PDEFoam.cxx

Go to the documentation of this file.

// @(#)root/tmva $Id$
// Author: S.Jadach, Tancredi Carli, Dominik Dannheim, Alexander Voigt

/**********************************************************************************
 * Project: TMVA - a Root-integrated toolkit for multivariate data analysis       *
 * Package: TMVA                                                                  *
 * Classes: PDEFoam                                                               *
 * Web    : http://tmva.sourceforge.net                                           *
 *                                                                                *
 * Description:                                                                   *
 *      Implementations                                                           *
 *                                                                                *
 * Authors (alphabetical):                                                        *
 *      Tancredi Carli   - CERN, Switzerland                                      *
 *      Dominik Dannheim - CERN, Switzerland                                      *
 *      S. Jadach        - Institute of Nuclear Physics, Cracow, Poland           *
 *      Alexander Voigt  - TU Dresden, Germany                                    *
 *      Peter Speckmayer - CERN, Switzerland                                      *
 *                                                                                *
 * Copyright (c) 2008, 2010:                                                      *
 *      CERN, Switzerland                                                         *
 *      MPI-K Heidelberg, Germany                                                 *
 *                                                                                *
 * Redistribution and use in source and binary forms, with or without             *
 * modification, are permitted according to the terms listed in LICENSE           *
 * (http://tmva.sourceforge.net/LICENSE)                                          *
 **********************************************************************************/

//_____________________________________________________________________
//
// Implementation of PDEFoam
//
// The PDEFoam method is an extension of the PDERS method, which uses
// self-adapting binning to divide the multi-dimensional phase space
// in a finite number of hyper-rectangles (boxes).
//
// For a given number of boxes, the binning algorithm adjusts the size
// and position of the boxes inside the multidimensional phase space,
// minimizing the variance of the signal and background densities inside
// the boxes. The binned density information is stored in binary trees,
// allowing for a very fast and memory-efficient classification of
// events.
//
// The implementation of the PDEFoam is based on the monte-carlo
// integration package TFoam included in the analysis package ROOT.
//
// The class TMVA::PDEFoam defines the default interface for the
// PDEFoam variants:
//
//   - PDEFoamEvent
//   - PDEFoamDiscriminant
//   - PDEFoamTarget
//   - PDEFoamMultiTarget
//   - PDEFoamDecisionTree
//
// Per default PDEFoam stores in the cells the number of events (event
// weights) and therefore acts as an event density estimator.
// However, the above listed derived classes override this behaviour
// to implement certain PDEFoam variations.
//
// In order to use PDEFoam the user has to set the density estimator
// of the type TMVA::PDEFoamDensityBase, which is used to during the foam
// build-up.  The default PDEFoam should be used with
// PDEFoamEventDensity.
// _____________________________________________________________________

#include "TMVA/PDEFoam.h"

#include "TMVA/Event.h"
#include "TMVA/MsgLogger.h"
#include "TMVA/PDEFoamKernelBase.h"
#include "TMVA/Timer.h"
#include "TMVA/Tools.h"
#include "TMVA/Types.h"

#include "TStyle.h"
#include "TObject.h"
#include "TH1D.h"
#include "TMath.h"
#include "TVectorT.h"
#include "TRandom3.h"
#include "TColor.h"
#include "TDirectory.h"
#include "TObjArray.h"

#include <cassert>
#include <fstream>
#include <iostream>
#include <iomanip>
#include <limits>
#include <sstream>

ClassImp(TMVA::PDEFoam)

static const Float_t kHigh= FLT_MAX;
static const Float_t kVlow=-FLT_MAX;

using namespace std;

////////////////////////////////////////////////////////////////////////////////
/// Default constructor for streamer, user should not use it.

TMVA::PDEFoam::PDEFoam() :
   fName("PDEFoam"),
   fDim(0),
   fNCells(0),
   fNBin(5),
   fNSampl(2000),
   fEvPerBin(0),
   fMaskDiv(0),
   fInhiDiv(0),
   fNoAct(1),
   fLastCe(-1),
   fCells(0),
   fHistEdg(0),
   fRvec(0),
   fPseRan(new TRandom3(4356)),
   fAlpha(0),
   fFoamType(kSeparate),
   fXmin(0),
   fXmax(0),
   fNElements(0),
   fNmin(100),
   fMaxDepth(0),
   fVolFrac(1.0/15.0),
   fFillFoamWithOrigWeights(kFALSE),
   fDTSeparation(kFoam),
   fPeekMax(kTRUE),
   fDistr(NULL),
   fTimer(new Timer(0, "PDEFoam", kTRUE)),
   fVariableNames(new TObjArray()),
   fLogger(new MsgLogger("PDEFoam"))
{
   // fVariableNames may delete it's heap-based content
   if (fVariableNames)
      fVariableNames->SetOwner(kTRUE);
}

////////////////////////////////////////////////////////////////////////////////
/// User constructor, to be employed by the user

TMVA::PDEFoam::PDEFoam(const TString& name) :
   fName(name),
   fDim(0),
   fNCells(1000),
   fNBin(5),
   fNSampl(2000),
   fEvPerBin(0),
   fMaskDiv(0),
   fInhiDiv(0),
   fNoAct(1),
   fLastCe(-1),
   fCells(0),
   fHistEdg(0),
   fRvec(0),
   fPseRan(new TRandom3(4356)),
   fAlpha(0),
   fFoamType(kSeparate),
   fXmin(0),
   fXmax(0),
   fNElements(0),
   fNmin(100),
   fMaxDepth(0),
   fVolFrac(1.0/15.0),
   fFillFoamWithOrigWeights(kFALSE),
   fDTSeparation(kFoam),
   fPeekMax(kTRUE),
   fDistr(NULL),
   fTimer(new Timer(1, "PDEFoam", kTRUE)),
   fVariableNames(new TObjArray()),
   fLogger(new MsgLogger("PDEFoam"))
{
   if(strlen(name) > 128)
      Log() << kFATAL << "Name too long " << name.Data() << Endl;

   // fVariableNames may delete it's heap-based content
   if (fVariableNames)
      fVariableNames->SetOwner(kTRUE);
}

////////////////////////////////////////////////////////////////////////////////
/// Default destructor

TMVA::PDEFoam::~PDEFoam()
{
   delete fVariableNames;
   delete fTimer;
   if (fDistr)  delete fDistr;
   if (fPseRan) delete fPseRan;
   if (fXmin) { delete [] fXmin;  fXmin=0; }
   if (fXmax) { delete [] fXmax;  fXmax=0; }

   ResetCellElements();
   if(fCells!= 0) {
      for(Int_t i=0; i<fNCells; i++) delete fCells[i]; // PDEFoamCell*[]
      delete [] fCells;
   }
   delete [] fRvec;    //double[]
   delete [] fAlpha;   //double[]
   delete [] fMaskDiv; //int[]
   delete [] fInhiDiv; //int[]

   delete fLogger;
}

////////////////////////////////////////////////////////////////////////////////
/// Copy Constructor  NOT IMPLEMENTED (NEVER USED)

TMVA::PDEFoam::PDEFoam(const PDEFoam &from) :
   TObject(from)
   , fDim(0)
   , fNCells(0)
   , fNBin(0)
   , fNSampl(0)
   , fEvPerBin(0)
   , fMaskDiv(0)
   , fInhiDiv(0)
   , fNoAct(0)
   , fLastCe(0)
   , fCells(0)
   , fHistEdg(0)
   , fRvec(0)
   , fPseRan(0)
   , fAlpha(0)
   , fFoamType(kSeparate)
   , fXmin(0)
   , fXmax(0)
   , fNElements(0)
   , fNmin(0)
   , fMaxDepth(0)
   , fVolFrac(1.0/15.0)
   , fFillFoamWithOrigWeights(kFALSE)
   , fDTSeparation(kFoam)
   , fPeekMax(kTRUE)
   , fDistr(0)
   , fTimer(0)
   , fVariableNames(0)
   , fLogger(new MsgLogger(*from.fLogger))
{
   Log() << kFATAL << "COPY CONSTRUCTOR NOT IMPLEMENTED" << Endl;

   // fVariableNames may delete it's heap-based content
   if (fVariableNames)
      fVariableNames->SetOwner(kTRUE);
}

////////////////////////////////////////////////////////////////////////////////
/// Sets dimension of cubical space

void TMVA::PDEFoam::SetDim(Int_t kDim)
{
   if (kDim < 1)
      Log() << kFATAL << "<SetDim>: Dimension is zero or negative!" << Endl;

   fDim = kDim;
   if (fXmin) delete [] fXmin;
   if (fXmax) delete [] fXmax;
   fXmin = new Double_t[GetTotDim()];
   fXmax = new Double_t[GetTotDim()];
}

////////////////////////////////////////////////////////////////////////////////
/// set lower foam bound in dimension idim

void TMVA::PDEFoam::SetXmin(Int_t idim, Double_t wmin)
{
   if (idim<0 || idim>=GetTotDim())
      Log() << kFATAL << "<SetXmin>: Dimension out of bounds!" << Endl;

   fXmin[idim]=wmin;
}

////////////////////////////////////////////////////////////////////////////////
/// set upper foam bound in dimension idim

void TMVA::PDEFoam::SetXmax(Int_t idim, Double_t wmax)
{
   if (idim<0 || idim>=GetTotDim())
      Log() << kFATAL << "<SetXmax>: Dimension out of bounds!" << Endl;

   fXmax[idim]=wmax;
}

////////////////////////////////////////////////////////////////////////////////
/// Basic initialization of FOAM invoked by the user.
/// IMPORTANT: Random number generator and the distribution object has to be
/// provided using SetPseRan and SetRho prior to invoking this initializator!
///
/// After the foam is grown, space for 2 variables is reserved in
/// every cell.  They are used for filling the foam cells.

void TMVA::PDEFoam::Create()
{
   Bool_t addStatus = TH1::AddDirectoryStatus();
   TH1::AddDirectory(kFALSE);

   if(fPseRan==0) Log() << kFATAL << "Random number generator not set" << Endl;
   if(fDistr==0)  Log() << kFATAL << "Distribution function not set" << Endl;
   if(fDim==0)    Log() << kFATAL << "Zero dimension not allowed" << Endl;

   /////////////////////////////////////////////////////////////////////////
   //                   ALLOCATE SMALL LISTS                              //
   //  it is done globally, not for each cell, to save on allocation time //
   /////////////////////////////////////////////////////////////////////////
   fRvec = new Double_t[fDim];   // Vector of random numbers
   if(fRvec==0)  Log() << kFATAL << "Cannot initialize buffer fRvec" << Endl;

   if(fDim>0){
      fAlpha = new Double_t[fDim];    // sum<1 for internal parametrization of the simplex
      if(fAlpha==0)  Log() << kFATAL << "Cannot initialize buffer fAlpha" << Endl;
   }

   //====== List of directions inhibited for division
   if(fInhiDiv == 0){
      fInhiDiv = new Int_t[fDim];
      for(Int_t i=0; i<fDim; i++) fInhiDiv[i]=0;
   }
   //====== Dynamic mask used in Explore for edge determination
   if(fMaskDiv == 0){
      fMaskDiv = new Int_t[fDim];
      for(Int_t i=0; i<fDim; i++) fMaskDiv[i]=1;
   }
   //====== Initialize list of histograms
   fHistEdg = new TObjArray(fDim);           // Initialize list of histograms
   for(Int_t i=0; i<fDim; i++){
      TString hname, htitle;
      hname   = fName+TString("_HistEdge_");
      hname  += i;
      htitle  = TString("Edge Histogram No. ");
      htitle += i;
      (*fHistEdg)[i] = new TH1D(hname.Data(),htitle.Data(),fNBin,0.0, 1.0); // Initialize histogram for each edge
      ((TH1D*)(*fHistEdg)[i])->Sumw2();
   }

   // ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| //
   //                     BUILD-UP of the FOAM                            //
   // ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| //

   // prepare PDEFoam for growing
   ResetCellElements(); // reset all cell elements

   // Define and explore root cell(s)
   InitCells();
   Grow();

   TH1::AddDirectory(addStatus);

   // prepare PDEFoam for the filling with events
   ResetCellElements(); // reset all cell elements
} // Create

////////////////////////////////////////////////////////////////////////////////
/// Internal subprogram used by Create.
/// It initializes "root part" of the FOAM of the tree of cells.

void TMVA::PDEFoam::InitCells()
{
   fLastCe =-1;                             // Index of the last cell
   if(fCells!= 0) {
      for(Int_t i=0; i<fNCells; i++) delete fCells[i];
      delete [] fCells;
   }

   fCells = new(nothrow) PDEFoamCell*[fNCells];
   if (!fCells) {
      Log() << kFATAL << "not enough memory to create " << fNCells
            << " cells" << Endl;
   }
   for(Int_t i=0; i<fNCells; i++){
      fCells[i]= new PDEFoamCell(fDim); // Allocate BIG list of cells
      fCells[i]->SetSerial(i);
   }

   /////////////////////////////////////////////////////////////////////////////
   //              Single Root Hypercube                                      //
   /////////////////////////////////////////////////////////////////////////////
   CellFill(1,   0);  //  0-th cell ACTIVE

   // Exploration of the root cell(s)
   for(Long_t iCell=0; iCell<=fLastCe; iCell++){
      Explore( fCells[iCell] );    // Exploration of root cell(s)
   }
}//InitCells

////////////////////////////////////////////////////////////////////////////////
/// Internal subprogram used by Create.
/// It initializes content of the newly allocated active cell.

Int_t TMVA::PDEFoam::CellFill(Int_t status, PDEFoamCell *parent)
{
   PDEFoamCell *cell;
   if (fLastCe==fNCells){
      Log() << kFATAL << "Too many cells" << Endl;
   }
   fLastCe++;   // 0-th cell is the first

   cell = fCells[fLastCe];

   cell->Fill(status, parent, 0, 0);

   cell->SetBest( -1);         // pointer for planning division of the cell
   cell->SetXdiv(0.5);         // factor for division
   Double_t xInt2,xDri2;
   if(parent!=0){
      xInt2  = 0.5*parent->GetIntg();
      xDri2  = 0.5*parent->GetDriv();
      cell->SetIntg(xInt2);
      cell->SetDriv(xDri2);
   }else{
      cell->SetIntg(0.0);
      cell->SetDriv(0.0);
   }
   return fLastCe;
}

////////////////////////////////////////////////////////////////////////////////
/// Internal subprogram used by Create.
/// It explores newly defined cell with help of special short MC sampling.
/// As a result, estimates of kTRUE and drive volume is defined/determined
/// Average and dispersion of the weight distribution will is found along
/// each edge and the best edge (minimum dispersion, best maximum weight)
/// is memorized for future use.
/// The optimal division point for eventual future cell division is
/// determined/recorded. Recorded are also minimum and maximum weight etc.
/// The volume estimate in all (inactive) parent cells is updated.
/// Note that links to parents and initial volume = 1/2 parent has to be
/// already defined prior to calling this routine.
///
/// If fNmin > 0 then the total number of (training) events found in
/// the cell during the exploration is stored in the cell.  This
/// information is used withing PeekMax() to avoid splitting cells
/// which contain less than fNmin events.

void TMVA::PDEFoam::Explore(PDEFoamCell *cell)
{
   Double_t wt, dx, xBest=0, yBest;
   Double_t intOld, driOld;

   Long_t iev;
   Double_t nevMC;
   Int_t i, j, k;
   Int_t nProj, kBest;
   Double_t ceSum[5], xproj;

   Double_t event_density = 0;
   Double_t totevents     = 0;
   Double_t toteventsOld  = 0;

   PDEFoamVect  cellSize(fDim);
   PDEFoamVect  cellPosi(fDim);

   cell->GetHcub(cellPosi,cellSize);

   PDEFoamCell  *parent;

   Double_t *xRand = new Double_t[fDim];

   Double_t *volPart=0;

   // calculate volume scale
   Double_t vol_scale = 1.0;
   for (Int_t idim = 0; idim < fDim; ++idim)
      vol_scale *= fXmax[idim] - fXmin[idim];

   cell->CalcVolume();
   dx = cell->GetVolume() * vol_scale;
   intOld = cell->GetIntg(); //memorize old values,
   driOld = cell->GetDriv(); //will be needed for correcting parent cells
   toteventsOld = GetCellElement(cell, 0);

   /////////////////////////////////////////////////////
   //    Special Short MC sampling to probe cell      //
   /////////////////////////////////////////////////////
   ceSum[0]=0;
   ceSum[1]=0;
   ceSum[2]=0;
   ceSum[3]=kHigh;  //wtmin
   ceSum[4]=kVlow;  //wtmax

   for (i=0;i<fDim;i++) ((TH1D *)(*fHistEdg)[i])->Reset(); // Reset histograms

   Double_t nevEff=0.;
   // ||||||||||||||||||||||||||BEGIN MC LOOP|||||||||||||||||||||||||||||
   for (iev=0;iev<fNSampl;iev++){
      MakeAlpha();               // generate uniformly vector inside hypercube

      if (fDim>0) for (j=0; j<fDim; j++) xRand[j]= cellPosi[j] +fAlpha[j]*(cellSize[j]);

      wt         = dx*Eval(xRand, event_density);
      totevents += event_density;

      nProj = 0;
      if (fDim>0) {
         for (k=0; k<fDim; k++) {
            xproj =fAlpha[k];
            ((TH1D *)(*fHistEdg)[nProj])->Fill(xproj,wt);
            nProj++;
         }
      }

      ceSum[0] += wt;    // sum of weights
      ceSum[1] += wt*wt; // sum of weights squared
      ceSum[2]++;        // sum of 1
      if (ceSum[3]>wt) ceSum[3]=wt;  // minimum weight;
      if (ceSum[4]<wt) ceSum[4]=wt;  // maximum weight
      // test MC loop exit condition
      if (ceSum[1]>0) nevEff = ceSum[0]*ceSum[0]/ceSum[1];
      else            nevEff = 0;
      if ( nevEff >= fNBin*fEvPerBin) break;
   }   // ||||||||||||||||||||||||||END MC LOOP|||||||||||||||||||||||||||||
   totevents *= dx;
   
   if (fNSampl>0) totevents /= fNSampl;

   // make shure that, if root cell is explored, more than zero
   // events were found.
   if (cell==fCells[0] && ceSum[0]<=0.0){
      if (ceSum[0]==0.0)
         Log() << kFATAL << "No events were found during exploration of "
               << "root cell.  Please check PDEFoam parameters nSampl "
               << "and VolFrac." << Endl;
      else
         Log() << kWARNING << "Negative number of events found during "
               << "exploration of root cell" << Endl;
   }

   //------------------------------------------------------------------
   //---  predefine logics of searching for the best division edge ---
   for (k=0; k<fDim;k++){
      fMaskDiv[k] =1;                       // default is all
      if ( fInhiDiv[k]==1) fMaskDiv[k] =0; // inhibit some...
   }
   kBest=-1;

   /////////////////////////////////////////////////////////////////////////////

   nevMC            = ceSum[2];
   Double_t intTrue = ceSum[0]/(nevMC+0.000001);
   Double_t intDriv=0.;

   if (kBest == -1) Varedu(ceSum,kBest,xBest,yBest); // determine the best edge,
   intDriv =sqrt(ceSum[1]/nevMC) -intTrue; // Foam build-up, sqrt(<w**2>) -<w>

   //=================================================================================
   cell->SetBest(kBest);
   cell->SetXdiv(xBest);
   cell->SetIntg(intTrue);
   cell->SetDriv(intDriv);
   SetCellElement(cell, 0, totevents);

   // correct/update integrals in all parent cells to the top of the tree
   Double_t  parIntg, parDriv;
   for (parent = cell->GetPare(); parent!=0; parent = parent->GetPare()){
      parIntg = parent->GetIntg();
      parDriv = parent->GetDriv();
      parent->SetIntg( parIntg   +intTrue -intOld );
      parent->SetDriv( parDriv   +intDriv -driOld );
      SetCellElement( parent, 0, GetCellElement(parent, 0) + totevents - toteventsOld);
   }
   delete [] volPart;
   delete [] xRand;
}

////////////////////////////////////////////////////////////////////////////////
/// Internal subrogram used by Create.
/// In determines the best edge candidate and the position of the cell division plane
/// in case of the variance reduction for future cell division,
/// using results of the MC exploration run stored in fHistEdg

void TMVA::PDEFoam::Varedu(Double_t ceSum[5], Int_t &kBest, Double_t &xBest, Double_t &yBest)
{
   Double_t nent   = ceSum[2];
   // Double_t swAll  = ceSum[0];
   Double_t sswAll = ceSum[1];
   Double_t ssw    = sqrt(sswAll)/sqrt(nent);
   //
   Double_t sswIn,sswOut,xLo,xUp;
   kBest =-1;
   xBest =0.5;
   yBest =1.0;
   Double_t maxGain=0.0;
   // Now go over all projections kProj
   for(Int_t kProj=0; kProj<fDim; kProj++) {
      if( fMaskDiv[kProj]) {
         // initialize search over bins
         // Double_t sigmIn =0.0; Double_t sigmOut =0.0;
         Double_t sswtBest = kHigh;
         Double_t gain =0.0;
         Double_t xMin=0.0; Double_t xMax=0.0;
         // Double loop over all pairs jLo<jUp
         for(Int_t jLo=1; jLo<=fNBin; jLo++) {
            Double_t aswIn=0;  Double_t asswIn=0;
            for(Int_t jUp=jLo; jUp<=fNBin;jUp++) {
               aswIn  +=     ((TH1D *)(*fHistEdg)[kProj])->GetBinContent(jUp);
               asswIn += Sqr(((TH1D *)(*fHistEdg)[kProj])->GetBinError(  jUp));
               xLo=(jLo-1.0)/fNBin;
               xUp=(jUp*1.0)/fNBin;
               // swIn  =        aswIn/nent;
               // swOut = (swAll-aswIn)/nent;
               if ( (xUp-xLo) < std::numeric_limits<double>::epsilon()) sswIn=0.;
               else sswIn = sqrt(asswIn)       /sqrt(nent*(xUp-xLo))     *(xUp-xLo);
               if ( (1.0-xUp+xLo) < std::numeric_limits<double>::epsilon()) sswOut=0.;
               else if ( sswAll-asswIn < std::numeric_limits<double>::epsilon()) sswOut=0.;
               else sswOut= sqrt(sswAll-asswIn)/sqrt(nent*(1.0-xUp+xLo)) *(1.0-xUp+xLo);
               if( (sswIn+sswOut) < sswtBest) {
                  sswtBest = sswIn+sswOut;
                  gain     = ssw-sswtBest;
                  // sigmIn   = sswIn -swIn;  // Debug
                  // sigmOut  = sswOut-swOut; // Debug
                  xMin    = xLo;
                  xMax    = xUp;
               }
            }//jUp
         }//jLo
         Int_t iLo = (Int_t) (fNBin*xMin);
         Int_t iUp = (Int_t) (fNBin*xMax);

         if(gain>=maxGain) {
            maxGain=gain;
            kBest=kProj; // <--- !!!!! The best edge
            xBest=xMin;
            yBest=xMax;
            if(iLo == 0)     xBest=yBest; // The best division point
            if(iUp == fNBin) yBest=xBest; // this is not really used
         }
      }
   } //kProj

   if( (kBest >= fDim) || (kBest<0) )
      Log() << kFATAL << "Something wrong with kBest" << Endl;
}          //PDEFoam::Varedu

////////////////////////////////////////////////////////////////////////////////
/// Internal subrogram used by Create.
/// Provides random vector Alpha  0< Alpha(i) < 1

void TMVA::PDEFoam::MakeAlpha()
{
   // simply generate and load kDim uniform random numbers
   fPseRan->RndmArray(fDim,fRvec);   // kDim random numbers needed
   for(Int_t k=0; k<fDim; k++) fAlpha[k] = fRvec[k];
} //MakeAlpha

////////////////////////////////////////////////////////////////////////////////
/// Internal subprogram used by Create.  It finds cell with maximal
/// driver integral for the purpose of the division.  This function
/// is overridden by the PDEFoam Class to apply cuts on the number
/// of events in the cell (fNmin) and the cell tree depth
/// (GetMaxDepth() > 0) during cell buildup.

Long_t TMVA::PDEFoam::PeekMax()
{
   Long_t iCell = -1;

   Long_t  i;
   Double_t  drivMax, driv, xDiv;
   Bool_t bCutNmin = kTRUE;
   Bool_t bCutMaxDepth = kTRUE;
   //   drivMax = kVlow;
   drivMax = 0;  // only split cells if gain>0 (this also avoids splitting at cell boundary)
   for(i=0; i<=fLastCe; i++) {//without root
      if( fCells[i]->GetStat() == 1 ) {
         // if driver integral < numeric limit, skip cell
         driv = fCells[i]->GetDriv();
         if (driv < std::numeric_limits<float>::epsilon())
            continue;

         // do not split cell at the edges
         xDiv = TMath::Abs(fCells[i]->GetXdiv());
         if (xDiv <= std::numeric_limits<Double_t>::epsilon() ||
             xDiv >= 1.0 - std::numeric_limits<Double_t>::epsilon())
            continue;

         // apply cut on depth
         if (GetMaxDepth() > 0)
            bCutMaxDepth = fCells[i]->GetDepth() < GetMaxDepth();

         // apply Nmin-cut
         if (GetNmin() > 0)
            bCutNmin = GetCellElement(fCells[i], 0) > GetNmin();

         // choose cell
         if(driv > drivMax && bCutNmin && bCutMaxDepth) {
            drivMax = driv;
            iCell = i;
         }
      }
   }

   if (iCell == -1){
      if (!bCutNmin)
         Log() << kVERBOSE << "Warning: No cell with more than "
               << GetNmin() << " events found!" << Endl;
      else if (!bCutMaxDepth)
         Log() << kVERBOSE << "Warning: Maximum depth reached: "
               << GetMaxDepth() << Endl;
      else
         Log() << kWARNING << "<PDEFoam::PeekMax>: no more candidate cells (drivMax>0) found for further splitting." << Endl;
   }

   return(iCell);
}

////////////////////////////////////////////////////////////////////////////////
/// Internal subrogram used by Create.
/// It divides cell iCell into two daughter cells.
/// The iCell is retained and tagged as inactive, daughter cells are appended
/// at the end of the buffer.
/// New vertex is added to list of vertices.
/// List of active cells is updated, iCell removed, two daughters added
/// and their properties set with help of MC sampling (PDEFoam_Explore)
/// Returns Code RC=-1 of buffer limit is reached,  fLastCe=fnBuf.

Int_t TMVA::PDEFoam::Divide(PDEFoamCell *cell)
{
   // Double_t xdiv;
   Int_t   kBest;

   if(fLastCe+1 >= fNCells) Log() << kFATAL << "Buffer limit is reached, fLastCe=fnBuf" << Endl;

   cell->SetStat(0); // reset cell as inactive
   fNoAct++;

   // xdiv  = cell->GetXdiv();
   kBest = cell->GetBest();
   if( kBest<0 || kBest>=fDim ) Log() << kFATAL << "Wrong kBest" << Endl;

   //////////////////////////////////////////////////////////////////
   //           define two daughter cells (active)                 //
   //////////////////////////////////////////////////////////////////

   Int_t d1 = CellFill(1,   cell);
   Int_t d2 = CellFill(1,   cell);
   cell->SetDau0((fCells[d1]));
   cell->SetDau1((fCells[d2]));

   Explore( (fCells[d1]) );
   Explore( (fCells[d2]) );

   return 1;
} // PDEFoam_Divide

////////////////////////////////////////////////////////////////////////////////
/// Internal subprogram.
/// Evaluates (training) distribution.

Double_t TMVA::PDEFoam::Eval(Double_t *xRand, Double_t &event_density)
{
   // Transform variable xRand, since Foam boundaries are [0,1] and
   // fDistr is filled with events which range in [fXmin,fXmax]
   //
   // Transformation:  [0, 1] --> [xmin, xmax]
   std::vector<Double_t> xvec;
   xvec.reserve(GetTotDim());
   for (Int_t idim = 0; idim < GetTotDim(); ++idim)
      xvec.push_back( VarTransformInvers(idim, xRand[idim]) );

   return GetDistr()->Density(xvec, event_density);
}

////////////////////////////////////////////////////////////////////////////////
/// Internal subrogram used by Create.
/// It grow new cells by the binary division process.
/// This function is overridden by the PDEFoam class to stop the foam buildup process
/// if one of the cut conditions stop the cell split.

void TMVA::PDEFoam::Grow()
{
   fTimer->Init(fNCells);

   Long_t iCell;
   PDEFoamCell* newCell;

   while ( (fLastCe+2) < fNCells ) {  // this condition also checked inside Divide
      iCell = PeekMax(); // peek up cell with maximum driver integral

      if ( (iCell<0) || (iCell>fLastCe) ) {
         Log() << kVERBOSE << "Break: "<< fLastCe+1 << " cells created" << Endl;
         // remove remaining empty cells
         for (Long_t jCell=fLastCe+1; jCell<fNCells; jCell++)
            delete fCells[jCell];
         fNCells = fLastCe+1;
         break;
      }
      newCell = fCells[iCell];

      OutputGrow();

      if ( Divide( newCell )==0) break;  // and divide it into two
   }
   OutputGrow( kTRUE );
   CheckAll(1);   // set arg=1 for more info

   Log() << kVERBOSE << GetNActiveCells() << " active cells created" << Endl;
}// Grow

////////////////////////////////////////////////////////////////////////////////
/// This can be called before Create, after setting kDim
/// It defines which variables are excluded in the process of the cell division.
/// For example 'FoamX->SetInhiDiv(1, 1);' inhibits division of y-variable.

void  TMVA::PDEFoam::SetInhiDiv(Int_t iDim, Int_t inhiDiv)
{
   if(fDim==0) Log() << kFATAL << "SetInhiDiv: fDim=0" << Endl;
   if(fInhiDiv == 0) {
      fInhiDiv = new Int_t[ fDim ];
      for(Int_t i=0; i<fDim; i++) fInhiDiv[i]=0;
   }
   //
   if( ( 0<=iDim) && (iDim<fDim)) {
      fInhiDiv[iDim] = inhiDiv;
   } else
      Log() << kFATAL << "Wrong iDim" << Endl;
}//SetInhiDiv

////////////////////////////////////////////////////////////////////////////////
///  User utility, miscellaneous and debug.
///  Checks all pointers in the tree of cells. This is useful autodiagnostic.
///  level=0, no printout, failures causes STOP
///  level=1, printout, failures lead to WARNINGS only

void TMVA::PDEFoam::CheckAll(Int_t level)
{
   Int_t errors, warnings;
   PDEFoamCell *cell;
   Long_t iCell;

   errors = 0; warnings = 0;
   if (level==1) Log() << kVERBOSE <<  "Performing consistency checks for created foam" << Endl;
   for(iCell=1; iCell<=fLastCe; iCell++) {
      cell = fCells[iCell];
      //  checking general rules
      if( ((cell->GetDau0()==0) && (cell->GetDau1()!=0) ) ||
          ((cell->GetDau1()==0) && (cell->GetDau0()!=0) ) ) {
         errors++;
         if (level==1) Log() << kFATAL << "ERROR: Cell's no %d has only one daughter " << iCell << Endl;
      }
      if( (cell->GetDau0()==0) && (cell->GetDau1()==0) && (cell->GetStat()==0) ) {
         errors++;
         if (level==1) Log() << kFATAL << "ERROR: Cell's no %d  has no daughter and is inactive " << iCell << Endl;
      }
      if( (cell->GetDau0()!=0) && (cell->GetDau1()!=0) && (cell->GetStat()==1) ) {
         errors++;
         if (level==1) Log() << kFATAL << "ERROR: Cell's no %d has two daughters and is active " << iCell << Endl;
      }

      // checking parents
      if( (cell->GetPare())!=fCells[0] ) { // not child of the root
         if ( (cell != cell->GetPare()->GetDau0()) && (cell != cell->GetPare()->GetDau1()) ) {
            errors++;
            if (level==1) Log() << kFATAL << "ERROR: Cell's no %d parent not pointing to this cell " << iCell << Endl;
         }
      }

      // checking daughters
      if(cell->GetDau0()!=0) {
         if(cell != (cell->GetDau0())->GetPare()) {
            errors++;
            if (level==1)  Log() << kFATAL << "ERROR: Cell's no %d daughter 0 not pointing to this cell " << iCell << Endl;
         }
      }
      if(cell->GetDau1()!=0) {
         if(cell != (cell->GetDau1())->GetPare()) {
            errors++;
            if (level==1) Log() << kFATAL << "ERROR: Cell's no %d daughter 1 not pointing to this cell " << iCell << Endl;
         }
      }
      if(cell->GetVolume()<1E-50) {
         errors++;
         if(level==1) Log() << kFATAL << "ERROR: Cell no. " << iCell << " has Volume of <1E-50" << Endl;
      }
   }// loop after cells;

   // Check for cells with Volume=0
   for(iCell=0; iCell<=fLastCe; iCell++) {
      cell = fCells[iCell];
      if( (cell->GetStat()==1) && (cell->GetVolume()<1E-11) ) {
         errors++;
         if(level==1) Log() << kFATAL << "ERROR: Cell no. " << iCell << " is active but Volume is 0 " <<  Endl;
      }
   }
   // summary
   if(level==1){
      Log() << kVERBOSE << "Check has found " << errors << " errors and " << warnings << " warnings." << Endl;
   }
   if(errors>0){
      Info("CheckAll","Check - found total %d  errors \n",errors);
   }
} // Check

////////////////////////////////////////////////////////////////////////////////
/// Prints geometry of and elements of 'iCell', as well as relations
/// to parent and daughter cells.

void TMVA::PDEFoam::PrintCell(Long_t iCell)
{
   if (iCell < 0 || iCell > fLastCe) {
      Log() << kWARNING << "<PrintCell(iCell=" << iCell
            << ")>: cell number " << iCell << " out of bounds!"
            << Endl;
      return;
   }

   PDEFoamVect cellPosi(fDim), cellSize(fDim);
   fCells[iCell]->GetHcub(cellPosi,cellSize);
   Int_t    kBest = fCells[iCell]->GetBest();
   Double_t xBest = fCells[iCell]->GetXdiv();

   Log() << "Cell[" << iCell << "]={ ";
   Log() << "  " << fCells[iCell] << "  " << Endl;  // extra DEBUG
   Log() << " Xdiv[abs. coord.]="
         << VarTransformInvers(kBest,cellPosi[kBest] + xBest*cellSize[kBest])
         << Endl;
   Log() << " Abs. coord. = (";
   for (Int_t idim=0; idim<fDim; idim++) {
      Log() << "dim[" << idim << "]={"
            << VarTransformInvers(idim,cellPosi[idim]) << ","
            << VarTransformInvers(idim,cellPosi[idim] + cellSize[idim])
            << "}";
      if (idim < fDim-1)
         Log() << ", ";
   }
   Log() << ")" << Endl;
   fCells[iCell]->Print("1");
   // print the cell elements
   Log() << "Elements: [";
   TVectorD *vec = (TVectorD*)fCells[iCell]->GetElement();
   if (vec != NULL){
      for (Int_t i=0; i<vec->GetNrows(); i++){
         if (i>0) Log() << ", ";
         Log() << GetCellElement(fCells[iCell], i);
      }
   } else
      Log() << "not set";
   Log() << "]" << Endl;
   Log()<<"}"<<Endl;
}

////////////////////////////////////////////////////////////////////////////////
/// Prints geometry of ALL cells of the FOAM

void TMVA::PDEFoam::PrintCells(void)
{
   for(Long_t iCell=0; iCell<=fLastCe; iCell++)
      PrintCell(iCell);
}

////////////////////////////////////////////////////////////////////////////////
/// This function fills a weight 'wt' into the PDEFoam cell, which
/// corresponds to the given event 'ev'.  Per default cell element 0
/// is filled with the weight 'wt', and cell element 1 is filled
/// with the squared weight.  This function can be overridden by a
/// subclass in order to change the values stored in the foam cells.

void TMVA::PDEFoam::FillFoamCells(const Event* ev, Float_t wt)
{
   // find corresponding foam cell
   std::vector<Float_t> values  = ev->GetValues();
   std::vector<Float_t> tvalues = VarTransform(values);
   PDEFoamCell *cell = FindCell(tvalues);

   // 0. Element: Sum of weights 'wt'
   // 1. Element: Sum of weights 'wt' squared
   SetCellElement(cell, 0, GetCellElement(cell, 0) + wt);
   SetCellElement(cell, 1, GetCellElement(cell, 1) + wt*wt);
}

////////////////////////////////////////////////////////////////////////////////
/// Remove the cell elements from all cells.

void TMVA::PDEFoam::ResetCellElements()
{
   if (!fCells) return;

   Log() << kVERBOSE << "Delete cell elements" << Endl;
   for (Long_t iCell = 0; iCell < fNCells; ++iCell) {
      TObject* elements = fCells[iCell]->GetElement();
      if (elements) {
         delete elements;
         fCells[iCell]->SetElement(NULL);
      }
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Returns true, if the value of the given cell is undefined.
/// Default value: kFALSE.  This function can be overridden by
/// sub-classes.

Bool_t TMVA::PDEFoam::CellValueIsUndefined( PDEFoamCell* /* cell */ )
{
   return kFALSE;
}

////////////////////////////////////////////////////////////////////////////////
/// This function finds the cell, which corresponds to the given
/// untransformed event vector 'xvec' and return its value, which is
/// given by the parameter 'cv'.  If kernel != NULL, then
/// PDEFoamKernelBase::Estimate() is called on the transformed event
/// variables.
///
/// Parameters:
///
/// - xvec - event vector (untransformed, [fXmin,fXmax])
///
/// - cv - the cell value to return
///
/// - kernel - PDEFoam kernel estimator.  If NULL is given, than the
///   pure cell value is returned
///
/// Return:
///
/// The cell value, corresponding to 'xvec', estimated by the given
/// kernel.

Float_t TMVA::PDEFoam::GetCellValue(const std::vector<Float_t> &xvec, ECellValue cv, PDEFoamKernelBase *kernel)
{
   std::vector<Float_t> txvec(VarTransform(xvec));
   if (kernel == NULL)
      return GetCellValue(FindCell(txvec), cv);
   else
      return kernel->Estimate(this, txvec, cv);
}

////////////////////////////////////////////////////////////////////////////////
/// This function finds all cells, which corresponds to the given
/// (incomplete) untransformed event vector 'xvec' and returns the
/// cell values, according to the parameter 'cv'.
///
/// Parameters:
///
/// - xvec - map for the untransformed vector.  The key (Int_t) is
///   the dimension, and the value (Float_t) is the event
///   coordinate.  Note that not all coordinates have to be
///   specified.
///
/// - cv - cell values to return
///
/// Return:
///
/// cell values from all cells that were found

std::vector<Float_t> TMVA::PDEFoam::GetCellValue( const std::map<Int_t,Float_t>& xvec, ECellValue cv )
{
   // transformed event
   std::map<Int_t,Float_t> txvec;
   for (std::map<Int_t,Float_t>::const_iterator it=xvec.begin(); it!=xvec.end(); ++it)
      txvec.insert(std::pair<Int_t, Float_t>(it->first, VarTransform(it->first, it->second)));

   // find all cells, which correspond to the transformed event
   std::vector<PDEFoamCell*> cells = FindCells(txvec);

   // get the cell values
   std::vector<Float_t> cell_values;
   cell_values.reserve(cells.size());
   for (std::vector<PDEFoamCell*>::const_iterator cell_it=cells.begin();
        cell_it != cells.end(); ++cell_it)
      cell_values.push_back(GetCellValue(*cell_it, cv));

   return cell_values;
}

////////////////////////////////////////////////////////////////////////////////
/// Find cell that contains 'xvec' (in foam coordinates [0,1]).
///
/// Loop to find cell that contains 'xvec' starting at root cell,
/// and traversing binary tree to find the cell quickly.  Note, that
/// if 'xvec' lies outside the foam, the cell which is nearest to
/// 'xvec' is returned.  (The returned pointer should never be
/// NULL.)
///
/// Parameters:
///
/// - xvec - event vector (in foam coordinates [0,1])
///
/// Return:
///
/// PDEFoam cell corresponding to 'xvec'

TMVA::PDEFoamCell* TMVA::PDEFoam::FindCell( const std::vector<Float_t> &xvec ) const
{
   PDEFoamVect  cellPosi0(GetTotDim()), cellSize0(GetTotDim());
   PDEFoamCell *cell, *cell0;

   cell=fCells[0]; // start with root cell
   Int_t idim=0;
   while (cell->GetStat()!=1) { //go down binary tree until cell is found
      idim=cell->GetBest();  // dimension that changed
      cell0=cell->GetDau0();
      cell0->GetHcub(cellPosi0,cellSize0);

      if (xvec.at(idim)<=cellPosi0[idim]+cellSize0[idim])
         cell=cell0;
      else
         cell=(cell->GetDau1());
   }
   return cell;
}

////////////////////////////////////////////////////////////////////////////////
/// This is a helper function for std::vector<PDEFoamCell*>
/// FindCells(...) and a generalisation of PDEFoamCell* FindCell().
/// It saves in 'cells' all cells, which contain the coordinates
/// specifies in 'txvec'.  Note, that not all coordinates have to be
/// specified in 'txvec'.
///
/// Parameters:
///
/// - txvec - event vector in foam coordinates [0,1].  The key is
///   the dimension and the value is the event coordinate.  Note,
///   that not all coordinates have to be specified.
///
/// - cell - cell to start searching with (usually root cell
///   fCells[0])
///
/// - cells - list of cells that were found

void TMVA::PDEFoam::FindCells(const std::map<Int_t, Float_t> &txvec, PDEFoamCell* cell, std::vector<PDEFoamCell*> &cells) const
{
   PDEFoamVect  cellPosi0(GetTotDim()), cellSize0(GetTotDim());
   PDEFoamCell *cell0;
   Int_t idim=0;

   while (cell->GetStat()!=1) { //go down binary tree until cell is found
      idim=cell->GetBest();  // dimension that changed

      // check if dimension 'idim' is specified in 'txvec'
      map<Int_t, Float_t>::const_iterator it = txvec.find(idim);

      if (it != txvec.end()){
         // case 1: cell is splitten in a dimension which is specified
         // in txvec
         cell0=cell->GetDau0();
         cell0->GetHcub(cellPosi0,cellSize0);
         // check, whether left daughter cell contains txvec
         if (it->second <= cellPosi0[idim] + cellSize0[idim])
            cell=cell0;
         else
            cell=cell->GetDau1();
      } else {
         // case 2: cell is splitten in target dimension
         FindCells(txvec, cell->GetDau0(), cells);
         FindCells(txvec, cell->GetDau1(), cells);
         return;
      }
   }
   cells.push_back(cell);
}

////////////////////////////////////////////////////////////////////////////////
/// Find all cells, that contain txvec.  This function can be used,
/// when the dimension of the foam is greater than the dimension of
/// txvec.  E.g. this is the case for multi-target regression.
///
/// Parameters:
///
/// - txvec - event vector of variables, transformed into foam
///   coordinates [0,1].  The size of txvec can be smaller than the
///   dimension of the foam.
///
/// Return value:
///
/// - vector of cells, that fit txvec

std::vector<TMVA::PDEFoamCell*> TMVA::PDEFoam::FindCells(const std::vector<Float_t> &txvec) const
{
   // copy the coordinates from 'txvec' into a map
   std::map<Int_t, Float_t> txvec_map;
   for (UInt_t i=0; i<txvec.size(); ++i)
      txvec_map.insert(std::pair<Int_t, Float_t>(i, txvec.at(i)));

   // the cells found
   std::vector<PDEFoamCell*> cells(0);

   // loop over all target dimensions
   FindCells(txvec_map, fCells[0], cells);

   return cells;
}

////////////////////////////////////////////////////////////////////////////////
/// Find all cells, that contain the coordinates specified in txvec.
/// The key in 'txvec' is the dimension, and the corresponding value
/// is the coordinate.  Note, that not all coordinates have to be
/// specified in txvec.
///
/// Parameters:
///
/// - txvec - map of coordinates (transformed into foam coordinates
///   [0,1])
///
/// Return value:
///
/// - vector of cells, that fit txvec

std::vector<TMVA::PDEFoamCell*> TMVA::PDEFoam::FindCells(const std::map<Int_t, Float_t> &txvec) const
{
   // the cells found
   std::vector<PDEFoamCell*> cells(0);

   // loop over all target dimensions
   FindCells(txvec, fCells[0], cells);

   return cells;
}

////////////////////////////////////////////////////////////////////////////////
/// Draws 1-dimensional foam (= histogram)
///
/// Parameters:
///
/// - cell_value - the cell value to draw
///
/// - nbin - number of bins of result histogram
///
/// - kernel - a PDEFoam kernel.

TH1D* TMVA::PDEFoam::Draw1Dim( ECellValue cell_value, Int_t nbin, PDEFoamKernelBase *kernel )
{
   // avoid plotting of wrong dimensions
   if ( GetTotDim()!=1 )
      Log() << kFATAL << "<Draw1Dim>: function can only be used for 1-dimensional foams!"
            << Endl;

   TString hname("h_1dim");
   TH1D* h1=(TH1D*)gDirectory->Get(hname);
   if (h1) delete h1;
   h1= new TH1D(hname, "1-dimensional Foam", nbin, fXmin[0], fXmax[0]);

   if (!h1) Log() << kFATAL << "ERROR: Can not create histo" << hname << Endl;

   // loop over all bins
   for (Int_t ibinx=1; ibinx<=h1->GetNbinsX(); ++ibinx) {
      // get event vector corresponding to bin
      std::vector<Float_t> txvec;
      txvec.push_back( VarTransform(0, h1->GetBinCenter(ibinx)) );
      Float_t val = 0;
      if (kernel != NULL) {
         // get cell value using the kernel
         val = kernel->Estimate(this, txvec, cell_value);
      } else {
         val = GetCellValue(FindCell(txvec), cell_value);
      }
      // fill value to histogram
      h1->SetBinContent(ibinx, val + h1->GetBinContent(ibinx));
   }

   return h1;
}

////////////////////////////////////////////////////////////////////////////////
/// Project foam variable idim1 and variable idim2 to histogram.
///
/// Parameters:
///
/// - idim1, idim2 - dimensions to project to
///
/// - cell_value - the cell value to draw
///
/// - kernel - a PDEFoam kernel (optional).  If NULL is given, the
///            kernel is ignored and the pure cell values are
///            plotted.
///
/// - nbin - number of bins in x and y direction of result histogram
///          (optional, default is 50).
///
/// Returns:
/// a 2-dimensional histogram

TH2D* TMVA::PDEFoam::Project2( Int_t idim1, Int_t idim2, ECellValue cell_value, PDEFoamKernelBase *kernel, UInt_t nbin )
{
   // avoid plotting of wrong dimensions
   if ((idim1>=GetTotDim()) || (idim1<0) ||
       (idim2>=GetTotDim()) || (idim2<0) ||
       (idim1==idim2) )
      Log() << kFATAL << "<Project2>: wrong dimensions given: "
            << idim1 << ", " << idim2 << Endl;

   // root can not handle too many bins in one histogram --> catch this
   // Furthermore, to have more than 1000 bins in the histogram doesn't make
   // sense.
   if (nbin>1000){
      Log() << kWARNING << "Warning: number of bins too big: " << nbin
            << " Using 1000 bins for each dimension instead." << Endl;
      nbin = 1000;
   } else if (nbin<1) {
      Log() << kWARNING << "Wrong bin number: " << nbin
            << "; set nbin=50" << Endl;
      nbin = 50;
   }

   // create result histogram
   TString hname(Form("h_%d_vs_%d",idim1,idim2));

   // if histogram with this name already exists, delete it
   TH2D* h1=(TH2D*)gDirectory->Get(hname.Data());
   if (h1) delete h1;
   h1= new TH2D(hname.Data(), Form("var%d vs var%d",idim1,idim2), nbin, fXmin[idim1], fXmax[idim1], nbin, fXmin[idim2], fXmax[idim2]);

   if (!h1) Log() << kFATAL << "ERROR: Can not create histo" << hname << Endl;

   // ============== start projection algorithm ================
   // loop over all histogram bins (2-dim)
   for (Int_t xbin = 1; xbin <= h1->GetNbinsX(); ++xbin) {
      for (Int_t ybin = 1; ybin <= h1->GetNbinsY(); ++ybin) {
         // calculate the phase space point, which corresponds to this
         // bin combination
         std::map<Int_t, Float_t> txvec;
         txvec[idim1] = VarTransform(idim1, h1->GetXaxis()->GetBinCenter(xbin));
         txvec[idim2] = VarTransform(idim2, h1->GetYaxis()->GetBinCenter(ybin));

         // find the cells, which corresponds to this phase space
         // point
         std::vector<TMVA::PDEFoamCell*> cells = FindCells(txvec);

         // loop over cells and fill the histogram with the cell
         // values
         Float_t sum_cv = 0; // sum of the cell values
         for (std::vector<TMVA::PDEFoamCell*>::const_iterator it = cells.begin();
              it != cells.end(); ++it) {
            // get cell position and size
            PDEFoamVect cellPosi(GetTotDim()), cellSize(GetTotDim());
            (*it)->GetHcub(cellPosi,cellSize);
            // Create complete event vector from txvec.  The missing
            // coordinates of txvec are set to the cell center.
            std::vector<Float_t> tvec;
            for (Int_t i=0; i<GetTotDim(); ++i) {
               if ( i != idim1 && i != idim2 )
                  tvec.push_back(cellPosi[i] + 0.5*cellSize[i]);
               else
                  tvec.push_back(txvec[i]);
            }
            if (kernel != NULL) {
               // get the cell value using the kernel
               sum_cv += kernel->Estimate(this, tvec, cell_value);
            } else {
               sum_cv += GetCellValue(FindCell(tvec), cell_value);
            }
         }

         // fill the bin content
         h1->SetBinContent(xbin, ybin, sum_cv + h1->GetBinContent(xbin, ybin));
      }
   }

   return h1;
}

////////////////////////////////////////////////////////////////////////////////
/// Returns the cell value of 'cell' corresponding to the given
/// option 'cv'.  This function should be overridden by the subclass
/// in order to specify which cell elements to return for a given
/// cell value 'cv'.  By default kValue returns cell element 0, and
/// kValueError returns cell element 1.

Float_t TMVA::PDEFoam::GetCellValue(const PDEFoamCell* cell, ECellValue cv)
{
   // calculate cell value (depending on the given option 'cv')
   switch (cv) {

   case kValue:
      return GetCellElement(cell, 0);

   case kValueError:
      return GetCellElement(cell, 1);

   case kValueDensity: {

      Double_t volume  = cell->GetVolume();
      if (volume > numeric_limits<double>::epsilon()) {
         return GetCellValue(cell, kValue)/volume;
      } else {
         if (volume<=0){
            cell->Print("1"); // debug output
            Log() << kWARNING << "<GetCellDensity(cell)>: ERROR: cell volume"
                  << " negative or zero!"
                  << " ==> return cell density 0!"
                  << " cell volume=" << volume
                  << " cell entries=" << GetCellValue(cell, kValue) << Endl;
         } else {
            Log() << kWARNING << "<GetCellDensity(cell)>: WARNING: cell volume"
                  << " close to zero!"
                  << " cell volume: " << volume << Endl;
         }
      }
   }
      return 0;

   case kMeanValue:
      return cell->GetIntg();

   case kRms:
      return cell->GetDriv();

   case kRmsOvMean:
      if (cell->GetIntg() != 0)
         return cell->GetDriv()/cell->GetIntg();
      else
         return 0;

   case kCellVolume:
      return cell->GetVolume();

   default:
      Log() << kFATAL << "<GetCellValue>: unknown cell value" << Endl;
      return 0;
   }

   return 0;
}

////////////////////////////////////////////////////////////////////////////////
/// Returns cell element i of cell 'cell'.  If the cell has no
/// elements or the index 'i' is out of range, than 0 is returned.

Double_t TMVA::PDEFoam::GetCellElement( const PDEFoamCell *cell, UInt_t i ) const
{
   // dynamic_cast doesn't seem to work here ?!
   TVectorD *vec = (TVectorD*)cell->GetElement();

   // if vec is not set or index out of range, return 0
   if (!vec || i >= (UInt_t) vec->GetNrows())
      return 0;

   return (*vec)(i);
}

////////////////////////////////////////////////////////////////////////////////
/// Set cell element i of cell to value.  If the cell element i does
/// not exist, it is created.

void TMVA::PDEFoam::SetCellElement( PDEFoamCell *cell, UInt_t i, Double_t value )
{
   TVectorD *vec = NULL;

   // if no cell elements are set, create TVectorD with i+1 entries,
   // ranging from [0,i]
   if (cell->GetElement() == NULL) {
      vec = new TVectorD(i+1);
      vec->Zero();       // set all values to zero
      (*vec)(i) = value; // set element i to value
      cell->SetElement(vec);
   } else {
      // dynamic_cast doesn't seem to work here ?!
      vec = (TVectorD*)cell->GetElement();
      if (!vec)
         Log() << kFATAL << "<SetCellElement> ERROR: cell element is not a TVectorD*" << Endl;
      // check vector size and resize if necessary
      if (i >= (UInt_t) vec->GetNrows())
         vec->ResizeTo(0,i);
      // set element i to value
      (*vec)(i) = value;
   }
}

////////////////////////////////////////////////////////////////////////////////
/// Overridden function of PDEFoam to avoid native foam output.
/// Draw TMVA-process bar instead.

void TMVA::PDEFoam::OutputGrow( Bool_t finished )
{
   if (finished) {
      Log() << kINFO << "Elapsed time: " + fTimer->GetElapsedTime()
            << "                                 " << Endl;
      return;
   }

   Int_t modulo = 1;

   if (fNCells        >= 100) modulo = Int_t(fNCells/100);
   if (fLastCe%modulo == 0)   fTimer->DrawProgressBar( fLastCe );
}

////////////////////////////////////////////////////////////////////////////////
/// Debugging tool which plots the cells of a 2-dimensional PDEFoam
/// as rectangles in C++ format readable for ROOT.
///
/// Parameters:
/// - filename - filename of ouput root macro
///
/// - opt - cell_value, rms, rms_ov_mean
///   If cell_value is set, the following values will be filled into
///   the result histogram:
///    - number of events - in case of classification with 2 separate
///                         foams or multi-target regression
///    - discriminator    - in case of classification with one
///                         unified foam
///    - target           - in case of mono-target regression
///   If none of {cell_value, rms, rms_ov_mean} is given, the cells
///   will not be filled.
///   If 'opt' contains the string 'cellnumber', the index of
///   each cell is draw in addition.
///
/// - createCanvas - whether to create a new canvas or not
///
/// - colors - whether to fill cells with colors or shades of grey
///
/// Example:
///
///   The following commands load a mono-target regression foam from
///   file 'foam.root' and create a ROOT macro 'output.C', which
///   draws all PDEFoam cells with little boxes.  The latter are
///   filled with colors according to the target value stored in the
///   cell.  Also the cell number is drawn.
///
///   TFile file("foam.root");
///   TMVA::PDEFoam *foam = (TMVA::PDEFoam*) gDirectory->Get("MonoTargetRegressionFoam");
///   foam->RootPlot2dim("output.C","cell_value,cellnumber");
///   gROOT->Macro("output.C");

void TMVA::PDEFoam::RootPlot2dim( const TString& filename, TString opt,
                                  Bool_t createCanvas, Bool_t colors )
{
   if (GetTotDim() != 2)
      Log() << kFATAL << "RootPlot2dim() can only be used with "
            << "two-dimensional foams!" << Endl;

   // select value to plot
   ECellValue cell_value = kValue;
   Bool_t plotcellnumber = kFALSE;
   Bool_t fillcells      = kTRUE;
   if (opt.Contains("cell_value")){
      cell_value = kValue;
   } else if (opt.Contains("rms_ov_mean")){
      cell_value = kRmsOvMean;
   } else if (opt.Contains("rms")){
      cell_value = kRms;
   } else {
      fillcells = kFALSE;
   }
   if (opt.Contains("cellnumber"))
      plotcellnumber = kTRUE;

   // open file (root macro)
   std::ofstream outfile(filename, std::ios::out);

   outfile<<"{" << std::endl;

   // declare boxes and set the fill styles
   if (!colors) { // define grayscale colors from light to dark,
      // starting from color index 1000
      outfile << "TColor *graycolors[100];" << std::endl;
      outfile << "for (Int_t i=0.; i<100; i++)" << std::endl;
      outfile << "  graycolors[i]=new TColor(1000+i, 1-(Float_t)i/100.,1-(Float_t)i/100.,1-(Float_t)i/100.);"<< std::endl;
   }
   if (createCanvas)
      outfile << "cMap = new TCanvas(\"" << fName << "\",\"Cell Map for "
              << fName << "\",600,600);" << std::endl;

   outfile<<"TBox*a=new TBox();"<<std::endl;
   outfile<<"a->SetFillStyle(0);"<<std::endl;  // big frame
   outfile<<"a->SetLineWidth(4);"<<std::endl;
   outfile<<"TBox *b1=new TBox();"<<std::endl;  // single cell
   outfile<<"TText*t=new TText();"<<std::endl;  // text for numbering
   if (fillcells) {
      outfile << (colors ? "gStyle->SetPalette(1, 0);" : "gStyle->SetPalette(0);")
              << std::endl;
      outfile <<"b1->SetFillStyle(1001);"<<std::endl;
      outfile<<"TBox *b2=new TBox();"<<std::endl;  // single cell
      outfile <<"b2->SetFillStyle(0);"<<std::endl;
   }
   else {
      outfile <<"b1->SetFillStyle(0);"<<std::endl;
   }

   if (fillcells)
      (colors ? gStyle->SetPalette(1, 0) : gStyle->SetPalette(0) );

   Float_t zmin = 1E8;  // minimal value (for color calculation)
   Float_t zmax = -1E8; // maximal value (for color calculation)

   // if cells shall be filled, calculate minimal and maximal plot
   // value --> store in zmin and zmax
   if (fillcells) {
      for (Long_t iCell=1; iCell<=fLastCe; iCell++) {
         if ( fCells[iCell]->GetStat() == 1) {
            Float_t value = GetCellValue(fCells[iCell], cell_value);
            if (value<zmin)
               zmin=value;
            if (value>zmax)
               zmax=value;
         }
      }
      outfile << "// observed minimum and maximum of distribution: " << std::endl;
      outfile << "// Float_t zmin = "<< zmin << ";" << std::endl;
      outfile << "// Float_t zmax = "<< zmax << ";" << std::endl;
   }

   outfile << "// used minimum and maximum of distribution (taking into account log scale if applicable): " << std::endl;
   outfile << "Float_t zmin = "<< zmin << ";" << std::endl;
   outfile << "Float_t zmax = "<< zmax << ";" << std::endl;

   Float_t x1,y1,x2,y2,x,y; // box and text coordintates
   Float_t offs  = 0.01;
   Float_t lpag  = 1-2*offs;
   Int_t ncolors  = colors ? gStyle->GetNumberOfColors() : 100;
   Float_t scale = (ncolors-1)/(zmax - zmin);
   PDEFoamVect cellPosi(GetTotDim()), cellSize(GetTotDim());

   // loop over cells and draw a box for every cell (and maybe the
   // cell number as well)
   outfile << "// =========== Rectangular cells  ==========="<< std::endl;
   for (Long_t iCell=1; iCell<=fLastCe; iCell++) {
      if ( fCells[iCell]->GetStat() == 1) {
         fCells[iCell]->GetHcub(cellPosi,cellSize);
         x1 = offs+lpag*(cellPosi[0]);
         y1 = offs+lpag*(cellPosi[1]);
         x2 = offs+lpag*(cellPosi[0]+cellSize[0]);
         y2 = offs+lpag*(cellPosi[1]+cellSize[1]);

         if (fillcells) {
            // get cell value
            Float_t value = GetCellValue(fCells[iCell], cell_value);

            // calculate fill color
            Int_t color;
            if (colors)
               color = gStyle->GetColorPalette(Int_t((value-zmin)*scale));
            else
               color = 1000+(Int_t((value-zmin)*scale));

            // set fill color of box b1
            outfile << "b1->SetFillColor(" << color << ");" << std::endl;
         }

         //     cell rectangle
         outfile<<"b1->DrawBox("<<x1<<","<<y1<<","<<x2<<","<<y2<<");"<<std::endl;
         if (fillcells)
            outfile<<"b2->DrawBox("<<x1<<","<<y1<<","<<x2<<","<<y2<<");"<<std::endl;

         //     cell number
         if (plotcellnumber) {
            outfile<<"t->SetTextColor(4);"<<std::endl;
            if(fLastCe<51)
               outfile<<"t->SetTextSize(0.025);"<<std::endl;  // text for numbering
            else if(fLastCe<251)
               outfile<<"t->SetTextSize(0.015);"<<std::endl;
            else
               outfile<<"t->SetTextSize(0.008);"<<std::endl;
            x = offs+lpag*(cellPosi[0]+0.5*cellSize[0]);
            y = offs+lpag*(cellPosi[1]+0.5*cellSize[1]);
            outfile<<"t->DrawText("<<x<<","<<y<<","<<"\""<<iCell<<"\""<<");"<<std::endl;
         }
      }
   }
   outfile<<"// ============== End Rectangles ==========="<< std::endl;

   outfile << "}" << std::endl;
   outfile.flush();
   outfile.close();
}

////////////////////////////////////////////////////////////////////////////////
/// Insert event to internal foam's density estimator
/// PDEFoamDensityBase.

void TMVA::PDEFoam::FillBinarySearchTree( const Event* ev )
{
   GetDistr()->FillBinarySearchTree(ev);
}

////////////////////////////////////////////////////////////////////////////////
/// Delete the foam's density estimator, which contains the binary
/// search tree.

void TMVA::PDEFoam::DeleteBinarySearchTree()
{
   if(fDistr) delete fDistr;
   fDistr = NULL;
}