Exemplo n.º 1
0
Asymmetry estimateAsymmetry(
    const TH1* hist, const TH2* cov, 
    const char * minName = "Minuit2",
    const char *algoName = "" )
{
    
    TH1* normHist=(TH1*)hist->Clone("normHist");
    TH2* normCov=(TH2*)cov->Clone("normCov");
    
    
    
    normHist->Scale(1.0/hist->Integral());
    normCov->Scale(1.0/hist->Integral()/hist->Integral());

    const int N = hist->GetNbinsX();

    TMatrixD covMatrix(N,N);
    
    for (int i=0; i<N;++i)
    {
        for (int j=0; j<N;++j)
        {
            covMatrix[i][j]=normCov->GetBinContent(i+1,j+1);
        }
    }
    TMatrixD invCovMatrix = TMatrixD(TMatrixD::kInverted,covMatrix);
    
    
    
    ROOT::Math::Minimizer* min = ROOT::Math::Factory::CreateMinimizer(minName, algoName);

    // set tolerance , etc...
    min->SetMaxFunctionCalls(1000000); // for Minuit/Minuit2 
    min->SetMaxIterations(10000);  // for GSL 
    min->SetTolerance(0.001);
    min->SetPrintLevel(1);
    //const double xx[1] = {0.5};
    std::function<double(const TH1*, const TMatrixD*, const double*)> unboundFct = chi2A;
    std::function<double(const double*)> boundFct = std::bind(unboundFct,normHist, &invCovMatrix, std::placeholders::_1);
    
    //boundFct(xx);
    ROOT::Math::Functor fct(boundFct,1); 


    min->SetFunction(fct);

    min->SetVariable(0,"A",0.2, 0.01);
    min->Minimize(); 

    const double *xs = min->X();
    const double *error = min->Errors();
    log(INFO,"min: %f\n",xs[0]);
    log(INFO,"err: %f\n",error[0]);
    Asymmetry res;
    res.mean=xs[0];
    res.uncertainty=error[0];
    return res;
}
Exemplo n.º 2
0
  void solve(TString outFileName){
    ROOT::Math::Minimizer* min = ROOT::Math::Factory::CreateMinimizer("Minuit2", "MIGRAD");
    min->SetMaxFunctionCalls(1000000);
    min->SetTolerance(0.001);
    min->SetPrintLevel(10);

        ROOT::Math::Functor f(&totalDist,4);
    double step[4] = {0.01,0.01,.01,.01};
    double variable[4] = { 0,0,50,0};
    min->SetFunction(f);
    min->SetVariable(0,"x"  ,variable[0], step[0]);
    min->SetVariable(1,"y"  ,variable[1], step[1]);
    min->SetVariable(2,"z"  ,variable[2], step[2]);
    min->SetVariable(3,"phi",variable[3], step[3]);

       // do the minimization
       min->Minimize();

       const double *xs = min->X();
       std::cout << "Minimum: f(" << xs[0] << "," << xs[1]<< "," << xs[2]<< "," << xs[3] << "): "
                 << min->MinValue()  << std::endl;


       setZ=xs[2];

       ROOT::Math::Minimizer* min2 = ROOT::Math::Factory::CreateMinimizer("Minuit2", "MIGRAD");
       min2->SetMaxFunctionCalls(1000000);
       min2->SetTolerance(0.001);
       min2->SetPrintLevel(10);

           ROOT::Math::Functor f2(&totalDistWithoutZ,3);
       double step2[3] = {0.01,0.01,.01};
       double variable2[3] = { xs[0],xs[1],xs[3]};
       min2->SetFunction(f2);
       min2->SetVariable(0,"x"  ,variable2[0], step2[0]);
       min2->SetVariable(1,"y"  ,variable2[1], step2[1]);
       min2->SetVariable(2,"phi",variable2[2], step2[2]);

          // do the minimization
          min2->Minimize();

          const double *xs2 = min2->X();
          std::cout << "Minimum: f(" << xs2[0] << "," << xs2[1]<< "," << xs2[2] << "): "
                    << min2->MinValue()  << std::endl;




//       // expected minimum is 0
//       if ( min->MinValue()  < 1.E-4  && f(xs) < 1.E-4)
//          std::cout << "   converged to the right minimum" << std::endl;
//       else {
//          std::cout << "   failed to converge !!!" << std::endl;
//          Error("NumericalMinimization","fail to converge");
//       }
  }
Exemplo n.º 3
0
void find_chisqMin()
{
  chisq=0.;
  for(int i=0; i<numSpectra; i++)
    {
      // for more information see minimizer class documentation
      // https://root.cern.ch/root/html/ROOT__Math__Minimizer.html
      char minName[132] = "Minuit";
      char algoName[132] = ""; // default conjugate gradient type method
      ROOT::Math::Minimizer* min = ROOT::Math::Factory::CreateMinimizer(minName, algoName);
  
      // set tolerance , etc...
      min->SetMaxFunctionCalls(1000000); // for Minuit
      min->SetMaxIterations(10000);      // for GSL 
      min->SetTolerance(0.001);
      min->SetPrintLevel(0);             // set to 1 for more info
      
      // communication to the likelihood ratio function
      // (via global parameters)
      for(int j=0; j<S32K; j++)
	{
	  expCurrent[j] = (double)expHist[spectrum[i]][j];
	  simCurrent[j] = (double)dOutHist[spectrum[i]][j];
	}
      spCurrent = i;
      
      // create funciton wrapper for minmizer
      // a IMultiGenFunction type 
      ROOT::Math::Functor lr(&lrchisq,3); 
      
      // behaves best when these are small
      // starting point    
      double variable[3] = {0.001,0.001,0.001};
      // step size
      double step[3] = {0.0001,0.0001,0.0001};
      
      min->SetFunction(lr);
      
      // Set pars for minimization
      min->SetVariable(0,"a0",variable[0],step[0]);
      min->SetVariable(1,"a1",variable[1],step[1]);
      min->SetVariable(2,"a2",variable[2],step[2]);
      
      // do the minimization
      min->Minimize(); 
      
      // grab parameters from minimum
      const double *xs = min->X();

      // print results
      /* std::cout << "Minimum: f(" << xs[0] << "," << xs[1] << "," << xs[2] << "): " */
      /* 		<< min->MinValue()  << std::endl; */

      // assuming 3 parameters
      // save pars
      for(int j=0;j<3;j++)
	aFinal[j][i] = xs[j];

      // add to total chisq
      chisq += min->MinValue();
    }
}
/* Main part of macro */
void fitData( TGraphErrors *gdata , TF1* ffit , double *startval )
{
  cout << "\n***** fitData.C: Starting fitting procedure... *****" << endl;

  g_data_global = gdata;
  f_fit_global = ffit;

  if ( g_data_global == NULL )
  {
    cout << "fitData.C: Did no find any data to fit." << endl;
    return NULL;
  }

  const char * minName = "Minuit2";
  const char *algoName = "Migrad";

  // create minimizer giving a name and a name (optionally) for the specific
  // algorithm
  // possible choices are:
  //     minName                  algoName
  // Minuit /Minuit2             Migrad, Simplex,Combined,Scan  (default is Migrad)
  //  Minuit2                     Fumili2
  //  Fumili
  //  GSLMultiMin                ConjugateFR, ConjugatePR, BFGS,
  //                              BFGS2, SteepestDescent
  //  GSLMultiFit
  //   GSLSimAn
  //   Genetic
  ROOT::Math::Minimizer* min =
  ROOT::Math::Factory::CreateMinimizer(minName, algoName);

  /* Alternatice constructor for Minuit */
  //ROOT::Minuit2::Minuit2Minimizer *min = new ROOT::Minuit2::Minuit2Minimizer();

  //TMinuit *min = new TMinuit();

  // set tolerance , etc...
  min->SetMaxFunctionCalls(1000000); // for Minuit/Minuit2
  min->SetMaxIterations(10000);  // for GSL
  min->SetTolerance(0.001);
  min->SetPrintLevel(1);

  // create funciton wrapper for minmizer
  // a IMultiGenFunction type
  ROOT::Math::Functor f(&Chi2_log,3);
  double step[3] = {0.1,0.1,10};

  // starting point
  double variable[3] = { startval[0],startval[1],startval[2]};

  // set function to minimize (this is the Chi2 function)
  min->SetFunction(f);

  // Set the free variables to be minimized!
  min->SetVariable(0,"x",variable[0], step[0]);
  min->SetVariable(1,"y",variable[1], step[1]);
  min->SetVariable(2,"z",variable[2], step[2]);

  // do the minimization
  min->Minimize();

  /* set function parameters to best fit results */
  const double *xs = min->X();

  f_fit_global->SetParameter(0, xs[0]);
  f_fit_global->SetParameter(1, xs[1]);
  f_fit_global->SetParameter(2, xs[2]);

  /* Print summaries of minimization process */
  std::cout << "Minimum: f(" << xs[0] << ", " << xs[1] << ", " << xs[2] << "): "
  << min->MinValue()  << std::endl;

  // expected minimum is 0
  if ( min->MinValue()  < 1.E-4  && f(xs) < 1.E-4)
  std::cout << "Minimizer " << minName << " - " << algoName
  << "   converged to the right minimum" << std::endl;
  else {
    std::cout << "Minimizer " << minName << " - " << algoName
    << "   failed to converge !!!" << std::endl;
    Error("NumericalMinimization","fail to converge");
  }

  /* Get degrees of freedom NDF */
  unsigned ndf = 0;

  /* get range of function used for fit */
  double fit_min, fit_max;
  f_fit_global->GetRange(fit_min,fit_max);

  /* count data points in range of function */
  for ( int p = 0; p < g_data_global->GetN(); p++ )
  {
    if ( g_data_global->GetX()[p] >= fit_min && g_data_global->GetX()[p] <= fit_max )
    {
      ndf++;
    }
  }
  ndf -= 3; // 3 parameters in fit

  cout << "Degrees of freedom: " << ndf << " --> chi2 / NDF = " << min->MinValue() / ndf << endl;

  /* Get error covariance matrix from minimizer */
  TMatrixD matrix0(3,3);
  for ( unsigned i = 0; i < 3; i++ )
  {
    for ( unsigned j = 0; j < 3; j++ )
    {
      matrix0[i][j] = min->CovMatrix(i,j);
    }
  }
  matrix0.Print();

  /* Get minos error */
  double par0_minos_error_up = 0;
  double par0_minos_error_low = 0;
  double par1_minos_error_up = 0;
  double par1_minos_error_low = 0;
  double par2_minos_error_up = 0;
  double par2_minos_error_low = 0;

  min->GetMinosError( 0, par0_minos_error_low, par0_minos_error_up );
  min->GetMinosError( 1, par1_minos_error_low, par1_minos_error_up );
  min->GetMinosError( 2, par2_minos_error_low, par2_minos_error_up );

  cout << "Minos uncertainty parameter 0: up = " << par0_minos_error_up << ", low = " << par0_minos_error_low << endl;
  cout << "Minos uncertainty parameter 1: up = " << par1_minos_error_up << ", low = " << par1_minos_error_low << endl;
  cout << "Minos uncertainty parameter 2: up = " << par2_minos_error_up << ", low = " << par2_minos_error_low << endl;

  /* Plot chi2 */
  /* sigmas symmetric from covariance matrix */
  //double sigmas[6] = {sqrt(matrix0[0][0]), sqrt(matrix0[0][0]), sqrt(matrix0[1][1]), sqrt(matrix0[1][1]), sqrt(matrix0[2][2]), sqrt(matrix0[2][2])};
  /* sigmas asymmetric from minos */
  double sigmas[6] = {par0_minos_error_low, par0_minos_error_up, par1_minos_error_low, par1_minos_error_up, par2_minos_error_low, par2_minos_error_up};
  plotChi2( g_data_global, f_fit_global, 3, sigmas );

  /* Draw contour plots */
  TGraph2D* gcontour3D = plotContour( min , 3 , ndf );

  /* Find error boundaries */
  TF1* flow = (TF1*)f_fit_global->Clone("flow");
  TF1* fup = (TF1*)f_fit_global->Clone("fup");
  flow->SetRange(0,100000);
  flow->SetLineColor(kBlue);
  flow->SetLineStyle(2);
  fup->SetRange(0,100000);
  fup->SetLineColor(kBlue);
  fup->SetLineStyle(2);
  findErrorBounds( f_fit_global, flow, fup, gcontour3D );

  /* plot residuals data w.r.t. fit */
  plotResiduals( g_data_global, f_fit_global, flow, fup );

  /* Draw data, best fit, and 1-sigma band */
  TCanvas *cfit = new TCanvas();
  g_data_global->Draw("AP");
  //f_fit_global->SetRange(0,4000);
  f_fit_global->Draw("same");
  flow->Draw("same");
  fup->Draw("same");

  cfit->Print("new_FitResult.png");

  /* Fit Extrapolation */
  double t_extrapolate_months = 6;
  double t_extrapolate_s = t_extrapolate_months * 30 * 24 * 60 * 60;
  cout << "Extrapolation to " << t_extrapolate_months
  << " months: " << ffit->Eval( t_extrapolate_s )
  << " , up: " << fup->Eval( t_extrapolate_s ) - ffit->Eval( t_extrapolate_s )
  << " , low: " << flow->Eval( t_extrapolate_s ) - ffit->Eval( t_extrapolate_s )
  << endl;


  return f_fit_global;
}
int main(int argc, char** argv)
{
//    ROOT::Math::Minimizer* minuit = ROOT::Math::Factory::CreateMinimizer("Genetic");  //---> next ROOT  release!
 ROOT::Math::Minimizer* minuit = ROOT::Math::Factory::CreateMinimizer("Minuit", "Migrad2");
 ROOT::Math::Functor functorChi2(&Chi2Func,6); 
 
 TString genCut; //==== (eleFBrem<0.8&&eleCharge>0)

 bool traslationX ;
 bool traslationY ;
 bool traslationZ ;
 bool rotationPhi ;
 bool rotationTheta ;
 bool rotationPsi ;
 
 std::string fileName (argv[1]) ;
 boost::shared_ptr<edm::ParameterSet> parameterSet = edm::readConfig(fileName) ;

 edm::ParameterSet subPSetInput = parameterSet->getParameter<edm::ParameterSet> ("inputTree") ;
 std::vector<std::string> nameFileIn = subPSetInput.getParameter<std::vector<std::string> > ("inputFiles") ;
 std::string nameTree = subPSetInput.getParameter<std::string> ("nameTree") ;
 std::string selection = subPSetInput.getParameter<std::string> ("selection") ;
 genCut = Form("%s",selection.c_str());
 traslationX = subPSetInput.getParameter<bool> ("traslationX") ;
 traslationY = subPSetInput.getParameter<bool> ("traslationY") ;
 traslationZ = subPSetInput.getParameter<bool> ("traslationZ") ;
 rotationPhi   = subPSetInput.getParameter<bool> ("rotationPhi") ;
 rotationTheta = subPSetInput.getParameter<bool> ("rotationTheta") ;
 rotationPsi   = subPSetInput.getParameter<bool> ("rotationPsi") ;
     
 double setRotationPhi     = subPSetInput.getUntrackedParameter<double> ("setRotationPhi",0) ;
 double setRotationTheta   = subPSetInput.getUntrackedParameter<double> ("setRotationTheta",0) ;
 double setRotationPsi     = subPSetInput.getUntrackedParameter<double> ("setRotationPsi",0) ;

 
 even = subPSetInput.getUntrackedParameter<bool> ("even",true) ;
 odd = subPSetInput.getUntrackedParameter<bool> ("odd",true) ;

 edm::ParameterSet subPSetOutput = parameterSet->getParameter<edm::ParameterSet> ("outputTree") ;
 std::string nameFileOut = subPSetOutput.getParameter<std::string> ("outputFile") ;

 //==== plot input/output ====
 std::cout << " nameFileIn = ";
 for (unsigned int i=0; i<nameFileIn.size(); i++ ) std::cout << "    " << nameFileIn.at(i) << std::endl;
 std::cout << " nameFileOut = " << nameFileOut << std::endl;
 std::cout << " genCut = " << genCut.Data() << std::endl;
  
 ///==== input DATA ==== 
 myTree = new TChain(nameTree.c_str());
 int numberInput = 0;
 for (std::vector<std::string>::const_iterator listIt = nameFileIn.begin () ; listIt != nameFileIn.end () ; ++listIt) {
  numberInput++;
  myTree->Add (listIt->c_str ()) ;
  if (numberInput%4 == 0) std::cerr << "Input number " << numberInput << " ... " << listIt->c_str () << std::endl;
 }


 ///==== bias functions ==== 
 
 std::string FunctionDetaName = subPSetInput.getUntrackedParameter<std::string> ("DetaBias","0") ; // x = eta, y = charge
 std::string FunctionDphiName = subPSetInput.getUntrackedParameter<std::string> ("DphiBias","0") ;

 FunctionDeta = new TF2 ("DetaBias",FunctionDetaName.c_str(),-5,5,-2,2);
 FunctionDphi = new TF2 ("DphiBias",FunctionDphiName.c_str(),-5,5,-2,2);

 //==== output DATA ====
 
 ///==== Input ECAL position ====
 std::string inputFilesPosition = subPSetInput.getUntrackedParameter<std::string> ("inputFilesPosition","") ;

 ///==== Build variables ====
 
 double DX_SC_Mean[4];
 double DX_SC_RMS[4];
 double DY_SC_Mean[4];
 double DY_SC_RMS[4];
 double DZ_SC_Mean[4];
 double DZ_SC_RMS[4];
 
 double DTHETAe_SC_Mean[4];
 double DTHETAe_SC_RMS[4];
 double DPSIe_SC_Mean[4];
 double DPSIe_SC_RMS[4];
 double DPHIe_SC_Mean[4];
 double DPHIe_SC_RMS[4];
 
 
 std::ifstream* file;
 if (inputFilesPosition != ""){
  file = new std::ifstream(inputFilesPosition.c_str());
  if(!file->is_open())
  {
   return false;
  }
 }
 
 for (int iSC = 0; iSC<4; iSC++){
  TString cut;
  cut = Form("%s && iDetEB < -10 && iDetEE == %d",genCut.Data(),iSC);
  std::cout << "  cut = " << cut.Data() << std::endl;
  
  ///===========================
  ///==== Chi2 minimization ====
  
  double inputDX = 0;
  double inputDY = 0;
  double inputDZ = 0;
  double inputDPHIe = 0;
  double inputDTHETAe = 0;
  double inputDPSIe = 0;
  if (inputFilesPosition != ""){
   std::string buffer;
   getline(*file,buffer);
   std::stringstream line( buffer );
   line >> inputDPHIe;
   line >> inputDTHETAe;
   line >> inputDPSIe;
   line >> inputDX; inputDX/=100;
   line >> inputDY; inputDY/=100;
   line >> inputDZ; inputDZ/=100; 
  }
  
  std::cerr << " inputDPHIe   = " << inputDPHIe << std::endl;
  std::cerr << " inputDTHETAe = " << inputDTHETAe << std::endl;
  std::cerr << " inputDPSIe   = " << inputDPSIe << std::endl;
  std::cerr << " inputDX      = " << inputDX << std::endl;
  std::cerr << " inputDY      = " << inputDY << std::endl;
  std::cerr << " inputDZ      = " << inputDZ << std::endl;

  
  std::cout << " Chi2 minimization " << std::endl;
  
  globalCut = cut;
  //   unsigned int iNoSteps = 1000;
  //   unsigned int iPar_NoBG = 0;
  minuit->SetFunction(functorChi2);
  minuit->SetMaxFunctionCalls(100000);
  minuit->SetMaxIterations(10000);
  minuit->SetTolerance(0.000002);
  
  if (traslationX)  minuit->SetLimitedVariable(0,"DX",inputDX, 0.00001,-0.050,0.050);
  else  minuit->SetFixedVariable(0,"DX",0);

  if (traslationY)  minuit->SetLimitedVariable(1,"DY",inputDY, 0.00001,-0.050,0.050);
  else  minuit->SetFixedVariable(1,"DY",0);

  if (traslationZ)  minuit->SetLimitedVariable(2,"DZ",inputDZ, 0.00001,-0.050,0.050);
  else  minuit->SetFixedVariable(2,"DZ",0);


  if (rotationPhi)  minuit->SetLimitedVariable(3,"DPHIe",inputDPHIe, 0.00001,-3.15,3.15);
  else  minuit->SetFixedVariable(3,"DPHIe",inputDPHIe);

  if (rotationTheta)  minuit->SetLimitedVariable(4,"DTHETAe",inputDTHETAe, 0.00001,-3.15,3.15);
  else  minuit->SetFixedVariable(4,"DTHETAe",inputDTHETAe);

  if (rotationPsi)  minuit->SetLimitedVariable(5,"DPSIe",inputDPSIe, 0.00001,-3.15,3.15);
  else  minuit->SetFixedVariable(5,"DPSIe",inputDPSIe);

 
  minuit->Minimize();
  minuit->PrintResults();
  
  DX_SC_Mean[iSC] = (minuit->X()[0]);
  DY_SC_Mean[iSC] = (minuit->X()[1]);
  DZ_SC_Mean[iSC] = (minuit->X()[2]);
  
  DX_SC_RMS[iSC] = (minuit->Errors()[0]);
  DY_SC_RMS[iSC] = (minuit->Errors()[1]);
  DZ_SC_RMS[iSC] = (minuit->Errors()[2]);
  
  DPHIe_SC_Mean[iSC] = (minuit->X()[3]);
  DTHETAe_SC_Mean[iSC] = (minuit->X()[4]);
  DPSIe_SC_Mean[iSC] = (minuit->X()[5]);
  
  DPHIe_SC_RMS[iSC] = (minuit->Errors()[3]);
  DTHETAe_SC_RMS[iSC] = (minuit->Errors()[4]);
  DPSIe_SC_RMS[iSC] = (minuit->Errors()[5]);
  
  ///==== end Chi2 minimization ====
  
  std::cout << " iSC = " << iSC << " DPhi =   " << DPHIe_SC_Mean[iSC]   << " +/- " << DPHIe_SC_RMS[iSC]   << std::endl;
  std::cout << " iSC = " << iSC << " DTheta = " << DTHETAe_SC_Mean[iSC] << " +/- " << DTHETAe_SC_RMS[iSC] << std::endl;
  std::cout << " iSC = " << iSC << " DPsi =   " << DPSIe_SC_Mean[iSC]   << " +/- " << DPSIe_SC_RMS[iSC]   << std::endl;
  std::cout << " iSC = " << iSC << " DX =     " << DX_SC_Mean[iSC]      << " +/- " << DX_SC_RMS[iSC]      << std::endl;
  std::cout << " iSC = " << iSC << " DY =     " << DY_SC_Mean[iSC]      << " +/- " << DY_SC_RMS[iSC]      << std::endl;
  std::cout << " iSC = " << iSC << " DZ =     " << DZ_SC_Mean[iSC]      << " +/- " << DZ_SC_RMS[iSC]      << std::endl;
  std::cout << "============================================================================" << std::endl;
  std::cout << "============================================================================" << std::endl;
  std::cout << "============================================================================" << std::endl;
  
 }
Exemplo n.º 6
0
int NumericalMinimization(const char * minName = "Minuit2",
                          const char *algoName = "" ,
                          int randomSeed = -1)
{
   // create minimizer giving a name and a name (optionally) for the specific
   // algorithm
   // possible choices are:
   //     minName                  algoName
   // Minuit /Minuit2             Migrad, Simplex,Combined,Scan  (default is Migrad)
   //  Minuit2                     Fumili2
   //  Fumili
   //  GSLMultiMin                ConjugateFR, ConjugatePR, BFGS,
   //                              BFGS2, SteepestDescent
   //  GSLMultiFit
   //   GSLSimAn
   //   Genetic
   ROOT::Math::Minimizer* minimum =
      ROOT::Math::Factory::CreateMinimizer(minName, algoName);

   // set tolerance , etc...
   minimum->SetMaxFunctionCalls(1000000); // for Minuit/Minuit2
   minimum->SetMaxIterations(10000);  // for GSL
   minimum->SetTolerance(0.001);
   minimum->SetPrintLevel(1);

   // create function wrapper for minimizer
   // a IMultiGenFunction type
   ROOT::Math::Functor f(&RosenBrock,2);
   double step[2] = {0.01,0.01};
   // starting point

   double variable[2] = { -1.,1.2};
   if (randomSeed >= 0) {
      TRandom2 r(randomSeed);
      variable[0] = r.Uniform(-20,20);
      variable[1] = r.Uniform(-20,20);
   }

   minimum->SetFunction(f);

   // Set the free variables to be minimized !
   minimum->SetVariable(0,"x",variable[0], step[0]);
   minimum->SetVariable(1,"y",variable[1], step[1]);

   // do the minimization
   minimum->Minimize();

   const double *xs = minimum->X();
   std::cout << "Minimum: f(" << xs[0] << "," << xs[1] << "): "
             << minimum->MinValue()  << std::endl;

   // expected minimum is 0
   if ( minimum->MinValue()  < 1.E-4  && f(xs) < 1.E-4)
      std::cout << "Minimizer " << minName << " - " << algoName
                << "   converged to the right minimum" << std::endl;
   else {
      std::cout << "Minimizer " << minName << " - " << algoName
                << "   failed to converge !!!" << std::endl;
      Error("NumericalMinimization","fail to converge");
   }

   return 0;
}