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
virtual unsigned int	Dimension ()
	return number of function variable (parameters) , i.e.
virtual std::vector< double >	Elements (std::vector< double > const &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 double	ErrorDef () const
	Error definition of the function.
virtual void	EvaluateAll (std::vector< double > const &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 std::vector< double >	G2 (std::vector< double > const &) const
	Return the diagonal elements of the Hessian (second derivatives).
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.
virtual const std::vector< double > &	Gradient () const
	Return cached Value of function Gradient estimated previously using the FumiliFCNBase::EvaluateAll method.
std::vector< double >	Gradient (std::vector< double > const &) const override
	Return the gradient vector of the function at the given parameter point.
virtual std::vector< double >	GradientWithPrevResult (std::vector< double > const &parameters, double , double , double *) const
virtual GradientParameterSpace	gradParameterSpace () const
virtual bool	HasG2 () const
bool	HasGradient () const override
virtual bool	HasHessian () const
std::vector< double >	Hessian (std::vector< double > const &) 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
const ParametricFunction *	ModelFunction () const
	Returns the model function used for the data.
double	operator() (std::vector< double > const &par) const override
	Calculates the sum of Elements squared, ie the chi-square.
virtual void	SetErrorDef (double)
	add interface to set dynamically a new error definition Re-implement this function if needed.
void	SetModelFunction (const ParametricFunction &modelFCN)
	Sets the model function for the data (for example gaussian+linear for a peak).
double	Up () const override
	!
virtual double	Value () const
	Return cached Value of objective function estimated previously using the FumiliFCNBase::EvaluateAll method.

Protected Member Functions
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)

Private Attributes
std::vector< double >	fGradient
std::vector< double >	fHessian
const ParametricFunction *	fModelFunction = nullptr
unsigned int	fNumberOfParameters
double	fValue

#include <Minuit2/FumiliChi2FCN.h>

Inheritance diagram for ROOT::Minuit2::FumiliChi2FCN:

Member Function Documentation

◆ Dimension()

virtual unsigned int ROOT::Minuit2::FumiliFCNBase::Dimension ( )

inlinevirtualinherited

return number of function variable (parameters) , i.e.

function dimension

Definition at line 121 of file FumiliFCNBase.h.

◆ Elements()

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

◆ ErrorDef()

virtual double ROOT::Minuit2::FCNBase::ErrorDef ( ) const

inlinevirtualinherited

Error definition of the function.

MINUIT defines Parameter errors as the change in Parameter Value required to change the function Value by up. Normally, for chisquared fits it is 1, and for negative log likelihood, its Value is 0.5. If the user wants instead the 2-sigma errors for chisquared fits, it becomes 4, as Chi2(x+n*sigma) = Chi2(x) + n*n.

Comment a little bit better with links!!!!!!!!!!!!!!!!!

Definition at line 70 of file FCNBase.h.

◆ EvaluateAll()

virtual void ROOT::Minuit2::FumiliFCNBase::EvaluateAll ( std::vector< double > const & par )

pure virtualinherited

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.

Parameters

par	vector of parameters

Implemented in ROOT::Minuit2::FumiliFCNAdapter< Function >, ROOT::Minuit2::FumiliStandardChi2FCN, and ROOT::Minuit2::FumiliStandardMaximumLikelihoodFCN.

◆ G2()

virtual std::vector< double > ROOT::Minuit2::FCNBase::G2 ( std::vector< double > const & ) const

inlinevirtualinherited

Return the diagonal elements of the Hessian (second derivatives).

By default, returns an empty vector. Override this method if analytic second derivatives (per-parameter curvature) are available.

Parameters

v	Parameter vector.

Returns: Vector of second derivatives with respect to each parameter.

Reimplemented in ROOT::Minuit2::FCNAdapter.

Definition at line 116 of file FCNBase.h.

◆ 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.

◆ Gradient() [1/3]

std::vector< double > & ROOT::Minuit2::FumiliFCNBase::Gradient ( )

inlineprotectedinherited

Definition at line 138 of file FumiliFCNBase.h.

◆ Gradient() [2/3]

virtual const std::vector< double > & ROOT::Minuit2::FumiliFCNBase::Gradient ( ) const

inlinevirtualinherited

Return cached Value of function Gradient estimated previously using the FumiliFCNBase::EvaluateAll method.

Definition at line 97 of file FumiliFCNBase.h.

◆ Gradient() [3/3]

std::vector< double > ROOT::Minuit2::FumiliFCNBase::Gradient ( std::vector< double > const & ) const

inlineoverridevirtualinherited

Return the gradient vector of the function at the given parameter point.

By default, returns an empty vector (no analytic gradient provided). Override this method if an analytic gradient is available.

Parameters

v	Parameter vector.

Returns: Gradient vector with respect to the parameters.

Reimplemented from ROOT::Minuit2::FCNBase.

Definition at line 98 of file FumiliFCNBase.h.

◆ GradientWithPrevResult()

virtual std::vector< double > ROOT::Minuit2::FCNBase::GradientWithPrevResult	(	std::vector< double > const &	parameters,
		double *	,
		double *	,
		double *	) const

inlinevirtualinherited

Warning: Not meant to be overridden! This is a requirement for an internal optimization in RooFit that might go away with any refactoring.

Definition at line 99 of file FCNBase.h.

◆ gradParameterSpace()

virtual GradientParameterSpace ROOT::Minuit2::FCNBase::gradParameterSpace ( ) const

inlinevirtualinherited

Warning: Not meant to be overridden! This is a requirement for an internal optimization in RooFit that might go away with any refactoring.

Definition at line 107 of file FCNBase.h.

◆ HasG2()

virtual bool ROOT::Minuit2::FCNBase::HasG2 ( ) const

inlinevirtualinherited

Reimplemented in ROOT::Minuit2::FCNAdapter.

Definition at line 129 of file FCNBase.h.

◆ HasGradient()

bool ROOT::Minuit2::FumiliFCNBase::HasGradient ( ) const

inlineoverridevirtualinherited

Reimplemented from ROOT::Minuit2::FCNBase.

Definition at line 56 of file FumiliFCNBase.h.

◆ HasHessian()

virtual bool ROOT::Minuit2::FCNBase::HasHessian ( ) const

inlinevirtualinherited

Reimplemented in ROOT::Minuit2::FCNAdapter.

Definition at line 127 of file FCNBase.h.

◆ Hessian() [1/3]

std::vector< double > & ROOT::Minuit2::FumiliFCNBase::Hessian ( )

inlineprotectedinherited

Definition at line 140 of file FumiliFCNBase.h.

◆ Hessian() [2/3]

std::vector< double > ROOT::Minuit2::FumiliFCNBase::Hessian ( std::vector< double > const & ) const

inlineoverridevirtualinherited

Return Value of the i-th j-th element of the Hessian matrix estimated previously using the FumiliFCNBase::EvaluateAll method.

Parameters

row	row Index of the matrix
col	col Index of the matrix

Reimplemented from ROOT::Minuit2::FCNBase.

Definition at line 107 of file FumiliFCNBase.h.

◆ Hessian() [3/3]

virtual double ROOT::Minuit2::FumiliFCNBase::Hessian	(	unsigned int	row,
		unsigned int	col ) const

inlinevirtualinherited

Definition at line 108 of file FumiliFCNBase.h.

◆ InitAndReset()

virtual void ROOT::Minuit2::FumiliFCNBase::InitAndReset ( unsigned int npar )

inlineprotectedvirtualinherited

initialize and reset values of gradien and Hessian

Definition at line 128 of file FumiliFCNBase.h.

◆ 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 70 of file FumiliChi2FCN.h.

◆ operator()()

double ROOT::Minuit2::FumiliChi2FCN::operator() ( std::vector< double > const & 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 128 of file FumiliChi2FCN.h.

◆ SetErrorDef()

virtual void ROOT::Minuit2::FCNBase::SetErrorDef ( double )

inlinevirtualinherited

add interface to set dynamically a new error definition Re-implement this function if needed.

Reimplemented in ROOT::Minuit2::FCNAdapter, and ROOT::Minuit2::FumiliFCNAdapter< Function >.

Definition at line 84 of file FCNBase.h.

◆ SetFCNValue()

void ROOT::Minuit2::FumiliFCNBase::SetFCNValue ( double value )

inlineprotectedinherited

Definition at line 136 of file FumiliFCNBase.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 60 of file FumiliChi2FCN.h.

◆ Up()

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

inlineoverridevirtual

!

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

Implements ROOT::Minuit2::FCNBase.

Definition at line 147 of file FumiliChi2FCN.h.

◆ Value()

virtual double ROOT::Minuit2::FumiliFCNBase::Value ( ) const

inlinevirtualinherited

Return cached Value of objective function estimated previously using the FumiliFCNBase::EvaluateAll method.

Definition at line 91 of file FumiliFCNBase.h.

Member Data Documentation

◆ fGradient

std::vector<double> ROOT::Minuit2::FumiliFCNBase::fGradient

privateinherited

Definition at line 145 of file FumiliFCNBase.h.

◆ fHessian

std::vector<double> ROOT::Minuit2::FumiliFCNBase::fHessian

privateinherited

Definition at line 146 of file FumiliFCNBase.h.

◆ fModelFunction

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

private

Definition at line 151 of file FumiliChi2FCN.h.

◆ fNumberOfParameters

unsigned int ROOT::Minuit2::FumiliFCNBase::fNumberOfParameters

privateinherited

Definition at line 143 of file FumiliFCNBase.h.

◆ fValue

double ROOT::Minuit2::FumiliFCNBase::fValue

privateinherited

Definition at line 144 of file FumiliFCNBase.h.

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

math/minuit2/inc/Minuit2/FumiliChi2FCN.h

Public Member Functions

Protected Member Functions

Private Attributes

Member Function Documentation

◆ Dimension()

◆ Elements()

◆ ErrorDef()

◆ EvaluateAll()

◆ G2()

◆ GetMeasurement()

◆ GetNumberOfMeasurements()

◆ Gradient() [1/3]

◆ Gradient() [2/3]

◆ Gradient() [3/3]

◆ GradientWithPrevResult()

◆ gradParameterSpace()

◆ HasG2()

◆ HasGradient()

◆ HasHessian()

◆ Hessian() [1/3]

◆ Hessian() [2/3]

◆ Hessian() [3/3]

◆ InitAndReset()

◆ ModelFunction()

◆ operator()()

◆ SetErrorDef()

◆ SetFCNValue()

◆ SetModelFunction()

◆ Up()

◆ Value()

Member Data Documentation

◆ fGradient

◆ fHessian

◆ fModelFunction

◆ fNumberOfParameters

◆ fValue