Histograms in ROOT

To find the maxim bin you can use TH1::GetMaximumBin if you don't want to loop at the bins yourself.

For zooming an histogram you can use TAxis::SetRange(firstbin,last bin) or TAxis::SetRangeUser(x1,x2). You can also do it with the GUI by selecting the axis range with the mouse.

#include "TH1.h"
#include "TRandom.h"
#include "TPad.h"
#include <iostream>

void exerciseHistogram1() { 


   TH1D * h1 = new TH1D("h1","flat+gaus histogram",200,0,10);

   for (int i = 0; i < 10000; ++i) { 
      h1->Fill( gRandom->Uniform(0,10) ); 
   }
   for (int i = 0; i < 1000; ++i) { 
      h1->Fill( gRandom->Gaus(5,0.2) ); 
   }

   h1->Draw();

   double ibinMax = h1->GetMaximumBin();
   std::cout << "Bin with maximum is " << ibinMax << " at x = " << h1->GetBinCenter(ibinMax) << std::endl;
   std::cout << "Maximum Content  is " << h1->GetBinContent(ibinMax) << " +/- " << h1->GetBinError(ibinMax) << std::endl;

   TAxis * axis = h1->GetXaxis();
   axis->SetRange( axis->FindBin(4.0001), axis->FindBin(5.9999) ); // add or subtract a small eps to avoid being at the edge of the bin
   // axis->SetRangeUser(4.,6. );   // alternativly you can use SetRangeUser

   gPad->Update();

}

To create the sub-histogram, you need first to find the bin numbers in the original histogram corresponding to 4 and 6. You can use for this TAxis:FindBin for this. Then you create the sub-histogram using as lower value for the axis, the lower edge of the bin corresponding to 4, and, as upper value, the upper edge of the bin corresponding to 6. Afterwards, by looping on the bins, you can copy the bin content from the original histogram into the new one. It is better to use a slightly value larger than 4 (e.g. 4.0001) and a value a little bit smaller than 6 (e.g. 5.999) to avoid the bin edges.

#include "TH1.h"
#include "TRandom.h"
#include "TPad.h"
#include <iostream>



void exerciseHistogram1b() { 


   TH1D * h1 = new TH1D("h1","flat+gaus histogram",200,0,10);

   for (int i = 0; i < 10000; ++i) { 
      h1->Fill( gRandom->Uniform(0,10) ); 
   }
   for (int i = 0; i < 1000; ++i) { 
      h1->Fill( gRandom->Gaus(5,0.2) ); 
   }

   h1->Draw();

   double ibinMax = h1->GetMaximumBin();
   std::cout << "Bin with maximum is " << ibinMax << " at x = " << h1->GetBinCenter(ibinMax) << std::endl;
   std::cout << "Maximum Content  is " << h1->GetBinContent(ibinMax) << " +/- " << h1->GetBinError(ibinMax) << std::endl;

   TAxis * axis = h1->GetXaxis();
   int ifirst =  axis->FindBin(4.001);
   int ilast =  axis->FindBin(5.9999);
   int nbins =  ilast - ifirst; 
   TH1D * h2 = new TH1D("h2","flat+gaus zoomed histogram",nbins, axis->GetBinLowEdge(ifirst), axis->GetBinUpEdge(ilast));
   std::cout << " Number of bins of zoomed histogram is " << nbins << std::endl;
   for (int i1 = ifirst; i1 <= ilast; ++i1) { 
      int i2 = i1 - ifirst + 1;
      //std::cout << " setting content for bin " << i2 << " from " << i1 << " c = " << h1->GetBinContent(i1) << std::endl;
      h2->SetBinContent( i2, h1->GetBinContent(i1) ); 
   }
   h2->Draw(); 
   gPad->Update();

   // to check if we did not screw-up,  we recompute maximum position
   double ibinMax2 = h2->GetMaximumBin();
   std::cout << "Bin with maximum is " << ibinMax2 << " at x = " << h2->GetBinCenter(ibinMax2) << std::endl; 

}

• Use TH1::Add to add the two histogram.
• Use TH1::Scale(10000/ 100000) to re-normalise the histogram.
• Use again TH1::Add to subtract the histogram, but with a second coefficient equal to -1. (TH1::Add(h1,h2,1,-1)).
• For getting the right errors you must call TH1::Sumw2= before doing the operations on the histograms (i.e. before scaling and before subtracting them)

#include "TH1.h"
#include "TRandom.h"
#include "TCanvas.h"
#include "TLine.h"
#include <iostream>

void exerciseHistogram2() { 


   TH1D * h1 = new TH1D("h1","flat histogram",100,0,10);
   for (int i = 0; i < 10000; ++i) { 
      h1->Fill( gRandom->Uniform(0,10) ); 
   }

   TH1D * h2 = new TH1D("h2","gaus histogram",100,0,10);
   for (int i = 0; i < 1000; ++i) { 
      h2->Fill( gRandom->Gaus(5,1) ); 
   }

   TH1D * h3 = new TH1D("h3","flat+gaus histogram",100,0,10);
   h3->Add(h1,h2);

   h3->Draw();


   TH1D * h4 = new TH1D("h4","second flat histogram",100,0,10);
   for (int i = 0; i < 100000; ++i) { 
      h4->Fill( gRandom->Uniform(0,10) ); 
   }

   // renormalize histogram
   //!! VERY IMPORTANT - NEED TO CALL Sumw2() to get right ERRORS!!!
   h4->Sumw2();
   h3->Sumw2();
   h4->Scale(0.1);

   // plot in a new Canvas
   new TCanvas("c2","c2");


  TH1D * h5 = new TH1D("h5","(flat+gaus) histogram - flat histogram",100,0,10);
  h5->Add(h3,h4,1.,-1.);
  h5->Draw("E");

  TLine * line = new TLine(0,0,10,0);
  line->Draw();
   

}

For rebinning in 4 times larger bins, use TH1::Rebin with ngroup=4.

Add these lines of code at the end of the macro

new TCanvas("c2","c2");

  TH1 * h6 = h5->Rebin(4,"h6");
  h6->SetTitle("Rebinned histogram");
  h6->Draw();

The option for plotting colour boxes is "COLZ" which draws also a palette for the scale on the Z axis (the bin content)

#include "TH2.h"
#include "TProfile.h"
#include "TRandom.h"
#include "TCanvas.h"
#include <iostream>

void exerciseHistogram3() { 


   TH2D * h2d = new TH2D("h2d","2d histogram",40,-5,5, 40, -5, 5);
   for (int i = 0; i < 100000; ++i) { 
      double u =  gRandom->Gaus(0,1);
      double w =  gRandom->Gaus(0,1);      
      double x = u; 
      double y = w + 0.5 * u;
      h2d->Fill( x,y ); 
   }

   h2d->Draw("COLZ");

   std::cout << "correlation factor " << h2d->GetCorrelationFactor() << std::endl;


}

For making the projection call TH1::ProjectionX and for making the profile call TH1::ProfileX

For dividing the canvas call TCanvas::Divide(1,2) and navigate in the pad contained in the canvas by calling TCanvas::cd(pad_number).

Add these lines of code at the end of the macro

TH1 * hx = h2d->ProjectionX(); 
   TH1 * px = h2d->ProfileX(); 

   TCanvas * c2 = new TCanvas("c2","c2"); 
   // divide in 2 pad in x and one in y
   c2->Divide(2,1);
   c2->cd(1); 
   hx->Draw(); 

   c2->cd(2);
   px->Draw();