BSFitter.cc

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#include "Minuit2/VariableMetricMinimizer.h"
#include "Minuit2/FunctionMinimum.h"
#include "Minuit2/MnPrint.h"
#include "Minuit2/MnMigrad.h"
#include "Minuit2/MnUserParameterState.h"
//#include "CLHEP/config/CLHEP.h"

// C++ standard
#include <vector>
#include <cmath>

// CMS
#include "RecoVertex/BeamSpotProducer/interface/BSFitter.h"
#include "FWCore/MessageLogger/interface/MessageLogger.h"
#include "FWCore/Utilities/interface/Exception.h"
#include "FWCore/Utilities/interface/isFinite.h"

// ROOT
#include "TMatrixD.h"
#include "TMatrixDSym.h"
#include "TDecompBK.h"
#include "TH1.h"
#include "TF1.h"
#include "TMinuitMinimizer.h"

using namespace ROOT::Minuit2;

//_____________________________________________________________________
BSFitter::BSFitter() {
  fbeamtype = reco::BeamSpot::Unknown;

  //In order to make fitting ROOT histograms thread safe
  // one must call this undocumented function
  TMinuitMinimizer::UseStaticMinuit(false);
}

//_____________________________________________________________________
BSFitter::BSFitter(const std::vector<BSTrkParameters> &BSvector) {
  //In order to make fitting ROOT histograms thread safe
  // one must call this undocumented function
  TMinuitMinimizer::UseStaticMinuit(false);

  ffit_type = "default";
  ffit_variable = "default";

  fBSvector = BSvector;

  fsqrt2pi = sqrt(2. * TMath::Pi());

  fpar_name[0] = "z0        ";
  fpar_name[1] = "SigmaZ0   ";
  fpar_name[2] = "X0        ";
  fpar_name[3] = "Y0        ";
  fpar_name[4] = "dxdz      ";
  fpar_name[5] = "dydz      ";
  fpar_name[6] = "SigmaBeam ";

  //if (theGausszFcn == 0 ) {
  thePDF = new BSpdfsFcn();

  //}
  //if (theFitter == 0 ) {

  theFitter = new VariableMetricMinimizer();

  //}

  fapplyd0cut = false;
  fapplychi2cut = false;
  ftmprow = 0;
  ftmp.ResizeTo(4, 1);
  ftmp.Zero();
  fnthite = 0;
  fMaxZ = 50.;         //cm
  fconvergence = 0.5;  // stop fit when 50% of the input collection has been removed.
  fminNtrks = 100;
  finputBeamWidth = -1;  // no input

  h1z = new TH1F("h1z", "z distribution", 200, -fMaxZ, fMaxZ);
}

//______________________________________________________________________
BSFitter::~BSFitter() {
  //delete fBSvector;
  delete thePDF;
  delete theFitter;
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit() { return this->Fit(nullptr); }

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit(double *inipar = nullptr) {
  fbeamtype = reco::BeamSpot::Unknown;
  if (ffit_variable == "z") {
    if (ffit_type == "chi2") {
      return Fit_z_chi2(inipar);

    } else if (ffit_type == "likelihood") {
      return Fit_z_likelihood(inipar);

    } else if (ffit_type == "combined") {
      reco::BeamSpot tmp_beamspot = Fit_z_chi2(inipar);
      double tmp_par[2] = {tmp_beamspot.z0(), tmp_beamspot.sigmaZ()};
      return Fit_z_likelihood(tmp_par);

    } else {
      throw cms::Exception("LogicError")
          << "Error in BeamSpotProducer/BSFitter: "
          << "Illegal fit type, options are chi2,likelihood or combined(ie. first chi2 then likelihood)";
    }
  } else if (ffit_variable == "d") {
    if (ffit_type == "d0phi") {
      this->d0phi_Init();
      return Fit_d0phi();

    } else if (ffit_type == "likelihood") {
      return Fit_d_likelihood(inipar);

    } else if (ffit_type == "combined") {
      this->d0phi_Init();
      reco::BeamSpot tmp_beamspot = Fit_d0phi();
      double tmp_par[4] = {tmp_beamspot.x0(), tmp_beamspot.y0(), tmp_beamspot.dxdz(), tmp_beamspot.dydz()};
      return Fit_d_likelihood(tmp_par);

    } else {
      throw cms::Exception("LogicError") << "Error in BeamSpotProducer/BSFitter: "
                                         << "Illegal fit type, options are d0phi, likelihood or combined";
    }
  } else if (ffit_variable == "d*z" || ffit_variable == "default") {
    if (ffit_type == "likelihood" || ffit_type == "default") {
      reco::BeamSpot::CovarianceMatrix matrix;
      // we are now fitting Z inside d0phi fitter
      // first fit z distribution using a chi2 fit
      //reco::BeamSpot tmp_z = Fit_z_chi2(inipar);
      //for (int j = 2 ; j < 4 ; ++j) {
      //for(int k = j ; k < 4 ; ++k) {
      //    matrix(j,k) = tmp_z.covariance()(j,k);
      //}
      //}

      // use d0-phi algorithm to extract transverse position
      this->d0phi_Init();
      //reco::BeamSpot tmp_d0phi= Fit_d0phi(); // change to iterative procedure:
      this->Setd0Cut_d0phi(4.0);
      reco::BeamSpot tmp_d0phi = Fit_ited0phi();

      //for (int j = 0 ; j < 2 ; ++j) {
      //    for(int k = j ; k < 2 ; ++k) {
      //        matrix(j,k) = tmp_d0phi.covariance()(j,k);
      //}
      //}
      // slopes
      //for (int j = 4 ; j < 6 ; ++j) {
      // for(int k = j ; k < 6 ; ++k) {
      //  matrix(j,k) = tmp_d0phi.covariance()(j,k);
      //  }
      //}

      // put everything into one object
      reco::BeamSpot spot(reco::BeamSpot::Point(tmp_d0phi.x0(), tmp_d0phi.y0(), tmp_d0phi.z0()),
                          tmp_d0phi.sigmaZ(),
                          tmp_d0phi.dxdz(),
                          tmp_d0phi.dydz(),
                          0.,
                          tmp_d0phi.covariance(),
                          fbeamtype);

      //reco::BeamSpot tmp_z = Fit_z_chi2(inipar);

      //reco::BeamSpot tmp_d0phi = Fit_d0phi();

      // log-likelihood fit
      if (ffit_type == "likelihood") {
        double tmp_par[7] = {
            tmp_d0phi.x0(), tmp_d0phi.y0(), tmp_d0phi.z0(), tmp_d0phi.sigmaZ(), tmp_d0phi.dxdz(), tmp_d0phi.dydz(), 0.0};

        double tmp_error_par[7];
        for (int s = 0; s < 6; s++) {
          tmp_error_par[s] = pow(tmp_d0phi.covariance()(s, s), 0.5);
        }
        tmp_error_par[6] = 0.0;

        reco::BeamSpot tmp_lh = Fit_d_z_likelihood(tmp_par, tmp_error_par);

        if (edm::isNotFinite(ff_minimum)) {
          edm::LogWarning("BSFitter")
              << "BSFitter: Result is non physical. Log-Likelihood fit to extract beam width did not converge."
              << std::endl;
          tmp_lh.setType(reco::BeamSpot::Unknown);
          return tmp_lh;
        }
        return tmp_lh;

      } else {
        edm::LogInfo("BSFitter") << "default track-based fit does not extract beam width." << std::endl;
        return spot;
      }

    } else if (ffit_type == "resolution") {
      reco::BeamSpot tmp_z = Fit_z_chi2(inipar);
      this->d0phi_Init();
      reco::BeamSpot tmp_d0phi = Fit_d0phi();

      double tmp_par[7] = {
          tmp_d0phi.x0(), tmp_d0phi.y0(), tmp_z.z0(), tmp_z.sigmaZ(), tmp_d0phi.dxdz(), tmp_d0phi.dydz(), 0.0};
      double tmp_error_par[7];
      for (int s = 0; s < 6; s++) {
        tmp_error_par[s] = pow(tmp_par[s], 0.5);
      }
      tmp_error_par[6] = 0.0;

      reco::BeamSpot tmp_beam = Fit_d_z_likelihood(tmp_par, tmp_error_par);

      double tmp_par2[7] = {tmp_beam.x0(),
                            tmp_beam.y0(),
                            tmp_beam.z0(),
                            tmp_beam.sigmaZ(),
                            tmp_beam.dxdz(),
                            tmp_beam.dydz(),
                            tmp_beam.BeamWidthX()};

      reco::BeamSpot tmp_lh = Fit_dres_z_likelihood(tmp_par2);

      if (edm::isNotFinite(ff_minimum)) {
        edm::LogWarning("BSFitter") << "Result is non physical. Log-Likelihood fit did not converge." << std::endl;
        tmp_lh.setType(reco::BeamSpot::Unknown);
        return tmp_lh;
      }
      return tmp_lh;

    } else {
      throw cms::Exception("LogicError") << "Error in BeamSpotProducer/BSFitter: "
                                         << "Illegal fit type, options are likelihood or resolution";
    }
  } else {
    throw cms::Exception("LogicError") << "Error in BeamSpotProducer/BSFitter: "
                                       << "Illegal variable type, options are \"z\", \"d\", or \"d*z\"";
  }
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit_z_likelihood(double *inipar) {
  //std::cout << "Fit_z(double *) called" << std::endl;
  //std::cout << "inipar[0]= " << inipar[0] << std::endl;
  //std::cout << "inipar[1]= " << inipar[1] << std::endl;

  std::vector<double> par(2, 0);
  std::vector<double> err(2, 0);

  par.push_back(0.0);
  par.push_back(7.0);
  err.push_back(0.0001);
  err.push_back(0.0001);
  //par[0] = 0.0; err[0] = 0.0;
  //par[1] = 7.0; err[1] = 0.0;

  thePDF->SetPDFs("PDFGauss_z");
  thePDF->SetData(fBSvector);
  //std::cout << "data loaded"<< std::endl;

  //FunctionMinimum fmin = theFitter->Minimize(*theGausszFcn, par, err, 1, 500, 0.1);
  MnUserParameters upar;
  upar.Add("X0", 0., 0.);
  upar.Add("Y0", 0., 0.);
  upar.Add("Z0", inipar[0], 0.001);
  upar.Add("sigmaZ", inipar[1], 0.001);

  MnMigrad migrad(*thePDF, upar);

  FunctionMinimum fmin = migrad();
  ff_minimum = fmin.Fval();
  //std::cout << " eval= " << ff_minimum
  //          << "/n params[0]= " << fmin.Parameters().Vec()(0) << std::endl;

  /*
    TMinuit *gmMinuit = new TMinuit(2);

    //gmMinuit->SetFCN(z_fcn);
    gmMinuit->SetFCN(myFitz_fcn);


    int ierflg = 0;
    double step[2] = {0.001,0.001};

    for (int i = 0; i<2; i++) {
        gmMinuit->mnparm(i,fpar_name[i].c_str(),inipar[i],step[i],0,0,ierflg);
    }
    gmMinuit->Migrad();
    */
  reco::BeamSpot::CovarianceMatrix matrix;

  for (int j = 2; j < 4; ++j) {
    for (int k = j; k < 4; ++k) {
      matrix(j, k) = fmin.Error().Matrix()(j, k);
    }
  }

  return reco::BeamSpot(reco::BeamSpot::Point(0., 0., fmin.Parameters().Vec()(2)),
                        fmin.Parameters().Vec()(3),
                        0.,
                        0.,
                        0.,
                        matrix,
                        fbeamtype);
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit_z_chi2(double *inipar) {
  // N.B. this fit is not performed anymore but now
  // Z is fitted in the same track set used in the d0-phi fit after
  // each iteration

  //std::cout << "Fit_z_chi2() called" << std::endl;
  // FIXME: include whole tracker z length for the time being
  // ==> add protection and z0 cut
  h1z = new TH1F("h1z", "z distribution", 200, -fMaxZ, fMaxZ);

  std::vector<BSTrkParameters>::const_iterator iparam = fBSvector.begin();

  // HERE check size of track vector

  for (iparam = fBSvector.begin(); iparam != fBSvector.end(); ++iparam) {
    h1z->Fill(iparam->z0());
    //std::cout<<"z0="<<iparam->z0()<<"; sigZ0="<<iparam->sigz0()<<std::endl;
  }

  //Use our own copy for thread safety
  // also do not add to global list of functions
  TF1 fgaus("fgaus", "gaus", 0., 1., TF1::EAddToList::kNo);
  h1z->Fit(&fgaus, "QLMN0 SERIAL");
  //std::cout << "fitted "<< std::endl;

  //std::cout << "got function" << std::endl;
  double fpar[2] = {fgaus.GetParameter(1), fgaus.GetParameter(2)};
  //std::cout<<"Debug fpar[2] = (" <<fpar[0]<<","<<fpar[1]<<")"<<std::endl;
  reco::BeamSpot::CovarianceMatrix matrix;
  // add matrix values.
  matrix(2, 2) = fgaus.GetParError(1) * fgaus.GetParError(1);
  matrix(3, 3) = fgaus.GetParError(2) * fgaus.GetParError(2);

  //delete h1z;

  return reco::BeamSpot(reco::BeamSpot::Point(0., 0., fpar[0]), fpar[1], 0., 0., 0., matrix, fbeamtype);
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit_ited0phi() {
  this->d0phi_Init();
  edm::LogInfo("BSFitter") << "number of total input tracks: " << fBSvector.size() << std::endl;

  reco::BeamSpot theanswer;

  if ((int)fBSvector.size() <= fminNtrks) {
    edm::LogWarning("BSFitter") << "need at least " << fminNtrks << " tracks to run beamline fitter." << std::endl;
    fbeamtype = reco::BeamSpot::Fake;
    theanswer.setType(fbeamtype);
    return theanswer;
  }

  theanswer = Fit_d0phi();  //get initial ftmp and ftmprow
  if (goodfit)
    fnthite++;
  //std::cout << "Initial tempanswer (iteration 0): " << theanswer << std::endl;

  reco::BeamSpot preanswer = theanswer;

  while (goodfit && ftmprow > fconvergence * fBSvector.size() && ftmprow > fminNtrks) {
    theanswer = Fit_d0phi();
    fd0cut /= 1.5;
    fchi2cut /= 1.5;
    if (goodfit && ftmprow > fconvergence * fBSvector.size() && ftmprow > fminNtrks) {
      preanswer = theanswer;
      //std::cout << "Iteration " << fnthite << ": " << preanswer << std::endl;
      fnthite++;
    }
  }
  // FIXME: return fit results from previous iteration for both bad fit and for >50% tracks thrown away
  //std::cout << "The last iteration, theanswer: " << theanswer << std::endl;
  theanswer = preanswer;
  //std::cout << "Use previous results from iteration #" << ( fnthite > 0 ? fnthite-1 : 0 ) << std::endl;
  //if ( fnthite > 1 ) std::cout << theanswer << std::endl;

  edm::LogInfo("BSFitter") << "Total number of successful iterations = " << (goodfit ? (fnthite + 1) : fnthite)
                           << std::endl;
  if (goodfit) {
    fbeamtype = reco::BeamSpot::Tracker;
    theanswer.setType(fbeamtype);
  } else {
    edm::LogWarning("BSFitter") << "Fit doesn't converge!!!" << std::endl;
    fbeamtype = reco::BeamSpot::Unknown;
    theanswer.setType(fbeamtype);
  }
  return theanswer;
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit_d0phi() {
  //LogDebug ("BSFitter") << " we will use " << fBSvector.size() << " tracks.";
  if (fnthite > 0)
    edm::LogInfo("BSFitter") << " number of tracks used: " << ftmprow << std::endl;
  //std::cout << " ftmp = matrix("<<ftmp.GetNrows()<<","<<ftmp.GetNcols()<<")"<<std::endl;
  //std::cout << " ftmp(0,0)="<<ftmp(0,0)<<std::endl;
  //std::cout << " ftmp(1,0)="<<ftmp(1,0)<<std::endl;
  //std::cout << " ftmp(2,0)="<<ftmp(2,0)<<std::endl;
  //std::cout << " ftmp(3,0)="<<ftmp(3,0)<<std::endl;

  h1z->Reset();

  TMatrixD x_result(4, 1);
  TMatrixDSym V_result(4);

  TMatrixDSym Vint(4);
  TMatrixD b(4, 1);

  //Double_t weightsum = 0;

  Vint.Zero();
  b.Zero();

  TMatrixD g(4, 1);
  TMatrixDSym temp(4);

  std::vector<BSTrkParameters>::iterator iparam = fBSvector.begin();
  ftmprow = 0;

  //edm::LogInfo ("BSFitter") << " test";

  //std::cout << "BSFitter: fit" << std::endl;

  for (iparam = fBSvector.begin(); iparam != fBSvector.end(); ++iparam) {
    //if(i->weight2 == 0) continue;

    //if (ftmprow==0) {
    //std::cout << "d0=" << iparam->d0() << " sigd0=" << iparam->sigd0()
    //<< " phi0="<< iparam->phi0() << " z0=" << iparam->z0() << std::endl;
    //std::cout << "d0phi_d0=" << iparam->d0phi_d0() << " d0phi_chi2="<<iparam->d0phi_chi2() << std::endl;
    //}
    g(0, 0) = sin(iparam->phi0());
    g(1, 0) = -cos(iparam->phi0());
    g(2, 0) = iparam->z0() * g(0, 0);
    g(3, 0) = iparam->z0() * g(1, 0);

    // average transverse beam width
    double sigmabeam2 = 0.006 * 0.006;
    if (finputBeamWidth > 0)
      sigmabeam2 = finputBeamWidth * finputBeamWidth;
    else {
      //edm::LogWarning("BSFitter") << "using in fit beam width = " << sqrt(sigmabeam2) << std::endl;
    }

    //double sigma2 = sigmabeam2 +  (iparam->sigd0())* (iparam->sigd0()) / iparam->weight2;
    // this should be 2*sigmabeam2?
    double sigma2 = sigmabeam2 + (iparam->sigd0()) * (iparam->sigd0());

    TMatrixD ftmptrans(1, 4);
    ftmptrans = ftmptrans.Transpose(ftmp);
    TMatrixD dcor = ftmptrans * g;
    double chi2tmp = (iparam->d0() - dcor(0, 0)) * (iparam->d0() - dcor(0, 0)) / sigma2;
    (*iparam) = BSTrkParameters(
        iparam->z0(), iparam->sigz0(), iparam->d0(), iparam->sigd0(), iparam->phi0(), iparam->pt(), dcor(0, 0), chi2tmp);

    bool pass = true;
    if (fapplyd0cut && fnthite > 0) {
      if (std::abs(iparam->d0() - dcor(0, 0)) > fd0cut)
        pass = false;
    }
    if (fapplychi2cut && fnthite > 0) {
      if (chi2tmp > fchi2cut)
        pass = false;
    }

    if (pass) {
      temp.Zero();
      for (int j = 0; j < 4; ++j) {
        for (int k = j; k < 4; ++k) {
          temp(j, k) += g(j, 0) * g(k, 0);
        }
      }

      Vint += (temp * (1 / sigma2));
      b += (iparam->d0() / sigma2 * g);
      //weightsum += sqrt(i->weight2);
      ftmprow++;
      h1z->Fill(iparam->z0());
    }
  }
  Double_t determinant;
  TDecompBK bk(Vint);
  bk.SetTol(1e-11);  //FIXME: find a better way to solve x_result
  if (!bk.Decompose()) {
    goodfit = false;
    edm::LogWarning("BSFitter") << "Decomposition failed, matrix singular ?" << std::endl
                                << "condition number = " << bk.Condition() << std::endl;
  } else {
    V_result = Vint.InvertFast(&determinant);
    x_result = V_result * b;
  }
  //        for(int j = 0 ; j < 4 ; ++j) {
  //      for(int k = 0 ; k < 4 ; ++k) {
  //        std::cout<<"V_result("<<j<<","<<k<<")="<<V_result(j,k)<<std::endl;
  //      }
  //        }
  //         for (int j=0;j<4;++j){
  //      std::cout<<"x_result("<<j<<",0)="<<x_result(j,0)<<std::endl;
  //    }
  //LogDebug ("BSFitter") << " d0-phi fit done.";
  //std::cout<< " d0-phi fit done." << std::endl;

  //Use our own copy for thread safety
  // also do not add to global list of functions
  TF1 fgaus("fgaus", "gaus", 0., 1., TF1::EAddToList::kNo);
  //returns 0 if OK
  //auto status = h1z->Fit(&fgaus,"QLM0","",h1z->GetMean() -2.*h1z->GetRMS(),h1z->GetMean() +2.*h1z->GetRMS());
  auto status =
      h1z->Fit(&fgaus, "QLN0 SERIAL", "", h1z->GetMean() - 2. * h1z->GetRMS(), h1z->GetMean() + 2. * h1z->GetRMS());

  //std::cout << "fitted "<< std::endl;

  //std::cout << "got function" << std::endl;
  if (status) {
    //edm::LogError("NoBeamSpotFit")<<"gaussian fit failed. no BS d0 fit";

    goodfit = false;
    return reco::BeamSpot();
  }
  double fpar[2] = {fgaus.GetParameter(1), fgaus.GetParameter(2)};

  reco::BeamSpot::CovarianceMatrix matrix;
  // first two parameters
  for (int j = 0; j < 2; ++j) {
    for (int k = j; k < 2; ++k) {
      matrix(j, k) = V_result(j, k);
    }
  }
  // slope parameters
  for (int j = 4; j < 6; ++j) {
    for (int k = j; k < 6; ++k) {
      matrix(j, k) = V_result(j - 2, k - 2);
    }
  }

  // Z0 and sigmaZ
  matrix(2, 2) = fgaus.GetParError(1) * fgaus.GetParError(1);
  matrix(3, 3) = fgaus.GetParError(2) * fgaus.GetParError(2);

  ftmp = x_result;

  // x0 and y0 are *not* x,y at z=0, but actually at z=0
  // to correct for this, we need to translate them to z=z0
  // using the measured slopes
  //
  double x0tmp = x_result(0, 0);
  double y0tmp = x_result(1, 0);

  x0tmp += x_result(2, 0) * fpar[0];
  y0tmp += x_result(3, 0) * fpar[0];

  return reco::BeamSpot(
      reco::BeamSpot::Point(x0tmp, y0tmp, fpar[0]), fpar[1], x_result(2, 0), x_result(3, 0), 0., matrix, fbeamtype);
}

//______________________________________________________________________
void BSFitter::Setd0Cut_d0phi(double d0cut) {
  fapplyd0cut = true;

  //fBSforCuts = BSfitted;
  fd0cut = d0cut;
}

//______________________________________________________________________
void BSFitter::SetChi2Cut_d0phi(double chi2cut) {
  fapplychi2cut = true;

  //fBSforCuts = BSfitted;
  fchi2cut = chi2cut;
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit_d_likelihood(double *inipar) {
  thePDF->SetPDFs("PDFGauss_d");
  thePDF->SetData(fBSvector);

  MnUserParameters upar;
  upar.Add("X0", inipar[0], 0.001);
  upar.Add("Y0", inipar[1], 0.001);
  upar.Add("Z0", 0., 0.001);
  upar.Add("sigmaZ", 0., 0.001);
  upar.Add("dxdz", inipar[2], 0.001);
  upar.Add("dydz", inipar[3], 0.001);

  MnMigrad migrad(*thePDF, upar);

  FunctionMinimum fmin = migrad();
  ff_minimum = fmin.Fval();

  reco::BeamSpot::CovarianceMatrix matrix;
  for (int j = 0; j < 6; ++j) {
    for (int k = j; k < 6; ++k) {
      matrix(j, k) = fmin.Error().Matrix()(j, k);
    }
  }

  return reco::BeamSpot(reco::BeamSpot::Point(fmin.Parameters().Vec()(0), fmin.Parameters().Vec()(1), 0.),
                        0.,
                        fmin.Parameters().Vec()(4),
                        fmin.Parameters().Vec()(5),
                        0.,
                        matrix,
                        fbeamtype);
}
//______________________________________________________________________
double BSFitter::scanPDF(double *init_pars, int &tracksfixed, int option) {
  if (option == 1)
    init_pars[6] = 0.0005;  //starting value for any given configuration

  //local vairables with initial values
  double fsqrt2pi = 0.0;
  double d_sig = 0.0;
  double d_dprime = 0.0;
  double d_result = 0.0;
  double z_sig = 0.0;
  double z_result = 0.0;
  double function = 0.0;
  double tot_pdf = 0.0;
  double last_minvalue = 1.0e+10;
  double init_bw = -99.99;
  int iters = 0;

  //used to remove tracks if far away from bs by this
  double DeltadCut = 0.1000;
  if (init_pars[6] < 0.0200) {
    DeltadCut = 0.0900;
  }  //worked for high 2.36TeV
  if (init_pars[6] < 0.0100) {
    DeltadCut = 0.0700;
  }  //just a guesss for 7 TeV but one should scan for actual values

  std::vector<BSTrkParameters>::const_iterator iparam = fBSvector.begin();

  if (option == 1)
    iters = 500;
  if (option == 2)
    iters = 1;

  for (int p = 0; p < iters; p++) {
    if (iters == 500)
      init_pars[6] += 0.0002;
    tracksfixed = 0;

    for (iparam = fBSvector.begin(); iparam != fBSvector.end(); ++iparam) {
      fsqrt2pi = sqrt(2. * TMath::Pi());
      d_sig = sqrt(init_pars[6] * init_pars[6] + (iparam->sigd0()) * (iparam->sigd0()));
      d_dprime = iparam->d0() - (((init_pars[0] + iparam->z0() * (init_pars[4])) * sin(iparam->phi0())) -
                                 ((init_pars[1] + iparam->z0() * (init_pars[5])) * cos(iparam->phi0())));

      //***Remove tracks before the fit which gives low pdf values to blow up the pdf
      if (std::abs(d_dprime) < DeltadCut && option == 2) {
        fBSvectorBW.push_back(*iparam);
      }

      d_result = (exp(-(d_dprime * d_dprime) / (2.0 * d_sig * d_sig))) / (d_sig * fsqrt2pi);
      z_sig = sqrt(iparam->sigz0() * iparam->sigz0() + init_pars[3] * init_pars[3]);
      z_result = (exp(-((iparam->z0() - init_pars[2]) * (iparam->z0() - init_pars[2])) / (2.0 * z_sig * z_sig))) /
                 (z_sig * fsqrt2pi);
      tot_pdf = z_result * d_result;

      //for those trcks which gives problems due to very tiny pdf_d values.
      //Update: This protection will NOT be used with the dprime cut above but still kept here to get
      // the intial value of beam width reasonably
      //A warning will appear if there were any tracks with < 10^-5 for pdf_d so that (d-dprime) cut can be lowered
      if (d_result < 1.0e-05) {
        tot_pdf = z_result * 1.0e-05;
        //if(option==2)std::cout<<"last Iter  d-d'   =  "<<(std::abs(d_dprime))<<std::endl;
        tracksfixed++;
      }

      function = function + log(tot_pdf);

    }  //loop over tracks

    function = -2.0 * function;
    if (function < last_minvalue) {
      init_bw = init_pars[6];
      last_minvalue = function;
    }
    function = 0.0;
  }  //loop over beam width

  if (init_bw > 0) {
    init_bw = init_bw + (0.20 * init_bw);  //start with 20 % more

  } else {
    if (option == 1) {
      edm::LogWarning("BSFitter")
          << "scanPDF:====>>>> WARNING***: The initial guess value of Beam width is negative!!!!!!" << std::endl
          << "scanPDF:====>>>> Assigning beam width a starting value of " << init_bw << "  cm" << std::endl;
      init_bw = 0.0200;
    }
  }

  return init_bw;
}

//________________________________________________________________________________
reco::BeamSpot BSFitter::Fit_d_z_likelihood(double *inipar, double *error_par) {
  int tracksFailed = 0;

  //estimate first guess of beam width and tame 20% extra of it to start
  inipar[6] = scanPDF(inipar, tracksFailed, 1);
  error_par[6] = (inipar[6]) * 0.20;

  //Here remove the tracks which give low pdf and fill into a new vector
  //std::cout<<"Size of Old vector = "<<(fBSvector.size())<<std::endl;
  /* double junk= */ scanPDF(inipar, tracksFailed, 2);
  //std::cout<<"Size of New vector = "<<(fBSvectorBW.size())<<std::endl;

  //Refill the fBSVector again with new sets of tracks
  fBSvector.clear();
  std::vector<BSTrkParameters>::const_iterator iparamBW = fBSvectorBW.begin();
  for (iparamBW = fBSvectorBW.begin(); iparamBW != fBSvectorBW.end(); ++iparamBW) {
    fBSvector.push_back(*iparamBW);
  }

  thePDF->SetPDFs("PDFGauss_d*PDFGauss_z");
  thePDF->SetData(fBSvector);
  MnUserParameters upar;

  upar.Add("X0", inipar[0], error_par[0]);
  upar.Add("Y0", inipar[1], error_par[1]);
  upar.Add("Z0", inipar[2], error_par[2]);
  upar.Add("sigmaZ", inipar[3], error_par[3]);
  upar.Add("dxdz", inipar[4], error_par[4]);
  upar.Add("dydz", inipar[5], error_par[5]);
  upar.Add("BeamWidthX", inipar[6], error_par[6]);

  MnMigrad migrad(*thePDF, upar);

  FunctionMinimum fmin = migrad();

  // std::cout<<"-----how the fit evoves------"<<std::endl;
  // std::cout<<fmin<<std::endl;

  ff_minimum = fmin.Fval();

  bool ff_nfcn = fmin.HasReachedCallLimit();
  bool ff_cov = fmin.HasCovariance();
  bool testing = fmin.IsValid();

  //Print WARNINGS if minimum did not converged
  if (!testing) {
    edm::LogWarning("BSFitter") << "===========>>>>>** WARNING: MINUIT DID NOT CONVERGES PROPERLY !!!!!!" << std::endl;
    if (ff_nfcn)
      edm::LogWarning("BSFitter") << "===========>>>>>** WARNING: No. of Calls Exhausted" << std::endl;
    if (!ff_cov)
      edm::LogWarning("BSFitter") << "===========>>>>>** WARNING: Covariance did not found" << std::endl;
  }

  edm::LogInfo("BSFitter") << "The Total # Tracks used for beam width fit = " << (fBSvectorBW.size()) << std::endl;

  //Checks after fit is performed
  double lastIter_pars[7];

  for (int ip = 0; ip < 7; ip++) {
    lastIter_pars[ip] = fmin.Parameters().Vec()(ip);
  }

  tracksFailed = 0;
  /* double lastIter_scan= */ scanPDF(lastIter_pars, tracksFailed, 2);

  edm::LogWarning("BSFitter") << "WARNING: # of tracks which have very low pdf value (pdf_d < 1.0e-05) are  = "
                              << tracksFailed << std::endl;

  //std::cout << " eval= " << ff_minimum
  //                << "/n params[0]= " << fmin.Parameters().Vec()(0) << std::endl;

  reco::BeamSpot::CovarianceMatrix matrix;

  for (int j = 0; j < 7; ++j) {
    for (int k = j; k < 7; ++k) {
      matrix(j, k) = fmin.Error().Matrix()(j, k);
    }
  }

  return reco::BeamSpot(
      reco::BeamSpot::Point(fmin.Parameters().Vec()(0), fmin.Parameters().Vec()(1), fmin.Parameters().Vec()(2)),
      fmin.Parameters().Vec()(3),
      fmin.Parameters().Vec()(4),
      fmin.Parameters().Vec()(5),
      fmin.Parameters().Vec()(6),

      matrix,
      fbeamtype);
}

//______________________________________________________________________
reco::BeamSpot BSFitter::Fit_dres_z_likelihood(double *inipar) {
  thePDF->SetPDFs("PDFGauss_d_resolution*PDFGauss_z");
  thePDF->SetData(fBSvector);

  MnUserParameters upar;
  upar.Add("X0", inipar[0], 0.001);
  upar.Add("Y0", inipar[1], 0.001);
  upar.Add("Z0", inipar[2], 0.001);
  upar.Add("sigmaZ", inipar[3], 0.001);
  upar.Add("dxdz", inipar[4], 0.001);
  upar.Add("dydz", inipar[5], 0.001);
  upar.Add("BeamWidthX", inipar[6], 0.0001);
  upar.Add("c0", 0.0010, 0.0001);
  upar.Add("c1", 0.0090, 0.0001);

  // fix beam width
  upar.Fix("BeamWidthX");
  // number of parameters in fit are 9-1 = 8

  MnMigrad migrad(*thePDF, upar);

  FunctionMinimum fmin = migrad();
  ff_minimum = fmin.Fval();

  reco::BeamSpot::CovarianceMatrix matrix;

  for (int j = 0; j < 6; ++j) {
    for (int k = j; k < 6; ++k) {
      matrix(j, k) = fmin.Error().Matrix()(j, k);
    }
  }

  //std::cout << " fill resolution values" << std::endl;
  //std::cout << " matrix size= " << fmin.Error().Matrix().size() << std::endl;
  //std::cout << " vec(6)="<< fmin.Parameters().Vec()(6) << std::endl;
  //std::cout << " vec(7)="<< fmin.Parameters().Vec()(7) << std::endl;

  fresolution_c0 = fmin.Parameters().Vec()(6);
  fresolution_c1 = fmin.Parameters().Vec()(7);
  fres_c0_err = sqrt(fmin.Error().Matrix()(6, 6));
  fres_c1_err = sqrt(fmin.Error().Matrix()(7, 7));

  for (int j = 6; j < 8; ++j) {
    for (int k = 6; k < 8; ++k) {
      fres_matrix(j - 6, k - 6) = fmin.Error().Matrix()(j, k);
    }
  }

  return reco::BeamSpot(
      reco::BeamSpot::Point(fmin.Parameters().Vec()(0), fmin.Parameters().Vec()(1), fmin.Parameters().Vec()(2)),
      fmin.Parameters().Vec()(3),
      fmin.Parameters().Vec()(4),
      fmin.Parameters().Vec()(5),
      inipar[6],
      matrix,
      fbeamtype);
}