GaussianSumUtilities< N > Class Template Reference

#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 (unsigned int i) const
	covariance matrix of a component More...
const Matrix &	covariance () const
	combined covariance 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 (unsigned int i) const
	mean value of a component More...
const Vector &	mean () const
	combined mean 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 (unsigned int i) const
	weight of a component More...
double	weight () const
	combined weight 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

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

Referenced by GaussianSumUtilities< N >::covariance().

template<unsigned int N>

Vector GaussianSumUtilities< N >::computeModeWithoutTransform ( ) const

protected

calculation of mode

Referenced by GaussianSumUtilities< N >::covariance().

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

Referenced by GaussianSumUtilities< N >::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(), GaussianSumUtilities< N >::d1LnPdf(), GaussianSumUtilities< N >::d1Pdf(), GaussianSumUtilities< N >::d2LnPdf(), GaussianSumUtilities< N >::d2Pdf(), mps_fire::i, GaussianSumUtilities< N >::lnPdf(), GaussianSumUtilities< N >::mode(), GaussianSumUtilities< N >::modeIsValid(), and GaussianSumUtilities< N >::pdf().

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

template<unsigned int N>

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

inline

combined covariance

Definition at line 89 of file GaussianSumUtilities.h.

References GaussianSumUtilities< N >::computeMode(), GaussianSumUtilities< N >::computeModeWithoutTransform(), GaussianSumUtilities< N >::constrainedState(), MultiGaussianState< N >::covariance(), edmIntegrityCheck::d, GaussianSumUtilities< N >::d1LnPdf(), GaussianSumUtilities< N >::d1Pdf(), GaussianSumUtilities< N >::d2LnPdf(), GaussianSumUtilities< N >::d2Pdf(), GaussianSumUtilities< N >::findMode(), GaussianSumUtilities< N >::gauss(), GaussianSumUtilities< N >::lnPdf(), GaussianSumUtilities< N >::localCovariance(), GaussianSumUtilities< N >::pdf(), GaussianSumUtilities< N >::pdfComponents(), GaussianSumUtilities< N >::setInvalidMode(), GaussianSumUtilities< N >::setMode(), GaussianSumUtilities< N >::tensorProduct(), GaussianSumUtilities< N >::theState, and x.

                                    {
    return theState.covariance();
  }

template<unsigned int N>

Vector GaussianSumUtilities< N >::d1LnPdf

(

const Vector &

)

const

gradient of ln(pdf)

Referenced by GaussianSumUtilities< N >::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 >::d1Pdf

(

const Vector &

)

const

gradient

Referenced by GaussianSumUtilities< N >::covariance().

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

Hessian of ln(pdf)

Referenced by GaussianSumUtilities< N >::covariance().

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 >::d2Pdf

(

const Vector &

)

const

Hessian.

Referenced by GaussianSumUtilities< N >::covariance().

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>

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

private

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

Referenced by GaussianSumUtilities< N >::covariance().

template<unsigned int N>

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

private

value of gaussian distribution

Referenced by GaussianSumUtilities< N >::covariance().

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

value of ln(pdf)

Referenced by GaussianSumUtilities< N >::covariance().

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>

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

private

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

Referenced by GaussianSumUtilities< N >::covariance().

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 mps_fire::i.

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

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 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

Referenced by GaussianSumUtilities< N >::covariance().

template<unsigned int N>

bool GaussianSumUtilities< N >::modeIsValid

(

)

const

mode status

Referenced by GaussianSumUtilities< N >::covariance().

template<unsigned int N>

double GaussianSumUtilities< N >::pdf

(

const Vector &

)

const

value of the p.d.f.

Referenced by GaussianSumUtilities< N >::covariance().

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>

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

private

pdf components

Referenced by GaussianSumUtilities< N >::covariance().

template<unsigned int N>

void GaussianSumUtilities< N >::setInvalidMode ( ) const

private

set mode "state" in case of failure

Referenced by GaussianSumUtilities< N >::covariance().

template<unsigned int N>

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

private

set mode "state" from solution of mode finding

Referenced by GaussianSumUtilities< N >::covariance().

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().

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

                                    {
    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)

Referenced by GaussianSumUtilities< N >::covariance().

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 mps_fire::i.

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

template<unsigned int N>

double GaussianSumUtilities< N >::weight ( void  ) const

inline

combined weight

Definition at line 81 of file GaussianSumUtilities.h.

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

                         {
    return theState.weight();
  }

Member Data Documentation

template<unsigned int N>

SingleGaussianState<N> GaussianSumUtilities< N >::theMode

mutableprivate

Definition at line 148 of file GaussianSumUtilities.h.

template<unsigned int N>

ModeStatus GaussianSumUtilities< N >::theModeStatus

mutableprivate

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().