TLinearFitter.cxx

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// @(#)root/minuit:$Id: TLinearFitter.cxx 36058 2010-10-04 14:38:48Z moneta $
// Author: Anna Kreshuk 04/03/2005

/*************************************************************************
 * Copyright (C) 1995-2005, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

#include "TLinearFitter.h"
#include "TMath.h"
#include "TDecompChol.h"
#include "TGraph.h"
#include "TGraph2D.h"
#include "TMultiGraph.h"
#include "TRandom2.h"
#include "TObjString.h"
#include "TF2.h"
#include "TH1.h"
#include "TList.h"


ClassImp(TLinearFitter)

//////////////////////////////////////////////////////////////////////////
//
// The Linear Fitter - fitting functions that are LINEAR IN PARAMETERS
//
// Linear fitter is used to fit a set of data points with a linear
// combination of specified functions. Note, that "linear" in the name
// stands only for the model dependency on parameters, the specified
// functions can be nonlinear.
// The general form of this kind of model is
//
//          y(x) = a[0] + a[1]*f[1](x)+...a[n]*f[n](x)
//
// Functions f are fixed functions of x. For example, fitting with a
// polynomial is linear fitting in this sense.
//
//                         The fitting method
//
// The fit is performed using the Normal Equations method with Cholesky
// decomposition.
//
//                         Why should it be used?
//
// The linear fitter is considerably faster than general non-linear
// fitters and doesn't require to set the initial values of parameters.
//
//                          Using the fitter:
//
// 1.Adding the data points:
//  1.1 To store or not to store the input data?
//      - There are 2 options in the constructor - to store or not
//        store the input data. The advantages of storing the data
//        are that you'll be able to reset the fitting model without
//        adding all the points again, and that for very large sets
//        of points the chisquare is calculated more precisely.
//        The obvious disadvantage is the amount of memory used to
//        keep all the points.
//      - Before you start adding the points, you can change the
//        store/not store option by StoreData() method.
//  1.2 The data can be added:
//      - simply point by point - AddPoint() method
//      - an array of points at once:
//        If the data is already stored in some arrays, this data
//        can be assigned to the linear fitter without physically
//        coping bytes, thanks to the Use() method of
//        TVector and TMatrix classes - AssignData() method
//
// 2.Setting the formula
//  2.1 The linear formula syntax:
//      -Additive parts are separated by 2 plus signes "++"
//       --for example "1 ++ x" - for fitting a straight line
//      -All standard functions, undrestood by TFormula, can be used
//       as additive parts
//       --TMath functions can be used too
//      -Functions, used as additive parts, shouldn't have any parameters,
//       even if those parameters are set.
//       --for example, if normalizing a sum of a gaus(0, 1) and a
//         gaus(0, 2), don't use the built-in "gaus" of TFormula,
//         because it has parameters, take TMath::Gaus(x, 0, 1) instead.
//      -Polynomials can be used like "pol3", .."polN"
//      -If fitting a more than 3-dimensional formula, variables should
//       be numbered as follows:
//       -- x[0], x[1], x[2]... For example, to fit  "1 ++ x[0] ++ x[1] ++ x[2] ++ x[3]*x[3]"
//  2.2 Setting the formula:
//    2.2.1 If fitting a 1-2-3-dimensional formula, one can create a
//          TF123 based on a linear expression and pass this function
//          to the fitter:
//          --Example:
//            TLinearFitter *lf = new TLinearFitter();
//            TF2 *f2 = new TF2("f2", "x ++ y ++ x*x*y*y", -2, 2, -2, 2);
//            lf->SetFormula(f2);
//          --The results of the fit are then stored in the function,
//            just like when the TH1::Fit or TGraph::Fit is used
//          --A linear function of this kind is by no means different
//            from any other function, it can be drawn, evaluated, etc.
//
//          --For multidimensional fitting, TFormulas of the form:
//            x[0]++...++x[n] can be used
//    2.2.2 There is no need to create the function if you don't want to,
//          the formula can be set by expression:
//          --Example:
//            // 2 is the number of dimensions
//            TLinearFitter *lf = new TLinearFitter(2);
//            lf->SetFormula("x ++ y ++ x*x*y*y");
//
//    2.2.3 The fastest functions to compute are polynomials and hyperplanes.
//          --Polynomials are set the usual way: "pol1", "pol2",...
//          --Hyperplanes are set by expression "hyp3", "hyp4", ...
//          ---The "hypN" expressions only work when the linear fitter
//             is used directly, not through TH1::Fit or TGraph::Fit.
//             To fit a graph or a histogram with a hyperplane, define
//             the function as "1++x++y".
//          ---A constant term is assumed for a hyperplane, when using
//             the "hypN" expression, so "hyp3" is in fact fitting with
//             "1++x++y++z" function.
//          --Fitting hyperplanes is much faster than fitting other
//            expressions so if performance is vital, calculate the
//            function values beforehand and give them to the fitter
//            as variables
//          --Example:
//            You want to fit "sin(x)|cos(2*x)" very fast. Calculate
//            sin(x) and cos(2*x) beforehand and store them in array *data.
//            Then:
//            TLinearFitter *lf=new TLinearFitter(2, "hyp2");
//            lf->AssignData(npoint, 2, data, y);
//
//  2.3 Resetting the formula
//    2.3.1 If the input data is stored (or added via AssignData() function),
//          the fitting formula can be reset without re-adding all the points.
//          --Example:
//            TLinearFitter *lf=new TLinearFitter("1++x++x*x");
//            lf->AssignData(n, 1, x, y, e);
//            lf->Eval()
//            //looking at the parameter significance, you see,
//            // that maybe the fit will improve, if you take out
//            // the constant term
//            lf->SetFormula("x++x*x");
//            lf->Eval();
//            ...
//    2.3.2 If the input data is not stored, the fitter will have to be
//          cleared and the data will have to be added again to try a
//          different formula.
//
// 3.Accessing the fit results
//  3.1 There are methods in the fitter to access all relevant information:
//      --GetParameters, GetCovarianceMatrix, etc
//      --the t-values of parameters and their significance can be reached by
//        GetParTValue() and GetParSignificance() methods
//  3.2 If fitting with a pre-defined TF123, the fit results are also
//      written into this function.
//
///////////////////////////////////////////////////////////////////////////
// 4.Robust fitting - Least Trimmed Squares regression (LTS)
//   Outliers are atypical(by definition), infrequant observations; data points
//   which do not appear to follow the characteristic distribution of the rest
//   of the data. These may reflect genuine properties of the underlying
//   phenomenon(variable), or be due to measurement errors or anomalies which
//   shouldn't be modelled. (StatSoft electronic textbook)
//
//   Even a single gross outlier can greatly influence the results of least-
//   squares fitting procedure, and in this case use of robust(resistant) methods
//   is recommended.
//
//   The method implemented here is based on the article and algorithm:
//   "Computing LTS Regression for Large Data Sets" by
//   P.J.Rousseeuw and Katrien Van Driessen
//   The idea of the method is to find the fitting coefficients for a subset
//   of h observations (out of n) with the smallest sum of squared residuals.
//   The size of the subset h should lie between (npoints + nparameters +1)/2
//   and n, and represents the minimal number of good points in the dataset.
//   The default value is set to (npoints + nparameters +1)/2, but of course
//   if you are sure that the data contains less outliers it's better to change
//   h according to your data.
//
//   To perform a robust fit, call EvalRobust() function instead of Eval() after
//   adding the points and setting the fitting function.
//   Note, that standard errors on parameters are not computed!
//
//////////////////////////////////////////////////////////////////////////



//______________________________________________________________________________
TLinearFitter::TLinearFitter() :
TVirtualFitter(),
   fParams(),
   fParCovar(),
   fTValues(),
   fDesign(),
   fDesignTemp(),
   fDesignTemp2(),
   fDesignTemp3(),
   fAtb(),
   fAtbTemp(),
   fAtbTemp2(),
   fAtbTemp3(),
   fFunctions(),
   fY(),
   fX(),
   fE(),
   fVal()
{
   //default c-tor, input data is stored
   //If you don't want to store the input data,
   //run the function StoreData(kFALSE) after constructor

   fChisquare =0;
   fNpoints   =0;
   fNdim      =0;
   fY2        =0;
   fY2Temp    =0;
   fNfixed    =0;
   fIsSet     =kFALSE;
   fFormula   =0;
   fFixedParams=0;
   fSpecial   =0;
   fInputFunction=0;
   fStoreData =kTRUE;
   fRobust    =kFALSE;
   fNfunctions = 0;
   fFormulaSize = 0;
   fH = 0; 
}

//______________________________________________________________________________
TLinearFitter::TLinearFitter(Int_t ndim) : 
   fVal() 
{
   //The parameter stands for number of dimensions in the fitting formula
   //The input data is stored. If you don't want to store the input data,
   //run the function StoreData(kFALSE) after constructor

   fNdim    =ndim;
   fNpoints =0;
   fY2      =0;
   fY2Temp  =0;
   fNfixed  =0;
   fFixedParams=0;
   fFormula =0;
   fIsSet   =kFALSE;
   fChisquare=0;
   fSpecial  =0;
   fInputFunction=0;
   fStoreData=kTRUE;
   fRobust = kFALSE;
   fNfunctions = 0;
   fFormulaSize = 0;
   fH = 0; 
}

//______________________________________________________________________________
TLinearFitter::TLinearFitter(Int_t ndim, const char *formula, Option_t *opt)
{
   //First parameter stands for number of dimensions in the fitting formula
   //Second parameter is the fitting formula: see class description for formula syntax
   //Options:
   //The option is to store or not to store the data
   //If you don't want to store the data, choose "" for the option, or run
   //StoreData(kFalse) member function after the constructor

   fNdim=ndim;
   fNpoints=0;
   fChisquare=0;
   fY2=0;
   fNfixed=0;
   fFixedParams=0;
   fSpecial=0;
   fInputFunction=0;
   fFormula = 0;
   TString option=opt;
   option.ToUpper();
   if (option.Contains("D"))
      fStoreData=kTRUE;
   else
      fStoreData=kFALSE;
   fRobust=kFALSE;
   SetFormula(formula);
}

//______________________________________________________________________________
TLinearFitter::TLinearFitter(TFormula *function, Option_t *opt)
{
   //This constructor uses a linear function. How to create it?
   //TFormula now accepts formulas of the following kind:
   //TFormula("f", "x++y++z++x*x") or
   //TFormula("f", "x[0]++x[1]++x[2]*x[2]");
   //Other than the look, it's in no
   //way different from the regular formula, it can be evaluated,
   //drawn, etc.
   //The option is to store or not to store the data
   //If you don't want to store the data, choose "" for the option, or run
   //StoreData(kFalse) member function after the constructor

   fNdim=function->GetNdim();
   if (!function->IsLinear()){
      Int_t number=function->GetNumber();
      if (number<299 || number>310){
         Error("TLinearFitter", "Trying to fit with a nonlinear function");
         return;
      }
   }
   fNpoints=0;
   fChisquare=0;
   fY2=0;
   fNfixed=0;
   fFixedParams=0;
   fSpecial=0;
   fFormula = 0;
   TString option=opt;
   option.ToUpper();
   if (option.Contains("D"))
      fStoreData=kTRUE;
   else
      fStoreData=kFALSE;
   fIsSet=kTRUE;
   fRobust=kFALSE;
   fInputFunction=0;

   SetFormula(function);
}

//______________________________________________________________________________
TLinearFitter::TLinearFitter(const TLinearFitter& tlf) :
   TVirtualFitter(tlf),
   fParams(tlf.fParams),
   fParCovar(tlf.fParCovar),
   fTValues(tlf.fTValues),
   fParSign(tlf.fParSign),
   fDesign(tlf.fDesign),
   fDesignTemp(tlf.fDesignTemp),
   fDesignTemp2(tlf.fDesignTemp2),
   fDesignTemp3(tlf.fDesignTemp3),
   fAtb(tlf.fAtb),
   fAtbTemp(tlf.fAtbTemp),
   fAtbTemp2(tlf.fAtbTemp2),
   fAtbTemp3(tlf.fAtbTemp3),
   fFunctions( * (TObjArray *)tlf.fFunctions.Clone()), 
   fY(tlf.fY),
   fY2(tlf.fY2),
   fY2Temp(tlf.fY2Temp),
   fX(tlf.fX),
   fE(tlf.fE),
   fInputFunction(tlf.fInputFunction), 
   fNpoints(tlf.fNpoints),
   fNfunctions(tlf.fNfunctions),
   fFormulaSize(tlf.fFormulaSize),
   fNdim(tlf.fNdim),
   fNfixed(tlf.fNfixed),
   fSpecial(tlf.fSpecial),
   fFormula(0),
   fIsSet(tlf.fIsSet),
   fStoreData(tlf.fStoreData),
   fChisquare(tlf.fChisquare),
   fH(tlf.fH),
   fRobust(tlf.fRobust),
   fFitsample(tlf.fFitsample), 
   fFixedParams(0)
{
   // Copy ctor

   // make a deep  copy of managed objects
   // fFormula, fFixedParams and fFunctions

   if ( tlf.fFixedParams && fNfixed > 0 ) {
      fFixedParams=new Bool_t[fNfixed];
      for(Int_t i=0; i<fNfixed; ++i) 
         fFixedParams[i]=tlf.fFixedParams[i];
   }
   if (tlf.fFormula) { 
      fFormula = new char[fFormulaSize+1]; 
      strlcpy(fFormula,tlf.fFormula,fFormulaSize+1);
   }

}


//______________________________________________________________________________
TLinearFitter::~TLinearFitter()
{
   // Linear fitter cleanup.

   if (fFormula) { 
      delete [] fFormula;
      fFormula = 0;
   }
   if (fFixedParams) { 
      delete [] fFixedParams;
      fFixedParams = 0;
   }
   fInputFunction = 0;
   fFunctions.Delete();

}

//______________________________________________________________________________
TLinearFitter& TLinearFitter::operator=(const TLinearFitter& tlf) 
{
   // Assignment operator

   if(this!=&tlf) {
      TVirtualFitter::operator=(tlf);
      fParams.ResizeTo(tlf.fParams);      fParams=tlf.fParams;
      fParCovar.ResizeTo(tlf.fParCovar);  fParCovar=tlf.fParCovar;
      fTValues.ResizeTo(tlf.fTValues);    fTValues=tlf.fTValues;
      fParSign.ResizeTo(tlf.fParSign);    fParSign=tlf.fParSign;
      fDesign.ResizeTo(tlf.fDesign);                fDesign=tlf.fDesign;
      fDesignTemp.ResizeTo(tlf.fDesignTemp);        fDesignTemp=tlf.fDesignTemp;
      fDesignTemp2.ResizeTo(tlf.fDesignTemp2);      fDesignTemp2=tlf.fDesignTemp2;
      fDesignTemp3.ResizeTo(tlf.fDesignTemp3);      fDesignTemp3=tlf.fDesignTemp3;
      fAtb.ResizeTo(tlf.fAtb);            fAtb=tlf.fAtb;
      fAtbTemp.ResizeTo(tlf.fAtbTemp);    fAtbTemp=tlf.fAtbTemp;
      fAtbTemp2.ResizeTo(tlf.fAtbTemp2);    fAtbTemp2=tlf.fAtbTemp2;
      fAtbTemp3.ResizeTo(tlf.fAtbTemp3);    fAtbTemp3=tlf.fAtbTemp3;
      
      if (fFormula) delete [] fFormula;  
      fFormula = 0; 
      if (tlf.fFormula) { 
         fFormula = new char[fFormulaSize+1]; 
         strlcpy(fFormula,tlf.fFormula,fFormulaSize+1);
      }

      if (fFixedParams)   delete [] fFixedParams;
      fFixedParams = 0; 
      if ( tlf.fFixedParams && fNfixed > 0 ) {
         fFixedParams=new Bool_t[tlf.fNfixed];
         for(Int_t i=0; i<tlf.fNfixed; ++i) 
            fFixedParams[i]=tlf.fFixedParams[i];
      }

      fFunctions.Delete(); 
      fFunctions= *(TObjArray*) tlf.fFunctions.Clone();
      fY=tlf.fY;
      fY2=tlf.fY2;
      fY2Temp=tlf.fY2Temp;
      fX=tlf.fX;
      fE=tlf.fE;
      fInputFunction=(TFormula*)tlf.fInputFunction;
      fNpoints=tlf.fNpoints;
      fNfunctions=tlf.fNfunctions;
      fFormulaSize=tlf.fFormulaSize;
      fNdim=tlf.fNdim;
      fNfixed=tlf.fNfixed;
      fSpecial=tlf.fSpecial;
      fIsSet=tlf.fIsSet;
      fStoreData=tlf.fStoreData;
      fChisquare=tlf.fChisquare;
      fH=tlf.fH;
      fRobust=tlf.fRobust;
      fFitsample=tlf.fFitsample;
   } 
   return *this;
}

//______________________________________________________________________________
void TLinearFitter::Add(TLinearFitter *tlf)
{
//Add another linear fitter to this linear fitter. Points and Design matrices
//are added, but the previos fitting results (if any) are deleted.
//Fitters must have same formulas (this is not checked). Fixed parameters are not changed

   fParams.Zero();
   fParCovar.Zero();
   fTValues.Zero();
   fParSign.Zero();

   fDesign += tlf->fDesign;

   fDesignTemp += tlf->fDesignTemp;
   fDesignTemp2 += tlf->fDesignTemp2;
   fDesignTemp3 += tlf->fDesignTemp3;
   fAtb += tlf->fAtb;
   fAtbTemp += tlf->fAtbTemp;
   fAtbTemp2 += tlf->fAtbTemp2;
   fAtbTemp3 += tlf->fAtbTemp3;

   if (fStoreData){
      Int_t size=fY.GetNoElements();
      Int_t newsize = fNpoints+tlf->fNpoints;
      if (size<newsize){
         fY.ResizeTo(newsize);
         fE.ResizeTo(newsize);
         fX.ResizeTo(newsize, fNdim);
      }
      for (Int_t i=fNpoints; i<newsize; i++){
         fY(i)=tlf->fY(i-fNpoints);
         fE(i)=tlf->fE(i-fNpoints);
         for (Int_t j=0; j<fNdim; j++){
            fX(i,j)=tlf->fX(i-fNpoints, j);
         }
      }
   }
   fY2 += tlf->fY2;
   fY2Temp += tlf->fY2Temp;
   fNpoints += tlf->fNpoints;  
   //fInputFunction=(TFormula*)tlf.fInputFunction->Clone();

   fChisquare=0;
   fH=0;
   fRobust=0;   
}

//______________________________________________________________________________
void TLinearFitter::AddPoint(Double_t *x, Double_t y, Double_t e)
{
   //Adds 1 point to the fitter.
   //First parameter stands for the coordinates of the point, where the function is measured
   //Second parameter - the value being fitted
   //Third parameter - weight(measurement error) of this point (=1 by default)

   Int_t size;
   fNpoints++;
   if (fStoreData){
      size=fY.GetNoElements();
      if (size<fNpoints){
         fY.ResizeTo(fNpoints+fNpoints/2);
         fE.ResizeTo(fNpoints+fNpoints/2);
         fX.ResizeTo(fNpoints+fNpoints/2, fNdim);
      }

      Int_t j=fNpoints-1;
      fY(j)=y;
      fE(j)=e;
      for (Int_t i=0; i<fNdim; i++)
         fX(j,i)=x[i];
   }
   //add the point to the design matrix, if the formula has been set
   // (LM: why condition !fRobust ?? - remove it to fix Coverity 11602)
   // when 100< fSpecial < 200 (Polynomial) fFunctions is not empty
   // (see implementation of SetFormula method)
   if (fFunctions.IsEmpty()&&(!fInputFunction)&&(fSpecial<=200)){
      Error("AddPoint", "Point can't be added, because the formula hasn't been set");
      return; 
   }
   if (!fRobust) AddToDesign(x, y, e);
}

//______________________________________________________________________________
void TLinearFitter::AssignData(Int_t npoints, Int_t xncols, Double_t *x, Double_t *y, Double_t *e)
{
   //This function is to use when you already have all the data in arrays
   //and don't want to copy them into the fitter. In this function, the Use() method
   //of TVectorD and TMatrixD is used, so no bytes are physically moved around.
   //First parameter - number of points to fit
   //Second parameter - number of variables in the model
   //Third parameter - the variables of the model, stored in the following way:
   //(x0(0), x1(0), x2(0), x3(0), x0(1), x1(1), x2(1), x3(1),...

   if (npoints<fNpoints){
      Error("AddData", "Those points are already added");
      return;
   }
   Bool_t same=kFALSE;
   if (fX.GetMatrixArray()==x && fY.GetMatrixArray()==y){
      if (e){
         if (fE.GetMatrixArray()==e)
            same=kTRUE;
      }
   }

   fX.Use(npoints, xncols, x);
   fY.Use(npoints, y);
   if (e)
      fE.Use(npoints, e);
   else {
      fE.ResizeTo(npoints);
      fE=1;
   }
   Int_t xfirst;
   if (!fFunctions.IsEmpty() || fInputFunction ||  fSpecial>200) {
      if (same)
         xfirst=fNpoints;

      else
         xfirst=0;
      for (Int_t i=xfirst; i<npoints; i++)
         AddToDesign(TMatrixDRow(fX, i).GetPtr(), fY(i), fE(i));
   }
   fNpoints=npoints;
}

//______________________________________________________________________________
void TLinearFitter::AddToDesign(Double_t *x, Double_t y, Double_t e)
{
   //Add a point to the AtA matrix and to the Atb vector.



   Int_t i, j, ii;
   y/=e;

//   Double_t fVal[1000];

   if ((fSpecial>100)&&(fSpecial<200)){
      //polynomial fitting
      Int_t npar=fSpecial-100;
      fVal[0]=1;
      for (i=1; i<npar; i++)
         fVal[i]=fVal[i-1]*x[0];
      for (i=0; i<npar; i++)
         fVal[i]/=e;
   } else if (fSpecial>200){
      //Hyperplane fitting. Constant term is added
      Int_t npar=fSpecial-201;
      fVal[0]=1./e;
      for (i=0; i<npar; i++)
         fVal[i+1]=x[i]/e;
   } else {
      //general case
      for (ii=0; ii<fNfunctions; ii++){
         if (!fFunctions.IsEmpty()){
            TFormula *f1 = (TFormula*)(fFunctions.UncheckedAt(ii));
            fVal[ii]=f1->EvalPar(x)/e;
         } else {
            TFormula *f=(TFormula*)fInputFunction->GetLinearPart(ii);
            fVal[ii]=f->EvalPar(x)/e;
         }
      }
   }
   //additional matrices for numerical stability
   for (i=0; i<fNfunctions; i++){
      for (j=0; j<i; j++)
         fDesignTemp3(j, i)+=fVal[i]*fVal[j];
      fDesignTemp3(i, i)+=fVal[i]*fVal[i];
      fAtbTemp3(i)+=fVal[i]*y;

   }
   fY2Temp+=y*y;
   fIsSet=kTRUE;

   if (fNpoints % 100 == 0 && fNpoints>100){
      fDesignTemp2+=fDesignTemp3;
      fDesignTemp3.Zero();
      fAtbTemp2+=fAtbTemp3;
      fAtbTemp3.Zero();
      if (fNpoints % 10000 == 0 && fNpoints>10000){
         fDesignTemp+=fDesignTemp2;
         fDesignTemp2.Zero();
         fAtbTemp+=fAtbTemp2;
         fAtbTemp2.Zero();
         fY2+=fY2Temp;
         fY2Temp=0;
         if (fNpoints % 1000000 == 0 && fNpoints>1000000){
            fDesign+=fDesignTemp;
            fDesignTemp.Zero();
            fAtb+=fAtbTemp;
            fAtbTemp.Zero();
         }
      }
   }
}

//______________________________________________________________________________
void TLinearFitter::AddTempMatrices()
{
   if (fDesignTemp3.GetNrows()>0){
      fDesignTemp2+=fDesignTemp3;
      fDesignTemp+=fDesignTemp2;
      fDesign+=fDesignTemp;
      fDesignTemp3.Zero();
      fDesignTemp2.Zero();
      fDesignTemp.Zero();
      fAtbTemp2+=fAtbTemp3;
      fAtbTemp+=fAtbTemp2;
      fAtb+=fAtbTemp;
      fAtbTemp3.Zero();
      fAtbTemp2.Zero();
      fAtbTemp.Zero();
      
      fY2+=fY2Temp;
      fY2Temp=0;
      }
}

//______________________________________________________________________________
void TLinearFitter::Clear(Option_t * /*option*/)
{
   //Clears everything. Used in TH1::Fit and TGraph::Fit().

   fParams.Clear();
   fParCovar.Clear();
   fTValues.Clear();
   fParSign.Clear();
   fDesign.Clear();
   fDesignTemp.Clear();
   fDesignTemp2.Clear();
   fDesignTemp3.Clear();
   fAtb.Clear();
   fAtbTemp.Clear();
   fAtbTemp2.Clear();
   fAtbTemp3.Clear();
   fFunctions.Clear();
   fInputFunction=0;
   fY.Clear();
   fX.Clear();
   fE.Clear();

   fNpoints=0;
   fNfunctions=0;
   fFormulaSize=0;
   fNdim=0;
   if (fFormula) delete [] fFormula;
   fFormula=0;
   fIsSet=0;
   if (fFixedParams) delete [] fFixedParams;
   fFixedParams=0;

   fChisquare=0;
   fY2=0;
   fSpecial=0;
   fRobust=kFALSE;
   fFitsample.Clear();
}

//______________________________________________________________________________
void TLinearFitter::ClearPoints()
{
   //To be used when different sets of points are fitted with the same formula.

   fDesign.Zero();
   fAtb.Zero();
   fDesignTemp.Zero();
   fDesignTemp2.Zero();
   fDesignTemp3.Zero();
   fAtbTemp.Zero();
   fAtbTemp2.Zero();
   fAtbTemp3.Zero();

   fParams.Zero();
   fParCovar.Zero();
   fTValues.Zero();
   fParSign.Zero();

   for (Int_t i=0; i<fNfunctions; i++)
      fFixedParams[i]=0;
   fChisquare=0;
   fNpoints=0;

}

//______________________________________________________________________________
void TLinearFitter::Chisquare()
{
   //Calculates the chisquare.

   Int_t i, j;
   Double_t sumtotal2;
   Double_t temp, temp2;

   if (!fStoreData){
      sumtotal2 = 0;
      for (i=0; i<fNfunctions; i++){
         for (j=0; j<i; j++){
            sumtotal2 += 2*fParams(i)*fParams(j)*fDesign(j, i);
         }
         sumtotal2 += fParams(i)*fParams(i)*fDesign(i, i);
         sumtotal2 -= 2*fParams(i)*fAtb(i);
      }
      sumtotal2 += fY2;
   } else {
      sumtotal2 = 0;
      if (fInputFunction){
         for (i=0; i<fNpoints; i++){
            temp = fInputFunction->EvalPar(TMatrixDRow(fX, i).GetPtr());
            temp2 = (fY(i)-temp)*(fY(i)-temp);
            temp2 /= fE(i)*fE(i);
            sumtotal2 += temp2;
         }
      } else {
         sumtotal2 = 0;
         Double_t val[100];
         for (Int_t point=0; point<fNpoints; point++){
            temp = 0;
            if ((fSpecial>100)&&(fSpecial<200)){
               Int_t npar = fSpecial-100;
               val[0] = 1;
               for (i=1; i<npar; i++)
                  val[i] = val[i-1]*fX(point, 0);
               for (i=0; i<npar; i++)
                  temp += fParams(i)*val[i];
            } else {
               if (fSpecial>200) {
                  //hyperplane case
                  Int_t npar = fSpecial-201;
                  temp+=fParams(0);
                  for (i=0; i<npar; i++)
                     temp += fParams(i+1)*fX(point, i);
               } else {
                  for (j=0; j<fNfunctions; j++) {
                     TFormula *f1 = (TFormula*)(fFunctions.UncheckedAt(j));
                     val[j] = f1->EvalPar(TMatrixDRow(fX, point).GetPtr());
                     temp += fParams(j)*val[j];
                  }
               }
            }
         temp2 = (fY(point)-temp)*(fY(point)-temp);
         temp2 /= fE(point)*fE(point);
         sumtotal2 += temp2;
         }
      }
   }
   fChisquare = sumtotal2;

}

//______________________________________________________________________________
void TLinearFitter::ComputeTValues()
{
   // Computes parameters' t-values and significance

   for (Int_t i=0; i<fNfunctions; i++){
      fTValues(i) = fParams(i)/(TMath::Sqrt(fParCovar(i, i)));
      fParSign(i) = 2*(1-TMath::StudentI(TMath::Abs(fTValues(i)),fNpoints-fNfunctions+fNfixed));
   }
}

//______________________________________________________________________________
Int_t TLinearFitter::Eval()
{
   // Perform the fit and evaluate the parameters
   // Returns 0 if the fit is ok, 1 if there are errors

   Double_t e;
   if (fFunctions.IsEmpty()&&(!fInputFunction)&&(fSpecial<=200)){
      Error("TLinearFitter::Eval", "The formula hasn't been set");
      return 1;
   }
   //
   fParams.ResizeTo(fNfunctions);
   fTValues.ResizeTo(fNfunctions);
   fParSign.ResizeTo(fNfunctions);
   fParCovar.ResizeTo(fNfunctions,fNfunctions);

   fChisquare=0;

   if (!fIsSet){
      Bool_t update = UpdateMatrix();
      if (!update){
         //no points to fit
         fParams.Zero();
         fParCovar.Zero();
         fTValues.Zero();
         fParSign.Zero();
         fChisquare=0;
         if (fInputFunction){
            fInputFunction->SetParameters(fParams.GetMatrixArray());
            for (Int_t i=0; i<fNfunctions; i++)
               ((TF1*)fInputFunction)->SetParError(i, 0);
            ((TF1*)fInputFunction)->SetChisquare(0);
            ((TF1*)fInputFunction)->SetNDF(0);
            ((TF1*)fInputFunction)->SetNumberFitPoints(0);
         }
         return 1;
      }
   }
  
   AddTempMatrices();

//fixing fixed parameters, if there are any
   Int_t i, ii, j=0;
   if (fNfixed>0){
      for (ii=0; ii<fNfunctions; ii++)
         fDesignTemp(ii, fNfixed) = fAtb(ii);
      for (i=0; i<fNfunctions; i++){
         if (fFixedParams[i]){
            for (ii=0; ii<i; ii++)
               fDesignTemp(ii, j) = fDesign(ii, i);
            for (ii=i; ii<fNfunctions; ii++)
               fDesignTemp(ii, j) = fDesign(i, ii);
            j++;
            for (ii=0; ii<fNfunctions; ii++){
               fAtb(ii)-=fParams(i)*(fDesignTemp(ii, j-1));
            }
         }
      }
      for (i=0; i<fNfunctions; i++){
         if (fFixedParams[i]){
            for (ii=0; ii<fNfunctions; ii++){
               fDesign(ii, i) = 0;
               fDesign(i, ii) = 0;
            }
            fDesign (i, i) = 1;
            fAtb(i) = fParams(i);
         }
      }
   }

   TDecompChol chol(fDesign);
   Bool_t ok;
   TVectorD coef(fNfunctions);
   coef=chol.Solve(fAtb, ok);
   if (!ok){
      Error("Eval","Matrix inversion failed");
      fParams.Zero();
      fParCovar.Zero();
      fTValues.Zero();
      fParSign.Zero();
      if (fInputFunction){
         fInputFunction->SetParameters(fParams.GetMatrixArray());
         if (fInputFunction->InheritsFrom(TF1::Class())){
            ((TF1*)fInputFunction)->SetChisquare(0);
            ((TF1*)fInputFunction)->SetNDF(fNpoints-fNfunctions+fNfixed);
            ((TF1*)fInputFunction)->SetNumberFitPoints(fNpoints);
         }
      }
      return 1;
   }
   fParams=coef;
   fParCovar=chol.Invert();

   if (fInputFunction){
      fInputFunction->SetParameters(fParams.GetMatrixArray());
      if (fInputFunction->InheritsFrom(TF1::Class())){
         for (i=0; i<fNfunctions; i++){
            e = TMath::Sqrt(fParCovar(i, i));
            ((TF1*)fInputFunction)->SetParError(i, e);
         }
         if (!fObjectFit)
            ((TF1*)fInputFunction)->SetChisquare(GetChisquare());
         ((TF1*)fInputFunction)->SetNDF(fNpoints-fNfunctions+fNfixed);
         ((TF1*)fInputFunction)->SetNumberFitPoints(fNpoints);
         }
   }

   //if parameters were fixed, change the design matrix back as it was before fixing
   j = 0;
   if (fNfixed>0){
      for (i=0; i<fNfunctions; i++){
         if (fFixedParams[i]){
            for (ii=0; ii<i; ii++){
               fDesign(ii, i) = fDesignTemp(ii, j);
               fAtb(ii) = fDesignTemp(ii, fNfixed);
            }
            for (ii=i; ii<fNfunctions; ii++){
               fDesign(i, ii) = fDesignTemp(ii, j);
               fAtb(ii) = fDesignTemp(ii, fNfixed);
            }
            j++;
         }
      }
   }
   return 0;
}

//______________________________________________________________________________
void TLinearFitter::FixParameter(Int_t ipar)
{
   //Fixes paramter #ipar at its current value.

   if (fParams.NonZeros()<1){
      Error("FixParameter", "no value available to fix the parameter");
      return;
   }
   if (ipar>fNfunctions || ipar<0){
      Error("FixParameter", "illegal parameter value");
      return;
   }
   if (fNfixed==fNfunctions) {
      Error("FixParameter", "no free parameters left");
      return;
   }
   if (!fFixedParams)
      fFixedParams = new Bool_t[fNfunctions];
   fFixedParams[ipar] = 1;
   fNfixed++;
}

//______________________________________________________________________________
void TLinearFitter::FixParameter(Int_t ipar, Double_t parvalue)
{
   //Fixes parameter #ipar at value parvalue.

   if (ipar>fNfunctions || ipar<0){
      Error("FixParameter", "illegal parameter value");
      return;
   }
   if (fNfixed==fNfunctions) {
      Error("FixParameter", "no free parameters left");
      return;
   }
   if(!fFixedParams)
      fFixedParams = new Bool_t[fNfunctions];
   fFixedParams[ipar] = 1;
   if (fParams.GetNoElements()<fNfunctions)
      fParams.ResizeTo(fNfunctions);
   fParams(ipar) = parvalue;
   fNfixed++;
}

//______________________________________________________________________________
void TLinearFitter::ReleaseParameter(Int_t ipar)
{
   //Releases parameter #ipar.

   if (ipar>fNfunctions || ipar<0){
      Error("ReleaseParameter", "illegal parameter value");
      return;
   }
   if (!fFixedParams[ipar]){
      Warning("ReleaseParameter","This parameter is not fixed\n");
      return;
   } else {
      fFixedParams[ipar] = 0;
      fNfixed--;
   }
}

//______________________________________________________________________________
void TLinearFitter::GetAtbVector(TVectorD &v)
{
   //Get the Atb vector - a vector, used for internal computations
   
   if (v.GetNoElements()!=fAtb.GetNoElements())
      v.ResizeTo(fAtb.GetNoElements());
   v = fAtb;
}

//______________________________________________________________________________
Double_t TLinearFitter::GetChisquare()
{
   // Get the Chisquare.

   if (fChisquare > 1e-16)
      return fChisquare;
   else {
      Chisquare();
      return fChisquare;
   }
}

//______________________________________________________________________________
void TLinearFitter::GetConfidenceIntervals(Int_t n, Int_t ndim, const Double_t *x, Double_t *ci, Double_t cl)
{
//Computes point-by-point confidence intervals for the fitted function
//Parameters:
//n - number of points
//ndim - dimensions of points
//x - points, at which to compute the intervals, for ndim > 1
//    should be in order: (x0,y0, x1, y1, ... xn, yn)
//ci - computed intervals are returned in this array
//cl - confidence level, default=0.95
//
//NOTE, that this method can only be used when the fitting function inherits from a TF1,
//so it's not possible when the fitting function was set as a string or as a pure TFormula

   if (fInputFunction){
      Double_t *grad = new Double_t[fNfunctions];
      Double_t *sum_vector = new Double_t[fNfunctions];
      Double_t c=0;
      Int_t df = fNpoints-fNfunctions+fNfixed;
      Double_t t = TMath::StudentQuantile(0.5 + cl/2, df);
      Double_t chidf = TMath::Sqrt(fChisquare/df);

      for (Int_t ipoint=0; ipoint<n; ipoint++){
         c=0;
         ((TF1*)(fInputFunction))->GradientPar(x+ndim*ipoint, grad);
         //multiply the covariance matrix by gradient
         for (Int_t irow=0; irow<fNfunctions; irow++){
            sum_vector[irow]=0;
            for (Int_t icol=0; icol<fNfunctions; icol++){
               sum_vector[irow]+=fParCovar(irow,icol)*grad[icol];
            }
         }
         for (Int_t i=0; i<fNfunctions; i++)
            c+=grad[i]*sum_vector[i];
         c=TMath::Sqrt(c);
         ci[ipoint]=c*t*chidf;
      }

      delete [] grad;
      delete [] sum_vector;
   }
}

//______________________________________________________________________________
void TLinearFitter::GetConfidenceIntervals(TObject *obj, Double_t cl)
{
//Computes confidence intervals at level cl. Default is 0.95
//The TObject parameter can be a TGraphErrors, a TGraph2DErrors or a TH123.
//For Graphs, confidence intervals are computed for each point,
//the value of the graph at that point is set to the function value at that
//point, and the graph y-errors (or z-errors) are set to the value of
//the confidence interval at that point
//For Histograms, confidence intervals are computed for each bin center
//The bin content of this bin is then set to the function value at the bin
//center, and the bin error is set to the confidence interval value.
//Allowed combinations:
//Fitted object               Passed object
//TGraph                      TGraphErrors, TH1
//TGraphErrors, AsymmErrors   TGraphErrors, TH1
//TH1                         TGraphErrors, TH1
//TGraph2D                    TGraph2DErrors, TH2
//TGraph2DErrors              TGraph2DErrors, TH2
//TH2                         TGraph2DErrors, TH2
//TH3                         TH3

   if (!fInputFunction) {
      Error("GetConfidenceIntervals", "The case of fitting not with a TFormula is not yet implemented");
      return;
   }

   //TGraph//////////////////

   if (obj->InheritsFrom(TGraph::Class())) {
      TGraph *gr = (TGraph*)obj;
      if (!gr->GetEY()){
         Error("GetConfidenceIntervals", "A TGraphErrors should be passed instead of a graph");
         return;
      }
      if (fObjectFit->InheritsFrom(TGraph2D::Class())){
         Error("GetConfidenceIntervals", "A TGraph2DErrors should be passed instead of a graph");
         return;
      }
      if (fObjectFit->InheritsFrom(TH1::Class())){
         if (((TH1*)(fObjectFit))->GetDimension()>1){
            Error("GetConfidenceIntervals", "A TGraph2DErrors or a TH23 should be passed instead of a graph");
            return;
         }
      }

      GetConfidenceIntervals(gr->GetN(),1,gr->GetX(), gr->GetEY(), cl);
      for (Int_t i=0; i<gr->GetN(); i++)
         gr->SetPoint(i, gr->GetX()[i], fInputFunction->Eval(gr->GetX()[i]));
   }

   //TGraph2D///////////////
   else if (obj->InheritsFrom(TGraph2D::Class())) {
      TGraph2D *gr2 = (TGraph2D*)obj;
      if (!gr2->GetEZ()){
         Error("GetConfidenceIntervals", "A TGraph2DErrors should be passed instead of a TGraph2D");
         return;
      }
      if (fObjectFit->InheritsFrom(TGraph::Class())){
         Error("GetConfidenceIntervals", "A TGraphErrors should be passed instead of a TGraph2D");
         return;
      }
      if (fObjectFit->InheritsFrom(TH1::Class())){
         if (((TH1*)(fObjectFit))->GetDimension()==1){
            Error("GetConfidenceIntervals", "A TGraphErrors or a TH1 should be passed instead of a graph");
            return;
         }
      }
      Double_t xy[2];
      Int_t np = gr2->GetN();
      Double_t *grad = new Double_t[fNfunctions];
      Double_t *sum_vector = new Double_t[fNfunctions];
      Double_t *x = gr2->GetX();
      Double_t *y = gr2->GetY();
      Double_t t = TMath::StudentQuantile(0.5 + cl/2, ((TF1*)(fInputFunction))->GetNDF());
      Double_t chidf = TMath::Sqrt(fChisquare/((TF1*)(fInputFunction))->GetNDF());
      Double_t c = 0;
      for (Int_t ipoint=0; ipoint<np; ipoint++){
         c=0;
         xy[0]=x[ipoint];
         xy[1]=y[ipoint];
         ((TF1*)(fInputFunction))->GradientPar(xy, grad);
         for (Int_t irow=0; irow<fNfunctions; irow++){
            sum_vector[irow]=0;
            for (Int_t icol=0; icol<fNfunctions; icol++)
               sum_vector[irow]+=fParCovar(irow, icol)*grad[icol];
         }
         for (Int_t i=0; i<fNfunctions; i++)
            c+=grad[i]*sum_vector[i];
         c=TMath::Sqrt(c);
         gr2->SetPoint(ipoint, xy[0], xy[1], fInputFunction->EvalPar(xy));
         gr2->GetEZ()[ipoint]=c*t*chidf;
      }
      delete [] grad;
      delete [] sum_vector;
   }

   //TH1////////////////////////
   else if (obj->InheritsFrom(TH1::Class())) {
      if (fObjectFit->InheritsFrom(TGraph::Class())){
         if (((TH1*)obj)->GetDimension()>1){
            Error("GetConfidenceIntervals", "Fitted graph and passed histogram have different number of dimensions");
            return;
         }
      }
      if (fObjectFit->InheritsFrom(TGraph2D::Class())){
         if (((TH1*)obj)->GetDimension()!=2){
            Error("GetConfidenceIntervals", "Fitted graph and passed histogram have different number of dimensions");
            return;
         }
      }
      if (fObjectFit->InheritsFrom(TH1::Class())){
         if (((TH1*)(fObjectFit))->GetDimension()!=((TH1*)(obj))->GetDimension()){
            Error("GetConfidenceIntervals", "Fitted and passed histograms have different number of dimensions");
            return;
         }
      }


      TH1 *hfit = (TH1*)obj;
      Double_t *grad = new Double_t[fNfunctions];
      Double_t *sum_vector = new Double_t[fNfunctions];
      Double_t x[3];
      Int_t hxfirst = hfit->GetXaxis()->GetFirst();
      Int_t hxlast  = hfit->GetXaxis()->GetLast();
      Int_t hyfirst = hfit->GetYaxis()->GetFirst();
      Int_t hylast  = hfit->GetYaxis()->GetLast();
      Int_t hzfirst = hfit->GetZaxis()->GetFirst();
      Int_t hzlast  = hfit->GetZaxis()->GetLast();

      TAxis *xaxis  = hfit->GetXaxis();
      TAxis *yaxis  = hfit->GetYaxis();
      TAxis *zaxis  = hfit->GetZaxis();
      Double_t t = TMath::StudentQuantile(0.5 + cl/2, ((TF1*)(fInputFunction))->GetNDF());
      Double_t chidf = TMath::Sqrt(fChisquare/((TF1*)(fInputFunction))->GetNDF());
      Double_t c=0;
      for (Int_t binz=hzfirst; binz<=hzlast; binz++){
         x[2]=zaxis->GetBinCenter(binz);
         for (Int_t biny=hyfirst; biny<=hylast; biny++) {
            x[1]=yaxis->GetBinCenter(biny);
            for (Int_t binx=hxfirst; binx<=hxlast; binx++) {
               x[0]=xaxis->GetBinCenter(binx);
               ((TF1*)(fInputFunction))->GradientPar(x, grad);
               c=0;
               for (Int_t irow=0; irow<fNfunctions; irow++){
                  sum_vector[irow]=0;
                  for (Int_t icol=0; icol<fNfunctions; icol++)
                     sum_vector[irow]+=fParCovar(irow, icol)*grad[icol];
               }
               for (Int_t i=0; i<fNfunctions; i++)
                  c+=grad[i]*sum_vector[i];
               c=TMath::Sqrt(c);
               hfit->SetBinContent(binx, biny, binz, fInputFunction->EvalPar(x));
               hfit->SetBinError(binx, biny, binz, c*t*chidf);
            }
         }
      }
      delete [] grad;
      delete [] sum_vector;
   }
   else {
      Error("GetConfidenceIntervals", "This object type is not supported");
      return;
   }
}

//______________________________________________________________________________
Double_t* TLinearFitter::GetCovarianceMatrix() const
{
//Returns covariance matrix

   Double_t *p = const_cast<Double_t*>(fParCovar.GetMatrixArray());
   return p;
}

//______________________________________________________________________________
void TLinearFitter::GetCovarianceMatrix(TMatrixD &matr)
{
//Returns covariance matrix

   if (matr.GetNrows()!=fNfunctions || matr.GetNcols()!=fNfunctions){
      matr.ResizeTo(fNfunctions, fNfunctions);
   }
   matr = fParCovar;
}

//______________________________________________________________________________
void TLinearFitter::GetDesignMatrix(TMatrixD &matr)
{
//Returns the internal design matrix
   if (matr.GetNrows()!=fNfunctions || matr.GetNcols()!=fNfunctions){
      matr.ResizeTo(fNfunctions, fNfunctions);
   }
   matr = fDesign;
}

//______________________________________________________________________________
void TLinearFitter::GetErrors(TVectorD &vpar)
{
//Returns parameter errors

   if (vpar.GetNoElements()!=fNfunctions) {
      vpar.ResizeTo(fNfunctions);
   }
   for (Int_t i=0; i<fNfunctions; i++)
      vpar(i) = TMath::Sqrt(fParCovar(i, i));

}

//______________________________________________________________________________
void TLinearFitter::GetParameters(TVectorD &vpar)
{
//Returns parameter values

   if (vpar.GetNoElements()!=fNfunctions) {
      vpar.ResizeTo(fNfunctions);
   }
   vpar=fParams;
}

//______________________________________________________________________________
Int_t TLinearFitter::GetParameter(Int_t ipar,char* name,Double_t& value,Double_t& /*verr*/,Double_t& /*vlow*/, Double_t& /*vhigh*/) const
{
//Returns the value and the name of the parameter #ipar
//NB: In the calling function he argument name must be set large enough

   if (ipar<0 || ipar>fNfunctions) {
      Error("GetParError", "illegal value of parameter");
      return 0;
   }
   value = fParams(ipar);
   if (fInputFunction)
      strcpy(name, fInputFunction->GetParName(ipar));
   else
      name = 0;
   return 1;
}


//______________________________________________________________________________
Double_t TLinearFitter::GetParError(Int_t ipar) const
{
//Returns the error of parameter #ipar

   if (ipar<0 || ipar>fNfunctions) {
      Error("GetParError", "illegal value of parameter");
      return 0;
   }

   return TMath::Sqrt(fParCovar(ipar, ipar));
}


//______________________________________________________________________________
const char *TLinearFitter::GetParName(Int_t ipar) const
{
//Returns name of parameter #ipar

   if (ipar<0 || ipar>fNfunctions) {
      Error("GetParError", "illegal value of parameter");
      return 0;
   }
   if (fInputFunction)
      return fInputFunction->GetParName(ipar);
   return "";
}

//______________________________________________________________________________
Double_t TLinearFitter::GetParTValue(Int_t ipar)
{
//Returns the t-value for parameter #ipar

   if (ipar<0 || ipar>fNfunctions) {
      Error("GetParTValue", "illegal value of parameter");
      return 0;
   }
   if (!fTValues.NonZeros())
      ComputeTValues();
   return fTValues(ipar);
}

//______________________________________________________________________________
Double_t TLinearFitter::GetParSignificance(Int_t ipar)
{
//Returns the significance of parameter #ipar

   if (ipar<0 || ipar>fNfunctions) {
      Error("GetParSignificance", "illegal value of parameter");
      return 0;
   }
   if (!fParSign.NonZeros())
      ComputeTValues();
   return fParSign(ipar);
}

//______________________________________________________________________________
void TLinearFitter::GetFitSample(TBits &bits)
{
//For robust lts fitting, returns the sample, on which the best fit was based

   if (!fRobust){
      Error("GetFitSample", "there is no fit sample in ordinary least-squares fit");
      return;
   }
   for (Int_t i=0; i<fNpoints; i++)
      bits.SetBitNumber(i, fFitsample.TestBitNumber(i));

}

//______________________________________________________________________________
Int_t TLinearFitter::Merge(TCollection *list)
{
   //Merge objects in list
   if (!list) return -1;
   TIter next(list);
   TLinearFitter *lfit = 0;
   while ((lfit = (TLinearFitter*)next())) {
      if (!lfit->InheritsFrom(TLinearFitter::Class())) {
         Error("Add","Attempt to add object of class: %s to a %s",lfit->ClassName(),this->ClassName());
         return -1;
      }
      Add(lfit);
   }
   return 0;   
}
//______________________________________________________________________________
void TLinearFitter::SetBasisFunctions(TObjArray * functions)
{
   //set the basis functions in case the fitting function is not 
   // set directly
   // The TLinearFitter will manage and delete the functions contained in the list

   fFunctions = *(functions);
   int size = fFunctions.GetEntries();

   fNfunctions=size;
   //change the size of design matrix
   fDesign.ResizeTo(size, size);
   fAtb.ResizeTo(size);
   fDesignTemp.ResizeTo(size, size);
   fDesignTemp2.ResizeTo(size, size);
   fDesignTemp3.ResizeTo(size, size);
   fAtbTemp.ResizeTo(size);
   fAtbTemp2.ResizeTo(size);
   fAtbTemp3.ResizeTo(size);
   if (fFixedParams)
      delete [] fFixedParams;
   fFixedParams=new Bool_t[size];
   fDesign.Zero();
   fAtb.Zero();
   fDesignTemp.Zero();
   fDesignTemp2.Zero();
   fDesignTemp3.Zero();
   fAtbTemp.Zero();
   fAtbTemp2.Zero();
   fAtbTemp3.Zero();
   fY2Temp=0;
   fY2=0;
   for (int i=0; i<size; i++)
      fFixedParams[i]=0;
   fIsSet=kFALSE;
   fChisquare=0;

}
   

//______________________________________________________________________________
void TLinearFitter::SetDim(Int_t ndim)
{
   //set the number of dimensions

   fNdim=ndim;
   fY.ResizeTo(ndim+1);
   fX.ResizeTo(ndim+1, ndim);
   fE.ResizeTo(ndim+1);

   fNpoints=0;
   fIsSet=kFALSE;
}

//______________________________________________________________________________
void TLinearFitter::SetFormula(const char *formula)
{
  //Additive parts should be separated by "++".
  //Examples (ai are parameters to fit):
  //1.fitting function: a0*x0 + a1*x1 + a2*x2
  //  input formula "x[0]++x[1]++x[2]"
  //2.TMath functions can be used:
  //  fitting function: a0*TMath::Gaus(x, 0, 1) + a1*y
  //  input formula:    "TMath::Gaus(x, 0, 1)++y"
  //fills the array of functions

   Int_t size, special = 0;
   Int_t i;
   Bool_t isHyper = kFALSE;
   //Int_t len = strlen(formula);
   if (fInputFunction)
      fInputFunction = 0;
   fFormulaSize = strlen(formula);
   fFormula = new char[fFormulaSize+1];
   strlcpy(fFormula, formula,fFormulaSize+1);
   fSpecial = 0;
   //in case of a hyperplane:
   char *fstring;
   fstring = (char *)strstr(fFormula, "hyp");
   if (fstring!=0){
      isHyper = kTRUE;
      fstring+=3;
      sscanf(fstring, "%d", &size);
      //+1 for the constant term
      size++;
      fSpecial=200+size;
   }

   if (fSpecial==0) {
      //in case it's not a hyperplane
      TString sstring(fFormula);
      sstring = sstring.ReplaceAll("++", 2, "|", 1);
      TString replaceformula;

      //count the number of functions

      TObjArray *oa = sstring.Tokenize("|");

      //change the size of functions array and clear it
      if (!fFunctions.IsEmpty())
         fFunctions.Clear();

      fNfunctions = oa->GetEntriesFast();
      fFunctions.Expand(fNfunctions);

      //check if the old notation of xi is used somewhere instead of x[i]
      char pattern[5];
      char replacement[6];
      for (i=0; i<fNdim; i++){
         snprintf(pattern,5, "x%d", i);
         snprintf(replacement,6, "x[%d]", i);
         sstring = sstring.ReplaceAll(pattern, Int_t(i/10)+2, replacement, Int_t(i/10)+4);
      }

      //fill the array of functions
      oa = sstring.Tokenize("|");
      for (i=0; i<fNfunctions; i++) {
         replaceformula = ((TObjString *)oa->UncheckedAt(i))->GetString();
         TFormula *f = new TFormula("f", replaceformula.Data());
         if (!f) {
            Error("TLinearFitter", "f_linear not allocated");
            return;
         }
         special=f->GetNumber();
         fFunctions.Add(f);
      }

      if ((fNfunctions==1)&&(special>299)&&(special<310)){
         //if fitting a polynomial
         size=special-299;
         fSpecial=100+size;
      } else
         size=fNfunctions;
      oa->Delete();
      delete oa;
   }
   fNfunctions=size;
   //change the size of design matrix
   fDesign.ResizeTo(size, size);
   fAtb.ResizeTo(size);
   fDesignTemp.ResizeTo(size, size);
   fDesignTemp2.ResizeTo(size, size);
   fDesignTemp3.ResizeTo(size, size);
   fAtbTemp.ResizeTo(size);
   fAtbTemp2.ResizeTo(size);
   fAtbTemp3.ResizeTo(size);
   if (fFixedParams)
      delete [] fFixedParams;
   fFixedParams=new Bool_t[size];
   fDesign.Zero();
   fAtb.Zero();
   fDesignTemp.Zero();
   fDesignTemp2.Zero();
   fDesignTemp3.Zero();
   fAtbTemp.Zero();
   fAtbTemp2.Zero();
   fAtbTemp3.Zero();
   fY2Temp=0;
   fY2=0;
   for (i=0; i<size; i++)
      fFixedParams[i]=0;
   fIsSet=kFALSE;
   fChisquare=0;

}

//______________________________________________________________________________
void TLinearFitter::SetFormula(TFormula *function)
{
   //Set the fitting function.

   Int_t special, size;
   fInputFunction=function;
   fNfunctions=fInputFunction->GetNpar();
   fSpecial = 0;
   special=fInputFunction->GetNumber();
   if (!fFunctions.IsEmpty())
      fFunctions.Delete();

   if ((special>299)&&(special<310)){
      //if fitting a polynomial
      size=special-299;
      fSpecial=100+size;
   } else
      size=fNfunctions;

   fNfunctions=size;
   //change the size of design matrix
   fDesign.ResizeTo(size, size);
   fAtb.ResizeTo(size);
   fDesignTemp.ResizeTo(size, size);
   fAtbTemp.ResizeTo(size);

   fDesignTemp2.ResizeTo(size, size);
   fDesignTemp3.ResizeTo(size, size);

   fAtbTemp2.ResizeTo(size);
   fAtbTemp3.ResizeTo(size);
   //
   if (fFixedParams)
      delete [] fFixedParams;
   fFixedParams=new Bool_t[size];
   fDesign.Zero();
   fAtb.Zero();
   fDesignTemp.Zero();
   fAtbTemp.Zero();

   fDesignTemp2.Zero();
   fDesignTemp3.Zero();

   fAtbTemp2.Zero();
   fAtbTemp3.Zero();
   fY2Temp=0;
   fY2=0;
   for (Int_t i=0; i<size; i++)
      fFixedParams[i]=0;
   //check if any parameters are fixed (not for pure TFormula)

   if (function->InheritsFrom(TF1::Class())){
      Double_t al,bl;
      for (Int_t i=0;i<fNfunctions;i++) {
         ((TF1*)function)->GetParLimits(i,al,bl);
         if (al*bl !=0 && al >= bl) {
            FixParameter(i, function->GetParameter(i));
         }
      }
   }

   fIsSet=kFALSE;
   fChisquare=0;

}

//______________________________________________________________________________
Bool_t TLinearFitter::UpdateMatrix()
{
   //Update the design matrix after the formula has been changed.

   if (fStoreData) {
      for (Int_t i=0; i<fNpoints; i++) {
         AddToDesign(TMatrixDRow(fX, i).GetPtr(), fY(i), fE(i));
      }
      return 1;
   } else
      return 0;

}

//______________________________________________________________________________
Int_t TLinearFitter::ExecuteCommand(const char *command, Double_t *args, Int_t /*nargs*/)
{
   //To use in TGraph::Fit and TH1::Fit().

   if (!strcmp(command, "FitGraph")){
      if (args)      return GraphLinearFitter(args[0]);
      else           return GraphLinearFitter(0);
   }
   if (!strcmp(command, "FitGraph2D")){
      if (args)      return Graph2DLinearFitter(args[0]);
      else           return Graph2DLinearFitter(0);
   }
   if (!strcmp(command, "FitMultiGraph")){
      if (args)     return  MultiGraphLinearFitter(args[0]);
      else          return  MultiGraphLinearFitter(0);
   }
   if (!strcmp(command, "FitHist"))       return HistLinearFitter();
//   if (!strcmp(command, "FitMultiGraph")) MultiGraphLinearFitter();

   return 0;
}

//______________________________________________________________________________
void TLinearFitter::PrintResults(Int_t level, Double_t /*amin*/) const
{
   // Level = 3 (to be consistent with minuit)  prints parameters and parameter
   // errors.

   if (level==3){
      if (!fRobust){
         printf("Fitting results:\nParameters:\nNO.\t\tVALUE\t\tERROR\n");
         for (Int_t i=0; i<fNfunctions; i++){
            printf("%d\t%e\t%e\n", i, fParams(i), TMath::Sqrt(fParCovar(i, i)));
         }
      } else {
         printf("Fitting results:\nParameters:\nNO.\t\tVALUE\n");
         for (Int_t i=0; i<fNfunctions; i++){
            printf("%d\t%e\n", i, fParams(i));
         }
      }
   }
}

//______________________________________________________________________________
Int_t TLinearFitter::GraphLinearFitter(Double_t h)
{
   //Used in TGraph::Fit().

   StoreData(kFALSE);
   TGraph *grr=(TGraph*)GetObjectFit();
   TF1 *f1=(TF1*)GetUserFunc();
   Foption_t fitOption=GetFitOption();

   //Int_t np=0;
   Double_t *x=grr->GetX();
   Double_t *y=grr->GetY();
   Double_t e;

   Int_t fitResult = 0;
   //set the fitting formula
   SetDim(1);
   SetFormula(f1);

   if (fitOption.Robust){
      fRobust=kTRUE;
      StoreData(kTRUE);
   }
   //put the points into the fitter
   Int_t n=grr->GetN();
   for (Int_t i=0; i<n; i++){
      if (!f1->IsInside(&x[i])) continue;
      e=grr->GetErrorY(i);
      if (e<0 || fitOption.W1)
         e=1;
      AddPoint(&x[i], y[i], e);
   }

   if (fitOption.Robust){
      return EvalRobust(h);
   }

   fitResult = Eval();

   //calculate the precise chisquare
   if (!fitResult){
      if (!fitOption.Nochisq){
         Double_t temp, temp2, sumtotal=0;
         for (Int_t i=0; i<n; i++){
            if (!f1->IsInside(&x[i])) continue;
            temp=f1->Eval(x[i]);
            temp2=(y[i]-temp)*(y[i]-temp);
            e=grr->GetErrorY(i);
            if (e<0 || fitOption.W1)
               e=1;
            temp2/=(e*e);
            
            sumtotal+=temp2;
         }
         fChisquare=sumtotal;
         f1->SetChisquare(fChisquare);
      }
   }
   return fitResult;
}

//______________________________________________________________________________
Int_t TLinearFitter::Graph2DLinearFitter(Double_t h)
{
   //Minimisation function for a TGraph2D
   StoreData(kFALSE);

   TGraph2D *gr=(TGraph2D*)GetObjectFit();
   TF2 *f2=(TF2*)GetUserFunc();

   Foption_t fitOption=GetFitOption();
   Int_t n        = gr->GetN();
   Double_t *gx   = gr->GetX();
   Double_t *gy   = gr->GetY();
   Double_t *gz   = gr->GetZ();
   Double_t x[2];
   Double_t z, e;
   Int_t fitResult=0;
   SetDim(2);
   SetFormula(f2);

   if (fitOption.Robust){
      fRobust=kTRUE;
      StoreData(kTRUE);
   }

   for (Int_t bin=0;bin<n;bin++) {
      x[0] = gx[bin];
      x[1] = gy[bin];
      if (!f2->IsInside(x)) {
         continue;
      }
      z   = gz[bin];
      e=gr->GetErrorZ(bin);
      if (e<0 || fitOption.W1)
         e=1;
      AddPoint(x, z, e);
   }

   if (fitOption.Robust){
      return EvalRobust(h);
   }

   fitResult = Eval();

   if (!fitResult){
      if (!fitOption.Nochisq){
         //calculate the precise chisquare
         Double_t temp, temp2, sumtotal=0;
         for (Int_t bin=0; bin<n; bin++){
            x[0] = gx[bin];
            x[1] = gy[bin];
            if (!f2->IsInside(x)) {
               continue;
            }
            z   = gz[bin];
            
            temp=f2->Eval(x[0], x[1]);
            temp2=(z-temp)*(z-temp);
            e=gr->GetErrorZ(bin);
            if (e<0 || fitOption.W1)
               e=1;
            temp2/=(e*e);
            
            sumtotal+=temp2;
         }
         fChisquare=sumtotal;
         f2->SetChisquare(fChisquare);
      }
   }
   return fitResult;
}

//______________________________________________________________________________
Int_t TLinearFitter::MultiGraphLinearFitter(Double_t h)
{
   //Minimisation function for a TMultiGraph
   Int_t n, i;
   Double_t *gx, *gy;
   Double_t e;
   TVirtualFitter *grFitter = TVirtualFitter::GetFitter();
   TMultiGraph *mg     = (TMultiGraph*)grFitter->GetObjectFit();
   TF1 *f1   = (TF1*)grFitter->GetUserFunc();
   Foption_t fitOption = grFitter->GetFitOption();
   Int_t fitResult=0;
   SetDim(1);

   if (fitOption.Robust){
      fRobust=kTRUE;
      StoreData(kTRUE);
   }
   SetFormula(f1);

   TGraph *gr;
   TIter next(mg->GetListOfGraphs());
   while ((gr = (TGraph*) next())) {
      n        = gr->GetN();
      gx   = gr->GetX();
      gy   = gr->GetY();
      for (i=0; i<n; i++){
         if (!f1->IsInside(&gx[i])) continue;
         e=gr->GetErrorY(i);
         if (e<0 || fitOption.W1)
            e=1;
         AddPoint(&gx[i], gy[i], e);
      }
   }

   if (fitOption.Robust){
      return EvalRobust(h);
   }

   fitResult = Eval();

   //calculate the chisquare
   if (!fitResult){
      if (!fitOption.Nochisq){
         Double_t temp, temp2, sumtotal=0;
         next.Reset();
         while((gr = (TGraph*)next())) {
            n        = gr->GetN();
            gx   = gr->GetX();
            gy   = gr->GetY();
            for (i=0; i<n; i++){
               if (!f1->IsInside(&gx[i])) continue;
               temp=f1->Eval(gx[i]);
               temp2=(gy[i]-temp)*(gy[i]-temp);
               e=gr->GetErrorY(i);
               if (e<0 || fitOption.W1)
                  e=1;
               temp2/=(e*e);
               
               sumtotal+=temp2;
            }
            
         }
         fChisquare=sumtotal;
         f1->SetChisquare(fChisquare);
      }
   }
   return fitResult;
}

//______________________________________________________________________________
Int_t TLinearFitter::HistLinearFitter()
{
   // Minimization function for H1s using a Chisquare method.

   StoreData(kFALSE);
   Double_t cu,eu;
   // Double_t dersum[100], grad[100];
   Double_t x[3];
   Int_t bin,binx,biny,binz;
   //   Axis_t binlow, binup, binsize;

   TH1 *hfit = (TH1*)GetObjectFit();
   TF1 *f1   = (TF1*)GetUserFunc();
   Int_t fitResult;
   Foption_t fitOption = GetFitOption();
   //SetDim(hfit->GetDimension());
   SetDim(f1->GetNdim());
   SetFormula(f1);

   Int_t hxfirst = GetXfirst();
   Int_t hxlast  = GetXlast();
   Int_t hyfirst = GetYfirst();
   Int_t hylast  = GetYlast();
   Int_t hzfirst = GetZfirst();
   Int_t hzlast  = GetZlast();
   TAxis *xaxis  = hfit->GetXaxis();
   TAxis *yaxis  = hfit->GetYaxis();
   TAxis *zaxis  = hfit->GetZaxis();

   for (binz=hzfirst;binz<=hzlast;binz++) {
      x[2]  = zaxis->GetBinCenter(binz);
      for (biny=hyfirst;biny<=hylast;biny++) {
         x[1]  = yaxis->GetBinCenter(biny);
         for (binx=hxfirst;binx<=hxlast;binx++) {
            x[0]  = xaxis->GetBinCenter(binx);
            if (!f1->IsInside(x)) continue;
            bin = hfit->GetBin(binx,biny,binz);
            cu  = hfit->GetBinContent(bin);
            if (f1->GetNdim() < hfit->GetDimension()) {
               if (hfit->GetDimension() > 2) cu = x[2];
               else                          cu = x[1];
            }
            if (fitOption.W1) {
               if (fitOption.W1==1 && cu == 0) continue;
               eu = 1;
            } else {
               eu  = hfit->GetBinError(bin);
               if (eu <= 0) continue;
            }
            AddPoint(x, cu, eu);
         }
      }
   }

   fitResult = Eval();

   if (!fitResult){
      if (!fitOption.Nochisq){
         Double_t temp, temp2, sumtotal=0;
         for (binz=hzfirst;binz<=hzlast;binz++) {
            x[2]  = zaxis->GetBinCenter(binz);
            for (biny=hyfirst;biny<=hylast;biny++) {
               x[1]  = yaxis->GetBinCenter(biny);
               for (binx=hxfirst;binx<=hxlast;binx++) {
                  x[0]  = xaxis->GetBinCenter(binx);
                  if (!f1->IsInside(x)) continue;
                  bin = hfit->GetBin(binx,biny,binz);
                  cu  = hfit->GetBinContent(bin);
                  
                  if (fitOption.W1) {
                     if (fitOption.W1==1 && cu == 0) continue;
                     eu = 1;
                  } else {
                     eu  = hfit->GetBinError(bin);
                     if (eu <= 0) continue;
                  }
                  temp=f1->EvalPar(x);
                  temp2=(cu-temp)*(cu-temp);
                  temp2/=(eu*eu);
                  sumtotal+=temp2;
               }
            }
         }
         
         fChisquare=sumtotal;
         f1->SetChisquare(fChisquare);
      }
   }
   return fitResult;
}

//____________________________________________________________________________
void TLinearFitter::Streamer(TBuffer &R__b)
{
   if (R__b.IsReading()) {
      Int_t old_matr_size = fNfunctions;
      R__b.ReadClassBuffer(TLinearFitter::Class(),this); 
      if (old_matr_size < fNfunctions) {
         fDesignTemp.ResizeTo(fNfunctions, fNfunctions);
         fAtbTemp.ResizeTo(fNfunctions);
         
         fDesignTemp2.ResizeTo(fNfunctions, fNfunctions);
         fDesignTemp3.ResizeTo(fNfunctions, fNfunctions);
         
         fAtbTemp2.ResizeTo(fNfunctions);
         fAtbTemp3.ResizeTo(fNfunctions);
      }
   } else {
      if (fAtb.NonZeros()==0) AddTempMatrices();
      R__b.WriteClassBuffer(TLinearFitter::Class(),this);
   }
} 

//______________________________________________________________________________
Int_t TLinearFitter::EvalRobust(Double_t h)
{
   //Finds the parameters of the fitted function in case data contains
   //outliers.
   //Parameter h stands for the minimal fraction of good points in the
   //dataset (h < 1, i.e. for 70% of good points take h=0.7).
   //The default value of h*Npoints is  (Npoints + Nparameters+1)/2
   //If the user provides a value of h smaller than above, default is taken
   //See class description for the algorithm details

   fRobust = kTRUE;
   Double_t kEps = 1e-13;
   Int_t nmini = 300;
   Int_t i, j, maxind=0, k, k1 = 500;
   Int_t nbest = 10;
   Double_t chi2 = -1;

   if (fFunctions.IsEmpty()&&(!fInputFunction)&&(fSpecial<=200)){
      Error("TLinearFitter::EvalRobust", "The formula hasn't been set");
      return 1;
   }


   Double_t *bestchi2 = new Double_t[nbest];
   for (i=0; i<nbest; i++)
      bestchi2[i]=1e30;

   Int_t hdef=Int_t((fNpoints+fNfunctions+1)/2);

   if (h<0.000001) fH = hdef;
   else if (h>0 && h<1 && fNpoints*h > hdef)
      fH = Int_t(fNpoints*h);
   else {
      Warning("Fitting:", "illegal value of H, default is taken");
      fH=hdef;
   }

   fDesign.ResizeTo(fNfunctions, fNfunctions);
   fAtb.ResizeTo(fNfunctions);
   fParams.ResizeTo(fNfunctions);

   Int_t *index = new Int_t[fNpoints];
   Double_t *residuals = new Double_t[fNpoints];

   if (fNpoints < 2*nmini) {
      //when number of cases is small

      //to store the best coefficients (columnwise)
      TMatrixD cstock(fNfunctions, nbest);
      for (k = 0; k < k1; k++) {
         CreateSubset(fNpoints, fH, index);
         chi2 = CStep(1, fH, residuals,index, index, -1, -1);
         chi2 = CStep(2, fH, residuals,index, index, -1, -1);
         maxind = TMath::LocMax(nbest, bestchi2);
         if (chi2 < bestchi2[maxind]) {
            bestchi2[maxind] = chi2;
            for (i=0; i<fNfunctions; i++)
               cstock(i, maxind) = fParams(i);
         }
      }

      //for the nbest best results, perform CSteps until convergence
      Int_t *bestindex = new Int_t[fH];
      Double_t currentbest;
      for (i=0; i<nbest; i++) {
         for (j=0; j<fNfunctions; j++)
            fParams(j) = cstock(j, i);
         chi2 = 1;
         while (chi2 > kEps) {
            chi2 = CStep(2, fH, residuals,index, index, -1, -1);
            if (TMath::Abs(chi2 - bestchi2[i]) < kEps)
               break;
            else
               bestchi2[i] = chi2;
         }
         currentbest = TMath::MinElement(nbest, bestchi2);
         if (chi2 <= currentbest + kEps) {
            for (j=0; j<fH; j++){
               bestindex[j]=index[j];
            }
            maxind = i;
         }
         for (j=0; j<fNfunctions; j++)
            cstock(j, i) = fParams(j);
      }
      //report the result with the lowest chisquare
      for (j=0; j<fNfunctions; j++)
         fParams(j) = cstock(j, maxind);
      fFitsample.SetBitNumber(fNpoints, kFALSE);
      for (j=0; j<fH; j++){
         //printf("bestindex[%d]=%d\n", j, bestindex[j]);
         fFitsample.SetBitNumber(bestindex[j]);
      }
      if (fInputFunction && fInputFunction->InheritsFrom(TF1::Class())) {
         ((TF1*)fInputFunction)->SetChisquare(bestchi2[maxind]);
         ((TF1*)fInputFunction)->SetNumberFitPoints(fH);
         ((TF1*)fInputFunction)->SetNDF(fH-fNfunctions);
      }
      delete [] index;
      delete [] bestindex;
      delete [] residuals;
      delete [] bestchi2;
      return 0;
   }
   //if n is large, the dataset should be partitioned
   Int_t indsubdat[5];
   for (i=0; i<5; i++)
      indsubdat[i] = 0;

   Int_t nsub = Partition(nmini, indsubdat);
   Int_t hsub;

   Int_t sum = TMath::Min(nmini*5, fNpoints);

   Int_t *subdat = new Int_t[sum]; //to store the indices of selected cases
   RDraw(subdat, indsubdat);

   TMatrixD cstockbig(fNfunctions, nbest*5);
   Int_t *beststock = new Int_t[nbest];
   Int_t i_start = 0;
   Int_t i_end = indsubdat[0];
   Int_t k2 = Int_t(k1/nsub);
   for (Int_t kgroup = 0; kgroup < nsub; kgroup++) {

      hsub = Int_t(fH * indsubdat[kgroup]/fNpoints);
      for (i=0; i<nbest; i++)
         bestchi2[i] = 1e16;
      for (k=0; k<k2; k++) {
         CreateSubset(indsubdat[kgroup], hsub, index);
         chi2 = CStep(1, hsub, residuals, index, subdat, i_start, i_end);
         chi2 = CStep(2, hsub, residuals, index, subdat, i_start, i_end);
         maxind = TMath::LocMax(nbest, bestchi2);
         if (chi2 < bestchi2[maxind]){
            for (i=0; i<fNfunctions; i++)
               cstockbig(i, nbest*kgroup + maxind) = fParams(i);
            bestchi2[maxind] = chi2;
         }
      }
      if (kgroup != nsub - 1){
         i_start += indsubdat[kgroup];
         i_end += indsubdat[kgroup+1];
      }
   }

   for (i=0; i<nbest; i++)
      bestchi2[i] = 1e30;
   //on the pooled subset
   Int_t hsub2 = Int_t(fH*sum/fNpoints);
   for (k=0; k<nbest*5; k++) {
      for (i=0; i<fNfunctions; i++)
         fParams(i)=cstockbig(i, k);
      chi2 = CStep(1, hsub2, residuals, index, subdat, 0, sum);
      chi2 = CStep(2, hsub2, residuals, index, subdat, 0, sum);
      maxind = TMath::LocMax(nbest, bestchi2);
      if (chi2 < bestchi2[maxind]){
         beststock[maxind] = k;
         bestchi2[maxind] = chi2;
      }
   }

   //now the array beststock keeps indices of 10 best candidates in cstockbig matrix
   for (k=0; k<nbest; k++) {
      for (i=0; i<fNfunctions; i++)
         fParams(i) = cstockbig(i, beststock[k]);
      chi2 = CStep(1, fH, residuals, index, index, -1, -1);
      chi2 = CStep(2, fH, residuals, index, index, -1, -1);
      bestchi2[k] = chi2;
   }

   maxind = TMath::LocMin(nbest, bestchi2);
   for (i=0; i<fNfunctions; i++)
      fParams(i)=cstockbig(i, beststock[maxind]);

   chi2 = 1;
   while (chi2 > kEps) {
      chi2 = CStep(2, fH, residuals, index, index, -1, -1);
      if (TMath::Abs(chi2 - bestchi2[maxind]) < kEps)
         break;
      else
         bestchi2[maxind] = chi2;
   }

   fFitsample.SetBitNumber(fNpoints, kFALSE);
   for (j=0; j<fH; j++)
      fFitsample.SetBitNumber(index[j]);
   if (fInputFunction){
      ((TF1*)fInputFunction)->SetChisquare(bestchi2[maxind]);
      ((TF1*)fInputFunction)->SetNumberFitPoints(fH);
      ((TF1*)fInputFunction)->SetNDF(fH-fNfunctions);
   }

   delete [] subdat;
   delete [] beststock;
   delete [] bestchi2;
   delete [] residuals;
   delete [] index;

   return 0;
}

//____________________________________________________________________________
void TLinearFitter::CreateSubset(Int_t ntotal, Int_t h, Int_t *index)
{
   //Creates a p-subset to start
   //ntotal - total number of points from which the subset is chosen

   Int_t i, j;
   Bool_t repeat=kFALSE;
   Int_t nindex=0;
   Int_t num;
   for(i=0; i<ntotal; i++)
      index[i] = ntotal+1;

   TRandom2 r;
   //create a p-subset
   for (i=0; i<fNfunctions; i++) {
      num=Int_t(r.Uniform(0, 1)*(ntotal-1));
      if (i>0){
         for(j=0; j<=i-1; j++) {
            if(index[j]==num)
               repeat = kTRUE;
         }
      }
      if(repeat==kTRUE) {
         i--;
         repeat = kFALSE;
      } else {
         index[i] = num;
         nindex++;
      }
   }

   //compute the coefficients of a hyperplane through the p-subset
   fDesign.Zero();
   fAtb.Zero();
   for (i=0; i<fNfunctions; i++){
      AddToDesign(TMatrixDRow(fX, index[i]).GetPtr(), fY(index[i]), fE(index[i]));
   }
   Bool_t ok;

   ok = Linf();

   //if the chosen points don't define a hyperplane, add more
   while (!ok && (nindex < h)) {
      repeat=kFALSE;
      do{
         num=Int_t(r.Uniform(0,1)*(ntotal-1));
         repeat=kFALSE;
         for(i=0; i<nindex; i++) {
            if(index[i]==num) {
               repeat=kTRUE;
               break;
            }
         }
      } while(repeat==kTRUE);

      index[nindex] = num;
      nindex++;
      //check if the system is of full rank now
      AddToDesign(TMatrixDRow(fX, index[nindex-1]).GetPtr(), fY(index[nindex-1]), fE(index[nindex-1]));
      ok = Linf();
   }
}

//____________________________________________________________________________
Double_t TLinearFitter::CStep(Int_t step, Int_t h, Double_t *residuals, Int_t *index, Int_t *subdat, Int_t start, Int_t end)
{
   //The CStep procedure, as described in the article

   R__ASSERT( !fFunctions.IsEmpty() || fInputFunction ||  fSpecial>200);

   Int_t i, j, itemp, n;
   Double_t func;
   Double_t val[100];
   Int_t npar;
   if (start > -1) {
      n = end - start;
      for (i=0; i<n; i++) {
         func = 0;
         itemp = subdat[start+i];
         if (fInputFunction){
            fInputFunction->SetParameters(fParams.GetMatrixArray());
            func=fInputFunction->EvalPar(TMatrixDRow(fX, itemp).GetPtr());
         } else {
            func=0;
            if ((fSpecial>100)&&(fSpecial<200)){
                  npar = fSpecial-100;
                  val[0] = 1;
                  for (j=1; j<npar; j++)
                     val[j] = val[j-1]*fX(itemp, 0);
                  for (j=0; j<npar; j++)
                     func += fParams(j)*val[j];
            } else if (fSpecial>200) {
               //hyperplane case
               npar = fSpecial-201;
               func+=fParams(0);
               for (j=0; j<npar; j++)
                  func += fParams(j+1)*fX(itemp, j);
            } else {
               // general case
               for (j=0; j<fNfunctions; j++) {
                  TF1 *f1 = (TF1*)(fFunctions.UncheckedAt(j));
                  val[j] = f1->EvalPar(TMatrixDRow(fX, itemp).GetPtr());
                  func += fParams(j)*val[j];
               }
            }
         }
         residuals[i] = (fY(itemp) - func)*(fY(itemp) - func)/(fE(i)*fE(i));
      }
   } else {
      n=fNpoints;
      for (i=0; i<fNpoints; i++) {
         func = 0;
         if (fInputFunction){
            fInputFunction->SetParameters(fParams.GetMatrixArray());
            func=fInputFunction->EvalPar(TMatrixDRow(fX, i).GetPtr());
         } else {
            func=0;
            if ((fSpecial>100)&&(fSpecial<200)){
               npar = fSpecial-100;
               val[0] = 1;
               for (j=1; j<npar; j++)
                  val[j] = val[j-1]*fX(i, 0);
               for (j=0; j<npar; j++)
                  func += fParams(j)*val[j];
            } else if (fSpecial>200) {
               //hyperplane case
               npar = fSpecial-201;
               func+=fParams(0);
               for (j=0; j<npar; j++)
                  func += fParams(j+1)*fX(i, j);
            } else {
               for (j=0; j<fNfunctions; j++) {
                  TF1 *f1 = (TF1*)(fFunctions.UncheckedAt(j));
                  val[j] = f1->EvalPar(TMatrixDRow(fX, i).GetPtr());
                  func += fParams(j)*val[j];
               }
            }
         }
         residuals[i] = (fY(i) - func)*(fY(i) - func)/(fE(i)*fE(i));
      }
   }
   //take h with smallest residuals
   TMath::KOrdStat(n, residuals, h-1, index);
   //add them to the design matrix
   fDesign.Zero();
   fAtb.Zero();
   for (i=0; i<h; i++)
      AddToDesign(TMatrixDRow(fX, index[i]).GetPtr(), fY(index[i]), fE(index[i]));

   Linf();

   //don't calculate the chisquare at the 1st cstep
   if (step==1) return 0;
   Double_t sum=0;


   if (start > -1) {
      for (i=0; i<h; i++) {
         itemp = subdat[start+index[i]];
         if (fInputFunction){
            fInputFunction->SetParameters(fParams.GetMatrixArray());
            func=fInputFunction->EvalPar(TMatrixDRow(fX, itemp).GetPtr());
         } else {
            func=0;
            if ((fSpecial>100)&&(fSpecial<200)){
                  npar = fSpecial-100;
                  val[0] = 1;
                  for (j=1; j<npar; j++)
                     val[j] = val[j-1]*fX(itemp, 0);
                  for (j=0; j<npar; j++)
                     func += fParams(j)*val[j];
            } else if (fSpecial>200) {
               //hyperplane case
               npar = fSpecial-201;
               func+=fParams(0);
               for (j=0; j<npar; j++)
                  func += fParams(j+1)*fX(itemp, j);
            } else {
               for (j=0; j<fNfunctions; j++) {
                  TF1 *f1 = (TF1*)(fFunctions.UncheckedAt(j));
                  val[j] = f1->EvalPar(TMatrixDRow(fX, itemp).GetPtr());
                  func += fParams(j)*val[j];
               }
            }
         }
         sum+=(fY(itemp)-func)*(fY(itemp)-func)/(fE(itemp)*fE(itemp));
      }
   } else {
      for (i=0; i<h; i++) {
         if (fInputFunction){
            fInputFunction->SetParameters(fParams.GetMatrixArray());
            func=fInputFunction->EvalPar(TMatrixDRow(fX, index[i]).GetPtr());
         } else {
            func=0;
            if ((fSpecial>100)&&(fSpecial<200)){
               npar = fSpecial-100;
               val[0] = 1;
               for (j=1; j<npar; j++)
                  val[j] = val[j-1]*fX(index[i], 0);
               for (j=0; j<npar; j++)
                  func += fParams(j)*val[j];
            } else {
               if (fSpecial>200) {
                  //hyperplane case
                  npar = fSpecial-201;
                  func+=fParams(0);
                  for (j=0; j<npar; j++)
                     func += fParams(j+1)*fX(index[i], j);
               } else {
                  for (j=0; j<fNfunctions; j++) {
                     TF1 *f1 = (TF1*)(fFunctions.UncheckedAt(j));
                     val[j] = f1->EvalPar(TMatrixDRow(fX, index[i]).GetPtr());
                     func += fParams(j)*val[j];
                  }
               }
            }
         }

         sum+=(fY(index[i])-func)*(fY(index[i])-func)/(fE(index[i])*fE(index[i]));
      }
   }

   return sum;
}

//____________________________________________________________________________
Bool_t TLinearFitter::Linf()
{

   //currently without the intercept term
   fDesignTemp2+=fDesignTemp3;
   fDesignTemp+=fDesignTemp2;
   fDesign+=fDesignTemp;
   fDesignTemp3.Zero();
   fDesignTemp2.Zero();
   fDesignTemp.Zero();
   fAtbTemp2+=fAtbTemp3;
   fAtbTemp+=fAtbTemp2;
   fAtb+=fAtbTemp;
   fAtbTemp3.Zero();
   fAtbTemp2.Zero();
   fAtbTemp.Zero();

   fY2+=fY2Temp;
   fY2Temp=0;


   TDecompChol chol(fDesign);
   TVectorD temp(fNfunctions);
   Bool_t ok;
   temp = chol.Solve(fAtb, ok);
   if (!ok){
      Error("Linf","Matrix inversion failed");
      //fDesign.Print();
      fParams.Zero();
      return kFALSE;
   }
   fParams = temp;
   return ok;
}

//____________________________________________________________________________
Int_t TLinearFitter::Partition(Int_t nmini, Int_t *indsubdat)
{
   //divides the elements into approximately equal subgroups
   //number of elements in each subgroup is stored in indsubdat
   //number of subgroups is returned

   Int_t nsub;

   if ((fNpoints>=2*nmini) && (fNpoints<=(3*nmini-1))) {
      if (fNpoints%2==1){
         indsubdat[0]=Int_t(fNpoints*0.5);
         indsubdat[1]=Int_t(fNpoints*0.5)+1;
      } else
         indsubdat[0]=indsubdat[1]=Int_t(fNpoints/2);
      nsub=2;
   }
   else{
      if((fNpoints>=3*nmini) && (fNpoints<(4*nmini -1))) {
         if(fNpoints%3==0){
            indsubdat[0]=indsubdat[1]=indsubdat[2]=Int_t(fNpoints/3);
         } else {
            indsubdat[0]=Int_t(fNpoints/3);
            indsubdat[1]=Int_t(fNpoints/3)+1;
            if (fNpoints%3==1) indsubdat[2]=Int_t(fNpoints/3);
            else indsubdat[2]=Int_t(fNpoints/3)+1;
         }
         nsub=3;
      }
      else{
         if((fNpoints>=4*nmini)&&(fNpoints<=(5*nmini-1))){
            if (fNpoints%4==0) indsubdat[0]=indsubdat[1]=indsubdat[2]=indsubdat[3]=Int_t(fNpoints/4);
            else {
               indsubdat[0]=Int_t(fNpoints/4);
               indsubdat[1]=Int_t(fNpoints/4)+1;
               if(fNpoints%4==1) indsubdat[2]=indsubdat[3]=Int_t(fNpoints/4);
               if(fNpoints%4==2) {
                  indsubdat[2]=Int_t(fNpoints/4)+1;
                  indsubdat[3]=Int_t(fNpoints/4);
               }
               if(fNpoints%4==3) indsubdat[2]=indsubdat[3]=Int_t(fNpoints/4)+1;
            }
            nsub=4;
         } else {
            for(Int_t i=0; i<5; i++)
               indsubdat[i]=nmini;
            nsub=5;
         }
      }
   }
   return nsub;
}

//____________________________________________________________________________
void TLinearFitter::RDraw(Int_t *subdat, Int_t *indsubdat)
{
   //Draws ngroup nonoverlapping subdatasets out of a dataset of size n
   //such that the selected case numbers are uniformly distributed from 1 to n

   Int_t jndex = 0;
   Int_t nrand;
   Int_t i, k, m, j;
   Int_t ngroup=0;
   for (i=0; i<5; i++) {
      if (indsubdat[i]!=0)
         ngroup++;
   }
   TRandom r;
   for (k=1; k<=ngroup; k++) {
      for (m=1; m<=indsubdat[k-1]; m++) {
         nrand = Int_t(r.Uniform(0, 1) * (fNpoints-jndex)) + 1;
         jndex++;
         if (jndex==1) {
            subdat[0] = nrand;
         } else {
            subdat[jndex-1] = nrand + jndex - 2;
            for (i=1; i<=jndex-1; i++) {
               if(subdat[i-1] > nrand+i-2) {
                  for(j=jndex; j>=i+1; j--) {
                     subdat[j-1] = subdat[j-2];
                  }
                  subdat[i-1] = nrand+i-2;
                  break;  //breaking the loop for(i=1...
               }
            }
         }
      }
   }
}

---