#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 More...

const Matrix &	covariance () const
	combined covariance More...

const Matrix &	covariance (unsigned int i) const
	covariance matrix of a component More...

Vector	d1LnPdf (const Vector &) const
	gradient of ln(pdf) More...

Vector	d1Pdf (const Vector &) const
	gradient More...

Matrix	d2LnPdf (const Vector &) const
	Hessian of ln(pdf) More...

Matrix	d2Pdf (const Vector &) const
	Hessian. More...

	GaussianSumUtilities (const MultiState &state)

double	lnPdf (const Vector &) const
	value of ln(pdf) More...

const Vector &	mean () const
	combined mean More...

const Vector &	mean (unsigned int i) const
	mean value of a component More...

const SingleGaussianState< N > &	mode () const

bool	modeIsValid () const
	mode status More...

double	pdf (const Vector &) const
	value of the p.d.f. More...

unsigned int	size () const
	number of components More...

const MultiState &	state () const
	multi-state More...

double	weight () const
	combined weight More...

double	weight (unsigned int i) const
	weight of a component More...

	~GaussianSumUtilities ()

Protected Member Functions
Vector	computeModeWithoutTransform () const
	calculation of mode More...

Private Types
enum	ModeStatus { Valid, NotValid, NotComputed }

Private Member Functions
void	computeMode () const
	calculation of mode with transformation of pdf More...

MultiGaussianState1D	constrainedState (const Vector &d, const Vector &x0) const
	state constrained to a line x = s*d+x0 More...

Vector	d1LnPdf (const Vector &, const std::vector< double > &) const
	gradient of ln(pdf) using the pdf components at the evaluation point More...

Vector	d1Pdf (const Vector &, const std::vector< double > &) const
	gradient using the pdf components at the evaluation point More...

Matrix	d2LnPdf (const Vector &, const std::vector< double > &) const
	Hessian of ln(pdf) using the pdf components at the evaluation point. More...

Matrix	d2Pdf (const Vector &, const std::vector< double > &) const
	Hessian using the pdf components at the evaluation point. More...

bool	findMode (Vector &mode, double &pdfAtMode, const Vector &xStart) const
	mode from starting value in ln(pdf); returns true on success More...

double	gauss (const double &, const double &, const double &) const
	value of gaussian distribution More...

double	gauss (const Vector &, const Vector &, const Matrix &) const
	value of multidimensional gaussian distribution More...

double	lnPdf (const Vector &, const std::vector< double > &) const
	value of ln(pdf) using the pdf components at the evaluation point More...

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 More...

std::vector< double >	pdfComponents (const Vector &) const
	pdf components More...

void	setInvalidMode () const
	set mode "state" in case of failure More...

void	setMode (const Vector &mode) const
	set mode "state" from solution of mode finding More...

Matrix	tensorProduct (const Vector &) const
	Symmetric Tensor Product (not recognized by standard ROOT Math) More...

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

◆ GenMatrix

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.

◆ Matrix

template<unsigned int N>

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

Definition at line 23 of file GaussianSumUtilities.h.

◆ MultiState

template<unsigned int N>

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

Definition at line 18 of file GaussianSumUtilities.h.

◆ SingleState

template<unsigned int N>

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

Definition at line 17 of file GaussianSumUtilities.h.

◆ SingleStateContainer

template<unsigned int N>

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

Definition at line 25 of file GaussianSumUtilities.h.

◆ SingleStatePtr

template<unsigned int N>

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

Definition at line 24 of file GaussianSumUtilities.h.

◆ Vector

template<unsigned int N>

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

Definition at line 22 of file GaussianSumUtilities.h.

Member Enumeration Documentation

◆ ModeStatus

template<unsigned int N>

enum GaussianSumUtilities::ModeStatus

private

Enumerator
Valid
NotValid
NotComputed

Definition at line 28 of file GaussianSumUtilities.h.

28 { Valid, NotValid, NotComputed };

Constructor & Destructor Documentation

◆ GaussianSumUtilities()

template<unsigned int N>

GaussianSumUtilities< N >::GaussianSumUtilities ( const MultiState & state )

inline

Definition at line 31 of file GaussianSumUtilities.h.

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

◆ ~GaussianSumUtilities()

template<unsigned int N>

GaussianSumUtilities< N >::~GaussianSumUtilities ( )

inline

Definition at line 35 of file GaussianSumUtilities.h.

35 {

36 }

Member Function Documentation

◆ components()

template<unsigned int N>

const SingleStateContainer& GaussianSumUtilities< N >::components ( ) const

inline

components

Definition at line 43 of file GaussianSumUtilities.h.

                                                   {
     return theState.components();
   }

References GaussianSumUtilities< N >::theState.

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

◆ computeMode()

template<unsigned int N>

void GaussianSumUtilities< N >::computeMode ( ) const

private

calculation of mode with transformation of pdf

◆ computeModeWithoutTransform()

template<unsigned int N>

Vector GaussianSumUtilities< N >::computeModeWithoutTransform ( ) const

protected

calculation of mode

◆ constrainedState()

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

◆ covariance() [1/2]

template<unsigned int N>

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

inline

combined covariance

Definition at line 89 of file GaussianSumUtilities.h.

                                     {
     return theState.covariance();
   }

References GaussianSumUtilities< N >::theState.

◆ covariance() [2/2]

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.

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

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

◆ d1LnPdf() [1/2]

template<unsigned int N>

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

gradient of ln(pdf)

◆ d1LnPdf() [2/2]

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

◆ d1Pdf() [1/2]

template<unsigned int N>

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

gradient

◆ d1Pdf() [2/2]

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

◆ d2LnPdf() [1/2]

template<unsigned int N>

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

Hessian of ln(pdf)

◆ d2LnPdf() [2/2]

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.

◆ d2Pdf() [1/2]

template<unsigned int N>

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

Hessian.

◆ d2Pdf() [2/2]

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.

◆ findMode()

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

◆ gauss() [1/2]

template<unsigned int N>

double GaussianSumUtilities< N >::gauss	(	const double &	,
		const double &	,
		const double &
	)		const

private

value of gaussian distribution

◆ gauss() [2/2]

template<unsigned int N>

double GaussianSumUtilities< N >::gauss	(	const Vector &	,
		const Vector &	,
		const Matrix &
	)		const

private

value of multidimensional gaussian distribution

◆ lnPdf() [1/2]

template<unsigned int N>

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

value of ln(pdf)

◆ lnPdf() [2/2]

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

◆ localCovariance()

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!

◆ mean() [1/2]

template<unsigned int N>

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

inline

combined mean

Definition at line 85 of file GaussianSumUtilities.h.

                               {
     return theState.mean();
   }

References GaussianSumUtilities< N >::theState.

◆ mean() [2/2]

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.

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

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

◆ mode()

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

◆ modeIsValid()

template<unsigned int N>

bool GaussianSumUtilities< N >::modeIsValid ( ) const

mode status

◆ pdf() [1/2]

template<unsigned int N>

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

value of the p.d.f.

◆ pdf() [2/2]

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

◆ pdfComponents()

template<unsigned int N>

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

private

pdf components

◆ setInvalidMode()

template<unsigned int N>

void GaussianSumUtilities< N >::setInvalidMode ( ) const

private

set mode "state" in case of failure

◆ setMode()

template<unsigned int N>

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

private

set mode "state" from solution of mode finding

◆ size()

template<unsigned int N>

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

inline

number of components

Definition at line 39 of file GaussianSumUtilities.h.

                                     {
     return components().size();
   }

References GaussianSumUtilities< N >::components().

Referenced by ntupleDataFormat._Collection::__iter__(), and ntupleDataFormat._Collection::__len__().

◆ state()

template<unsigned int N>

const MultiState& GaussianSumUtilities< N >::state ( ) const

inline

multi-state

Definition at line 47 of file GaussianSumUtilities.h.

                                    {
     return theState;
   }

References GaussianSumUtilities< N >::theState.

◆ tensorProduct()

template<unsigned int N>

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

private

Symmetric Tensor Product (not recognized by standard ROOT Math)

◆ weight() [1/2]

template<unsigned int N>

double GaussianSumUtilities< N >::weight ( ) const

inline

combined weight

Definition at line 81 of file GaussianSumUtilities.h.

                          {
     return theState.weight();
   }

References GaussianSumUtilities< N >::theState.

◆ weight() [2/2]

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.

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

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

Member Data Documentation

◆ theMode

template<unsigned int N>

SingleGaussianState<N> GaussianSumUtilities< N >::theMode

mutableprivate

Definition at line 148 of file GaussianSumUtilities.h.

◆ theModeStatus

template<unsigned int N>

ModeStatus GaussianSumUtilities< N >::theModeStatus

mutableprivate

Definition at line 146 of file GaussianSumUtilities.h.

◆ theState

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().

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

◆ GenMatrix

◆ Matrix

◆ MultiState

◆ SingleState

◆ SingleStateContainer

◆ SingleStatePtr

◆ Vector

Member Enumeration Documentation

◆ ModeStatus

Constructor & Destructor Documentation

◆ GaussianSumUtilities()

◆ ~GaussianSumUtilities()

Member Function Documentation

◆ components()

◆ computeMode()

◆ computeModeWithoutTransform()

◆ constrainedState()

◆ covariance() [1/2]

◆ covariance() [2/2]

◆ d1LnPdf() [1/2]

◆ d1LnPdf() [2/2]

◆ d1Pdf() [1/2]

◆ d1Pdf() [2/2]

◆ d2LnPdf() [1/2]

◆ d2LnPdf() [2/2]

◆ d2Pdf() [1/2]

◆ d2Pdf() [2/2]

◆ findMode()

◆ gauss() [1/2]

◆ gauss() [2/2]

◆ lnPdf() [1/2]

◆ lnPdf() [2/2]

◆ localCovariance()

◆ mean() [1/2]

◆ mean() [2/2]

◆ mode()

◆ modeIsValid()

◆ pdf() [1/2]

◆ pdf() [2/2]

◆ pdfComponents()

◆ setInvalidMode()

◆ setMode()

◆ size()

◆ state()

◆ tensorProduct()

◆ weight() [1/2]

◆ weight() [2/2]

Member Data Documentation

◆ theMode

◆ theModeStatus

◆ theState

template<unsigned int N>
class GaussianSumUtilities< N >