Small helper class to collect all results, All input parameters are set by class LTF The user can access all input and output quantities. More...

#include <LTF.h>

Public Member Functions
double	DoLiTeFit ()
	Run linear template fit (LiTeFit,LTF) with previously set input parameters. More...

double	DoLiTeFit (int mPolN, int mOrdInfrc, const Eigen::VectorXd &ahat)
	Run non-linear template fit with previously set input parameters. More...

double	DoIterativeFitNewton (int nIter=3, int nPol=2, int nInfrc=1)
	Run an non-linear template fit with iterative improvements. More...

double	DoIterativeFitTaylor (int nIter=4, double StepSize=0.6, int nPol=2, int nInfrc=1)
	Run an non-linear template fit with iterative improvements. More...

void	ApplyLogNormalDistribution ()
	Assume underlying log-normal distributed probability density functions. More...

void	RescaleInputErrors (std::vector< double > values)

void	RescaleInputErrors (const Eigen::VectorXd &values)
	Rescale uncertainties. See LTF::RescaleErrors() for more details.

void	PrintShort () const
	Print results (short version)

void	PrintFull () const
	Print all results. Do not print covariance or correlation matrices though.

Eigen::MatrixXd	Mc (int nPow=1, int nInfrc=0) const
	calculated matrix M^+ from matrix M More...

Eigen::VectorXd	a0pow (int nPow, int nInfrc, const Eigen::VectorXd &ahat) const
	calculated vector (a0,a0^2,infrc) to be multiplied with Mc More...

Eigen::MatrixXd	McApprox (int powmax, int intfrc, const Eigen::VectorXd &ahat) const
	calculated approximate matrix M^+ from non-linear matrix M^+ More...

Eigen::MatrixXd	W () const
	calculate inverse covariance matrix from V's More...

Eigen::MatrixXd	VFit () const
	calculate covariance matrix of all uncertainties included in fit

Eigen::MatrixXd	VExt () const
	calculate covariance matrix of all uncertainties included in fit

bool	GetLogNormal () const
	return boolean if fit was performed with relative uncertainties

Eigen::VectorXd	CalculatePrediction (double v) const

Eigen::VectorXd	CalculatePrediction (std::vector< double > v) const

Eigen::VectorXd	CalculatePrediction (Eigen::VectorXd v) const
	Calculate the prediction as it is used by the fit for a given parameter value.

Eigen::VectorXd	ComputeLinearTemplateFit (int mPolN=1, int mOrdInfrc=0, const Eigen::VectorXd &ahat=Eigen::VectorXd()) const
	Solve the (linear) template fit The equations of the linear template fit are applied and the best estimator(s) are determined. More...

Eigen::VectorXd	ComputeNewtonEstimator (int mPolN=1, int mOrdInfrc=0, const Eigen::VectorXd &ahat=Eigen::VectorXd())
	Solve (linear) template fit. More...

Public Attributes
Eigen::VectorXd	Dt
	data distribution

Eigen::MatrixXd	M
	Matrix M (reference values)

Eigen::MatrixXd	Y
	Matrix Y (templates)

Eigen::MatrixXd	X
	Matrix X (templates) [only required for error propagation].

Eigen::MatrixXd	A
	Response matrix (optional) [only used for (relative) error propagation].

std::vector< std::pair< std::string, Eigen::MatrixXd > >	Vs
	(uncor./Cov) uncertainties

std::vector< std::pair< std::string, Eigen::VectorXd > >	Sys
	(correlated) systematic uncertainties

std::map< std::string, Eigen::MatrixXd >	VsExt
	external (uncor./Cov) uncertainties

std::map< std::string, Eigen::VectorXd >	SysExt
	external (correlated) systematic uncertainties

std::map< std::string, LTF::Uncertainty >	SysIsConstr
	uncertainty specification for Sys

std::map< std::string, Eigen::MatrixXd >	SysY
	uncertainty of the templates

std::map< std::string, Eigen::MatrixXd >	SysA
	uncertainty of the response matrix

std::map< std::string, double >	corrSys
	Correlation coefficient of the systematic uncertainties.

vector< double >	Gamma
	Use non-linear Gamma-factor.

double	a0 = 0
	Fit result.

double	a0_errorFit = 0
	uncertainty from all uncertainties included in fit (no 'external' uncertainties)

double	a0_errorExt = 0
	uncertainty from 'external' uncertainties

double	a0_errorTmpl = 0
	uncertainty from templates

double	a0_errorRespMat = 0
	uncertainty from response matrix

double	chisq = 0
	chi^2

double	chisq_error = 0
	uncertainty of chi^2

Eigen::MatrixXd	F
	Projection matrix of LiTeFit.

Eigen::VectorXd	chisq_y
	chi^2 for each template

std::map< std::string, double >	chisq_part
	'partial' chi^2 for each error source

Eigen::VectorXd	ahat
	results (a0, a1, ..., epsilon1, epsilon2,...)

Eigen::VectorXd	ahat_errorFit
	Uncertainties included in fit.

Eigen::VectorXd	ahat_errorExt
	Uncertainties not included in fit.

Eigen::VectorXd	ahat_errorTmpl
	Uncertainties from templates.

Eigen::VectorXd	ahat_errorRespMat
	Uncertainties from response matrix.

Eigen::VectorXd	TheoFit
	best-fit theory predictions

std::map< std::string, Eigen::MatrixXd >	Vsource
	Covariance matrices from uncorr. and cov. uncertainties.

std::map< std::string, Eigen::VectorXd >	DeltaSys
	Correlated systematic uncertainties.

std::map< std::string, Eigen::MatrixXd >	VsourceExt
	Covariance matrices from 'external' uncorr. and cov. uncertainties.

std::map< std::string, Eigen::VectorXd >	DeltaSysExt
	'external' correlated systematic uncertainty

std::map< std::string, Eigen::VectorXd >	DeltaSysY
	systematic uncertainty from the templates

std::map< std::string, Eigen::VectorXd >	DeltaSysA
	systematic uncertainty from the response matrix

Eigen::VectorXd	achk
	result from polynomial fit to chi2's of templates

Eigen::VectorXd	achk_errorFit
	result from polynomial fit to chi2's of templates

double	achk_chisq
	chisq_min from polynomial fit to chi2's of templates

Eigen::VectorXd	ahat21
	result from linearized second-order model approximation (incl. interference)

Eigen::VectorXd	EDM21
	expected distance to minimum (EDM), calculating the newton step for a non-linear model

double	EDM21_chisq
	expected distance to minimum (EDM), calculating the newton step for a non-linear model

Eigen::VectorXd	delta_m21
	uncertainty on M from linearized second-order model (incl. interference)

Protected Member Functions
void	ApplyGamma (std::map< std::string, Eigen::VectorXd > &Delta) const
	Compute the value of the next Newton step, when using a higher-order model approximation. More...

void	ApplyGamma (std::map< std::string, Eigen::MatrixXd > &VMat) const
	apply gamma factor to the uncertainties

Protected Attributes
bool	LogNormal = false
	Use LogNormal distributed uncertainties, i.e. normal-distibuted relative uncertainties.

std::vector< std::pair< std::string, Eigen::MatrixXd > >	SysAX
	uncertainty of the response matrix when using log-normal

Eigen::VectorXd	ErrorScale
	Reference values for error rescaling (default: data)

Eigen::VectorXd	ybar

Eigen::MatrixXd	Ytil

Detailed Description

Small helper class to collect all results, All input parameters are set by class LTF The user can access all input and output quantities.

Member Function Documentation

◆ a0pow()

Eigen::VectorXd LTF::LiTeFit::a0pow	(	int	nPow,
		int	nInfrc,
		const Eigen::VectorXd &	ahat
	)		const

calculated vector (a0,a0^2,infrc) to be multiplied with Mc

Compute vector a to be multiplied with Mc.

Parameters

nPow	maximum power of polynomial model approximation (nPow=1,2)
nInfrc	maximum power of interference terms (nInfrc=0,1) (only applicable for nPow>=2)
ahat	input values for parameters alpha

Return vector may be similar to [and includes the gamma factors] a0pow = ( 1 a0 a1 a0^2 a1^2 a1*a2 )

◆ ApplyGamma()

void LTF::LiTeFit::ApplyGamma ( std::map< std::string, Eigen::VectorXd > & Delta ) const

protected

Compute the value of the next Newton step, when using a higher-order model approximation.

apply gamma factor to the uncertainties

◆ ApplyLogNormalDistribution()

void LTF::LiTeFit::ApplyLogNormalDistribution ( )

Assume underlying log-normal distributed probability density functions.

Modify input paramters in order to obtain relative uncertainties.

◆ CalculatePrediction() [1/2]

Eigen::VectorXd LTF::LiTeFit::CalculatePrediction ( double v ) const

inline

<Calculate the prediction as it is used by the fit for a given parameter value

◆ CalculatePrediction() [2/2]

Eigen::VectorXd LTF::LiTeFit::CalculatePrediction ( std::vector< double > v ) const

inline

<Calculate the prediction as it is used by the fit for a given parameter value

◆ ComputeLinearTemplateFit()

Eigen::VectorXd LTF::LiTeFit::ComputeLinearTemplateFit	(	int	mPolN = `1`,
		int	mOrdInfrc = `0`,
		const Eigen::VectorXd &	aexp = `Eigen::VectorXd()`
	)		const

Solve the (linear) template fit The equations of the linear template fit are applied and the best estimator(s) are determined.

With default arguments, the linear template fit

is applied.

Non-linear approximations of the model are

performed for mPolN > 1, while only mPolN=2 is

implemented (quadratic function)

In addition interference terms can be considered with mOrdInfrc=1

◆ ComputeNewtonEstimator()

Eigen::VectorXd LTF::LiTeFit::ComputeNewtonEstimator	(	int	mPolN = `1`,
		int	mOrdInfrc = `0`,
		const Eigen::VectorXd &	ahat = `Eigen::VectorXd()`
	)

Solve (linear) template fit.

Compute the value of the next Newton step, when using higher-order model approximation.

◆ DoIterativeFitNewton()

double LTF::LiTeFit::DoIterativeFitNewton	(	int	nIter = `3`,
		int	nPol = `2`,
		int	nInfrc = `1`
	)

Run an non-linear template fit with iterative improvements.

Run the linear template fit iteratively with non-linear model approximation.

using the Newton algorithm

Parameters

nIter	Number of iterations beyond first linear template fit
nPol	polynomial of model approximation (default =2, 1: linear template fit)
nInfrc	polynomial of interference terms for nPol>=2 (default =1)

◆ DoIterativeFitTaylor()

double LTF::LiTeFit::DoIterativeFitTaylor	(	int	nIter = `4`,
		double	StepSize = `0.6`,
		int	nPol = `2`,
		int	nInfrc = `1`
	)

Run an non-linear template fit with iterative improvements.

Run the linear template fit iteratively with non-linear model approximation.

using a taylor expansion of the non-linear model

Parameters

nIter	Number of iterations beyond first linear template fit
StepSize	Learning rate, 0<StepSize<=1
nPol	polynomial of model approximation (default =2, 1: linear template fit)
nInfrc	polynomial of interference terms for nPol>=2 (default =1)

◆ DoLiTeFit() [1/2]

double LTF::LiTeFit::DoLiTeFit ( )

Run linear template fit (LiTeFit,LTF) with previously set input parameters.

Run linear template fit (LiTeFit,LTF) with previously set input parameters This function fills all member variables of LiTeFit. All results are collected in the member variables For a printout of the results, call PrintFull() or PrintShort()

◆ DoLiTeFit() [2/2]

double LTF::LiTeFit::DoLiTeFit	(	int	mPolN,
		int	mOrdInfrc,
		const Eigen::VectorXd &	ahat
	)

Run non-linear template fit with previously set input parameters.

Run linear template fit (LiTeFit,LTF) with previously set input parameters This function fills all member variables of LiTeFit. All results are collected in the member variables For a printout of the results, call PrintFull() or PrintShort()

◆ Mc()

Eigen::MatrixXd LTF::LiTeFit::Mc	(	int	powmax = `1`,
		int	interference = `0`
	)		const

calculated matrix M^+ from matrix M

calculate matrix called M^+ M^+ = ( M^T W M )^-1 M^T W with W=1, since we use unweighted linear regression

exponential Gamma-factor is applied for each fit-parameter

The function returns the g-inverse for n-th-order regression: powmax = 1: linear regression powmax = 2: second order polynomial etc.... powmax=1 is the default

◆ McApprox()

Eigen::MatrixXd LTF::LiTeFit::McApprox	(	int	mPolN,
		int	mOrdInfrc,
		const Eigen::VectorXd &	aexp0
	)		const

calculated approximate matrix M^+ from non-linear matrix M^+

< Return matrix Mc that is obtained from first-order approximation of non-linear Mc aexp specifies the expansion point

◆ RescaleInputErrors()

void LTF::LiTeFit::RescaleInputErrors ( std::vector< double > values )

inline

<Rescale uncertainties. See LTF::RescaleErrors() for more details

◆ W()

Eigen::MatrixXd LTF::LiTeFit::W ( ) const

calculate inverse covariance matrix from V's

Calculate inverse (covariance) matrix Input are all covariance matrices in V Note: at least one (uncorrelated) uncertainty must be present in the fit.

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

LTF/LTF.h
src/LTF.cxx

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ a0pow()

◆ ApplyGamma()

◆ ApplyLogNormalDistribution()

◆ CalculatePrediction() [1/2]

◆ CalculatePrediction() [2/2]

◆ ComputeLinearTemplateFit()

◆ ComputeNewtonEstimator()

◆ DoIterativeFitNewton()

◆ DoIterativeFitTaylor()

◆ DoLiTeFit() [1/2]

◆ DoLiTeFit() [2/2]

◆ Mc()

◆ McApprox()

◆ RescaleInputErrors()

◆ W()