+
+void TStatToolkit::MedianFilter(TH1 * his1D, Int_t nmedian){
+ //
+ // Algorithm to filter histogram
+ // author: marian.ivanov@cern.ch
+ // Details of algorithm:
+ // http://en.wikipedia.org/w/index.php?title=Median_filter&oldid=582191524
+ // Input parameters:
+ // his1D - input histogam - to be modiefied by Medianfilter
+ // nmendian - number of bins in median filter
+ //
+ Int_t nbins = his1D->GetNbinsX();
+ TVectorD vectorH(nbins);
+ for (Int_t ibin=0; ibin<nbins; ibin++) vectorH[ibin]=his1D->GetBinContent(ibin+1);
+ for (Int_t ibin=0; ibin<nbins; ibin++) {
+ Int_t index0=ibin-nmedian;
+ Int_t index1=ibin+nmedian;
+ if (index0<0) {index1+=-index0; index0=0;}
+ if (index1>=nbins) {index0-=index1-nbins+1; index1=nbins-1;}
+ Double_t value= TMath::Median(index1-index0,&(vectorH.GetMatrixArray()[index0]));
+ his1D->SetBinContent(ibin+1, value);
+ }
+}
+
+Bool_t TStatToolkit::LTMHisto(TH1 *his1D, TVectorD ¶ms , Float_t fraction){
+ //
+ // LTM : Trimmed mean on histogram - Modified version for binned data
+ //
+ // Robust statistic to estimate properties of the distribution
+ // To handle binning error special treatment
+ // for definition of unbinned data see:
+ // http://en.wikipedia.org/w/index.php?title=Trimmed_estimator&oldid=582847999
+ //
+ // Function parameters:
+ // his1D - input histogram
+ // params - vector with parameters
+ // - 0 - area
+ // - 1 - mean
+ // - 2 - rms
+ // - 3 - error estimate of mean
+ // - 4 - error estimate of RMS
+ // - 5 - first accepted bin position
+ // - 6 - last accepted bin position
+ //
+ Int_t nbins = his1D->GetNbinsX();
+ Int_t nentries = (Int_t)his1D->GetEntries();
+ const Double_t kEpsilon=0.0000000001;
+
+ if (nentries<=0) return 0;
+ if (fraction>1) fraction=0;
+ if (fraction<0) return 0;
+ TVectorD vectorX(nbins);
+ TVectorD vectorMean(nbins);
+ TVectorD vectorRMS(nbins);
+ Double_t sumCont=0;
+ for (Int_t ibin0=1; ibin0<=nbins; ibin0++) sumCont+=his1D->GetBinContent(ibin0);
+ //
+ Double_t minRMS=his1D->GetRMS()*10000;
+ Int_t maxBin=0;
+ //
+ for (Int_t ibin0=1; ibin0<nbins; ibin0++){
+ Double_t sum0=0, sum1=0, sum2=0;
+ Int_t ibin1=ibin0;
+ for ( ibin1=ibin0; ibin1<nbins; ibin1++){
+ Double_t cont=his1D->GetBinContent(ibin1);
+ Double_t x= his1D->GetBinCenter(ibin1);
+ sum0+=cont;
+ sum1+=cont*x;
+ sum2+=cont*x*x;
+ if ( (ibin0!=ibin1) && sum0>=fraction*sumCont) break;
+ }
+ vectorX[ibin0]=his1D->GetBinCenter(ibin0);
+ if (sum0<fraction*sumCont) continue;
+ //
+ // substract fractions of bin0 and bin1 to keep sum0=fration*sumCont
+ //
+ Double_t diff = sum0-fraction*sumCont;
+ Double_t mean = sum1/sum0;
+ //
+ Double_t x0=his1D->GetBinCenter(ibin0);
+ Double_t x1=his1D->GetBinCenter(ibin1);
+ Double_t y0=his1D->GetBinContent(ibin0);
+ Double_t y1=his1D->GetBinContent(ibin1);
+ //
+ Double_t d = y0+y1-diff; //enties to keep
+ Double_t w0=0,w1=0;
+ if (y0<=kEpsilon&&y1>kEpsilon){
+ w1=d/y1;
+ }
+ if (y1<=kEpsilon&&y0>kEpsilon){
+ w0=d/y0;
+ }
+ if (y0>kEpsilon && y1>kEpsilon && x1>x0 ){
+ w0 = (d*(x1-mean))/((x1-x0)*y0);
+ w1 = (d-y0*w0)/y1;
+ //
+ if (w0>1) {w1+=(w0-1)*y0/y1; w0=1;}
+ if (w1>1) {w0+=(w1-1)*y1/y0; w1=1;}
+ }
+ if ( (x1>x0) &&TMath::Abs(y0*w0+y1*w1-d)>kEpsilon*sum0){
+ printf(" TStatToolkit::LTMHisto error\n");
+ }
+ sum0-=y0+y1;
+ sum1-=y0*x0;
+ sum1-=y1*x1;
+ sum2-=y0*x0*x0;
+ sum2-=y1*x1*x1;
+ //
+ Double_t xx0=his1D->GetXaxis()->GetBinUpEdge(ibin0)-0.5*w0*his1D->GetBinWidth(ibin0);
+ Double_t xx1=his1D->GetXaxis()->GetBinLowEdge(ibin1)+0.5*w1*his1D->GetBinWidth(ibin1);
+ sum0+=y0*w0+y1*w1;
+ sum1+=y0*w0*xx0;
+ sum1+=y1*w1*xx1;
+ sum2+=y0*w0*xx0*xx0;
+ sum2+=y1*w1*xx1*xx1;
+
+ //
+ // choose the bin with smallest rms
+ //
+ if (sum0>0){
+ vectorMean[ibin0]=sum1/sum0;
+ vectorRMS[ibin0]=TMath::Sqrt(TMath::Abs(sum2/sum0-vectorMean[ibin0]*vectorMean[ibin0]));
+ if (vectorRMS[ibin0]<minRMS){
+ minRMS=vectorRMS[ibin0];
+ params[0]=sum0;
+ params[1]=vectorMean[ibin0];
+ params[2]=vectorRMS[ibin0];
+ params[3]=vectorRMS[ibin0]/TMath::Sqrt(sumCont*fraction);
+ params[4]=0; // what is the formula for error of RMS???
+ params[5]=ibin0;
+ params[6]=ibin1;
+ params[7]=his1D->GetBinCenter(ibin0);
+ params[8]=his1D->GetBinCenter(ibin1);
+ maxBin=ibin0;
+ }
+ }else{
+ break;
+ }
+ }
+ return kTRUE;
+}
+
+