#include "TMath.h"
#include "AliMathBase.h"
#include "Riostream.h"
+#include "TH1F.h"
+#include "TH3.h"
+#include "TF1.h"
+#include "TLinearFitter.h"
+
+//
+// includes neccessary for test functions
+//
+
+#include "TSystem.h"
+#include "TRandom.h"
+#include "TStopwatch.h"
+#include "TTreeStream.h"
ClassImp(AliMathBase) // Class implementation to enable ROOT I/O
AliMathBase::AliMathBase() : TObject()
{
-// Default constructor
+ //
+ // Default constructor
+ //
}
///////////////////////////////////////////////////////////////////////////
AliMathBase::~AliMathBase()
{
-// Destructor
+ //
+ // Destructor
+ //
}
Double_t sumx2 =0;
Int_t bestindex = -1;
Double_t bestmean = 0;
- Double_t bestsigma = data[index[nvectors-1]]-data[index[0]]; // maximal possible sigma
+ Double_t bestsigma = (data[index[nvectors-1]]-data[index[0]]+1.); // maximal possible sigma
+ bestsigma *=bestsigma;
+
for (Int_t i=0; i<hh; i++){
sumx += data[index[i]];
sumx2 += data[index[i]]*data[index[i]];
return countPos;
}
+
+//___AliMathBase__________________________________________________________________________
+void AliMathBase::TruncatedMean(TH1F * his, TVectorD *param, Float_t down, Float_t up, Bool_t verbose){
+ //
+ //
+ //
+ Int_t nbins = his->GetNbinsX();
+ Float_t nentries = his->GetEntries();
+ Float_t sum =0;
+ Float_t mean = 0;
+ Float_t sigma2 = 0;
+ Float_t ncumul=0;
+ for (Int_t ibin=1;ibin<nbins; ibin++){
+ ncumul+= his->GetBinContent(ibin);
+ Float_t fraction = Float_t(ncumul)/Float_t(nentries);
+ if (fraction>down && fraction<up){
+ sum+=his->GetBinContent(ibin);
+ mean+=his->GetBinCenter(ibin)*his->GetBinContent(ibin);
+ sigma2+=his->GetBinCenter(ibin)*his->GetBinCenter(ibin)*his->GetBinContent(ibin);
+ }
+ }
+ mean/=sum;
+ sigma2= TMath::Sqrt(TMath::Abs(sigma2/sum-mean*mean));
+ if (param){
+ (*param)[0] = his->GetMaximum();
+ (*param)[1] = mean;
+ (*param)[2] = sigma2;
+
+ }
+ if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma2);
+}
+
+void AliMathBase::LTM(TH1F * his, TVectorD *param , Float_t fraction, Bool_t verbose){
+ //
+ // LTM
+ //
+ Int_t nbins = his->GetNbinsX();
+ Int_t nentries = (Int_t)his->GetEntries();
+ Double_t *data = new Double_t[nentries];
+ Int_t npoints=0;
+ for (Int_t ibin=1;ibin<nbins; ibin++){
+ Float_t entriesI = his->GetBinContent(ibin);
+ Float_t xcenter= his->GetBinCenter(ibin);
+ for (Int_t ic=0; ic<entriesI; ic++){
+ if (npoints<nentries){
+ data[npoints]= xcenter;
+ npoints++;
+ }
+ }
+ }
+ Double_t mean, sigma;
+ Int_t npoints2=TMath::Min(Int_t(fraction*Float_t(npoints)),npoints-1);
+ npoints2=TMath::Max(Int_t(0.5*Float_t(npoints)),npoints2);
+ AliMathBase::EvaluateUni(npoints, data, mean,sigma,npoints2);
+ delete [] data;
+ if (verbose) printf("Mean\t%f\t Sigma2\t%f\n", mean,sigma);if (param){
+ (*param)[0] = his->GetMaximum();
+ (*param)[1] = mean;
+ (*param)[2] = sigma;
+ }
+}
+
+Double_t AliMathBase::FitGaus(TH1F* his, TVectorD *param, TMatrixD *matrix, Float_t xmin, Float_t xmax, Bool_t verbose){
+ //
+ // Fit histogram with gaussian function
+ //
+ // Prameters:
+ // return value- chi2 - if negative ( not enough points)
+ // his - input histogram
+ // param - vector with parameters
+ // xmin, xmax - range to fit - if xmin=xmax=0 - the full histogram range used
+ // Fitting:
+ // 1. Step - make logarithm
+ // 2. Linear fit (parabola) - more robust - always converge
+ // 3. In case of small statistic bins are averaged
+ //
+ static TLinearFitter fitter(3,"pol2");
+ TVectorD par(3);
+ TVectorD sigma(3);
+ TMatrixD mat(3,3);
+ if (his->GetMaximum()<4) return -1;
+ if (his->GetEntries()<12) return -1;
+ if (his->GetRMS()<mat.GetTol()) return -1;
+ Float_t maxEstimate = his->GetEntries()*his->GetBinWidth(1)/TMath::Sqrt((TMath::TwoPi()*his->GetRMS()));
+ Int_t dsmooth = TMath::Nint(6./TMath::Sqrt(maxEstimate));
+
+ if (maxEstimate<1) return -1;
+ Int_t nbins = his->GetNbinsX();
+ Int_t npoints=0;
+ //
+
+
+ if (xmin>=xmax){
+ xmin = his->GetXaxis()->GetXmin();
+ xmax = his->GetXaxis()->GetXmax();
+ }
+ for (Int_t iter=0; iter<2; iter++){
+ fitter.ClearPoints();
+ npoints=0;
+ for (Int_t ibin=1;ibin<nbins+1; ibin++){
+ Int_t countB=1;
+ Float_t entriesI = his->GetBinContent(ibin);
+ for (Int_t delta = -dsmooth; delta<=dsmooth; delta++){
+ if (ibin+delta>1 &&ibin+delta<nbins-1){
+ entriesI += his->GetBinContent(ibin+delta);
+ countB++;
+ }
+ }
+ entriesI/=countB;
+ Double_t xcenter= his->GetBinCenter(ibin);
+ if (xcenter<xmin || xcenter>xmax) continue;
+ Double_t error=1./TMath::Sqrt(countB);
+ Float_t cont=2;
+ if (iter>0){
+ if (par[0]+par[1]*xcenter+par[2]*xcenter*xcenter>20) return 0;
+ cont = TMath::Exp(par[0]+par[1]*xcenter+par[2]*xcenter*xcenter);
+ if (cont>1.) error = 1./TMath::Sqrt(cont*Float_t(countB));
+ }
+ if (entriesI>1&&cont>1){
+ fitter.AddPoint(&xcenter,TMath::Log(Float_t(entriesI)),error);
+ npoints++;
+ }
+ }
+ if (npoints>3){
+ fitter.Eval();
+ fitter.GetParameters(par);
+ }else{
+ break;
+ }
+ }
+ if (npoints<=3){
+ return -1;
+ }
+ fitter.GetParameters(par);
+ fitter.GetCovarianceMatrix(mat);
+ if (TMath::Abs(par[1])<mat.GetTol()) return -1;
+ if (TMath::Abs(par[2])<mat.GetTol()) return -1;
+ Double_t chi2 = fitter.GetChisquare()/Float_t(npoints);
+ //fitter.GetParameters();
+ if (!param) param = new TVectorD(3);
+ if (!matrix) matrix = new TMatrixD(3,3);
+ (*param)[1] = par[1]/(-2.*par[2]);
+ (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
+ (*param)[0] = TMath::Exp(par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1]);
+ if (verbose){
+ par.Print();
+ mat.Print();
+ param->Print();
+ printf("Chi2=%f\n",chi2);
+ TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",his->GetXaxis()->GetXmin(),his->GetXaxis()->GetXmax());
+ f1->SetParameter(0, (*param)[0]);
+ f1->SetParameter(1, (*param)[1]);
+ f1->SetParameter(2, (*param)[2]);
+ f1->Draw("same");
+ }
+ return chi2;
+}
+
+Double_t AliMathBase::FitGaus(Float_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, TVectorD *param, TMatrixD *matrix, Bool_t verbose){
+ //
+ // Fit histogram with gaussian function
+ //
+ // Prameters:
+ // nbins: size of the array and number of histogram bins
+ // xMin, xMax: histogram range
+ // param: paramters of the fit (0-Constant, 1-Mean, 2-Sigma, 3-Sum)
+ // matrix: covariance matrix -- not implemented yet, pass dummy matrix!!!
+ //
+ // Return values:
+ // >0: the chi2 returned by TLinearFitter
+ // -3: only three points have been used for the calculation - no fitter was used
+ // -2: only two points have been used for the calculation - center of gravity was uesed for calculation
+ // -1: only one point has been used for the calculation - center of gravity was uesed for calculation
+ // -4: invalid result!!
+ //
+ // Fitting:
+ // 1. Step - make logarithm
+ // 2. Linear fit (parabola) - more robust - always converge
+ //
+ static TLinearFitter fitter(3,"pol2");
+ static TMatrixD mat(3,3);
+ static Double_t kTol = mat.GetTol();
+ fitter.StoreData(kFALSE);
+ fitter.ClearPoints();
+ TVectorD par(3);
+ TVectorD sigma(3);
+ TMatrixD A(3,3);
+ TMatrixD b(3,1);
+ Float_t rms = TMath::RMS(nBins,arr);
+ Float_t max = TMath::MaxElement(nBins,arr);
+ Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
+
+ Float_t meanCOG = 0;
+ Float_t rms2COG = 0;
+ Float_t sumCOG = 0;
+
+ Float_t entries = 0;
+ Int_t nfilled=0;
+
+ for (Int_t i=0; i<nBins; i++){
+ entries+=arr[i];
+ if (arr[i]>0) nfilled++;
+ }
+ (*param)[0] = 0;
+ (*param)[1] = 0;
+ (*param)[2] = 0;
+ (*param)[3] = 0;
+
+ if (max<4) return -4;
+ if (entries<12) return -4;
+ if (rms<kTol) return -4;
+
+ (*param)[3] = entries;
+
+ Int_t npoints=0;
+ for (Int_t ibin=0;ibin<nBins; ibin++){
+ Float_t entriesI = arr[ibin];
+ if (entriesI>1){
+ Double_t xcenter = xMin+(ibin+0.5)*binWidth;
+ Float_t error = 1./TMath::Sqrt(entriesI);
+ Float_t val = TMath::Log(Float_t(entriesI));
+ fitter.AddPoint(&xcenter,val,error);
+ if (npoints<3){
+ A(npoints,0)=1;
+ A(npoints,1)=xcenter;
+ A(npoints,2)=xcenter*xcenter;
+ b(npoints,0)=val;
+ meanCOG+=xcenter*entriesI;
+ rms2COG +=xcenter*entriesI*xcenter;
+ sumCOG +=entriesI;
+ }
+ npoints++;
+ }
+ }
+
+ Double_t chi2 = 0;
+ if (npoints>=3){
+ if ( npoints == 3 ){
+ //analytic calculation of the parameters for three points
+ A.Invert();
+ TMatrixD res(1,3);
+ res.Mult(A,b);
+ par[0]=res(0,0);
+ par[1]=res(0,1);
+ par[2]=res(0,2);
+ chi2 = -3.;
+ } else {
+ // use fitter for more than three points
+ fitter.Eval();
+ fitter.GetParameters(par);
+ fitter.GetCovarianceMatrix(mat);
+ chi2 = fitter.GetChisquare()/Float_t(npoints);
+ }
+ if (TMath::Abs(par[1])<kTol) return -4;
+ if (TMath::Abs(par[2])<kTol) return -4;
+
+ if (!param) param = new TVectorD(4);
+ if ( param->GetNrows()<4 ) param->ResizeTo(4);
+ if (!matrix) matrix = new TMatrixD(3,3); // !!!!might be a memory leek. use dummy matrix pointer to call this function!
+
+ (*param)[1] = par[1]/(-2.*par[2]);
+ (*param)[2] = 1./TMath::Sqrt(TMath::Abs(-2.*par[2]));
+ Double_t lnparam0 = par[0]+ par[1]* (*param)[1] + par[2]*(*param)[1]*(*param)[1];
+ if ( lnparam0>307 ) return -4;
+ (*param)[0] = TMath::Exp(lnparam0);
+ if (verbose){
+ par.Print();
+ mat.Print();
+ param->Print();
+ printf("Chi2=%f\n",chi2);
+ TF1 * f1= new TF1("f1","[0]*exp(-(x-[1])^2/(2*[2]*[2]))",xMin,xMax);
+ f1->SetParameter(0, (*param)[0]);
+ f1->SetParameter(1, (*param)[1]);
+ f1->SetParameter(2, (*param)[2]);
+ f1->Draw("same");
+ }
+ return chi2;
+ }
+
+ if (npoints == 2){
+ //use center of gravity for 2 points
+ meanCOG/=sumCOG;
+ rms2COG /=sumCOG;
+ (*param)[0] = max;
+ (*param)[1] = meanCOG;
+ (*param)[2] = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
+ chi2=-2.;
+ }
+ if ( npoints == 1 ){
+ meanCOG/=sumCOG;
+ (*param)[0] = max;
+ (*param)[1] = meanCOG;
+ (*param)[2] = binWidth/TMath::Sqrt(12);
+ chi2=-1.;
+ }
+ return chi2;
+
+}
+
+
+Float_t AliMathBase::GetCOG(Short_t *arr, Int_t nBins, Float_t xMin, Float_t xMax, Float_t *rms, Float_t *sum)
+{
+ //
+ // calculate center of gravity rms and sum for array 'arr' with nBins an a x range xMin to xMax
+ // return COG; in case of failure return xMin
+ //
+ Float_t meanCOG = 0;
+ Float_t rms2COG = 0;
+ Float_t sumCOG = 0;
+ Int_t npoints = 0;
+
+ Float_t binWidth = (xMax-xMin)/(Float_t)nBins;
+
+ for (Int_t ibin=0; ibin<nBins; ibin++){
+ Float_t entriesI = (Float_t)arr[ibin];
+ Double_t xcenter = xMin+(ibin+0.5)*binWidth;
+ if ( entriesI>0 ){
+ meanCOG += xcenter*entriesI;
+ rms2COG += xcenter*entriesI*xcenter;
+ sumCOG += entriesI;
+ npoints++;
+ }
+ }
+ if ( sumCOG == 0 ) return xMin;
+ meanCOG/=sumCOG;
+
+ if ( rms ){
+ rms2COG /=sumCOG;
+ (*rms) = TMath::Sqrt(TMath::Abs(meanCOG*meanCOG-rms2COG));
+ if ( npoints == 1 ) (*rms) = binWidth/TMath::Sqrt(12);
+ }
+
+ if ( sum )
+ (*sum) = sumCOG;
+
+ return meanCOG;
+}
+
+
+
+///////////////////////////////////////////////////////////////
+////////////// TEST functions /////////////////////////
+///////////////////////////////////////////////////////////////
+
+
+
+
+
+void AliMathBase::TestGausFit(Int_t nhistos){
+ //
+ // Test performance of the parabolic - gaussian fit - compare it with
+ // ROOT gauss fit
+ // nhistos - number of histograms to be used for test
+ //
+ TTreeSRedirector *pcstream = new TTreeSRedirector("fitdebug.root");
+
+ Float_t *xTrue = new Float_t[nhistos];
+ Float_t *sTrue = new Float_t[nhistos];
+ TVectorD **par1 = new TVectorD*[nhistos];
+ TVectorD **par2 = new TVectorD*[nhistos];
+ TMatrixD dummy(3,3);
+
+
+ TH1F **h1f = new TH1F*[nhistos];
+ TF1 *myg = new TF1("myg","gaus");
+ TF1 *fit = new TF1("fit","gaus");
+ gRandom->SetSeed(0);
+
+ //init
+ for (Int_t i=0;i<nhistos; i++){
+ par1[i] = new TVectorD(3);
+ par2[i] = new TVectorD(3);
+ h1f[i] = new TH1F(Form("h1f%d",i),Form("h1f%d",i),20,-10,10);
+ xTrue[i]= gRandom->Rndm();
+ gSystem->Sleep(2);
+ sTrue[i]= .75+gRandom->Rndm()*.5;
+ myg->SetParameters(1,xTrue[i],sTrue[i]);
+ h1f[i]->FillRandom("myg");
+ }
+
+ TStopwatch s;
+ s.Start();
+ //standard gaus fit
+ for (Int_t i=0; i<nhistos; i++){
+ h1f[i]->Fit(fit,"0q");
+ (*par1[i])(0) = fit->GetParameter(0);
+ (*par1[i])(1) = fit->GetParameter(1);
+ (*par1[i])(2) = fit->GetParameter(2);
+ }
+ s.Stop();
+ printf("Gaussian fit\t");
+ s.Print();
+
+ s.Start();
+ //AliMathBase gaus fit
+ for (Int_t i=0; i<nhistos; i++){
+ AliMathBase::FitGaus(h1f[i]->GetArray()+1,h1f[i]->GetNbinsX(),h1f[i]->GetXaxis()->GetXmin(),h1f[i]->GetXaxis()->GetXmax(),par2[i],&dummy);
+ }
+
+ s.Stop();
+ printf("Parabolic fit\t");
+ s.Print();
+ //write stream
+ for (Int_t i=0;i<nhistos; i++){
+ Float_t xt = xTrue[i];
+ Float_t st = sTrue[i];
+ (*pcstream)<<"data"
+ <<"xTrue="<<xt
+ <<"sTrue="<<st
+ <<"pg.="<<(par1[i])
+ <<"pa.="<<(par2[i])
+ <<"\n";
+ }
+ //delete pointers
+ for (Int_t i=0;i<nhistos; i++){
+ delete par1[i];
+ delete par2[i];
+ delete h1f[i];
+ }
+ delete pcstream;
+ delete []h1f;
+ delete []xTrue;
+ delete []sTrue;
+ //
+ delete []par1;
+ delete []par2;
+
+}
+
+
+
+TGraph2D * AliMathBase::MakeStat2D(TH3 * his, Int_t delta0, Int_t delta1, Int_t type){
+ //
+ //
+ //
+ // delta - number of bins to integrate
+ // type - 0 - mean value
+
+ TAxis * xaxis = his->GetXaxis();
+ TAxis * yaxis = his->GetYaxis();
+ // TAxis * zaxis = his->GetZaxis();
+ Int_t nbinx = xaxis->GetNbins();
+ Int_t nbiny = yaxis->GetNbins();
+ char name[1000];
+ Int_t icount=0;
+ TGraph2D *graph = new TGraph2D(nbinx*nbiny);
+ TF1 f1("f1","gaus");
+ for (Int_t ix=0; ix<nbinx;ix++)
+ for (Int_t iy=0; iy<nbiny;iy++){
+ Float_t xcenter = xaxis->GetBinCenter(ix);
+ Float_t ycenter = yaxis->GetBinCenter(iy);
+ sprintf(name,"%s_%d_%d",his->GetName(), ix,iy);
+ TH1 *projection = his->ProjectionZ(name,ix-delta0,ix+delta0,iy-delta1,iy+delta1);
+ Float_t stat= 0;
+ if (type==0) stat = projection->GetMean();
+ if (type==1) stat = projection->GetRMS();
+ if (type==2 || type==3){
+ TVectorD vec(3);
+ AliMathBase::LTM((TH1F*)projection,&vec,0.7);
+ if (type==2) stat= vec[1];
+ if (type==3) stat= vec[0];
+ }
+ if (type==4|| type==5){
+ projection->Fit(&f1);
+ if (type==4) stat= f1.GetParameter(1);
+ if (type==5) stat= f1.GetParameter(2);
+ }
+ //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
+ graph->SetPoint(icount,xcenter, ycenter, stat);
+ icount++;
+ }
+ return graph;
+}
+
+TGraph * AliMathBase::MakeStat1D(TH3 * his, Int_t delta1, Int_t type){
+ //
+ //
+ //
+ // delta - number of bins to integrate
+ // type - 0 - mean value
+
+ TAxis * xaxis = his->GetXaxis();
+ TAxis * yaxis = his->GetYaxis();
+ // TAxis * zaxis = his->GetZaxis();
+ Int_t nbinx = xaxis->GetNbins();
+ Int_t nbiny = yaxis->GetNbins();
+ char name[1000];
+ Int_t icount=0;
+ TGraph *graph = new TGraph(nbinx);
+ TF1 f1("f1","gaus");
+ for (Int_t ix=0; ix<nbinx;ix++){
+ Float_t xcenter = xaxis->GetBinCenter(ix);
+ // Float_t ycenter = yaxis->GetBinCenter(iy);
+ sprintf(name,"%s_%d",his->GetName(), ix);
+ TH1 *projection = his->ProjectionZ(name,ix-delta1,ix+delta1,0,nbiny);
+ Float_t stat= 0;
+ if (type==0) stat = projection->GetMean();
+ if (type==1) stat = projection->GetRMS();
+ if (type==2 || type==3){
+ TVectorD vec(3);
+ AliMathBase::LTM((TH1F*)projection,&vec,0.7);
+ if (type==2) stat= vec[1];
+ if (type==3) stat= vec[0];
+ }
+ if (type==4|| type==5){
+ projection->Fit(&f1);
+ if (type==4) stat= f1.GetParameter(1);
+ if (type==5) stat= f1.GetParameter(2);
+ }
+ //printf("%d\t%f\t%f\t%f\n", icount,xcenter, ycenter, stat);
+ graph->SetPoint(icount,xcenter, stat);
+ icount++;
+ }
+ return graph;
+}
+
+Double_t AliMathBase::TruncatedGaus(Double_t mean, Double_t sigma, Double_t cutat)
+{
+ // return number generated according to a gaussian distribution N(mean,sigma) truncated at cutat
+ //
+ Double_t value;
+ do{
+ value=gRandom->Gaus(mean,sigma);
+ }while(TMath::Abs(value-mean)>cutat);
+ return value;
+}
+
+Double_t AliMathBase::TruncatedGaus(Double_t mean, Double_t sigma, Double_t leftCut, Double_t rightCut)
+{
+ // return number generated according to a gaussian distribution N(mean,sigma)
+ // truncated at leftCut and rightCut
+ //
+ Double_t value;
+ do{
+ value=gRandom->Gaus(mean,sigma);
+ }while((value-mean)<-leftCut || (value-mean)>rightCut);
+ return value;
+}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff