/// \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();
}