X-Git-Url: http://git.uio.no/git/?a=blobdiff_plain;f=STEER%2FAliMathBase.cxx;h=cdae2369d06d0477342b06bbae8e26c2f9a8c7d2;hb=b5db117133fb58fc8399a368a6333ff795d99d8a;hp=1c8c5ec30f341f3f760a11a6745153e7c2a10811;hpb=f6659a9d8b9d1566f930bcdb14fb130a0a9039e8;p=u%2Fmrichter%2FAliRoot.git

diff --git a/STEER/AliMathBase.cxx b/STEER/AliMathBase.cxx
index 1c8c5ec30f3..cdae2369d06 100644
--- a/STEER/AliMathBase.cxx
+++ b/STEER/AliMathBase.cxx
@@ -25,19 +25,35 @@
 #include "AliMathBase.h"
 #include "Riostream.h"
 #include "TH1F.h"
+#include "TH3.h"
 #include "TF1.h"
 #include "TLinearFitter.h"
+
+#include "AliExternalTrackParam.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
+  //
 }
 
 
@@ -68,7 +84,9 @@ void AliMathBase::EvaluateUni(Int_t nvectors, Double_t *data, Double_t &mean
   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]];
@@ -280,7 +298,7 @@ Double_t  AliMathBase::FitGaus(TH1F* his, TVectorD *param, TMatrixD *matrix, Flo
   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((2.*TMath::Pi()*his->GetRMS()));  
+  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;
@@ -296,7 +314,7 @@ Double_t  AliMathBase::FitGaus(TH1F* his, TVectorD *param, TMatrixD *matrix, Flo
   for (Int_t iter=0; iter<2; iter++){
     fitter.ClearPoints();
     npoints=0;
-    for (Int_t ibin=1;ibin<nbins-1; ibin++){      
+    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++){
@@ -355,4 +373,415 @@ Double_t  AliMathBase::FitGaus(TH1F* his, TVectorD *param, TMatrixD *matrix, Flo
   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;
+}
+
 
+Double_t AliMathBase::ErfcFast(Double_t x){
+  // Fast implementation of the complementary error function
+  // The error of the approximation is |eps(x)| < 5E-4
+  // See Abramowitz and Stegun, p.299, 7.1.27
+
+  Double_t z = TMath::Abs(x);
+  Double_t ans = 1+z*(0.278393+z*(0.230389+z*(0.000972+z*0.078108)));
+  ans = 1.0/ans;
+  ans *= ans;
+  ans *= ans;
+
+  return (x>=0.0 ? ans : 2.0 - ans);
+}
+
+///////////////////////////////////////////////////////////////
+//////////////         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;
+}
+
+Double_t AliMathBase::BetheBlochAleph(Double_t bg,
+         Double_t kp1,
+         Double_t kp2,
+         Double_t kp3,
+         Double_t kp4,
+         Double_t kp5) {
+  //
+  // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
+  // It is normalized to 1 at the minimum.
+  //
+  // bg - beta*gamma
+  // 
+  // The default values for the kp* parameters are for ALICE TPC.
+  // The returned value is in MIP units
+  //
+
+  return AliExternalTrackParam::BetheBlochAleph(bg,kp1,kp2,kp3,kp4,kp5);
+}