities< N >::pdfComponents ( const Vector & ) const [private]

pdf components

template<unsigned int N>

void GaussianSumUtilities< N >::setInvalidMode ( ) const [private]

set mode "state" in case of failure

template<unsigned int N>

void GaussianSumUtilities< N >::setMode ( const Vector & mode ) const [private]

set mode "state" from solution of mode finding

template<unsigned int N>

unsigned int GaussianSumUtilities< N >::size ( void ) const [inline]

number of components

Definition at line 39 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::components().

                                    {
    return components().size();
  }

template<unsigned int N>

const MultiState& GaussianSumUtilities< N >::state ( ) const [inline]

multi-state

Definition at line 47 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::theState.

                                   {
    return theState;
  }

template<unsigned int N>

Matrix GaussianSumUtilities< N >::tensorProduct ( const Vector & ) const [private]

Symmetric Tensor Product (not recognized by standard ROOT Math)

template<unsigned int N>

double GaussianSumUtilities< N >::weight ( ) const [inline]

combined weight

Definition at line 81 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::theState, and MultiGaussianState< N >::weight().

                         {
    return theState.weight();
  }

template<unsigned int N>

double GaussianSumUtilities< N >::weight ( unsigned int i ) const [inline]

weight of a component

Definition at line 51 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::components(), and i.

                                              {
    return components()[i]->weight();
  }

Member Data Documentation

template<unsigned int N>

SingleGaussianState<N> GaussianSumUtilities< N >::theMode [mutable, private]

Definition at line 148 of file GaussianSumUtilities.h.

template<unsigned int N>

ModeStatus GaussianSumUtilities< N >::theModeStatus [mutable, private]

Definition at line 146 of file GaussianSumUtilities.h.

template<unsigned int N>

const MultiState& GaussianSumUtilities< N >::theState [private]

Definition at line 143 of file GaussianSumUtilities.h.

Referenced by GaussianSumUtilities< N >::components(), GaussianSumUtilities< N >::covariance(), GaussianSumUtilities< N >::mean(), GaussianSumUtilities< N >::state(), and GaussianSumUtilities< N >::weight().

GaussianSumUtilities< N > Class Template Reference

Public Types

Public Member Functions

Protected Member Functions

Private Types

Private Member Functions

Private Attributes

Detailed Description

template<unsigned int N> class GaussianSumUtilities< N >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<unsigned int N>
class GaussianSumUtilities< N >