HFitInterface.cxx

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// @(#)root/hist:$Id$
// Author: L. Moneta Thu Aug 31 10:40:20 2006

/**********************************************************************
 *                                                                    *
 * Copyright (c) 2006  LCG ROOT Math Team, CERN/PH-SFT                *
 *                                                                    *
 *                                                                    *
 **********************************************************************/

// Implementation file for class TH1Interface

#include "HFitInterface.h"

#include "Fit/BinData.h"
#include "Fit/SparseData.h"
#include "Fit/FitResult.h"
#include "Math/IParamFunction.h"

#include <vector>

#include <cassert>
#include <cmath>

#include "TH1.h"
#include "THnBase.h"
#include "TF1.h"
#include "TGraph2D.h"
#include "TGraph.h"
#include "TGraphErrors.h"
// #include "TGraphErrors.h"
// #include "TGraphBentErrors.h"
// #include "TGraphAsymmErrors.h"
#include "TMultiGraph.h"
#include "TList.h"
#include "TError.h"


//#define DEBUG
#ifdef DEBUG
#include "TClass.h"
#include <iostream>
#endif


namespace ROOT {

namespace Fit {

// add a namespace to distinguish from the Graph functions
namespace HFitInterface {


bool IsPointOutOfRange(const TF1 * func, const double * x) {
   // function to check if a point is outside range
   if (func ==0) return false;
   return !func->IsInside(x);
}

bool AdjustError(const DataOptions & option, double & error, double value = 1) {
   // adjust the given error according to the option
   // return false when point must be skipped.
   // When point error = 0, the point is kept if the option UseEmpty is set or if
   // fErrors1 is set and the point value is not zero.
   // The value should be used only for points representing counts (histograms), not for the graph.
   // In the graph points with zero errors are by default skipped indepentently of the value.
   // If one wants to keep the points, the option fUseEmpty must be set

   if (error <= 0) {
      if (option.fUseEmpty || (option.fErrors1 && std::abs(value) > 0 ) )
         error = 1.; // set error to 1
      else
         return false;   // skip  bins with zero errors or empty
   } else if (option.fErrors1)
      error = 1;   // set all error to 1 for non-empty bins
   return true;
}

void ExamineRange(const TAxis * axis, std::pair<double,double> range,int &hxfirst,int &hxlast) {
   // examine the range given with the pair on the given histogram axis
   // correct in case the bin values hxfirst hxlast
   double xlow   = range.first;
   double xhigh  = range.second;
#ifdef DEBUG
   std::cout << "xlow " << xlow << " xhigh = " << xhigh << std::endl;
#endif
   // ignore ranges specified outside histogram range
   int ilow = axis->FindFixBin(xlow);
   int ihigh = axis->FindFixBin(xhigh);
   if (ilow > hxlast || ihigh < hxfirst) { 
      Warning("ROOT::Fit::FillData","fit range is outside histogram range, no fit data for %s",axis->GetName()); 
   }
   // consider only range defined with-in histogram not oustide. Always exclude underflow/overflow
   hxfirst =  std::min( std::max( ilow, hxfirst), hxlast+1) ;
   hxlast  =  std::max( std::min( ihigh, hxlast), hxfirst-1) ;
   // exclude bins where range coverage is less than half bin width
   if (hxfirst < hxlast) {
      if ( axis->GetBinCenter(hxfirst) < xlow)  hxfirst++;
      if ( axis->GetBinCenter(hxlast)  > xhigh) hxlast--;
   }
}


} // end namespace HFitInterface


void FillData(BinData & dv, const TH1 * hfit, TF1 * func)
{
   // Function to fill the binned Fit data structure from a TH1
   // The dimension of the data is the same of the histogram dimension
   // The function pointer is need in case of integral is used and to reject points
   // rejected in the function

   // the TF1 pointer cannot be constant since EvalPar and InitArgs are not const methods

   // get fit option
   const DataOptions & fitOpt = dv.Opt();


   // store instead of bin center the bin edges
   bool useBinEdges = fitOpt.fIntegral || fitOpt.fBinVolume;

   assert(hfit != 0);

   //std::cout << "creating Fit Data from histogram " << hfit->GetName() << std::endl;

   int hxfirst = hfit->GetXaxis()->GetFirst();
   int hxlast  = hfit->GetXaxis()->GetLast();

   int hyfirst = hfit->GetYaxis()->GetFirst();
   int hylast  = hfit->GetYaxis()->GetLast();

   int hzfirst = hfit->GetZaxis()->GetFirst();
   int hzlast  = hfit->GetZaxis()->GetLast();

   // function by default has same range (use that one if requested otherwise use data one)


   //  get the range (add the function range ??)
   // to check if inclusion/exclusion at end/point
   const DataRange & range = dv.Range();
   if (range.Size(0) != 0) {
      HFitInterface::ExamineRange( hfit->GetXaxis(), range(0), hxfirst, hxlast);
      if (range.Size(0) > 1  ) {
         Warning("ROOT::Fit::FillData","support only one range interval for X coordinate");
      }
   }

   if (hfit->GetDimension() > 1 && range.Size(1) != 0) {
      HFitInterface::ExamineRange( hfit->GetYaxis(), range(1), hyfirst, hylast);
      if (range.Size(1) > 1  )
         Warning("ROOT::Fit::FillData","support only one range interval for Y coordinate");
   }

   if (hfit->GetDimension() > 2 && range.Size(2) != 0) {
      HFitInterface::ExamineRange( hfit->GetZaxis(), range(2), hzfirst, hzlast);
      if (range.Size(2) > 1  )
         Warning("ROOT::Fit::FillData","support only one range interval for Z coordinate");
   }


   int n = (hxlast-hxfirst+1)*(hylast-hyfirst+1)*(hzlast-hzfirst+1);

#ifdef DEBUG
   std::cout << "THFitInterface: ifirst = " << hxfirst << " ilast =  " << hxlast
             << " total bins  " << n
             << std::endl;
#endif

   // reserve n for more efficient usage
   //dv.Data().reserve(n);

   int hdim =  hfit->GetDimension();
   int ndim = hdim;
   // case of function dimension less than histogram
   if (func !=0 && func->GetNdim() == hdim-1) ndim = hdim-1;
  
   assert( ndim > 0 );
   //typedef  BinPoint::CoordData CoordData;
   //CoordData x = CoordData( hfit->GetDimension() );
   dv.Initialize(n,ndim);

   double x[3];
   double s[3];

   int binx = 0;
   int biny = 0;
   int binz = 0;

   const TAxis *xaxis  = hfit->GetXaxis();
   const TAxis *yaxis  = hfit->GetYaxis();
   const TAxis *zaxis  = hfit->GetZaxis();

   for ( binx = hxfirst; binx <= hxlast; ++binx) {
      if (useBinEdges) {
         x[0] = xaxis->GetBinLowEdge(binx);
         s[0] = xaxis->GetBinUpEdge(binx);
      }
      else
         x[0] = xaxis->GetBinCenter(binx);


      for ( biny = hyfirst; biny <= hylast; ++biny) {
         if (useBinEdges) {
            x[1] = yaxis->GetBinLowEdge(biny);
            s[1] = yaxis->GetBinUpEdge(biny);
         }
         else
            x[1] = yaxis->GetBinCenter(biny);

         for ( binz = hzfirst; binz <= hzlast; ++binz) {
            if (useBinEdges) {
               x[2] = zaxis->GetBinLowEdge(binz);
               s[2] = zaxis->GetBinUpEdge(binz);
            }
            else
               x[2] = zaxis->GetBinCenter(binz);

            // need to evaluate function to know about rejected points
            // hugly but no other solutions
            if (func != 0) {
               TF1::RejectPoint(false);
               (*func)( &x[0] );  // evaluate using stored function parameters
               if (TF1::RejectedPoint() ) continue;
            }


            double value =  hfit->GetBinContent(binx, biny, binz);
            double error =  hfit->GetBinError(binx, biny, binz);
            if (!HFitInterface::AdjustError(fitOpt,error,value) ) continue;

            if (ndim == hdim -1) {
               // case of fitting a function with  dimension -1
               // point error is bin width y / sqrt(N) where N is nuber of entries in the bin
               // normalization of error will be wrong - but they will be rescaled in the fit
               if (hdim == 2)  dv.Add(  x,  x[1],  yaxis->GetBinWidth(biny) / error  );
               if (hdim == 3)  dv.Add(  x,  x[2],  zaxis->GetBinWidth(binz) / error  );
            } else {
               dv.Add(   x,  value, error  );
               if (useBinEdges) {
                  dv.AddBinUpEdge( s );
               }
            }


#ifdef DEBUG
            std::cout << "bin " << binx << " add point " << x[0] << "  " << hfit->GetBinContent(binx) << std::endl;
#endif

         }  // end loop on z bins
      }  // end loop on y bins
   }   // end loop on x axis


#ifdef DEBUG
   std::cout << "THFitInterface::FillData: Hist FitData size is " << dv.Size() << std::endl;
#endif

}

////////////////////////////////////////////////////////////////////////////////
///   -*-*-*-*Compute rough values of parameters for an  exponential
///           ===================================================

void InitExpo(const ROOT::Fit::BinData & data, TF1 * f1)
{
   unsigned int n = data.Size();
   if (n == 0) return;

   // find xmin and xmax of the data
   double valxmin;
   double xmin = *(data.GetPoint(0,valxmin));
   double xmax = xmin;
   double valxmax = valxmin;

   for (unsigned int i = 1; i < n; ++ i) {
      double val;
      double x = *(data.GetPoint(i,val) );
      if (x < xmin) {
         xmin = x;
         valxmin = val;
      }
      else if (x > xmax) {
         xmax = x;
         valxmax = val;
      }
   }

   // avoid negative values of valxmin/valxmax
   if (valxmin <= 0 && valxmax > 0 ) valxmin = valxmax;
   else if (valxmax <=0 && valxmin > 0) valxmax = valxmin;
   else if (valxmin <=0 && valxmax <= 0) { valxmin = 1; valxmax = 1; }

   double slope = std::log( valxmax/valxmin) / (xmax - xmin);
   double constant = std::log(valxmin) - slope * xmin;
   f1->SetParameters(constant, slope);
}


////////////////////////////////////////////////////////////////////////////////
///   -*-*-*-*Compute Initial values of parameters for a gaussian
///           derivaed from function H1InitGaus defined in TH1.cxx
///           ===================================================

void InitGaus(const ROOT::Fit::BinData & data, TF1 * f1)
{

   static const double sqrtpi = 2.506628;

   //   - Compute mean value and RMS of the data
   unsigned int n = data.Size();
   if (n == 0) return;
   double sumx = 0;
   double sumx2 = 0;
   double allcha = 0;
   double valmax = 0;
   double rangex = data.Coords(n-1)[0] - data.Coords(0)[0];
   // to avoid binwidth = 0 set arbitrarly to 1
   double binwidth = 1;
   if ( rangex > 0) binwidth = rangex;
   double x0 = 0;
   for (unsigned int i = 0; i < n; ++ i) {
      double val;
      double x = *(data.GetPoint(i,val) );
      sumx  += val*x;
      sumx2 += val*x*x;
      allcha += val;
      if (val > valmax) valmax = val;
      if (i > 0) {
         double dx = x - x0;
         if (dx < binwidth) binwidth = dx;
      }
      x0 = x;
   }

   if (allcha <= 0) return;
   double mean = sumx/allcha;
   double rms  = sumx2/allcha - mean*mean;


   if (rms > 0)
      rms  = std::sqrt(rms);
   else
      rms  = binwidth*n/4;


    //if the distribution is really gaussian, the best approximation
   //is binwidx*allcha/(sqrtpi*rms)
   //However, in case of non-gaussian tails, this underestimates
   //the normalisation constant. In this case the maximum value
   //is a better approximation.
   //We take the average of both quantities

//   printf("valmax %f other %f bw %f allcha %f rms %f  \n",valmax, binwidth*allcha/(sqrtpi*rms),
//          binwidth, allcha,rms  );

   double constant = 0.5*(valmax+ binwidth*allcha/(sqrtpi*rms));


   //In case the mean value is outside the histo limits and
   //the RMS is bigger than the range, we take
   //  mean = center of bins
   //  rms  = half range
//    Double_t xmin = curHist->GetXaxis()->GetXmin();
//    Double_t xmax = curHist->GetXaxis()->GetXmax();
//    if ((mean < xmin || mean > xmax) && rms > (xmax-xmin)) {
//       mean = 0.5*(xmax+xmin);
//       rms  = 0.5*(xmax-xmin);
//    }

   f1->SetParameter(0,constant);
   f1->SetParameter(1,mean);
   f1->SetParameter(2,rms);
   f1->SetParLimits(2,0,10*rms);


#ifdef DEBUG
   std::cout << "Gaussian initial par values" << constant << "   " << mean << "  " << rms << std::endl;
#endif

}

////////////////////////////////////////////////////////////////////////////////
///   -*-*-*-*Compute Initial values of parameters for a gaussian
///           derivaed from function H1InitGaus defined in TH1.cxx
///           ===================================================

void Init2DGaus(const ROOT::Fit::BinData & data, TF1 * f1)
{

   static const double sqrtpi = 2.506628;

   //   - Compute mean value and RMS of the data
   unsigned int n = data.Size();
   if (n == 0) return;
   double sumx = 0, sumy = 0;
   double sumx2 = 0, sumy2 = 0;
   double allcha = 0;
   double valmax = 0;
   double rangex = data.Coords(n-1)[0] - data.Coords(0)[0];
   double rangey = data.Coords(n-1)[1] - data.Coords(0)[1];
   // to avoid binwidthx = 0 set arbitrarly to 1
   double binwidthx = 1, binwidthy = 1;
   if ( rangex > 0) binwidthx = rangex;
   if ( rangey > 0) binwidthy = rangey;
   double x0 = 0, y0 = 0;
   for (unsigned int i = 0; i < n; ++i) {
      double val;
      const double *coords = data.GetPoint(i,val);
      double x = coords[0], y = coords[1];
      sumx  += val*x;
      sumy  += val*y;
      sumx2 += val*x*x;
      sumy2 += val*y*y;
      allcha += val;
      if (val > valmax) valmax = val;
      if (i > 0) {
         double dx = x - x0;
         if (dx < binwidthx) binwidthx = dx;
         double dy = y - y0;
         if (dy < binwidthy) binwidthy = dy;
      }
      x0 = x;
      y0 = y;
   }

   if (allcha <= 0) return;
   double meanx = sumx/allcha, meany = sumy/allcha;
   double rmsx  = sumx2/allcha - meanx*meanx;
   double rmsy  = sumy2/allcha - meany*meany;


   if (rmsx > 0)
      rmsx  = std::sqrt(rmsx);
   else
      rmsx  = binwidthx*n/4;

   if (rmsy > 0)
      rmsy  = std::sqrt(rmsy);
   else
      rmsy  = binwidthy*n/4;


    //if the distribution is really gaussian, the best approximation
   //is binwidx*allcha/(sqrtpi*rmsx)
   //However, in case of non-gaussian tails, this underestimates
   //the normalisation constant. In this case the maximum value
   //is a better approximation.
   //We take the average of both quantities

   double constant = 0.5 * (valmax+ binwidthx*allcha/(sqrtpi*rmsx))*
                           (valmax+ binwidthy*allcha/(sqrtpi*rmsy));

   f1->SetParameter(0,constant);
   f1->SetParameter(1,meanx);
   f1->SetParameter(2,rmsx);
   f1->SetParLimits(2,0,10*rmsx);
   f1->SetParameter(3,meany);
   f1->SetParameter(4,rmsy);
   f1->SetParLimits(4,0,10*rmsy);

#ifdef DEBUG
   std::cout << "2D Gaussian initial par values"
             << constant << "   "
             << meanx    << "   "
             << rmsx
             << meany    << "   "
             << rmsy
             << std::endl;
#endif

}

// filling fit data from TGraph objects

BinData::ErrorType GetDataType(const TGraph * gr, DataOptions & fitOpt) {
   // get type of data for TGraph objects
   double *ex = gr->GetEX();
   double *ey = gr->GetEY();
   double * eyl = gr->GetEYlow();
   double * eyh = gr->GetEYhigh();


   // default case for graphs (when they have errors)
   BinData::ErrorType type = BinData::kValueError;
   // if all errors are zero set option of using errors to 1
   if (fitOpt.fErrors1 || ( ey == 0 && ( eyl == 0 || eyh == 0 ) ) ) {
      type =  BinData::kNoError;
   }
   // need to treat case when all errors are zero
   // note that by default fitOpt.fCoordError is true
   else if ( ex != 0 && fitOpt.fCoordErrors)  {
      // check that all errors are not zero
      int i = 0;
      while (i < gr->GetN() && type != BinData::kCoordError) {
         if (ex[i] > 0) type = BinData::kCoordError;
         ++i;
      }
   }
   // case of asymmetric errors (by default fAsymErrors is true)
   else if ( ( eyl != 0 && eyh != 0)  && fitOpt.fAsymErrors)  {
      // check also if that all errors are non zero's
      int i = 0;
      bool zeroErrorX = true;
      bool zeroErrorY = true;
      while (i < gr->GetN() && (zeroErrorX || zeroErrorY)) {
         double e2X = ( gr->GetErrorXlow(i) + gr->GetErrorXhigh(i) );
         double e2Y = eyl[i] + eyh[i];
         zeroErrorX &= (e2X <= 0);
         zeroErrorY &= (e2Y <= 0);
         ++i;
      }
      if (zeroErrorX && zeroErrorY)
         type = BinData::kNoError;
      else if (!zeroErrorX && zeroErrorY)
         type = BinData::kCoordError;
      else if (zeroErrorX && !zeroErrorY) {
         type = BinData::kAsymError;
         fitOpt.fCoordErrors = false;
      }
      else {
         type = BinData::kAsymError;
      }
   }

   // need to look also a case when all errors in y are zero
   if ( ey != 0 && type != BinData::kCoordError )  {
      int i = 0;
      bool zeroError = true;
      while (i < gr->GetN() && zeroError) {
         if (ey[i] > 0) zeroError = false;;
         ++i;
      }
      if (zeroError) type = BinData::kNoError;
   }


#ifdef DEBUG
   std::cout << "type is " << type << " graph type is " << gr->IsA()->GetName() << std::endl;
#endif

   return type;
}

BinData::ErrorType GetDataType(const TGraph2D * gr, const DataOptions & fitOpt) {
   // get type of data for TGraph2D object
   double *ex = gr->GetEX();
   double *ey = gr->GetEY();
   double *ez = gr->GetEZ();

   // default case for graphs (when they have errors)
   BinData::ErrorType type = BinData::kValueError;
   // if all errors are zero set option of using errors to 1
   if (fitOpt.fErrors1 || ez == 0 ) {
      type =  BinData::kNoError;
   }
   else if ( ex != 0 && ey!=0 && fitOpt.fCoordErrors)  {
      // check that all errors are not zero
      int i = 0;
      while (i < gr->GetN() && type != BinData::kCoordError) {
         if (ex[i] > 0 || ey[i] > 0) type = BinData::kCoordError;
         ++i;
      }
   }


#ifdef DEBUG
   std::cout << "type is " << type << " graph2D type is " << gr->IsA()->GetName() << std::endl;
#endif

   return type;
}



void DoFillData ( BinData  & dv,  const TGraph * gr,  BinData::ErrorType type, TF1 * func ) {
   // internal method to do the actual filling of the data
   // given a graph and a multigraph

   // get fit option
   DataOptions & fitOpt = dv.Opt();

   int  nPoints = gr->GetN();
   double *gx = gr->GetX();
   double *gy = gr->GetY();

   const DataRange & range = dv.Range();
   bool useRange = ( range.Size(0) > 0);
   double xmin = 0;
   double xmax = 0;
   range.GetRange(xmin,xmax);

   dv.Initialize(nPoints,1, type);

#ifdef DEBUG
   std::cout << "DoFillData: graph npoints = " << nPoints << " type " << type << std::endl;
   if (func) {
      double a1,a2; func->GetRange(a1,a2); std::cout << "func range " << a1 << "  " << a2 << std::endl;
   }
#endif

   double x[1];
   for ( int i = 0; i < nPoints; ++i) {

      x[0] = gx[i];


      if (useRange && (  x[0] < xmin || x[0] > xmax) ) continue;

      // need to evaluate function to know about rejected points
      // hugly but no other solutions
      if (func) {
         TF1::RejectPoint(false);
         (*func)( x ); // evaluate using stored function parameters
         if (TF1::RejectedPoint() ) continue;
      }


      if (fitOpt.fErrors1)
         dv.Add( gx[i], gy[i] );

      // for the errors use the getters by index to avoid cases when the arrays are zero
      // (like in a case of a graph)
      else if (type == BinData::kValueError)  {
         double errorY =  gr->GetErrorY(i);
         // should consider error = 0 as 1 ? Decide to skip points with zero errors
         // in case want to keep points with error = 0 as errrors=1 need to set the option UseEmpty
         if (!HFitInterface::AdjustError(fitOpt,errorY) ) continue;
         dv.Add( gx[i], gy[i], errorY );

#ifdef DEBUG
         std::cout << "Point " << i << "  " << gx[i] <<  "  " << gy[i]  << "  " << errorY << std::endl;
#endif


      }
      else { // case use error in x or asym errors
         double errorX = 0;
         if (fitOpt.fCoordErrors)
            // shoulkd take combined average (sqrt(0.5(e1^2+e2^2))  or math average ?
            // gr->GetErrorX(i) returns combined average
            // use math average for same behaviour as before
            errorX =  std::max( 0.5 * ( gr->GetErrorXlow(i) + gr->GetErrorXhigh(i) ) , 0. ) ;


         // adjust error in y according to option
         double errorY = std::max(gr->GetErrorY(i), 0.);
         // we do not check the return value since we check later if error in X and Y is zero for skipping the point
         HFitInterface::AdjustError(fitOpt, errorY);

         // skip points with total error = 0
         if ( errorX <=0 && errorY <= 0 ) continue;


         if (type == BinData::kAsymError)   {
            // asymmetric errors
            dv.Add( gx[i], gy[i], errorX, gr->GetErrorYlow(i), gr->GetErrorYhigh(i) );
         }
         else {
            // case symmetric Y errors
            dv.Add( gx[i], gy[i], errorX, errorY );
         }
      }

   }

#ifdef DEBUG
   std::cout << "TGraphFitInterface::FillData Graph FitData size is " << dv.Size() << std::endl;
#endif

}

void FillData(SparseData & dv, const TH1 * h1, TF1 * /*func*/)
{
   const int dim = h1->GetDimension();
   std::vector<double> min(dim);
   std::vector<double> max(dim);

   int ncells = h1->GetNcells();
   for ( int i = 0; i < ncells; ++i ) {
//       printf("i: %d; OF: %d; UF: %d; C: %f\n"
//              , i
//              , h1->IsBinOverflow(i) , h1->IsBinUnderflow(i)
//              , h1->GetBinContent(i));
      if ( !( h1->IsBinOverflow(i) || h1->IsBinUnderflow(i) )
           && h1->GetBinContent(i))
      {
         int x,y,z;
         h1->GetBinXYZ(i, x, y, z);

//          std::cout << "FILLDATA: h1(" << i << ")"
//               << "[" << h1->GetXaxis()->GetBinLowEdge(x) << "-" << h1->GetXaxis()->GetBinUpEdge(x) << "]";
//          if ( dim >= 2 )
//             std::cout   << "[" << h1->GetYaxis()->GetBinLowEdge(y) << "-" << h1->GetYaxis()->GetBinUpEdge(y) << "]";
//          if ( dim >= 3 )
//             std::cout   << "[" << h1->GetZaxis()->GetBinLowEdge(z) << "-" << h1->GetZaxis()->GetBinUpEdge(z) << "]";

//          std::cout << h1->GetBinContent(i) << std::endl;

         min[0] = h1->GetXaxis()->GetBinLowEdge(x);
         max[0] = h1->GetXaxis()->GetBinUpEdge(x);
         if ( dim >= 2 )
         {
            min[1] = h1->GetYaxis()->GetBinLowEdge(y);
            max[1] = h1->GetYaxis()->GetBinUpEdge(y);
         }
         if ( dim >= 3 ) {
            min[2] = h1->GetZaxis()->GetBinLowEdge(z);
            max[2] = h1->GetZaxis()->GetBinUpEdge(z);
         }

         dv.Add(min, max, h1->GetBinContent(i), h1->GetBinError(i));
      }
   }
}

void FillData(SparseData & dv, const THnBase * h1, TF1 * /*func*/)
{
   const int dim = h1->GetNdimensions();
   std::vector<double> min(dim);
   std::vector<double> max(dim);
   std::vector<Int_t>  coord(dim);

   ULong64_t nEntries = h1->GetNbins();
   for ( ULong64_t i = 0; i < nEntries; i++ )
   {
      double value = h1->GetBinContent( i, &coord[0] );
      if ( !value ) continue;

//       std::cout << "FILLDATA(SparseData): h1(" << i << ")";

      // Exclude underflows and oveflows! (defect behaviour with the TH1*)
      bool insertBox = true;
      for ( int j = 0; j < dim && insertBox; ++j )
      {
         TAxis* axis = h1->GetAxis(j);
         if ( ( axis->GetBinLowEdge(coord[j]) < axis->GetXmin() ) ||
              ( axis->GetBinUpEdge(coord[j])  > axis->GetXmax() ) ) {
            insertBox = false;
         }
         min[j] = h1->GetAxis(j)->GetBinLowEdge(coord[j]);
         max[j] = h1->GetAxis(j)->GetBinUpEdge(coord[j]);
      }
      if ( !insertBox ) {
//          std::cout << "NOT INSERTED!"<< std::endl;
         continue;
      }

//       for ( int j = 0; j < dim; ++j )
//       {
//          std::cout << "[" << h1->GetAxis(j)->GetBinLowEdge(coord[j])
//               << "-" << h1->GetAxis(j)->GetBinUpEdge(coord[j]) << "]";
//       }
//       std::cout << h1->GetBinContent(i) << std::endl;

      dv.Add(min, max, value, h1->GetBinError(i));
   }
}

void FillData(BinData & dv, const THnBase * s1, TF1 * func)
{
   // Fill the Range of the THnBase
   unsigned int const ndim = s1->GetNdimensions();
   std::vector<double> xmin(ndim);
   std::vector<double> xmax(ndim);
   for ( unsigned int i = 0; i < ndim; ++i ) {
      TAxis* axis = s1->GetAxis(i);
      xmin[i] = axis->GetXmin();
      xmax[i] = axis->GetXmax();
   }

   // Put default options, needed for the likelihood fitting of sparse
   // data.
   ROOT::Fit::DataOptions& dopt = dv.Opt();
   dopt.fUseEmpty = true;
   // when using sparse data need to set option to use normalized bin volume, because sparse bins are merged together
   //if (!dopt.fIntegral) dopt.fBinVolume = true;
   dopt.fBinVolume = true; 
   dopt.fNormBinVolume = true;

   // Get the sparse data
   ROOT::Fit::SparseData d(ndim, &xmin[0], &xmax[0]);
   ROOT::Fit::FillData(d, s1, func);

//    std::cout << "FillData(BinData & dv, const THnBase * s1, TF1 * func) (1)" << std::endl;

   // Create the bin data from the sparse data
   d.GetBinDataIntegral(dv);

}

void FillData ( BinData  & dv, const TGraph * gr,  TF1 * func ) {
   //  fill the data vector from a TGraph. Pass also the TF1 function which is
   // needed in case to exclude points rejected by the function
   assert(gr != 0);

   // get fit option
   DataOptions & fitOpt = dv.Opt();

   BinData::ErrorType type = GetDataType(gr,fitOpt);
   // adjust option according to type
   fitOpt.fErrors1 = (type == BinData::kNoError);
   // set this if we want to have error=1 for points with zero errors (by default they are skipped)
   // fitOpt.fUseEmpty = true;

   // use coordinate or asym  errors in case option is set  and type is consistent
   fitOpt.fCoordErrors &= (type ==  BinData::kCoordError) ||  (type ==  BinData::kAsymError) ;
   fitOpt.fAsymErrors &= (type ==  BinData::kAsymError);


   // if data are filled already check if there are consistent - otherwise do nothing
   if (dv.Size() > 0 && dv.NDim() == 1 ) {
      // check if size is correct otherwise flag an errors
      if (dv.PointSize() == 2 && type != BinData::kNoError ) {
         Error("FillData","Inconsistent TGraph with previous data set- skip all graph data");
         return;
      }
      if (dv.PointSize() == 3 && type != BinData::kValueError ) {
         Error("FillData","Inconsistent TGraph with previous data set- skip all graph data");
         return;
      }
      if (dv.PointSize() == 4 && type != BinData::kCoordError ) {
         Error("FillData","Inconsistent TGraph with previous data set- skip all graph data");
         return;
      }
      if (dv.PointSize() == 5 && type != BinData::kAsymError ) {
         Error("FillData","Inconsistent TGraph with previous data set- skip all graph data");
         return;
      }
   }

   DoFillData(dv, gr, type, func);

}

void FillData ( BinData  & dv, const TMultiGraph * mg, TF1 * func ) {
   //  fill the data vector from a TMultiGraph. Pass also the TF1 function which is
   // needed in case to exclude points rejected by the function
   assert(mg != 0);

   TList * grList = mg->GetListOfGraphs();
   assert(grList != 0);

#ifdef DEBUG
//   grList->Print();
   TIter itr(grList, kIterBackward);
   TObject *obj;
   std::cout << "multi-graph list of graps: " << std::endl;
   while ((obj = itr())) {
      std::cout << obj->IsA()->GetName() << std::endl;
   }

#endif

   // get fit option
   DataOptions & fitOpt = dv.Opt();

   // loop on the graphs to get the data type (use maximum)
   TIter next(grList);

   BinData::ErrorType type = BinData::kNoError;
   TGraph *gr = 0;
   while ((gr = (TGraph*) next())) {
      BinData::ErrorType t = GetDataType(gr,fitOpt);
      if (t > type ) type = t;
   }
   // adjust option according to type
   fitOpt.fErrors1 = (type == BinData::kNoError);
   fitOpt.fCoordErrors = (type ==  BinData::kCoordError);
   fitOpt.fAsymErrors = (type ==  BinData::kAsymError);


#ifdef DEBUG
   std::cout << "Fitting MultiGraph of type  " << type << std::endl;
#endif

   // fill the data now
   next = grList;
   while ((gr = (TGraph*) next())) {
      DoFillData( dv, gr, type, func);
   }

#ifdef DEBUG
   std::cout << "TGraphFitInterface::FillData MultiGraph FitData size is " << dv.Size() << std::endl;
#endif

}

void FillData ( BinData  & dv, const TGraph2D * gr, TF1 * func ) {
   //  fill the data vector from a TGraph2D. Pass also the TF1 function which is
   // needed in case to exclude points rejected by the function
   // in case of a pure TGraph
   assert(gr != 0);

   // get fit option
   DataOptions & fitOpt = dv.Opt();
   BinData::ErrorType type = GetDataType(gr,fitOpt);
   // adjust option according to type
   fitOpt.fErrors1 = (type == BinData::kNoError);
   fitOpt.fCoordErrors = (type ==  BinData::kCoordError);
   fitOpt.fAsymErrors = false; // a TGraph2D with asymmetric errors does not exist

   int  nPoints = gr->GetN();
   double *gx = gr->GetX();
   double *gy = gr->GetY();
   double *gz = gr->GetZ();

   // if all errors are zero set option of using errors to 1
   if ( gr->GetEZ() == 0) fitOpt.fErrors1 = true;

   double x[2];
   double ex[2];

   // look at data  range
   const DataRange & range = dv.Range();
   bool useRangeX = ( range.Size(0) > 0);
   bool useRangeY = ( range.Size(1) > 0);
   double xmin = 0;
   double xmax = 0;
   double ymin = 0;
   double ymax = 0;
   range.GetRange(xmin,xmax,ymin,ymax);

   dv.Initialize(nPoints,2, type);

   for ( int i = 0; i < nPoints; ++i) {

      x[0] = gx[i];
      x[1] = gy[i];

      //if (fitOpt.fUseRange && HFitInterface::IsPointOutOfRange(func, x) ) continue;
      if (useRangeX && (  x[0] < xmin || x[0] > xmax) ) continue;
      if (useRangeY && (  x[1] < ymin || x[1] > ymax) ) continue;

      // need to evaluate function to know about rejected points
      // hugly but no other solutions
      if (func) {
         TF1::RejectPoint(false);
         (*func)( x ); // evaluate using stored function parameters
         if (TF1::RejectedPoint() ) continue;
      }

      if (type == BinData::kNoError) {
         dv.Add( x, gz[i] );
         continue;
      }

      double errorZ = gr->GetErrorZ(i);
      if (!HFitInterface::AdjustError(fitOpt,errorZ) ) continue;

      if (type == BinData::kValueError)  {
         dv.Add( x, gz[i], errorZ );
      }
      else if (type == BinData::kCoordError) { // case use error in coordinates (x and y)
         ex[0] = std::max(gr->GetErrorX(i), 0.);
         ex[1] = std::max(gr->GetErrorY(i), 0.);
         dv.Add( x, gz[i], ex, errorZ );
      }
      else
         assert(0); // should not go here

#ifdef DEBUG
         std::cout << "Point " << i << "  " << gx[i] <<  "  " << gy[i]  << "  " << errorZ << std::endl;
#endif

   }

#ifdef DEBUG
   std::cout << "THFitInterface::FillData Graph2D FitData size is " << dv.Size() << std::endl;
#endif

}


// confidence intervals
bool GetConfidenceIntervals(const TH1 * h1, const ROOT::Fit::FitResult  & result, TGraphErrors * gr, double cl ) {
   if (h1->GetDimension() != 1) {
      Error("GetConfidenceIntervals","Invalid object used for storing confidence intervals");
      return false;
   }
   // fill fit data sets with points to estimate cl.
   BinData d;
   FillData(d,h1,0);
   gr->Set(d.NPoints() );
   double * ci = gr->GetEY(); // make CL values error of the graph
   result.GetConfidenceIntervals(d,ci,cl);
   // put function value as abscissa of the graph
   for (unsigned int ipoint = 0; ipoint < d.NPoints(); ++ipoint) {
      const double * x = d.Coords(ipoint);
      const ROOT::Math::IParamMultiFunction * func = result.FittedFunction();
      gr->SetPoint(ipoint, x[0], (*func)(x) );
   }
   return true;
}


} // end namespace Fit

} // end namespace ROOT