The AliTMinuitToolkit serves as an easy to use interface for the TMinuit. More...

#include <AliTMinuitToolkit.h>

Inheritance diagram for AliTMinuitToolkit:

Public Types
enum	EVerboseFlags { kPrintMinuit =0x00001, kSysInfo =0x00002, kPrintAll =0x00004, kStreamFcn =0x00010, kStreamFcnPoint =0x00020, kFCNInfo =0x000400 }

enum	EFitFlags { kCovarFailed =0x0001 }

Public Member Functions
	AliTMinuitToolkit (const char streamerName=nullptr, const char mode="recreate")

virtual	~AliTMinuitToolkit ()

void	SetStreamer (const char streamerName, const char mode="recreate")
	Set stream for writing info into TTree. see examples(STEER/STEERBase/TTreeStream.cxx) More...

TTreeSRedirector *	GetStreamer ()

void	ClearData ()

void	Fit (Option_t *option="")
	Internal function that calls the fitter. More...

void	FitHistogram (const TH1 his, Option_t option="")
	Fit a one dimensional histogram. More...

void	FitGraph (const TGraph gr, Option_t option="")
	Fit a TGraph object. More...

Long64_t	FillFitter (TTree *inputTree, TString values, TString variables, TString selection, Int_t firstEntry, Int_t nEntries, Bool_t doReset=kTRUE)
	Fill input matrices of the fitter. More...

TString	GetFitFunctionAsAlias (Option_t option="", TTree tree=nullptr)
	Format alias string for the for tree alias or for fit title. More...

void	Bootstrap (ULong_t nIter, const char reportName, Option_t option=nullptr)
	Bootstrap minimization. More...

void	TwoFoldCrossValidation (UInt_t nIter, const char reportName, Option_t option=nullptr)

void	MISAC (Int_t nFitPoints, UInt_t nIter, const char reportName, Option_t option=nullptr)
	Fitting with outlier removal inspired by RANSAC - see https://en.wikipedia.org/w/index.php?title=Random_sample_consensus&oldid=767657742. More...

void	SetFitFunction (TF1 *formula, Bool_t doReset)
	Set formula of the fitted function and reset parameter. See doReset. More...

void	SetInitialParam (const TMatrixD *initialParam)
	Set initial parameters matrix. More...

TMatrixD *	GetInitialParam ()

void	SetLogLikelihoodFunction (TF1 *logLikelihood)

void	SetFitAlgorithm (Char_t *const name)

void	SetMaxCalls (Int_t calls)

void	SetTolerance (Double_t tol)

void	SetPoints (TMatrixD *points)

void	SetValues (TMatrixD *values)

void	EnableRobust (Bool_t b)

const TMatrixD *	GetPoints () const

const TMatrixD *	GetValues () const

TF1 *	GetFormula () const

const TF1 *	GetLogLikelihoodFunction () const

const TVectorD *	GetParameters () const

const TVectorD *	GetRMSEstimator () const

const TMatrixD *	GetCovarianceMatrix () const

const TMatrixD *	GetMISACEstimators () const

Double_t	GetChisquare ()

Int_t	GetStatus ()

Bool_t	IsHuberCost () const

TObjArray *	GetListOfVariables ()

void	SetVerbose (Int_t verbose)

Bool_t	IsVerbose (Int_t flag)

Static Public Member Functions
static void	FitterFCN (int &nParam, double info, double &chi2, double gin, int iflag)
	Internal function used in the TMinuit minimization. More...

static AliTMinuitToolkit *	Fit (TH1 his, const char fitterName, Option_t fitOption="", Option_t hisOption="", Option_t *funOption="", Double_t xMin=0, Double_t xMax=0)
	Make histogram fit. More...

static AliTMinuitToolkit *	Fit (TGraph graph, const char fitterName, Option_t fitOption="", Option_t graphOption="", Option_t *funOption="", Double_t xMin=0, Double_t xMax=0)
	Make graph fit. More...

static AliTMinuitToolkit *	GetPredefinedFitter (const std::string &fitterName)

static void	SetPredefinedFitter (const std::string &fitterName, AliTMinuitToolkit *fitter)

static void	RegisterDefaultFitters ()

static AliTMinuitToolkit *	RegisterPlaneFitter (Int_t nPlanes, Int_t logLikeType)
	Register default fitters. More...

static Double_t	GaussCachyLogLike (const Double_t x, const Double_t p)

static Double_t	HuberLogLike (const Double_t x, const Double_t p)

static Double_t	PseudoHuberLogLike (const Double_t x, const Double_t p)

static Double_t	GausKurtosisSkewness (const Double_t x, const Double_t p)
	Gaus convoluted with Erf to emulate kurtosis and skewness. More...

static Double_t	RndmGaus (Double_t mean=0, Double_t sigma=1)
	Random gaus generator as static function (to use in root TFormula, TTreeFormula) More...

static Double_t	RndmLandau (Double_t mean=0, Double_t sigma=1)
	Random gaus generator as static function (to use in root TFormula, TTreeFormula) More...

static void	SetFunctionDrawOption (TF1 fun, Option_t option)

Private Member Functions
	AliTMinuitToolkit (const AliTMinuitToolkit &)

AliTMinuitToolkit &	operator= (const AliTMinuitToolkit &)

Private Attributes
TTreeSRedirector *	fStreamer

Int_t	fVerbose

TF1 *	fFormula

TF1 *	fLogLikelihoodFunction

TString	fFitAlgorithm

TMatrixD *	fPoints

TMatrixD *	fValues

TObjArray *	fVarNames

TObjArray *	fValueNames

TArrayI	fPointIndex

TMatrixD *	fInitialParam

TVectorD *	fParam

TVectorD *	fRMSEstimator

TMatrixD *	fMISACEstimators

TMatrixD *	fCovar

Int_t	fStatus

Double_t	fChi2

Int_t	fMaxCalls

Double_t	fPrecision

Bool_t	fIsHuberCost

Int_t	fFCNCounter

Static Private Attributes
static std::map< std::string, AliTMinuitToolkit * >	fPredefinedFitters

Detailed Description

The AliTMinuitToolkit serves as an easy to use interface for the TMinuit.

Usage:

1.) Setting the fit formula:
- Set fit function:
  void SetFitFunction(TFormula * formula, Bool_t doReset)".
2.) Adding the data points
- Direct specification of the points is possible via
  void SetPoints(TMatrixD * points)
  - Each point corresponds to one row in the matrix.
- The fitter is then started with the command
  void Fit()
- In order to fit a histogram, graphs in once use:
  AliTMinuitToolkit::FitHistogram(const TH1 * his, Option_t *option)
  
  AliTMinuitToolkit::FitGraph(const TGraph * gr, Option_t *option)
  
  AliTMinuitToolkit::Fit(TH1* his, const char *fitterName, Option_t* option, Option_t* goption,Option_t* foption, Double_t xMin, Double_t xMax)
  
  AliTMinuitToolkit::Fit(TGraph *graph, const char *fitterName, Option_t* option, Option_t* goption, Option_t* foption, Double_t xMin, Double_t xMax)
- Filling input points using TTree queries (example)
  tool1D->FillFitter(inputTree,"test1D+noise:1/sqrt(12.+0)","testx0", "", 0,fitEntries);
3.) Accessing the fit results
- The N parameters of the formula are stored in a N-dimensional vector which is returned by
  - TVectorD * GetParameters()
- The covariance (NxN) matrix of the fit
  - TMatrixD * GetCovarianceMatrix()
4.) Log likelihood minimization
- see example
  $ALICE_ROOT/../src/STAT/test/AliTMinuitToolkitTest.C:Test1D()
  
  Even a few outliers can lead to wrong results of a least-squares fitting procedure. In this case the use of robust(resistant) methods can be helpful, but a stronger dependence on starting values or convergence to local minimum can occur.
- Cost (log likelihood) functions
  1. By default chi2 minimization is invoked.
  2. Optionally more robust log likelihood- Huber cost function can be specified instead of chi^2. For small deviations the function behaves like x^2 and for larger deviations like |x| - the so called Huber estimator:
    h(x) = x^2 , for x < 2.5*sigma
    h(x) = 2*(2.5*sigma)*x - (2.5*sigma)^2 , for x > 2.5*sigma
    - REFERENCE for non-linear robust fitting:
      - Ekblom H. and Madsen K. (1988), Algorithms for non-linear Huber estimation,
      - BIT Numerical Mathematics 29 (1989) 60-76.
      - internet: http://www.springerlink.com/content/m277218542988344/
  3. User defined log likelihood function can be specified
    TF1 * f1Cost = new TF1("1","abs(x)<10?-log(0.8*exp(-x**2)+0.2/(1+x**2)):-log(0.2/(1+x**2))",-20,20); // 80 % gaus + 20% cachy
    tool1D->SetLogLikelihoodFunction(f1Cost);
    tool1D->Fit();
5.) Additional fitting strategy (options)
- Bootstrap
- MISAC (similar to RANSAC algorithm - https://en.wikipedia.org/wiki/Random_sample_consensus)
- cross validation
- Example usage (.x $AliRoot_SRC/STAT/test/AliTMinuitToolkitTestLinear.C+(2000,3))
  AliTMinuitToolkit::RegisterDefaultFitters();
  AliTMinuitToolkit*fitter4 = AliTMinuitToolkit::Fit(gr,"pol1H","", "", "funOption(2,3,2)");
  fit4=*(fitter4->GetParameters()); rms4=*(fitter3->GetCovarianceMatrix());
  AliTMinuitToolkit*fitter5 = AliTMinuitToolkit::Fit(gr,"pol1R","bootstrap20", "","funOption(6,3,4)"); // bootstrap20
  fit5=*(fitter5->GetParameters()); rms5=*(fitter5->GetRMSEstimator());
  AliTMinuitToolkit*fitter6 = AliTMinuitToolkit::Fit(gr,"pol1R","bootstrap50", "", "funOption(3,3,5)" ); // bootstrap50
  fit6=*(fitter6->GetParameters()); rms6=*(fitter6->GetRMSEstimator());
  AliTMinuitToolkit*fitter7 = AliTMinuitToolkit::Fit(gr,"pol1R","misac(4,20)","","funOption(3,3,6)"); // misac 20
  fit7=*(fitter7->GetParameters()); rms7=*(fitter7->GetRMSEstimator());
  AliTMinuitToolkit*fitter8 = AliTMinuitToolkit::Fit(gr,"pol1R","misac(4,50)","","funOption(3,3,6)"); // misac 50
6.) Work in progress
- Multidimensional fits (more than one observable)
  - e.g fitting Er and Erphi in parallel
- Regularization
  - e.g positive definite, monotonous function
    Author
    Marian Ivanov maria.nosp@m.n.iv.nosp@m.anov@.nosp@m.cern.nosp@m..ch

Example usage in the $AliRoot_SRC/STAT/test/

TODO - save example images in the doxygen/html directory (STEERING part ?) - currently saved by hand - to check with OFFLINE
$AliRoot_SRC/STAT/test/AliTMinuitToolkitTest.C+
$AliRoot_SRC/STAT/test/AliTMinuitToolkitTestLinear.C+
- compare fits example with different likelihood/resp fits strategies for data with outliers
- compare performance fits example with different likelihood/resp fits strategies for data with outliers

Definition at line 104 of file AliTMinuitToolkit.h.

Member Enumeration Documentation

enum AliTMinuitToolkit::EFitFlags

Enumerator
kCovarFailed

Definition at line 115 of file AliTMinuitToolkit.h.

enum AliTMinuitToolkit::EVerboseFlags

Enumerator
kPrintMinuit
kSysInfo
kPrintAll
kStreamFcn
kStreamFcnPoint
kFCNInfo

Definition at line 106 of file AliTMinuitToolkit.h.

Constructor & Destructor Documentation

AliTMinuitToolkit::AliTMinuitToolkit	(	const char *	streamerName = `nullptr`,
		const char *	mode = `"recreate"`
	)

Definition at line 43 of file AliTMinuitToolkit.cxx.

Referenced by MISAC(), RegisterPlaneFitter(), and SetPredefinedFitter().

AliTMinuitToolkit::~AliTMinuitToolkit ( )

virtual

Definition at line 78 of file AliTMinuitToolkit.cxx.

AliTMinuitToolkit::AliTMinuitToolkit ( const AliTMinuitToolkit & )

private

Member Function Documentation

void AliTMinuitToolkit::Bootstrap	(	ULong_t	nIter,
		const char *	reportName,
		Option_t *	option = `nullptr`
	)

Bootstrap minimization.

fitting parameters done several times on modified data sample (random samples with replacement)
- to emulate different data population
- reduce problem with local minimum in the M-estimator estimated parameters - robust mean/median
- obtained RMS used to estimate error (take into account also model error)
TODO - parameters robust estimator setting
Parameters

nIter - number of iteration

reportName - report name - in case results streamed

option - fit option

Definition at line 582 of file AliTMinuitToolkit.cxx.

Referenced by Fit(), GetStreamer(), and Test1D().

void AliTMinuitToolkit::ClearData ( )

Definition at line 107 of file AliTMinuitToolkit.cxx.

Referenced by FillFitter(), FitGraph(), FitHistogram(), and GetStreamer().

void AliTMinuitToolkit::EnableRobust ( Bool_t b )

inline

Definition at line 144 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkit_TestHistogram(), and Test1D().

Long64_t AliTMinuitToolkit::FillFitter	(	TTree *	inputTree,
		TString	values,
		TString	variables,
		TString	selection,
		Int_t	firstEntry,
		Int_t	nEntries,
		Bool_t	doReset = `kTRUE`
	)

Fill input matrices of the fitter.

TODO - add better working example (using code/trees from the test directory)

Parameters

inputTree	- pointer to input tree
values	- values description (parameter:<error>)
variables	- variables array (var0:<var1>)
selection	- tree selection
firstEntry	- first entry to query
nEntries	- number of entries to query
doReset	- switch reset previous/or append

Returns

Example: TPC occupancy 6 dimensional hyperplane fit

AliTMinuitToolkit * hyp6R= AliTMinuitToolkit::GetPredefinedFitter("hyp6R");
hyp6R->FillFitter(treeQA, "NoThreshold.fElements:0.1*NoThreshold.fElements", "1:dRNorm:Phi2Norm:QNorm:gxNorm:gyNorm", "region&&occFitCut&&rndm<0.2", 0, 10000000);
hyp6R->Fit();

Definition at line 415 of file AliTMinuitToolkit.cxx.

Referenced by GetStreamer(), and Test1D().

void AliTMinuitToolkit::Fit ( Option_t * option = "" )

Internal function that calls the fitter.

Parameters

option

bootstrap[0-9]* -
twofold[0-9]* -
misac([0-9]*,[0-9]*) -

Definition at line 275 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkit_TestHistogram(), AliTMinuitToolkitTestLinear(), Bootstrap(), FitGraph(), FitHistogram(), GetStreamer(), IsVerbose(), MISAC(), Test1D(), and TwoFoldCrossValidation().

AliTMinuitToolkit * AliTMinuitToolkit::Fit	(	TH1 *	his,
		const char *	fitterName,
		Option_t *	fitOption = `""`,
		Option_t *	hisOption = `""`,
		Option_t *	funOption = `""`,
		Double_t	xMin = `0`,
		Double_t	xMax = `0`
	)

static

Make histogram fit.

TODO- add example code snippet - using the code from test directory

Parameters

his	- pointer to histogram
fitterName	- fitter name ()
fitOption	- fit Option
hisOption	- graphic option for histogram
funOption	- graphic option for function drawing
xMin	- fit range min
xMax	- fit range max

Returns: - pointer to the fitter

Definition at line 943 of file AliTMinuitToolkit.cxx.

AliTMinuitToolkit * AliTMinuitToolkit::Fit	(	TGraph *	graph,
		const char *	fitterName,
		Option_t *	fitOption = `""`,
		Option_t *	graphOption = `""`,
		Option_t *	funOption = `""`,
		Double_t	xMin = `0`,
		Double_t	xMax = `0`
	)

static

Make graph fit.

TODO- add example code snippet - using the code from test directory

Parameters

graph	- pointer to graph
fitterName	- fitter name ()
fitOption	- fitter setting option
graphOption	- graphic option
funOption	- graphic option for function
xMin	- fit range min
xMax	- fit range max

Returns: - pointer to the fitter

Definition at line 979 of file AliTMinuitToolkit.cxx.

void AliTMinuitToolkit::FitGraph	(	const TGraph *	gr,
		Option_t *	option = `""`
	)

Fit a TGraph object.

Parameters

gr	- const TGraph object
option	- fit option e.g (default, bootstrap20,misac .... ) In alternative usage more option and graph range can be specified Fit(TGraph* graph, const char fitterName, Option_t fitOption = "", Option_t* graphOption = "", Option_t* funOption="",Double_t xMin = 0, Double_t xMax = 0)

Definition at line 169 of file AliTMinuitToolkit.cxx.

Referenced by Fit(), and GetStreamer().

void AliTMinuitToolkit::FitHistogram	(	const TH1 *	his,
		Option_t *	option = `""`
	)

Fit a one dimensional histogram.

Parameters

his	- const TH1 object
option	- fit option e.g (default, bootstrap20,misac ... ) In alternative usage more option and histogram range can be specified Fit(TH1* his, const char fitterName, Option_t fitOption = "", Option_t* hisOption = "", Option_t *funOption="", Double_t xMin = 0, Double_t xMax = 0)

Definition at line 150 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkit_TestHistogram(), Fit(), and GetStreamer().

void AliTMinuitToolkit::FitterFCN	(	int &	nParam,
		double *	info,
		double &	chi2,
		double *	gin,
		int	iflag
	)

static

Internal function used in the TMinuit minimization.

see documentation for FCN parameters g.g in ROOT- TMinuit::Eval

Parameters

nPar	- not used in our interface
grad	- gradient of cost function
chi2(fVal))	- cost function to minimize (chi2/log-likelihood/)
gin(par)	- function parameters
iflag(flag)	- flag used by root (1.) print/ 2.) derivative/ 3. final fit) in our interface also possible to specify stream data (kStreamFcnPoint,kStreamFcn) typedef void(* FCNFunc_t) (Int_t &nPar, Double_t gin, Double_t &f, Double_t u, Int_t flag)

Original documentation in TMinuit::Eval documentation in root
- Input parameters:
  - nPar: number of currently variable parameters
  - par: array of (constant and variable) parameters
  - flag: Indicates what is to be calculated (see example below) ()
  - grad: array of gradients
- Output parameters:
  - fVal: The calculated function value.
  - grad: The (optional) vector of first derivatives).

Definition at line 205 of file AliTMinuitToolkit.cxx.

Referenced by Bootstrap(), Fit(), MISAC(), SetValues(), and TwoFoldCrossValidation().

Double_t AliTMinuitToolkit::GausKurtosisSkewness	(	const Double_t *	x,
		const Double_t *	p
	)

static

Gaus convoluted with Erf to emulate kurtosis and skewness.

Parameters

x
p	p[0],p[1],p[2] - as for gauss p[3] - Kurtosis - tails - proportional to 4 moment p[4] - Asymmetry - proportional to 3 moment

Returns

Definition at line 562 of file AliTMinuitToolkit.cxx.

Referenced by SetPredefinedFitter().

Double_t AliTMinuitToolkit::GaussCachyLogLike	(	const Double_t *	x,
		const Double_t *	p
	)

static

Log likelihood for the gaus+cauchy - used for Log likelihood minimization of distribution with tails

Parameters

x	-
p	- p[0] - gaus fraction p[1] - cauchy 0.5*FWHM

Returns: log likelihood for the mixture of gaus and cauchy distribution representation as in https://en.wikipedia.org/wiki/Cauchy_distribution

Definition at line 524 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkit_TestHistogram(), MISAC(), RegisterGaussFitters(), RegisterPlaneFitter(), and SetPredefinedFitter().

Double_t AliTMinuitToolkit::GetChisquare ( )

inline

Definition at line 155 of file AliTMinuitToolkit.h.

const TMatrixD* AliTMinuitToolkit::GetCovarianceMatrix ( ) const

inline

Definition at line 152 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkitTestLinear().

TString AliTMinuitToolkit::GetFitFunctionAsAlias	(	Option_t *	option = `""`,
		TTree *	tree = `nullptr`
	)

Format alias string for the for tree alias or for fit title.

Parameters

option - use latex in case of title request

Returns: - string description

Definition at line 465 of file AliTMinuitToolkit.cxx.

Referenced by GetStreamer(), and Test1D().

TF1* AliTMinuitToolkit::GetFormula ( ) const

inline

Definition at line 148 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkit_TestHistogram(), Fit(), and FitterFCN().

TMatrixD* AliTMinuitToolkit::GetInitialParam ( )

inline

Definition at line 136 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkitTestLinear().

TObjArray* AliTMinuitToolkit::GetListOfVariables ( )

inline

Definition at line 158 of file AliTMinuitToolkit.h.

Referenced by GetFitFunctionAsAlias().

const TF1* AliTMinuitToolkit::GetLogLikelihoodFunction ( ) const

inline

Definition at line 149 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkitTestLinear().

const TMatrixD* AliTMinuitToolkit::GetMISACEstimators ( ) const

inline

Definition at line 153 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkitTestLinear().

const TVectorD* AliTMinuitToolkit::GetParameters ( ) const

inline

Definition at line 150 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkit_TestHistogram(), AliTMinuitToolkitTestLinear(), Fit(), and Test1D().

const TMatrixD* AliTMinuitToolkit::GetPoints ( ) const

inline

Definition at line 146 of file AliTMinuitToolkit.h.

Referenced by FitterFCN().

static AliTMinuitToolkit* AliTMinuitToolkit::GetPredefinedFitter ( const std::string & fitterName )

inlinestatic

Definition at line 164 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkitTestLinear(), and Fit().

const TVectorD* AliTMinuitToolkit::GetRMSEstimator ( ) const

inline

Definition at line 151 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkitTestLinear(), and GetFitFunctionAsAlias().

Int_t AliTMinuitToolkit::GetStatus ( )

inline

Definition at line 156 of file AliTMinuitToolkit.h.

TTreeSRedirector* AliTMinuitToolkit::GetStreamer ( )

inline

Definition at line 122 of file AliTMinuitToolkit.h.

const TMatrixD* AliTMinuitToolkit::GetValues ( ) const

inline

Definition at line 147 of file AliTMinuitToolkit.h.

Referenced by FitterFCN().

Double_t AliTMinuitToolkit::HuberLogLike	(	const Double_t *	x,
		const Double_t *	p
	)

static

Huber loss is a loss function used in robust regression - representation as in https://en.wikipedia.org/w/index.php?title=Huber_loss&diff=809252384&oldid=798150659

Parameters

x	-
p	- p[0] - gaus region boundary

Returns: - loss function (used as a log likelihood)

Definition at line 536 of file AliTMinuitToolkit.cxx.

Referenced by SetPredefinedFitter().

Bool_t AliTMinuitToolkit::IsHuberCost ( ) const

inline

Definition at line 157 of file AliTMinuitToolkit.h.

Referenced by FitterFCN().

Bool_t AliTMinuitToolkit::IsVerbose ( Int_t flag )

inline

Definition at line 160 of file AliTMinuitToolkit.h.

Referenced by FitterFCN().

void AliTMinuitToolkit::MISAC	(	Int_t	nFitPoints,
		UInt_t	nIter,
		const char *	reportName,
		Option_t *	option = `nullptr`
	)

Fitting with outlier removal inspired by RANSAC - see https://en.wikipedia.org/w/index.php?title=Random_sample_consensus&oldid=767657742.

TODO: Make robust n-dimensional estimator
Parameters

nFitPoints - number of points used in one fit

nIter - number of iterations

reportName - report name (!=NULL- specified stream to save intermediate data)

option - fit option
Algorithm:
- 0.) Generate permutations of data
- 1.) Calculate fit parameters for small subset of data
- 2.) Calculate normalized distance between each fit vector
- 3.) Reject outliers and calculate robust mean
- 4.) Extract combined statistic
- 5.) Dump results into tree in verbose mode

TODO- check failure of the fit

Definition at line 720 of file AliTMinuitToolkit.cxx.

Referenced by Fit(), and GetStreamer().

AliTMinuitToolkit& AliTMinuitToolkit::operator= ( const AliTMinuitToolkit & )

private

Referenced by SetPredefinedFitter().

Double_t AliTMinuitToolkit::PseudoHuberLogLike	(	const Double_t *	x,
		const Double_t *	p
	)

static

Pseudo Huber loss is a loss function used in robust regression - representation as in https://en.wikipedia.org/w/index.php?title=Huber_loss&diff=809252384&oldid=798150659

Parameters

x	-
p	- p[0] - gaus region boundary

Returns: - loss function (used as a log likelihood)

Definition at line 547 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkit_TestHistogram(), MISAC(), RegisterPlaneFitter(), and SetPredefinedFitter().

static void AliTMinuitToolkit::RegisterDefaultFitters ( )

static

Referenced by AliTMinuitToolkitTestLinear(), MISAC(), and SetPredefinedFitter().

AliTMinuitToolkit * AliTMinuitToolkit::RegisterPlaneFitter	(	Int_t	nPlanes,
		Int_t	logLikeType
	)

static

Register default fitters.

Registered function can be used in standard minimization using sting identifier, e.g:
- AliTMinuitToolkit::Fit(TH1* his, const char *fitterName, Option_t* option, Option_t* goption,Option_t* foption, Double_t xMin, Double_t xMax)
- AliTMinuitToolkit::Fit(TH1* his, const char *fitterName, Option_t* option, Option_t* goption,Option_t* foption, Double_t xMin, Double_t xMax)
Registered fitter can be accessed - eventually modified (e.g to set initial values)
- AliTMinuitToolkit * pol1R= AliTMinuitToolkit::GetPredefinedFitter("pol1R");\endocode
  * Default fitters:
  * formula: pol<N>, gauss
  * log-likelihood: chi2, likeGausCachy, huber norm
  void AliTMinuitToolkit::RegisterDefaultFitters(){
  TF1 *likeGausCachy = new TF1("likeGausCachy", AliTMinuitToolkit::GaussCachyLogLike,-10,10,2);
  TF1 *likePseudoHuber = new TF1("likePseudoHuber", AliTMinuitToolkit::PseudoHuberLogLike,-10,10,1);
  likeGausCachy->SetParameters(0.8,1);
  likePseudoHuber->SetParameter(0,3);
  likeGausCachy->GetXaxis()->SetTitle("#Delta");
  likeGausCachy->GetYaxis()->SetTitle("-logLikelihood");
  likeGausCachy->SetLineColor(2);
  likePseudoHuber->GetXaxis()->SetTitle("#Delta");
  likePseudoHuber->GetYaxis()->SetTitle("-logLikelihood");
  likePseudoHuber->SetLineColor(4);
  //
  for (Int_t iPol=0; iPol<10; iPol++){ //register polynomial fitters
  TMatrixD initPar(iPol+1,4);
  for (Int_t iPar=0; iPar<iPol+1; iPar++) initPar(iPar,1)=1;
  //
  TF1 *fpol = new TF1(TString::Format("fpol%d",iPol).Data(),TString::Format("pol%d",iPol).Data());
  AliTMinuitToolkit * fitter1D = new AliTMinuitToolkit();
  fitter1D->SetVerbose(0x1); fitter1D->SetFitFunction(fpol,kTRUE);
  fitter1D->SetInitialParam(&initPar);
  fitter1D->SetName(TString::Format("pol%d",iPol).Data());
  AliTMinuitToolkit::SetPredefinedFitter(fitter1D->GetName(),fitter1D);
  // gaus log likelihood cost function
  AliTMinuitToolkit * fitter1DR = new AliTMinuitToolkit();
  fitter1DR->SetVerbose(0x1); fitter1DR->SetFitFunction(fpol,kTRUE);
  fitter1DR->SetLogLikelihoodFunction(likeGausCachy);
  fitter1DR->SetInitialParam(&initPar);
  fitter1DR->SetName(TString::Format("pol%dR",iPol).Data());
  AliTMinuitToolkit::SetPredefinedFitter(fitter1DR->GetName(),fitter1DR);
  // huber cost function
  AliTMinuitToolkit * fitter1DH = new AliTMinuitToolkit();
  fitter1DH->SetVerbose(0x1); fitter1DH->SetFitFunction(fpol,kTRUE);
  fitter1DH->SetInitialParam(&initPar);
  //fitter1DH->EnableRobust(true);
  fitter1DH->SetLogLikelihoodFunction(likePseudoHuber);
  fitter1DH->SetName(TString::Format("pol%dH",iPol).Data());
  AliTMinuitToolkit::SetPredefinedFitter(fitter1DH->GetName(),fitter1DH);
  }
  //
  TF1 *fGaus = new TF1("fgaus","gaus");
  TMatrixD initPar(3,4);
  initPar(0,0)=0; initPar(0,1)=1;
  initPar(1,0)=0; initPar(1,1)=1;
  initPar(2,0)=1; initPar(2,1)=1;
  AliTMinuitToolkit * fitterGR = new AliTMinuitToolkit();
  fitterGR->SetVerbose(0x1); fitterGR->SetFitFunction(fGaus,kTRUE);
  fitterGR->SetLogLikelihoodFunction(likeGausCachy);
  fitterGR->SetInitialParam(&initPar);
  AliTMinuitToolkit::SetPredefinedFitter("gausR",fitterGR);
  //
  //
  // TFormulaPrimitive::AddFormula(new TFormulaPrimitive("GausKS","GausKS",(TFormulaPrimitive::GenFuncG)AliTMinuitToolkit::GausKurtosisSkewness,5));
  // hack number of arguments in the primitive (protected member) - //TODO - fix ROOT
  // TFormulaPrimitive * p = TFormulaPrimitive::FindFormula("GausKS");
  // TDataMember *m = (TDataMember*)p->IsA()->GetListOfDataMembers()->FindObject("fNArguments");
  // *((Int_t*)(((char*)p)+m->GetOffset()))=1;
  }
  \breief Register plane fitters (As in the TLinearFitter)
  Global registered fitters can be obtained e.g :
  \code AliTMinuitToolkit * hyp2R= AliTMinuitToolkit::GetPredefinedFitter("hyp2R");
  Parameters
  nPlanes - number of planes
  
  logLikeType - type of the log likelihood
  
  0) chi2, 1.) gaus+cauchy, 2.) pseudo-huber
  Returns
  return registered fitter

Definition at line 902 of file AliTMinuitToolkit.cxx.

Referenced by SetPredefinedFitter().

Double_t AliTMinuitToolkit::RndmGaus	(	Double_t	mean = `0`,
		Double_t	sigma = `1`
	)

static

Random gaus generator as static function (to use in root TFormula, TTreeFormula)

Parameters

mean	- mean Gaus
sigma	- sigma gaus

Returns

Definition at line 505 of file AliTMinuitToolkit.cxx.

Referenced by SetPredefinedFitter().

Double_t AliTMinuitToolkit::RndmLandau	(	Double_t	mean = `0`,
		Double_t	sigma = `1`
	)

static

Random gaus generator as static function (to use in root TFormula, TTreeFormula)

Parameters

mean
sigma

Returns

Definition at line 513 of file AliTMinuitToolkit.cxx.

Referenced by SetPredefinedFitter().

void AliTMinuitToolkit::SetFitAlgorithm ( Char_t *const name )

inline

Definition at line 138 of file AliTMinuitToolkit.h.

void AliTMinuitToolkit::SetFitFunction	(	TF1 *	formula,
		Bool_t	doReset
	)

Set formula of the fitted function and reset parameter. See doReset.

Parameters

formula	- formula of the fitted function
doReset	- if true reset parameters related to the fit function

Definition at line 120 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkit_TestHistogram(), GetStreamer(), MISAC(), RegisterGaussFitters(), RegisterPlaneFitter(), and Test1D().

void AliTMinuitToolkit::SetFunctionDrawOption	(	TF1 *	fun,
		Option_t *	option
	)

static

Parse draw option for function

Parameters

fun	- pointer to function to change
option	- draw option for function TODO- add example using the code from test directory Example usage: AliTMinuitToolkit::SetFunctionDrawOption(fpol1,"funOption(1,1,1)")

Definition at line 1014 of file AliTMinuitToolkit.cxx.

Referenced by Fit(), and SetPredefinedFitter().

void AliTMinuitToolkit::SetInitialParam ( const TMatrixD * paramLimits )

Set initial parameters matrix.

Parameters

paramLimits

- Initialization matrix

number of lines = number of parameters
4 columns
- [0] - initial value
- [1] - initial error
- [2],[3] - optional parameters to specify minimum and maximum of the parameter (see TMinuit)

Definition at line 140 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkit_TestHistogram(), GetStreamer(), MISAC(), RegisterGaussFitters(), RegisterPlaneFitter(), and Test1D().

void AliTMinuitToolkit::SetLogLikelihoodFunction ( TF1 * logLikelihood )

inline

Definition at line 137 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkit_TestHistogram(), MISAC(), RegisterGaussFitters(), RegisterPlaneFitter(), and Test1D().

void AliTMinuitToolkit::SetMaxCalls ( Int_t calls )

inline

Definition at line 139 of file AliTMinuitToolkit.h.

void AliTMinuitToolkit::SetPoints ( TMatrixD * points )

inline

Definition at line 141 of file AliTMinuitToolkit.h.

static void AliTMinuitToolkit::SetPredefinedFitter	(	const std::string &	fitterName,
		AliTMinuitToolkit *	fitter
	)

inlinestatic

Definition at line 165 of file AliTMinuitToolkit.h.

Referenced by AliTMinuitToolkit_TestHistogram(), MISAC(), RegisterGaussFitters(), and RegisterPlaneFitter().

void AliTMinuitToolkit::SetStreamer	(	const char *	streamerName,
		const char *	mode = `"recreate"`
	)

Set stream for writing info into TTree. see examples(STEER/STEERBase/TTreeStream.cxx)

Parameters

streamerName	- Name of .root file
mode	- option for .root file open recreate update ....

Definition at line 99 of file AliTMinuitToolkit.cxx.

Referenced by AliTMinuitToolkitTestLinear().

void AliTMinuitToolkit::SetTolerance ( Double_t tol )

inline

Definition at line 140 of file AliTMinuitToolkit.h.

void AliTMinuitToolkit::SetValues ( TMatrixD * values )

inline

Definition at line 142 of file AliTMinuitToolkit.h.

void AliTMinuitToolkit::SetVerbose ( Int_t verbose )

inline

Definition at line 159 of file AliTMinuitToolkit.h.

Referenced by MISAC(), RegisterGaussFitters(), and Test1D().

void AliTMinuitToolkit::TwoFoldCrossValidation	(	UInt_t	nIter,
		const char *	reportName,
		Option_t *	option = `nullptr`
	)

Two fold cross validation - https://en.wikipedia.org/wiki/Cross-validation_(statistics)

Sample randomly divided to the independent training set and complementary test set (Repeated random sub-sampling validation)
log likelihood cost function calculated for training fit set
TODO - Used for fit model validation. Report - Post processing using streamer not available for the moment
TODO - Add: The results are then averaged over the splits as described in the wiki section - (Repeated random sub-sampling validation)
Parameters

nIter - number of iterations

reportName - report name (identifier in the streamer)

option - fit option

Definition at line 637 of file AliTMinuitToolkit.cxx.

Referenced by Fit(), GetStreamer(), and Test1D().

Member Data Documentation

Double_t AliTMinuitToolkit::fChi2

private

Definition at line 197 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), Fit(), GetChisquare(), and MISAC().

TMatrixD* AliTMinuitToolkit::fCovar

private

Definition at line 195 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), Fit(), GetCovarianceMatrix(), MISAC(), SetFitFunction(), TwoFoldCrossValidation(), and ~AliTMinuitToolkit().

Int_t AliTMinuitToolkit::fFCNCounter

private

Definition at line 201 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), FitterFCN(), and TwoFoldCrossValidation().

TString AliTMinuitToolkit::fFitAlgorithm

private

Definition at line 185 of file AliTMinuitToolkit.h.

Referenced by Fit(), and SetFitAlgorithm().

TF1* AliTMinuitToolkit::fFormula

private

Definition at line 183 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), Fit(), FitterFCN(), GetFitFunctionAsAlias(), GetFormula(), MISAC(), SetFitFunction(), and TwoFoldCrossValidation().

TMatrixD* AliTMinuitToolkit::fInitialParam

private

Definition at line 191 of file AliTMinuitToolkit.h.

Referenced by Fit(), GetInitialParam(), SetInitialParam(), and ~AliTMinuitToolkit().

Bool_t AliTMinuitToolkit::fIsHuberCost

private

Definition at line 200 of file AliTMinuitToolkit.h.

Referenced by EnableRobust(), and IsHuberCost().

TF1* AliTMinuitToolkit::fLogLikelihoodFunction

private

Definition at line 184 of file AliTMinuitToolkit.h.

Referenced by FitterFCN(), GetLogLikelihoodFunction(), and SetLogLikelihoodFunction().

Int_t AliTMinuitToolkit::fMaxCalls

private

Definition at line 198 of file AliTMinuitToolkit.h.

Referenced by Fit(), and SetMaxCalls().

TMatrixD* AliTMinuitToolkit::fMISACEstimators

private

Definition at line 194 of file AliTMinuitToolkit.h.

Referenced by GetMISACEstimators(), MISAC(), and ~AliTMinuitToolkit().

TVectorD* AliTMinuitToolkit::fParam

private

Definition at line 192 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), Fit(), GetFitFunctionAsAlias(), GetParameters(), MISAC(), SetFitFunction(), TwoFoldCrossValidation(), and ~AliTMinuitToolkit().

TArrayI AliTMinuitToolkit::fPointIndex

private

Definition at line 190 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), FitterFCN(), MISAC(), and TwoFoldCrossValidation().

TMatrixD* AliTMinuitToolkit::fPoints

private

Definition at line 186 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), ClearData(), FillFitter(), FitGraph(), FitHistogram(), GetPoints(), MISAC(), SetPoints(), TwoFoldCrossValidation(), and ~AliTMinuitToolkit().

Double_t AliTMinuitToolkit::fPrecision

private

Definition at line 199 of file AliTMinuitToolkit.h.

Referenced by Fit(), and SetTolerance().

std::map< std::string, AliTMinuitToolkit * > AliTMinuitToolkit::fPredefinedFitters

staticprivate

Definition at line 202 of file AliTMinuitToolkit.h.

Referenced by GetPredefinedFitter(), and SetPredefinedFitter().

TVectorD* AliTMinuitToolkit::fRMSEstimator

private

Definition at line 193 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), GetRMSEstimator(), MISAC(), SetFitFunction(), and ~AliTMinuitToolkit().

Int_t AliTMinuitToolkit::fStatus

private

Definition at line 196 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), Fit(), GetStatus(), MISAC(), and TwoFoldCrossValidation().

TTreeSRedirector* AliTMinuitToolkit::fStreamer

private

Definition at line 181 of file AliTMinuitToolkit.h.

Referenced by Bootstrap(), FitterFCN(), GetStreamer(), MISAC(), SetStreamer(), TwoFoldCrossValidation(), and ~AliTMinuitToolkit().

TObjArray* AliTMinuitToolkit::fValueNames

private

Definition at line 189 of file AliTMinuitToolkit.h.

Referenced by FillFitter().

TMatrixD* AliTMinuitToolkit::fValues

private

Definition at line 187 of file AliTMinuitToolkit.h.

Referenced by ClearData(), FillFitter(), Fit(), FitGraph(), FitHistogram(), GetValues(), SetValues(), and ~AliTMinuitToolkit().

TObjArray* AliTMinuitToolkit::fVarNames

private

Definition at line 188 of file AliTMinuitToolkit.h.

Referenced by FillFitter(), GetFitFunctionAsAlias(), and GetListOfVariables().

Int_t AliTMinuitToolkit::fVerbose

private

Definition at line 182 of file AliTMinuitToolkit.h.

Referenced by Fit(), IsVerbose(), and SetVerbose().

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

STAT/AliTMinuitToolkit.h
STAT/AliTMinuitToolkit.cxx

nIter	- number of iteration
reportName	- report name - in case results streamed
option	- fit option

nFitPoints	- number of points used in one fit
nIter	- number of iterations
reportName	- report name (!=NULL- specified stream to save intermediate data)
option	- fit option

nPlanes	- number of planes
logLikeType	- type of the log likelihood 0) chi2, 1.) gaus+cauchy, 2.) pseudo-huber

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Usage:

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation