kdTreeBinning.C

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/// \file
/// \ingroup tutorial_math
/// \notebook
/// kdTreeBinning tutorial: bin the data in cells of equal content using a kd-tree
///
/// Using TKDTree wrapper class as a data binning structure
///  Plot the 2D data using the TH2Poly class
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Bartolomeu Rabacal

#include <math.h>

#include "TKDTreeBinning.h"
#include "TH2D.h"
#include "TH2Poly.h"
#include "TStyle.h"
#include "TGraph2D.h"
#include "TRandom3.h"
#include "TCanvas.h"
#include <iostream>

void kdTreeBinning() {

   // -----------------------------------------------------------------------------------------------
   //  Create random sample with regular binning plotting

   const UInt_t DATASZ = 10000;
   const UInt_t DATADIM = 2;
   const UInt_t NBINS = 50;

   Double_t smp[DATASZ * DATADIM];

   double mu[2] = {0,2};
   double sig[2] = {2,3};
   TRandom3 r;
   r.SetSeed(1);
   for (UInt_t i = 0; i < DATADIM; ++i)
      for (UInt_t j = 0; j < DATASZ; ++j)
         smp[DATASZ * i + j] = r.Gaus(mu[i], sig[i]);

   UInt_t h1bins = (UInt_t) sqrt(NBINS);

   TH2D* h1 = new TH2D("h1BinTest", "Regular binning", h1bins, -5., 5., h1bins, -5., 5.);
   for (UInt_t j = 0; j < DATASZ; ++j)
      h1->Fill(smp[j], smp[DATASZ + j]);


   // ---------------------------------------------------------------------------------------------
   // Create KDTreeBinning object with TH2Poly plotting

   TKDTreeBinning* kdBins = new TKDTreeBinning(DATASZ, DATADIM, smp, NBINS);

   UInt_t nbins = kdBins->GetNBins();
   UInt_t dim   = kdBins->GetDim();

   const Double_t* binsMinEdges = kdBins->GetBinsMinEdges();
   const Double_t* binsMaxEdges = kdBins->GetBinsMaxEdges();

   TH2Poly* h2pol = new TH2Poly("h2PolyBinTest", "KDTree binning", kdBins->GetDataMin(0), kdBins->GetDataMax(0), kdBins->GetDataMin(1), kdBins->GetDataMax(1));

   for (UInt_t i = 0; i < nbins; ++i) {
      UInt_t edgeDim = i * dim;
      h2pol->AddBin(binsMinEdges[edgeDim], binsMinEdges[edgeDim + 1], binsMaxEdges[edgeDim], binsMaxEdges[edgeDim + 1]);
   }

   for (UInt_t i = 1; i <= kdBins->GetNBins(); ++i)
      h2pol->SetBinContent(i, kdBins->GetBinDensity(i - 1));

   std::cout << "Bin with minimum density: " << kdBins->GetBinMinDensity() << std::endl;
   std::cout << "Bin with maximum density: " << kdBins->GetBinMaxDensity() << std::endl;

   TCanvas* c1 = new TCanvas("glc1", "TH2Poly from a kdTree",0,0,600,800);
   c1->Divide(1,3);
   c1->cd(1);
   h1->Draw("lego");

   c1->cd(2);
   h2pol->Draw("COLZ L");
   c1->Update();

   //-------------------------------------------------
   // Draw an equivalent plot showing the data points 


   std::vector<Double_t> z = std::vector<Double_t>(DATASZ, 0.);
   for (UInt_t i = 0; i < DATASZ; ++i)
      z[i] = (Double_t) h2pol->GetBinContent(h2pol->FindBin(smp[i], smp[DATASZ + i]));

   TGraph2D *g = new TGraph2D(DATASZ, smp, &smp[DATASZ], &z[0]);
   g->SetMarkerStyle(20);

   c1->cd(3);
   g->Draw("pcol");
   c1->Update();

   // ---------------------------------------------------------
   // make a new TH2Poly where bins are ordered by the density

   TH2Poly* h2polrebin = new TH2Poly("h2PolyBinTest", "KDTree binning", kdBins->GetDataMin(0), kdBins->GetDataMax(0), kdBins->GetDataMin(1), kdBins->GetDataMax(1));
   h2polrebin->SetFloat();

   //---------------------------------
   // Sort the bins by their density  

   kdBins->SortBinsByDensity();

   for (UInt_t i = 0; i < kdBins->GetNBins(); ++i) {
      const Double_t* binMinEdges = kdBins->GetBinMinEdges(i);
      const Double_t* binMaxEdges = kdBins->GetBinMaxEdges(i);
      h2polrebin->AddBin(binMinEdges[0], binMinEdges[1], binMaxEdges[0], binMaxEdges[1]);
   }

   for (UInt_t i = 1; i <= kdBins->GetNBins(); ++i){
      h2polrebin->SetBinContent(i, kdBins->GetBinDensity(i - 1));}

   std::cout << "Bin with minimum density: " << kdBins->GetBinMinDensity() << std::endl;
   std::cout << "Bin with maximum density: " << kdBins->GetBinMaxDensity() << std::endl;

   // now make a vector with bin number vs position
   for (UInt_t i = 0; i < DATASZ; ++i)
     z[i] = (Double_t) h2polrebin->FindBin(smp[i], smp[DATASZ + i]);

   TGraph2D *g2 = new TGraph2D(DATASZ, smp, &smp[DATASZ], &z[0]);
   g2->SetMarkerStyle(20);


   // plot new TH2Poly (ordered one) and TGraph2D
   // The new TH2Poly has to be same as old one and the TGraph2D should be similar to
   // the previous one. It is now made using as z value the bin number

   TCanvas* c4 = new TCanvas("glc4", "TH2Poly from a kdTree (Ordered)",50,50,800,800);

   c4->Divide(2,2);
   c4->cd(1);
   h2polrebin->Draw("COLZ L");  // draw as scatter plot

   c4->cd(2);
   g2->Draw("pcol");

   c4->Update();

   // make also the 1D binned histograms

   TKDTreeBinning* kdX = new TKDTreeBinning(DATASZ, 1, &smp[0], 20);
   TKDTreeBinning* kdY = new TKDTreeBinning(DATASZ, 1, &smp[DATASZ], 40);


  kdX->SortOneDimBinEdges();
  kdY->SortOneDimBinEdges();

  TH1* hX=new TH1F("hX", "X projection", kdX->GetNBins(), kdX->GetOneDimBinEdges());
  for(int i=0; i<kdX->GetNBins(); ++i){
    hX->SetBinContent(i+1, kdX->GetBinDensity(i));
  }

  TH1* hY=new TH1F("hY", "Y Projection", kdY->GetNBins(), kdY->GetOneDimBinEdges());
  for(int i=0; i<kdY->GetNBins(); ++i){
    hY->SetBinContent(i+1, kdY->GetBinDensity(i));
  }

  c4->cd(3);
  hX->Draw();
  c4->cd(4);
  hY->Draw();
}