Extension of the FCNBase for the Fumili method.

Fumili applies only to minimization problems used for fitting. The method is based on a linearization of the model function negleting second derivatives. User needs to provide the model function. The figure-of-merit describing the difference between the model function and the actual measurements in the case of chi-square is the sum of the squares of the figures-of-merit calculated for each measurement point, which is implemented by the operator() member function. The user still has to implement the calculation of the individual figures-of-merit (which in the majority of the cases will be the (measured Value - the Value predicted by the model)/standard deviation implemented by the FumiliStandardChi2FCN; however this form can become more complicated (see for an example Numerical Recipes' section on "Straight-Line Data with Errors in Both Coordinates")).

Author: Andras Zsenei and Lorenzo Moneta, Creation date: 24 Aug 2004

See also: MINUIT Tutorial on function minimization, section 5; FumiliStandardChi2FCN

Definition at line 49 of file FumiliChi2FCN.h.

Public Member Functions
	FumiliChi2FCN ()

	~FumiliChi2FCN () override

virtual std::vector< double >	Elements (const std::vector< double > &par) const =0
	Evaluates the model function for the different measurement points and the Parameter values supplied, calculates a figure-of-merit for each measurement and returns a vector containing the result of this evaluation.

virtual const std::vector< double > &	GetMeasurement (int Index) const =0
	Accessor to the parameters of a given measurement.

virtual int	GetNumberOfMeasurements () const =0
	Accessor to the number of measurements used for calculating the present figure of merit.

const ParametricFunction *	ModelFunction () const
	Returns the model function used for the data.

double	operator() (const std::vector< double > &par) const override
	Calculates the sum of Elements squared, ie the chi-square.

void	SetModelFunction (const ParametricFunction &modelFCN)
	Sets the model function for the data (for example gaussian+linear for a peak)

double	Up () const override
	!!!!!!!!!!!! to be commented

Public Member Functions inherited from ROOT::Minuit2::FumiliFCNBase
	FumiliFCNBase ()
	Default Constructor.

	FumiliFCNBase (unsigned int npar)
	Constructor which initializes the class with the function provided by the user for modeling the data.

	~FumiliFCNBase () override

virtual unsigned int	Dimension ()
	return number of function variable (parameters) , i.e.

virtual void	EvaluateAll (const std::vector< double > &par)=0
	Evaluate function Value, Gradient and Hessian using Fumili approximation, for values of parameters p The result is cached inside and is return from the FumiliFCNBase::Value , FumiliFCNBase::Gradient and FumiliFCNBase::Hessian methods.

virtual const std::vector< double > &	Gradient () const
	Return cached Value of function Gradient estimated previously using the FumiliFCNBase::EvaluateAll method.

std::vector< double >	Gradient (const std::vector< double > &) const override

std::vector< double >	Hessian (const std::vector< double > &) const override
	Return Value of the i-th j-th element of the Hessian matrix estimated previously using the FumiliFCNBase::EvaluateAll method.

virtual double	Hessian (unsigned int row, unsigned int col) const

virtual double	Value () const
	Return cached Value of objective function estimated previously using the FumiliFCNBase::EvaluateAll method.

Public Member Functions inherited from ROOT::Minuit2::FCNGradientBase
	~FCNGradientBase () override

virtual bool	CheckGradient () const

virtual std::vector< double >	G2 (const std::vector< double > &) const
	return second derivatives (diagonal of the Hessian matrix)

virtual std::vector< double >	GradientWithPrevResult (const std::vector< double > &parameters, double , double , double *) const

virtual GradientParameterSpace	gradParameterSpace () const

virtual bool	HasG2 () const

virtual bool	HasHessian () const

Public Member Functions inherited from ROOT::Minuit2::FCNBase
	~FCNBase () override

virtual double	ErrorDef () const
	Error definition of the function.

virtual void	SetErrorDef (double)
	add interface to set dynamically a new error definition Re-implement this function if needed.

Public Member Functions inherited from ROOT::Minuit2::GenericFunction
virtual	~GenericFunction ()

Private Attributes
const ParametricFunction *	fModelFunction = nullptr

Additional Inherited Members
Protected Member Functions inherited from ROOT::Minuit2::FumiliFCNBase
std::vector< double > &	Gradient ()

std::vector< double > &	Hessian ()

virtual void	InitAndReset (unsigned int npar)
	initialize and reset values of gradien and Hessian

void	SetFCNValue (double value)

#include <Minuit2/FumiliChi2FCN.h>

Inheritance diagram for ROOT::Minuit2::FumiliChi2FCN:

[legend]

Constructor & Destructor Documentation

◆ FumiliChi2FCN()

ROOT::Minuit2::FumiliChi2FCN::FumiliChi2FCN ( )

inline

Definition at line 52 of file FumiliChi2FCN.h.

◆ ~FumiliChi2FCN()

ROOT::Minuit2::FumiliChi2FCN::~FumiliChi2FCN ( )

inlineoverride

Definition at line 54 of file FumiliChi2FCN.h.

Member Function Documentation

◆ Elements()

virtual std::vector< double > ROOT::Minuit2::FumiliChi2FCN::Elements ( const std::vector< double > & par ) const

pure virtual

Evaluates the model function for the different measurement points and the Parameter values supplied, calculates a figure-of-merit for each measurement and returns a vector containing the result of this evaluation.

Parameters

par	vector of Parameter values to feed to the model function.

Returns: A vector containing the figures-of-merit for the model function evaluated for each set of measurements.

Implemented in ROOT::Minuit2::FumiliStandardChi2FCN.

◆ GetMeasurement()

virtual const std::vector< double > & ROOT::Minuit2::FumiliChi2FCN::GetMeasurement ( int Index ) const

pure virtual

Accessor to the parameters of a given measurement.

For example in the case of a chi-square fit with a one-dimensional Gaussian, the Parameter characterizing the measurement will be the position. It is the Parameter that is passed to the model function.

Parameters

Index Index of the measueremnt the parameters of which to return

Returns: A reference to a vector containing the values characterizing a measurement

Implemented in ROOT::Minuit2::FumiliStandardChi2FCN.

◆ GetNumberOfMeasurements()

virtual int ROOT::Minuit2::FumiliChi2FCN::GetNumberOfMeasurements ( ) const

pure virtual

Accessor to the number of measurements used for calculating the present figure of merit.

Returns: the number of measurements

Implemented in ROOT::Minuit2::FumiliStandardChi2FCN.

◆ ModelFunction()

const ParametricFunction * ROOT::Minuit2::FumiliChi2FCN::ModelFunction ( ) const

inline

Returns the model function used for the data.

Returns: Returns a pointer to the model function.

Definition at line 74 of file FumiliChi2FCN.h.

◆ operator()()

double ROOT::Minuit2::FumiliChi2FCN::operator() ( const std::vector< double > & par ) const

inlineoverridevirtual

Calculates the sum of Elements squared, ie the chi-square.

The user must implement in a class which inherits from FumiliChi2FCN the member function Elements() which will supply the Elements for the sum.

Parameters

par	vector containing the Parameter values for the model function

Returns: The sum of Elements squared

See also: FumiliFCNBase::elements

Implements ROOT::Minuit2::FCNBase.

Definition at line 132 of file FumiliChi2FCN.h.

◆ SetModelFunction()

void ROOT::Minuit2::FumiliChi2FCN::SetModelFunction ( const ParametricFunction & modelFCN )

inline

Sets the model function for the data (for example gaussian+linear for a peak)

Parameters

modelFCN a reference to the model function.

Definition at line 64 of file FumiliChi2FCN.h.

◆ Up()

double ROOT::Minuit2::FumiliChi2FCN::Up ( ) const

inlineoverridevirtual

!!!!!!!!!!!! to be commented

Implements ROOT::Minuit2::FCNBase.

Definition at line 151 of file FumiliChi2FCN.h.

Member Data Documentation

◆ fModelFunction

const ParametricFunction* ROOT::Minuit2::FumiliChi2FCN::fModelFunction = nullptr

private

Definition at line 155 of file FumiliChi2FCN.h.

Libraries for ROOT::Minuit2::FumiliChi2FCN:

[legend]

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

math/minuit2/inc/Minuit2/FumiliChi2FCN.h

Public Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ FumiliChi2FCN()

◆ ~FumiliChi2FCN()

Member Function Documentation

◆ Elements()

◆ GetMeasurement()

◆ GetNumberOfMeasurements()

◆ ModelFunction()

◆ operator()()

◆ SetModelFunction()

◆ Up()

Member Data Documentation

◆ fModelFunction