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. In this cased the function to be minimized is the sum of the logarithms of the model function for the different measurements times -1.

Author: Andras Zsenei and Lorenzo Moneta, Creation date: 3 Sep 2004

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

Definition at line 46 of file FumiliMaximumLikelihoodFCN.h.

Public Member Functions
	FumiliMaximumLikelihoodFCN ()

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 std::vector< double >	GradientWithPrevResult (std::vector< double > const &parameters, double previous_grad, double previous_g2, double *previous_gstep, double) const
	Variant of GradientWithPrevResult() that additionally receives the already-known function value at `parameters` (e.g.

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 function for the maximum likelihood method.

virtual bool	SecondDerivativeAlwaysVanishes (unsigned int, unsigned int) const
	Indicate whether the mixed second order derivative with respect to parameters i and j is identically zero, i.e.

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

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

unsigned int	fNumberOfParameters

double	fValue

#include <Minuit2/FumiliMaximumLikelihoodFCN.h>

Inheritance diagram for ROOT::Minuit2::FumiliMaximumLikelihoodFCN:

[legend]

Constructor & Destructor Documentation

◆ FumiliMaximumLikelihoodFCN()

ROOT::Minuit2::FumiliMaximumLikelihoodFCN::FumiliMaximumLikelihoodFCN ( )

inline

Definition at line 49 of file FumiliMaximumLikelihoodFCN.h.

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::FumiliMaximumLikelihoodFCN::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::FumiliStandardMaximumLikelihoodFCN.

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

◆ 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 130 of file FCNBase.h.

◆ GetMeasurement()

virtual const std::vector< double > & ROOT::Minuit2::FumiliMaximumLikelihoodFCN::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 vector containing the values characterizing a measurement

Implemented in ROOT::Minuit2::FumiliStandardMaximumLikelihoodFCN.

◆ GetNumberOfMeasurements()

virtual int ROOT::Minuit2::FumiliMaximumLikelihoodFCN::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::FumiliStandardMaximumLikelihoodFCN.

◆ 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() [1/2]

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.

◆ GradientWithPrevResult() [2/2]

virtual std::vector< double > ROOT::Minuit2::FCNBase::GradientWithPrevResult	(	std::vector< double > const &	parameters,
		double *	previous_grad,
		double *	previous_g2,
		double *	previous_gstep,
		double	) const

inlinevirtualinherited

Variant of GradientWithPrevResult() that additionally receives the already-known function value at parameters (e.g.

from the line search that preceded the gradient request), so implementations can avoid re-evaluating the function at the central point.

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 112 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 121 of file FCNBase.h.

◆ HasG2()

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

inlinevirtualinherited

Reimplemented in ROOT::Minuit2::FCNAdapter.

Definition at line 143 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 141 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::FumiliMaximumLikelihoodFCN::ModelFunction ( ) const

inline

Returns the model function used for the data.

Returns: Returns a pointer to the model function.

Definition at line 69 of file FumiliMaximumLikelihoodFCN.h.

◆ operator()()

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

inlineoverridevirtual

Calculates the function for the maximum likelihood method.

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 the natural logarithm of the Elements multiplied by -1

See also: FumiliFCNBase::elements

Implements ROOT::Minuit2::FCNBase.

Definition at line 127 of file FumiliMaximumLikelihoodFCN.h.

◆ SecondDerivativeAlwaysVanishes()

virtual bool ROOT::Minuit2::FCNBase::SecondDerivativeAlwaysVanishes	(	unsigned int	,
		unsigned int	) const

inlinevirtualinherited

Indicate whether the mixed second order derivative with respect to parameters i and j is identically zero, i.e.

zero for all parameter values. This can help to avoid expensive function calls in numerical Hessian evaluations (see MnHesse).

The contract for implementations:

The indices refer to the FCN's own full (external) parameter space, including any parameters that are fixed in the minimizer. Callers that work with internal indices, like MnHesse, must translate them via MnUserTransformation::ExtOfInt() before calling this function.
The result must be symmetric in i and j.
Only return true if the second derivative vanishes for any value of the parameters: the result may be cached and is used at arbitrary points in parameter space.
The diagonal (i == j) is never queried by Minuit2, so its return value has no effect.

Reimplemented in ROOT::Minuit2::FCNAdapter.

Definition at line 163 of file FCNBase.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::FumiliMaximumLikelihoodFCN::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 59 of file FumiliMaximumLikelihoodFCN.h.

◆ Up()

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

inlineoverridevirtual

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

Implements ROOT::Minuit2::FCNBase.

Definition at line 151 of file FumiliMaximumLikelihoodFCN.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::FumiliMaximumLikelihoodFCN::fModelFunction

private

Definition at line 155 of file FumiliMaximumLikelihoodFCN.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.

Libraries for ROOT::Minuit2::FumiliMaximumLikelihoodFCN:

[legend]

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

math/minuit2/inc/Minuit2/FumiliMaximumLikelihoodFCN.h

Public Member Functions

Protected Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ FumiliMaximumLikelihoodFCN()

Member Function Documentation

◆ Dimension()

◆ Elements()

◆ ErrorDef()

◆ EvaluateAll()

◆ G2()

◆ GetMeasurement()

◆ GetNumberOfMeasurements()

◆ Gradient() [1/3]

◆ Gradient() [2/3]

◆ Gradient() [3/3]

◆ GradientWithPrevResult() [1/2]

◆ GradientWithPrevResult() [2/2]

◆ gradParameterSpace()

◆ HasG2()

◆ HasGradient()

◆ HasHessian()

◆ Hessian() [1/3]

◆ Hessian() [2/3]

◆ Hessian() [3/3]

◆ InitAndReset()

◆ ModelFunction()

◆ operator()()

◆ SecondDerivativeAlwaysVanishes()

◆ SetErrorDef()

◆ SetFCNValue()

◆ SetModelFunction()

◆ Up()

◆ Value()

Member Data Documentation

◆ fGradient

◆ fHessian

◆ fModelFunction

◆ fNumberOfParameters

◆ fValue