X-Git-Url: http://git.uio.no/git/?a=blobdiff_plain;f=STEER%2FAliMathBase.cxx;h=89d9a87c40a4a93f4eff770a3bd99e9b350c7790;hb=86ee89e6a8f3b6a0cd5b84a8615847f971bcde12;hp=7d02171e8d2816fff2973fc8a35be7b9efe5d230;hpb=284050f74c33ba291c793e202ee72cdfa446b08e;p=u%2Fmrichter%2FAliRoot.git

diff --git a/STEER/AliMathBase.cxx b/STEER/AliMathBase.cxx
index 7d02171e8d2..89d9a87c40a 100644
--- a/STEER/AliMathBase.cxx
+++ b/STEER/AliMathBase.cxx
@@ -24,17 +24,33 @@
 #include "TMath.h"
 #include "AliMathBase.h"
 #include "Riostream.h"
+#include "TH1F.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
+  //
 }
 
 
@@ -59,13 +75,15 @@ void AliMathBase::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean
   TMath::Sort(nvectors, data, index, kFALSE);
   
   Int_t    nquant = TMath::Min(Int_t(Double_t(((hh*1./nvectors)-0.5)*40))+1, 11);
-  Double_t factor = faclts[nquant-1];
+  Double_t factor = faclts[TMath::Max(0,nquant-1)];
   
   Double_t sumx  =0;
   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]];
@@ -194,3 +212,433 @@ Int_t AliMathBase::Freq(Int_t n, const Int_t *inlist
   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)
+  //     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++;
+  }
+
+  if (max<4) return -4;
+  if (entries<12) return -4;
+  if (rms<kTol) return -4;
+
+  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(3);
+      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;
+
+}
+
+
+
+