/// \file
/// \ingroup tutorial_unfold5
///
/// Version 17.0 example for multi-dimensional unfolding
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Stefan Schmitt, DESY
#include <iostream>
#include <cmath>
#include <map>
#include <TMath.h>
#include <TCanvas.h>
#include <TStyle.h>
#include <TGraph.h>
#include <TFile.h>
#include <TH1.h>
#include "TUnfoldDensity.h"

using namespace std;

// #define PRINT_MATRIX_L

void testUnfold5d()
{
  // switch on histogram errors
  TH1::SetDefaultSumw2();

  //==============================================
  // step 1 : open output file
  TFile *outputFile=new TFile("testUnfold5_results.root","recreate");

  //==============================================
  // step 2 : read binning schemes and input histograms
  TFile *inputFile=new TFile("testUnfold5_histograms.root");

  outputFile->cd();

  TUnfoldBinning *detectorBinning,*generatorBinning;

  inputFile->GetObject("detector",detectorBinning);
  inputFile->GetObject("generator",generatorBinning);

  if((!detectorBinning)||(!generatorBinning)) {
     cout<<"problem to read binning schemes\n";
  }

  // save binning schemes to output file
  detectorBinning->Write();
  generatorBinning->Write();

  // read histograms
  TH1 *histDataReco,*histDataTruth;
  TH2 *histMCGenRec;

  inputFile->GetObject("histDataReco",histDataReco);
  inputFile->GetObject("histDataTruth",histDataTruth);
  inputFile->GetObject("histMCGenRec",histMCGenRec);

  histDataReco->Write();
  histDataTruth->Write();
  histMCGenRec->Write();

  if((!histDataReco)||(!histDataTruth)||(!histMCGenRec)) {
     cout<<"problem to read input histograms\n";
  }

  //========================
  // Step 3: unfolding

 // preserve the area
  TUnfold::EConstraint constraintMode= TUnfold::kEConstraintArea;

  // basic choice of regularisation scheme:
  //    curvature (second derivative)
  TUnfold::ERegMode regMode = TUnfold::kRegModeCurvature;

  // density flags
  TUnfoldDensity::EDensityMode densityFlags=
    TUnfoldDensity::kDensityModeBinWidth;

  // detailed steering for regularisation
  const char *REGULARISATION_DISTRIBUTION=0;
  const char *REGULARISATION_AXISSTEERING="*[B]";

  // set up matrix of migrations
  TUnfoldDensity unfold(histMCGenRec,TUnfold::kHistMapOutputHoriz,
                        regMode,constraintMode,densityFlags,
                        generatorBinning,detectorBinning,
                        REGULARISATION_DISTRIBUTION,
                        REGULARISATION_AXISSTEERING);

  // define the input vector (the measured data distribution)
  unfold.SetInput(histDataReco /* ,0.0,1.0 */);

  // print matrix of regularisation conditions
#ifdef PRINT_MATRIX_L
  TH2 *histL= unfold.GetL("L");
  for(Int_t j=1;j<=histL->GetNbinsY();j++) {
     cout<<"L["<<unfold.GetLBinning()->GetBinName(j)<<"]";
     for(Int_t i=1;i<=histL->GetNbinsX();i++) {
        Double_t c=histL->GetBinContent(i,j);
        if(c!=0.0) cout<<" ["<<i<<"]="<<c;
     }
     cout<<"\n";
  }
#endif
  // run the unfolding
  //
  // here, tau is determined by scanning the global correlation coefficients

  Int_t nScan=30;
  TSpline *rhoLogTau=0;
  TGraph *lCurve=0;

  // for determining tau, scan the correlation coefficients
  // correlation coefficients may be probed for all distributions
  // or only for selected distributions
  // underflow/overflow bins may be included/excluded
  //
  const char *SCAN_DISTRIBUTION="signal";
  const char *SCAN_AXISSTEERING=0;

  Int_t iBest=unfold.ScanTau(nScan,0.,0.,&rhoLogTau,
                             TUnfoldDensity::kEScanTauRhoMax,
                             SCAN_DISTRIBUTION,SCAN_AXISSTEERING,
                             &lCurve);

  // create graphs with one point to visualize best choice of tau
  Double_t t[1],rho[1],x[1],y[1];
  rhoLogTau->GetKnot(iBest,t[0],rho[0]);
  lCurve->GetPoint(iBest,x[0],y[0]);
  TGraph *bestRhoLogTau=new TGraph(1,t,rho);
  TGraph *bestLCurve=new TGraph(1,x,y);
  Double_t *tAll=new Double_t[nScan],*rhoAll=new Double_t[nScan];
  for(Int_t i=0;i<nScan;i++) {
     rhoLogTau->GetKnot(i,tAll[i],rhoAll[i]);
  }
  TGraph *knots=new TGraph(nScan,tAll,rhoAll);

  cout<<"chi**2="<<unfold.GetChi2A()<<"+"<<unfold.GetChi2L()
      <<" / "<<unfold.GetNdf()<<"\n";


  //===========================
  // Step 4: retreive and plot unfolding results

  // get unfolding output
  TH1 *histDataUnfold=unfold.GetOutput("unfolded signal",0,0,0,kFALSE);
  // get MOnte Carlo reconstructed data
  TH1 *histMCReco=histMCGenRec->ProjectionY("histMCReco",0,-1,"e");
  TH1 *histMCTruth=histMCGenRec->ProjectionX("histMCTruth",0,-1,"e");
  Double_t scaleFactor=histDataTruth->GetSumOfWeights()/
     histMCTruth->GetSumOfWeights();
  histMCReco->Scale(scaleFactor);
  histMCTruth->Scale(scaleFactor);
  // get matrix of probabilities
  TH2 *histProbability=unfold.GetProbabilityMatrix("histProbability");
  // get global correlation coefficients
  TH1 *histGlobalCorr=unfold.GetRhoItotal("histGlobalCorr",0,0,0,kFALSE);
  TH1 *histGlobalCorrScan=unfold.GetRhoItotal
     ("histGlobalCorrScan",0,SCAN_DISTRIBUTION,SCAN_AXISSTEERING,kFALSE);
  TH2 *histCorrCoeff=unfold.GetRhoIJtotal("histCorrCoeff",0,0,0,kFALSE);

  TCanvas *canvas = new TCanvas();
  canvas->Print("testUnfold5.ps[");

  //========== page 1 ============
  // unfolding control plots
  // input, matrix, output
  // tau-scan, global correlations, correlation coefficients
  canvas->Clear();
  canvas->Divide(3,2);

  // (1) all bins, compare to original MC distribution
  canvas->cd(1);
  histDataReco->SetMinimum(0.0);
  histDataReco->Draw("E");
  histMCReco->SetLineColor(kBlue);
  histMCReco->Draw("SAME HIST");
  // (2) matrix of probabilities
  canvas->cd(2);
  histProbability->Draw("BOX");
  // (3) unfolded data, data truth, MC truth
  canvas->cd(3);
  gPad->SetLogy();
  histDataUnfold->Draw("E");
  histDataTruth->SetLineColor(kBlue);
  histDataTruth->Draw("SAME HIST");
  histMCTruth->SetLineColor(kRed);
  histMCTruth->Draw("SAME HIST");
  // (4) scan of correlation vs tau
  canvas->cd(4);
  rhoLogTau->Draw();
  knots->Draw("*");
  bestRhoLogTau->SetMarkerColor(kRed);
  bestRhoLogTau->Draw("*");
  // (5) global correlation coefficients for the distributions
  //     used during the scan
  canvas->cd(5);
  //histCorrCoeff->Draw("BOX");
  histGlobalCorrScan->Draw("HIST");
  // (6) L-curve
  canvas->cd(6);
  lCurve->Draw("AL");
  bestLCurve->SetMarkerColor(kRed);
  bestLCurve->Draw("*");


  canvas->Print("testUnfold5.ps");

  canvas->Print("testUnfold5.ps]");

}