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AliTMinuitToolkit.cxx
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AliTMinuitToolkit.cxx
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/**************************************************************************
* Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
* *
* Author: The ALICE Off-line Project. *
* Contributors are mentioned in the code where appropriate. *
* *
* Permission to use, copy, modify and distribute this software and its *
* documentation strictly for non-commercial purposes is hereby granted *
* without fee, provided that the above copyright notice appears in all *
* copies and that both the copyright notice and this permission notice *
* appear in the supporting documentation. The authors make no claims *
* about the suitability of this software for any purpose. It is *
* provided "as is" without express or implied warranty. *
**************************************************************************/
/* $Id$ */
#include <TCanvas.h>
#include <TF1.h>
#include <TH1F.h>
#include <TMath.h>
#include <TMatrix.h>
#include <TRandom.h>
#include <TVector.h>
#include <TVectorD.h>
#include <TVirtualFitter.h>
#include <TLegend.h>
#include <TStyle.h>
#include <TTree.h>
#include <TTreeStream.h>
#include "AliTMinuitToolkit.h"
#include "TGraph.h"
#include "TPRegexp.h"
#include "TStatToolkit.h"
//#include "TFormulaPrimitive.h"
#include "TDataMember.h"
std::map<std::string, AliTMinuitToolkit*> AliTMinuitToolkit::fPredefinedFitters;
ClassImp(AliTMinuitToolkit)
AliTMinuitToolkit::AliTMinuitToolkit(const char *streamerName, const char *mode) :
TNamed(),
fStreamer(nullptr),
fVerbose(0),
fFormula(nullptr),
fLogLikelihoodFunction(nullptr),
fFitAlgorithm(""),
fPoints(nullptr),
fValues(nullptr),
fVarNames(nullptr), // variable names
fValueNames(nullptr), // value names
fPointIndex(0), // point index - to specify points for likelihood calculation (used for Bootstrap and CrossValidation)
fParam(nullptr),
fInitialParam(nullptr),
fRMSEstimator(nullptr), // parameter spread as estimated in Bootstrap resp. TwoFold cross validation
fMISACEstimators(nullptr), // MISAC estimators - median, mean, rms
fCovar(nullptr),
fChi2(0),
fMaxCalls(0),
fPrecision(0),
fIsHuberCost(0),
fFCNCounter(0) // cost function call counter
{
//
// standard constructor
//
fMaxCalls = 500;
fPrecision = 1;
fIsHuberCost = false;
if (streamerName!= nullptr) fStreamer= new TTreeSRedirector(streamerName,mode);
}
AliTMinuitToolkit::~AliTMinuitToolkit(){
//
// destructor
//
delete fPoints;
delete fValues;
delete fInitialParam;
// delete fFormula;
delete fParam;
delete fRMSEstimator;
delete fMISACEstimators;
delete fCovar;
delete fStreamer;
}
/// \brief Set stream for writing info into TTree.
/// see examples(STEER/STEERBase/TTreeStream.cxx)
/// \param streamerName - Name of .root file
/// \param mode - option for .root file open
/// * recreate
/// * update
/// * ....
void AliTMinuitToolkit::SetStreamer(const char *streamerName, const char *mode){
//
// set streamer
delete fStreamer;
fStreamer= new TTreeSRedirector(streamerName,mode);
}
void AliTMinuitToolkit::ClearData(){
delete fPoints;
fPoints= nullptr;
delete fValues;
fValues= nullptr;
// delete fParam;
// fParam=0;
// delete fCovar;
// fCovar=0;
}
/// \brief Set formula of the fitted function and reset parameter. See doReset
/// \param formula - formula of the fitted function
/// \param doReset - if true reset parameters related to the fit function
void AliTMinuitToolkit::SetFitFunction(TF1 * formula, Bool_t doReset) {
//
fFormula=formula;
if (doReset){
delete fParam;
delete fRMSEstimator;
delete fCovar;
fParam=new TVectorD(formula->GetNpar());
fRMSEstimator=new TVectorD(formula->GetNpar());
fCovar=new TMatrixD(formula->GetNpar(),formula->GetNpar());
}
}
/// \brief Set initial parameters matrix
/// \param 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)
void AliTMinuitToolkit::SetInitialParam(const TMatrixD * paramLimits) {
fInitialParam=new TMatrixD(*paramLimits);
};
/// \brief Fit a one dimensional histogram
/// \param his - const TH1 object
/// \param option - fit option e.g (default, bootstrap20,misac ... )
/// * In alternative usage more option and histogram range can be specified
/// \code Fit(TH1* his, const char *fitterName, Option_t* fitOption = "", Option_t* hisOption = "", Option_t *funOption="", Double_t xMin = 0, Double_t xMax = 0)\endcode
void AliTMinuitToolkit::FitHistogram(const TH1 * his, Option_t *option) {
ClearData();
fPoints = new TMatrixD(his->GetNbinsX(), 1);
fValues = new TMatrixD(his->GetNbinsX(), 2);
for(Int_t iBin=0; iBin < his->GetNbinsX(); iBin++) {
Double_t x = his->GetXaxis()->GetBinCenter(iBin+1);
Double_t y = his->GetBinContent(iBin+1);
(*fPoints)(iBin, 0) = x;
Double_t err=his->GetBinError(iBin+1);
(*fValues)(iBin,0)=y;
(*fValues)(iBin,1)=(err>0)? 1./err:0;
}
Fit(option);
}
/// \brief Fit a TGraph object
/// \param gr - const TGraph object
/// \param option - fit option e.g (default, bootstrap20,misac .... )
/// * In alternative usage more option and graph range can be specified
/// \code Fit(TGraph* graph, const char *fitterName, Option_t* fitOption = "", Option_t* graphOption = "", Option_t* funOption="",Double_t xMin = 0, Double_t xMax = 0)\endcode
void AliTMinuitToolkit::FitGraph(const TGraph * gr, Option_t *option) {
ClearData();
Int_t nPoints=gr->GetN();
fPoints = new TMatrixD(nPoints, 1);
fValues = new TMatrixD(nPoints, 2);
for(Int_t ip=0; ip < nPoints; ip++) {
Double_t x = gr->GetX()[ip];
Double_t y = gr->GetY()[ip];
(*fPoints)(ip, 0) = x;
Double_t err=gr->GetErrorY(ip);
(*fValues)(ip,0)=y;
(*fValues)(ip,1)=(err>0)? 1./err:0;
}
Fit(option);
}
/// \brief Internal function used in the TMinuit minimization
/// * see documentation for FCN parameters g.g in ROOT- TMinuit::Eval
///
/// \param nPar - not used in our interface
/// \param grad - gradient of cost function
/// \param chi2(fVal)) - cost function to minimize (chi2/log-likelihood/)
/// \param gin(par) - function parameters
/// \param 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).
void AliTMinuitToolkit::FitterFCN(int &/*nPar*/, double */*grad*/, double &chi2, double *gin, int iflag){
AliTMinuitToolkit * fitter = (AliTMinuitToolkit*)TVirtualFitter::GetFitter()->GetObjectFit();
if (!fitter) return;
Int_t &fcnCounter=fitter->fFCNCounter;
TF1 *logLike=fitter->fLogLikelihoodFunction;
const Double_t* likeParam= (logLike!= nullptr) ? logLike->GetParameters(): nullptr;
chi2 = 0;
const TMatrixD & variables= (*fitter->GetPoints());
const TMatrixD & values= (*fitter->GetValues());
Int_t nVars = variables.GetNcols();
Int_t nPoints = variables.GetNrows();
TVectorD param(fitter->fFormula->GetNpar(), gin);
// calculate log likelihood
//
if (fitter->fPointIndex.GetSize()>0) {
nPoints=fitter->fPointIndex.GetSize();
}
for (Int_t jPoint=0; jPoint<nPoints; jPoint++){
Int_t iPoint=(fitter->fPointIndex.GetSize()>0) ? fitter->fPointIndex[jPoint]:jPoint;
Double_t x[100];
for (Int_t ivar=0; ivar<nVars; ivar++){
x[ivar] = variables(iPoint, ivar);
}
Double_t funX = (fitter->GetFormula())->EvalPar(x,gin);
Double_t value=values(iPoint,0);
Double_t weight=values(iPoint,1);
Double_t delta = (value - funX);
Double_t toAdd=0;
if (logLike){
Double_t normDelta = delta*weight;
toAdd=logLike->EvalPar(&normDelta,likeParam);
}else{
if (fitter->IsHuberCost() != 0) { //hubert norm
delta = TMath::Abs(delta*weight); // normalization
if (delta <= 2.5) toAdd= delta*delta; // new metric: Huber-k-estimator
if (delta > 2.5) toAdd= 2*(2.5)*delta - (2.5*2.5);
} else {
Double_t lChi2 = delta*weight;
lChi2*=lChi2;
toAdd=lChi2; // chi2 (log likelihood)
}
}
//
if (fitter->IsVerbose(kStreamFcnPoint) || (iflag&kStreamFcnPoint)){
TVectorD vecX(nVars, x);
(*(fitter->fStreamer))<<"fcnDebugPoint"<<
"toAdd="<<toAdd<< // log likelihood to add
"val="<<value<< // "measurement"
"w="<<weight<< // wight of point
"fun="<<funX<< // function value
"x.="<<&vecX<< // variable vector
"p.="<<¶m<< // parameter vector
"\n";
}
chi2+=toAdd;
}
if (fitter->IsVerbose(kStreamFcn) || (iflag&kStreamFcn )){
(*(fitter->fStreamer))<<"fcnDebug"<<
"chi2="<<chi2<<
"p.="<<¶m<<
"\n";
}
fcnCounter++;
}
/// \brief Internal function that calls the fitter
/// \param option:
/// * bootstrap[0-9]* -
/// * twofold[0-9]* -
/// * misac\([0-9]*,[0-9]*\) -
void AliTMinuitToolkit::Fit(Option_t *option) {
TString sOption=(option== nullptr)?"":option;
TPRegexp regBootstrap("bootstrap[0-9]*");
TPRegexp regTwofold("twofold[0-9]*");
TPRegexp regMISAC("misac\\([0-9]*,[0-9]*\\)");
// run bootstrap if specified
if (regBootstrap.Match(sOption)>0){ // run bootstrap
TString newOption=sOption;
regBootstrap.Substitute(newOption,"");
UInt_t nPoints= static_cast<UInt_t>(TString(&(sOption.Data()[sOption.Index(regBootstrap) + 9])).Atoi());
if (nPoints<0) nPoints=5;
return Bootstrap(nPoints, nullptr,newOption.Data());
}
// run two fold minimization if specified
if (regTwofold.Match(sOption)>0){ // run twofold minimization
TString newOption=sOption;
regTwofold.Substitute(newOption,"");
UInt_t nPoints= static_cast<UInt_t>(TString(&(sOption.Data()[sOption.Index(regTwofold) + 7])).Atoi());
if (nPoints<0) nPoints=5;
return TwoFoldCrossValidation(nPoints, nullptr,newOption.Data());
}
// run MISAC
if (regMISAC.Match(sOption)>0){ // run MISAC minimization - mix of RANSAC and KFold
TString newOption=sOption;
regMISAC.Substitute(newOption,"");
Int_t index1=sOption.Index(regMISAC)+6;
Int_t index2=sOption.Index(",",index1+1)+1;
Int_t nPoints=TString(&(sOption.Data()[index1])).Atoi();
UInt_t nIter= static_cast<UInt_t>(TString(&(sOption.Data()[index2])).Atoi());
if (nPoints<0) nPoints=5;
return MISAC(nPoints,nIter, nullptr,newOption.Data());
}
fStatus=0;
Int_t nParam = fFormula->GetNpar();
// create "initial param" in case not set before
if (fParam== nullptr) fParam=new TVectorD(nParam);
if (fInitialParam == nullptr) {
::Info("AliTMinuitToolkit::Fit","Default initial parameters set");
fInitialParam= new TMatrixD(nParam,4);
for (Int_t iParam=0; iParam<nParam; iParam++) {
(*fInitialParam)(iParam,0)=0;
(*fInitialParam)(iParam,1)=1000;
(*fInitialParam)(iParam,2)=0;
(*fInitialParam)(iParam,3)=0;
}
}
// migrad fit algorithm as default
if (fFitAlgorithm == "") {
fFitAlgorithm = "migrad";
}
// assign weights
if (fValues == nullptr) {
::Error("AliTMinuitToolkit::Fit()","Invalid fit. Values not set");
return ;
}
// set up the fitter
TVirtualFitter *minuit = TVirtualFitter::Fitter(nullptr, nParam);
minuit->SetObjectFit(this);
minuit->SetFCN(AliTMinuitToolkit::FitterFCN);
if ((fVerbose& kPrintMinuit)==0){ // MAKE minuit QUIET!!
double p1 = -1;
minuit->ExecuteCommand("SET PRINTOUT",&p1,1);
}
if ((fVerbose& kPrintAll)>0){ // MAKE minuit verbose!!
double pprint=2;
minuit->ExecuteCommand("SET PRINTOUT",&pprint,1);
}
// initialize parameters (step size???)
for (Int_t iParam=0; iParam<nParam; iParam++){
if (sOption.Contains("rndmInit")){
Double_t initValue=(*fInitialParam)(iParam, 0)+gRandom->Gaus()*(*fInitialParam)(iParam,1);
minuit->SetParameter(iParam, Form("p[%d]",iParam), initValue, (*fInitialParam)(iParam,1), (*fInitialParam)(iParam, 2), (*fInitialParam)(iParam, 3));
}else{
minuit->SetParameter(iParam, Form("p[%d]",iParam), (*fInitialParam)(iParam,0), (*fInitialParam)(iParam,1), (*fInitialParam)(iParam, 2), (*fInitialParam)(iParam, 3));
}
/*
if (doReset){
minuit->SetParameter(iParam, Form("p[%d]",iParam), (*fInitialParam)(iParam,0), (*fInitialParam)(iParam,1), (*fInitialParam)(iParam, 2), (*fInitialParam)(iParam, 3));
}else{
minuit->SetParameter(iParam, Form("p[%d]",iParam), (*fParam)(iParam), TMath::Sqrt((*fCovar)(iParam,iParam)), (*fInitialParam)(iParam, 2), (*fInitialParam)(iParam, 3));
}
*/
}
//
Double_t argList[2];
argList[0] = fMaxCalls; //maximal number of calls
argList[1] = fPrecision; //tolerance normalized to 0.001
//if (fMaxCalls == 500 && fPrecision == 1) minuit->ExecuteCommand(fFitAlgorithm, 0, 0);
//if (fMaxCalls != 500 || fPrecision != 1)
minuit->ExecuteCommand(fFitAlgorithm, argList, 2);
// two additional arguments can be specified ExecuteCommand("migrad", argList, 2) - use 0,0 for default
// fStatus = (((TFitter*)minuit)->GetMinuit())->GetStatus(); // we should add separate status for Minuit and AliTMinuitToolkit
// fill parameter vector
for (Int_t ivar=0; ivar<nParam; ivar++){
(*fParam)(ivar) = minuit->GetParameter(ivar);
fFormula->SetParameter(ivar, minuit->GetParameter(ivar));
//fFormula->SetPar(ivar, minuit->GetParameter(ivar));
}
FitterFCN(nParam, nullptr,fChi2, fParam->GetMatrixArray(),0);
// fill parameter vector
for (Int_t ivar=0; ivar<nParam; ivar++){
(*fParam)(ivar) = minuit->GetParameter(ivar);
fFormula->SetParameter(ivar, minuit->GetParameter(ivar));
}
// fill covariance matrix
if (fCovar== nullptr) fCovar = new TMatrixD(nParam, nParam);
if (minuit->GetCovarianceMatrix()){
fCovar->SetMatrixArray(minuit->GetCovarianceMatrix());
}else{
fStatus|=kCovarFailed;
}
}
/// \brief Fill input matrices of the fitter
/// * TODO - add better working example (using code/trees from the test directory)
/// \param inputTree - pointer to input tree
/// \param values - values description (parameter:<error>)
/// \param variables - variables array (var0:<var1>)
/// \param selection - tree selection
/// \param firstEntry - first entry to query
/// \param nEntries - number of entries to query
/// \param doReset - switch reset previous/or append
/// \return
/*!
* Example: TPC occupancy 6 dimensional hyperplane fit
\code
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();
\endcode
*/
Long64_t AliTMinuitToolkit::FillFitter(TTree * inputTree, TString values, TString variables, TString selection, Int_t firstEntry, Int_t nEntries, Bool_t doReset ){
TString query=values;
query+=":";
query+=variables;
if (inputTree== nullptr){
::Error("AliTMinuitToolkit::FillFitter","Input tree==NULL");
return -1;
}
fValueNames=values.Tokenize(":");
fVarNames=variables.Tokenize(":");
Int_t nVal= fValueNames->GetEntries();
Int_t nVars= fVarNames->GetEntries();
if (doReset == 0 && fPoints != nullptr){
if (fPoints->GetNrows()!=nVars){
::Error("AliTMinuitToolkit::FillFitter","Non compatible number of variables: %d instead of %d: variables: %s",nVars, fPoints->GetNrows(), query.Data());
return -1;
}
}
Long64_t entries = inputTree->Draw(query.Data(),selection.Data(),"goff para",nEntries,firstEntry);
if (entries<=0) {
::Error("AliTMinuitToolkit::FillFitter","badly formatted values or variables: %s",query.Data());
::Error("AliTMinuitToolkit::FillFitter","valueDescription: %s",values.Data());
::Error("AliTMinuitToolkit::FillFitter","variables: %s",variables.Data());
return -1;
}
Int_t index0=0;
if (doReset || fPoints== nullptr) {
ClearData();
fPoints=new TMatrixD(entries,nVars);
fValues=new TMatrixD(entries,nVal);
}else{
index0= fPoints->GetNrows();
fPoints->ResizeTo(index0+Int_t(entries),nVars);
fValues->ResizeTo(index0+Int_t(entries),nVal);
}
for (Int_t iPoint=0; iPoint<entries; iPoint++){
for (Int_t iVar=0; iVar<nVars; iVar++){
(*fPoints)(index0+iPoint,iVar)=inputTree->GetVal(iVar+nVal)[iPoint];
}
for (Int_t iVal=0; iVal<nVal; iVal++){
(*fValues)(index0+iPoint,iVal)=inputTree->GetVal(iVal)[iPoint];
}
}
return entries;
}
/// \brief Format alias string for the for tree alias or for fit title
/// \param option - use latex in case of title request
/// \return - string description
TString AliTMinuitToolkit::GetFitFunctionAsAlias(Option_t *option, TTree * tree){
//
// construct string TTree alias for fit function
TString inputString(fFormula->GetTitle());
TString sOption(option);
sOption.ToLower();
if (fVarNames== nullptr){
::Error("AliTMinuitToolkit::GetFitFunctionAsAlias","Variable names not defined");
return "";
}
for (Int_t iDim=0; iDim<fFormula->GetNdim(); iDim++){
TString varName=GetListOfVariables()->At(iDim)->GetName();
if (sOption.Contains("latex") &&tree){
TNamed * meta = TStatToolkit::GetMetadata(tree,varName+".Title");
if (meta) varName=meta->GetTitle();
}
inputString.ReplaceAll(TString::Format("x[%d]",iDim).Data(), varName.Data());
}
for (Int_t iPar=0; iPar<fFormula->GetNpar(); iPar++){
if (sOption.Contains("latex")==0){
inputString.ReplaceAll(TString::Format("[%d]",iPar).Data(), TString::Format("(%f)",(*fParam)[iPar]).Data());
}else{
if ((*GetRMSEstimator())[0]>0) {
inputString.ReplaceAll(TString::Format("[%d]", iPar).Data(),
TString::Format("(%2.2f#pm%2.2f)", (*fParam)[iPar], (*GetRMSEstimator())[iPar]).Data());
}else{
inputString.ReplaceAll(TString::Format("[%d]", iPar).Data(),
TString::Format("(%2.2f#pm%2.2f)", (*fParam)[iPar], (*GetRMSEstimator())[iPar]).Data());
}
}
}
return inputString;
}
/// \brief Random gaus generator as static function (to use in root TFormula, TTreeFormula)
/// \param mean - mean Gaus
/// \param sigma - sigma gaus
/// \return
Double_t AliTMinuitToolkit::RndmGaus(Double_t mean, Double_t sigma){
return gRandom->Gaus(mean,sigma);
}
/// \brief Random gaus generator as static function (to use in root TFormula, TTreeFormula)
/// \param mean
/// \param sigma
/// \return
Double_t AliTMinuitToolkit::RndmLandau(Double_t mean, Double_t sigma){
return gRandom->Landau(mean,sigma);
}
/// Log likelihood for the gaus+cauchy - used for Log likelihood minimization of distribution with tails
/// \param x -
/// \param p - p[0] - gaus fraction
/// - p[1] - cauchy 0.5*FWHM
/// \return log likelihood for the mixture of gaus and cauchy distribution
/// representation as in https://en.wikipedia.org/wiki/Cauchy_distribution
Double_t AliTMinuitToolkit::GaussCachyLogLike(const Double_t *x, const Double_t *p){
Double_t vCauchy=p[1]/(TMath::Pi()*(p[1]*p[1]+(*x)*(*x)));
Double_t vGaus=(TMath::Abs(*x)<20) ? TMath::Gaus(*x,0,1.,kTRUE):0.;
Double_t p0= p[0]*TMath::Gaus(0,0,1,kTRUE)+(1-p[0])/(TMath::Pi()*p[1]);
return -2.*TMath::Log((p[0]*vGaus+(1-p[0])*vCauchy)/p0);
}
/// 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
/// \param x -
/// \param p - p[0] - gaus region boundary
/// \return - loss function (used as a log likelihood)
///
Double_t AliTMinuitToolkit::HuberLogLike(const Double_t *x, const Double_t *p){
Double_t absX=TMath::Abs(x[0]);
if (absX<p[0]) return absX*absX;
return p[0]*(2*absX-p[0]);
}
/// 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
/// \param x -
/// \param p - p[0] - gaus region boundary
/// \return - loss function (used as a log likelihood)
///
Double_t AliTMinuitToolkit::PseudoHuberLogLike(const Double_t *x, const Double_t *p){
Double_t p2=p[0]*p[0];
Double_t x2=x[0]*x[0];
Double_t result=2.*p2*(TMath::Sqrt(1.+x2/p2)-1.);
return result;
}
/// \brief Gaus convoluted with Erf to emulate kurtosis and skewness
///
/// \param x
/// \param 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
/// \return
Double_t AliTMinuitToolkit::GausKurtosisSkewness(const Double_t *x, const Double_t *p){
// TODO add protection against out of range
static Float_t msqrt2=1./TMath::Sqrt(2.);
Double_t gaussPart=p[0]*TMath::Exp(-(TMath::Power(TMath::Abs(x[0]-p[1])/p[2],p[3])));
Double_t erfPart=(1.+TMath::Erf(p[4]*(x[0]-p[1])/p[2]*msqrt2));
return gaussPart*erfPart;
}
/// \brief 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
/// \param nIter - number of iteration
/// \param reportName - report name - in case results streamed
/// \param option - fit option
void AliTMinuitToolkit::Bootstrap(ULong_t nIter, const char * reportName, Option_t *option){
Int_t nPoints= fPoints->GetNrows();
fPointIndex.Set(nPoints);
// Double_t info[3]={0,0,0};
Int_t nPar= fFormula->GetNpar();
Int_t fcnP=-1;
TObjString rName("bootstrap");
if (reportName!= nullptr) rName=reportName;
std::vector< std::vector<double> > vecPar(static_cast<unsigned long>(nPar), std::vector<double>(nIter));
for (Int_t iter=0; iter<nIter; iter++){
for (Int_t iPoint=0; iPoint<nPoints; iPoint++){
fPointIndex[iPoint]= static_cast<Int_t>(gRandom->Rndm() * nPoints);
}
Fit(option);
FitterFCN(nPar, nullptr,fChi2, fParam->GetMatrixArray(),0);
if (fcnP<0) fcnP=fFCNCounter;
Int_t fcnCounter=fFCNCounter-fcnP;
fcnP=fFCNCounter;
for (UInt_t iPar=0; iPar<nPar;iPar++) vecPar[iPar][iter]=(*fParam)(iPar);
if (fStreamer){
(*fStreamer)<<"bootstrap"<<
"iter="<<iter<<
"fStatus="<<fStatus<< // minuit status
"reportName.="<<&rName<<
"nPoints="<<nPoints<<
"fChi2="<<fChi2<<
"fcnCounterI="<<fFCNCounter<<
"fcnCounter="<<fcnCounter<<
"fParam.="<<fParam<<
"fCovar.="<<fCovar<<
"\n";
}
}
if (fRMSEstimator== nullptr) fRMSEstimator=new TVectorD(*fParam);
TVectorD &par=*fParam;
TVectorD &rms=*fRMSEstimator;
for (Int_t iPar=0; iPar<nPar;iPar++) {
Double_t rmsF,meanF;
TStatToolkit::EvaluateUni(static_cast<Int_t>(nIter), vecPar[iPar].data(), meanF, rmsF,
static_cast<Int_t>(TMath::Max(nIter * 0.75, 1.)));
par[iPar]=TMath::Median(static_cast<Long64_t>(nIter), vecPar[iPar].data());
rms[iPar]=rmsF;
}
fPointIndex.Set(0);
}
///\breief 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)
/// \param nIter - number of iterations
/// \param reportName - report name (identifier in the streamer)
/// \param option - fit option
void AliTMinuitToolkit::TwoFoldCrossValidation(UInt_t nIter, const char *reportName, Option_t *option) {
Int_t nPoints = fPoints->GetNrows();
TArrayI indexFold(nPoints);
TArrayD rndmCV(nPoints);
fPointIndex.Set(nPoints);
Double_t chi2_00, chi2_01, /*chi2_10,*/ chi2_11;
//Double_t info[3] = {0, 0, 0};
Int_t nPar = fFormula->GetNpar();
Int_t fcnP = -1;
TObjString rName(reportName);
std::vector<std::vector<double> > vecPar(static_cast<unsigned long>(2 * nPar + 4), std::vector<double>(nIter)); //store vectors and chi2
for (Int_t iter = 0; iter < nIter; iter++) {
for (Int_t iPoint = 0; iPoint < nPoints; iPoint++) {
rndmCV[iPoint] = gRandom->Rndm() * nPoints;
}
TMath::Sort(nPoints, rndmCV.GetArray(), indexFold.GetArray());
//
fPointIndex.Set(nPoints / 2, indexFold.GetArray());
Fit(option);
for (Int_t iPar = 0; iPar < nPar; iPar++) vecPar[iPar][iter] = (*fParam)(iPar);
TVectorD param0(*fParam);
TMatrixD covar0(*fCovar);
FitterFCN(nPar, nullptr, chi2_00, fParam->GetMatrixArray(), 0);
//
fPointIndex.Set(nPoints - nPoints / 2, &(indexFold.GetArray()[nPoints / 2]));
FitterFCN(nPar, nullptr, chi2_01, fParam->GetMatrixArray(), 0);
Fit(option);
for (Int_t iPar = 0; iPar < nPar; iPar++) vecPar[nPar + iPar][iter] = (*fParam)(iPar);
FitterFCN(nPar, nullptr, chi2_11, fParam->GetMatrixArray(), 0);
vecPar[2 * nPar][iter] = chi2_00 + chi2_01 + chi2_11;
TVectorD param1(*fParam);
TMatrixD covar1(*fCovar);
// param distance
TMatrixD covar(covar0);
covar += covar1;
covar.Invert();
TMatrixD delta(nPar, 1, (param1 - param0).GetMatrixArray());
TMatrixD delta2(covar, TMatrixD::kMult, delta);
delta.T();
TMatrixD chi2(delta, TMatrixD::kMult, delta2);
chi2 *= vecPar[2 * nPar][iter];
vecPar[2 * nPar + 1][iter] = chi2(0, 0);
Double_t logLike = chi2_00 + chi2_01 + chi2_11;
Double_t normDistance = TMath::Sqrt(chi2(0, 0));
//
if (fcnP < 0) fcnP = fFCNCounter;
Int_t fcnCounter = fFCNCounter - fcnP;
fcnP = fFCNCounter;
if (fStreamer) {
(*fStreamer) << "crossValidation" <<
"reportName.=" << &rName <<
"iter=" << iter << // iteration
"fStatus=" << fStatus << // minuit status
"nPoints=" << nPoints << // number of points
"chi2_00=" << chi2_00 << // log likelihood for training sample
"chi2_01=" << chi2_01 << // log likelihood for test sample using training fit
"chi2_11=" << chi2_11 << // log likelihood for test sample using test fit
"fcnCounterI=" << fFCNCounter << // fcn counter integral
"fcnCounter=" << fcnCounter << // fcn counter per fit
"param0.=" << ¶m0 << // parameters estimate training sample
"covar0.=" << &covar0 << // covariance for training sample
"param1.=" << ¶m1 << // parameters for complementary subsample
"covar1.=" << &covar1 << // covariance for complementary subsample
"logLike=" << logLike << "normDistance=" << normDistance << // parameters normalized distance
"\n";
}
}
fPointIndex.Set(0);
}
/// \brief 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
/// \param nFitPoints - number of points used in one fit
/// \param nIter - number of iterations
/// \param reportName - report name (!=NULL- specified stream to save intermediate data)
/// \param 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
void AliTMinuitToolkit::MISAC(Int_t nFitPoints, UInt_t nIter, const char * reportName, Option_t *option){
TObjString rName(reportName);
const Double_t kRelMedDistanceCut=2; // outlier rejection cut - should be parameter
Int_t nPoints= fPoints->GetNrows(); //
Int_t nPar=fFormula->GetNpar(); //
Int_t nSamples=nFitPoints*nIter; // number of fit samples
Int_t nRepeat=(1+(nSamples/nPoints)); //
Int_t *permutationIndex= new Int_t[nRepeat*nPoints]; // generate random permutations
Double_t *xrndm=new Double_t[nPoints];
std::vector<TMatrixD*> paramArray(nIter); // fit parameters
std::vector<TMatrixD*> covarArray(nIter); // fit covariance
std::vector<double> logLike(nIter); // fit to points
std::vector<double> medDistance(nIter); // fit to other fits
std::vector<int> fitStatus(nIter); // fit status
if (nullptr == fRMSEstimator){
fRMSEstimator=new TVectorD(nPar);
}
// 0. Generate permutations of data
for (Int_t iR=0; iR<nRepeat; iR++){ // make nRepeat random permutations of points
for (Int_t iPoint=0; iPoint<nPoints; iPoint++){
xrndm[iPoint]=gRandom->Rndm();
}
TMath::Sort(nPoints, xrndm, &(permutationIndex[iR*nPoints]));
}
// 1.) Calculate fit parameters for small subset of data
for (UInt_t iter=0; iter<nIter; iter++){
fPointIndex.Set(nFitPoints, &(permutationIndex[iter*nFitPoints]));
Fit(option);
fitStatus[iter]=fStatus;
FitterFCN(nPar, nullptr,fChi2, fParam->GetMatrixArray(),0);
logLike[iter]=fChi2;
paramArray[iter] = new TMatrixD(nPar,1,fParam->GetMatrixArray());
covarArray[iter] = new TMatrixD(*fCovar);
}
// 2. Calculate normalized distance between each fits
std::vector< std::vector<double> > logDistance(nIter, std::vector<double>(nIter)); //store vectors and chi2
for (Int_t iter0=0; iter0<nIter; iter0++){
for (Int_t iter1=0; iter1<nIter; iter1++){
if ( ((fitStatus[iter0]&kCovarFailed)==0 && (fitStatus[iter1]&kCovarFailed))==0){
TMatrixD covar(*(covarArray[iter0]));
covar+=*(covarArray[iter1]);
covar.Invert();
TMatrixD delta(*(paramArray[iter0]));
delta-=*(paramArray[iter1]);
TMatrixD delta2(covar,TMatrixD::kMult,delta);
delta.T();
TMatrixD chi2(delta,TMatrixD::kMult,delta2);
chi2*=logLike[iter0]+logLike[iter1];
if (chi2(0,0)>0) {
Double_t normDistance = TMath::Sqrt(chi2(0, 0));
logDistance[iter0][iter1] = normDistance;
}else{
logDistance[iter0][iter1]=-1.; ///TODO- check failure of the fit
};
}else{
logDistance[iter0][iter1]=-1.;
}
}
}
// 3. Reject outliers and calculate robust mean
for (Int_t iter=0; iter<nIter; iter++){
medDistance[iter]=TMath::Median(nIter, logDistance[iter].data());
}
Double_t medMedDistance=TMath::Median(nIter,medDistance.data());
// 4. Extract combined statistic
// 4.a 1D median,mean,rms
// 4.b nD ?
if (fMISACEstimators== nullptr) fMISACEstimators = new TMatrixD(4,nPar);
for (Int_t iPar=0;iPar<nPar; iPar++){
std::vector<double>workingArray(nIter);
Int_t nAccepted=0;
for (Int_t iter=0; iter<nIter; iter++){
if (medDistance[iter]<0) continue;
if (medDistance[iter]/medMedDistance>kRelMedDistanceCut) continue;
workingArray[nAccepted]=(*(paramArray[iter]))(iPar,0);
nAccepted++;
}
if (nAccepted>0){
(*fMISACEstimators)(0,iPar)=TMath::Median(nAccepted,workingArray.data());
(*fMISACEstimators)(1,iPar)=TMath::Mean(nAccepted,workingArray.data());
(*fMISACEstimators)(2,iPar)=TMath::RMS(nAccepted,workingArray.data());
}
(*fParam)(iPar)=(*fMISACEstimators)(0,iPar);
(*fRMSEstimator)(iPar)=(*fMISACEstimators)(2,iPar);
}
// 5. Dump results into tree in verbose mode
if (fStreamer){
for (Int_t iter=0; iter<nIter; iter++){
(*fStreamer)<<"misac"<<
"iter="<<iter<< // iteration
"reportName.="<<&rName<<
"fStatus="<<fStatus<< // minuit status
"nPoints="<<nPoints<< // number of points
"param.="<<paramArray[iter]<<
"covar.="<<covarArray[iter]<<
"medDistance="<<medDistance[iter]<<
"medMedDistance="<<medMedDistance<<
"misacE.="<<fMISACEstimators<< // estimator matrix (estimator(median,mean,rms),param)
"\n";
}
}
fPointIndex.Set(0);
delete [] xrndm;
delete [] permutationIndex;
}
/// \brief Register default fitters
/// * Registered function can be used in standard minimization using sting identifier, e.g:
/// * \code AliTMinuitToolkit::Fit(TH1* his, const char *fitterName, Option_t* option, Option_t* goption,Option_t* foption, Double_t xMin, Double_t xMax) \endcode
/// * \code AliTMinuitToolkit::Fit(TH1* his, const char *fitterName, Option_t* option, Option_t* goption,Option_t* foption, Double_t xMin, Double_t xMax) \endcode
/// * Registered fitter can be accessed - eventually modified (e.g to set initial values)
/// * \code 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"); \endcode
/// \param nPlanes - number of planes
/// \param logLikeType - type of the log likelihood
/// * 0) chi2, 1.) gaus+cauchy, 2.) pseudo-huber
/// \return return registered fitter
AliTMinuitToolkit * AliTMinuitToolkit::RegisterPlaneFitter(Int_t nPlanes, Int_t logLikeType){
AliTMinuitToolkit *fitter = new AliTMinuitToolkit(TString::Format("AliTMinuitToolkitTest%d.root", nPlanes));
TString sFormula = "[0]*x[0]";
for (Int_t iPlane=1; iPlane<nPlanes; iPlane++) sFormula+=TString::Format("+[%d]*x[%d]", iPlane,iPlane);
TFormula *formula = new TFormula(TString::Format("hyp%dR",nPlanes).Data(), sFormula.Data());
fitter->SetFitFunction((TF1 *) formula, kTRUE);
//
if (logLikeType==0) { // standard minimization
TF1 *likeGaus = new TF1("likeGausCachy", "x*x*0.5", -10, 10);
fitter->SetLogLikelihoodFunction(likeGaus);
fitter->SetName(TString::Format("hyp%d", nPlanes).Data());
}
if (logLikeType==1){
TF1 *likeGausCachy = new TF1("likeGausCachy", AliTMinuitToolkit::GaussCachyLogLike, -10, 10, 2);
likeGausCachy->SetParameters(0.8, 1);
fitter->SetLogLikelihoodFunction(likeGausCachy);
fitter->SetName(TString::Format("hyp%dR", nPlanes).Data());
}
if (logLikeType==2){
TF1 *likePseudoHuber = new TF1("likePseudoHuber", AliTMinuitToolkit::PseudoHuberLogLike, -10, 10, 1);
likePseudoHuber->SetParameter(0,3);
fitter->SetLogLikelihoodFunction(likePseudoHuber);
fitter->SetName(TString::Format("hyp%dH", nPlanes).Data());
}
fitter->SetInitialParam(new TMatrixD(nPlanes,4));
AliTMinuitToolkit::SetPredefinedFitter(fitter->GetName(), fitter);
return fitter;
}
/// \brief Make histogram fit
/// * TODO- add example code snippet - using the code from test directory
/// \param his - pointer to histogram
/// \param fitterName - fitter name ()
/// \param fitOption - fit Option
/// \param hisOption - graphic option for histogram
/// \param funOption - graphic option for function drawing
/// \param xMin - fit range min
/// \param xMax - fit range max
/// \return - pointer to the fitter
AliTMinuitToolkit * AliTMinuitToolkit::Fit(TH1* his, const char *fitterName, Option_t* fitOption, Option_t* hisOption,Option_t* funOption, Double_t xMin, Double_t xMax){
AliTMinuitToolkit *fitter=GetPredefinedFitter(fitterName);
if (fitter== nullptr){
::Error("AliTMinuitToolkit::Fit","Non supported fitter %s. \nfitter can be added to the list using. SetPredefinedFitter", fitterName);
return nullptr;
}
if (his== nullptr){
::Error("AliTMinuitToolkit::Fit","NULL pointer");
return nullptr;
}
fitter->FitHistogram(his,fitOption);
TF1 * fitFun = (TF1*)(fitter->GetFormula()->Clone());
fitFun->SetParameters(fitter->GetParameters()->GetMatrixArray());
SetFunctionDrawOption(fitFun,funOption);
his->GetListOfFunctions()->AddLast(fitFun);
if (xMin<xMax) {
fitFun->SetRange(xMin,xMax);
}else{
fitFun->SetRange(his->GetXaxis()->GetXmin(), his->GetXaxis()->GetXmax());
}
if (hisOption) his->Draw(hisOption);
return fitter;
}
/// \brief Make graph fit
/// * TODO- add example code snippet - using the code from test directory
/// \param graph - pointer to graph
/// \param fitterName - fitter name ()
/// \param fitOption - fitter setting option
/// \param graphOption - graphic option
/// \param funOption - graphic option for function
/// \param xMin - fit range min
/// \param xMax - fit range max
/// \return - pointer to the fitter
AliTMinuitToolkit * AliTMinuitToolkit::Fit(TGraph *graph, const char *fitterName, Option_t* fitOption, Option_t* graphOption, Option_t* funOption, Double_t xMin, Double_t xMax){
//
//
AliTMinuitToolkit *fitter=GetPredefinedFitter(fitterName);
if (fitter== nullptr){
::Error("AliTMinuitToolkit::Fit","Non supported fitter %s. \nfitter can be added to the list using. SetPredefinedFitter", fitterName);
return nullptr;
}
if (graph== nullptr){
::Error("AliTMinuitToolkit::Fit","NULL pointer");
return nullptr;
}
fitter->FitGraph(graph,fitOption);
TF1 * fitFun = (TF1*)(fitter->GetFormula()->Clone());
fitFun->SetParameters(fitter->GetParameters()->GetMatrixArray());
fitFun->SetName(TString::Format("%s:%s",fitter->GetName(), fitOption).Data());
fitFun->SetTitle(TString::Format("%s:%s",fitter->GetName(), fitOption).Data());
SetFunctionDrawOption(fitFun,funOption);
graph->GetListOfFunctions()->AddLast(fitFun);
if (xMin<xMax) {