TKinFitter.cc

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// Classname: TKinFitter
// Author: Jan E. Sundermann, Verena Klose (TU Dresden)

//________________________________________________________________
//
// TKinFitter::
// --------------------
//
// Class to perform kinematic fit with non-linear constraints
//

#include <iostream>
#include <iomanip>
#include "FWCore/MessageLogger/interface/MessageLogger.h"
#include "PhysicsTools/KinFitter/interface/TKinFitter.h"
#include "PhysicsTools/KinFitter/interface/TAbsFitParticle.h"
#include "PhysicsTools/KinFitter/interface/TAbsFitConstraint.h"

TKinFitter::TKinFitter()
    : TNamed("UnNamed", "UnTitled"),
      _A(1, 1),
      _AT(1, 1),
      _B(1, 1),
      _BT(1, 1),
      _V(1, 1),
      _Vinv(1, 1),
      _VB(1, 1),
      _VBinv(1, 1),
      _VA(1, 1),
      _VAinv(1, 1),
      _c(1, 1),
      _C11(1, 1),
      _C11T(1, 1),
      _C21(1, 1),
      _C21T(1, 1),
      _C22(1, 1),
      _C22T(1, 1),
      _C31(1, 1),
      _C31T(1, 1),
      _C32(1, 1),
      _C32T(1, 1),
      _C33(1, 1),
      _C33T(1, 1),
      _deltaA(1, 1),
      _deltaY(1, 1),
      _deltaAstar(1, 1),
      _deltaYstar(1, 1),
      _lambda(1, 1),
      _lambdaT(1, 1),
      _lambdaVFit(1, 1),
      _yaVFit(1, 1),
      _constraints(0),
      _measParticles(0),
      _unmeasParticles(0) {
  reset();
}

TKinFitter::TKinFitter(const TString& name, const TString& title)
    : TNamed(name, title),
      _A(1, 1),
      _AT(1, 1),
      _B(1, 1),
      _BT(1, 1),
      _V(1, 1),
      _Vinv(1, 1),
      _VB(1, 1),
      _VBinv(1, 1),
      _VA(1, 1),
      _VAinv(1, 1),
      _c(1, 1),
      _C11(1, 1),
      _C11T(1, 1),
      _C21(1, 1),
      _C21T(1, 1),
      _C22(1, 1),
      _C22T(1, 1),
      _C31(1, 1),
      _C31T(1, 1),
      _C32(1, 1),
      _C32T(1, 1),
      _C33(1, 1),
      _C33T(1, 1),
      _deltaA(1, 1),
      _deltaY(1, 1),
      _deltaAstar(1, 1),
      _deltaYstar(1, 1),
      _lambda(1, 1),
      _lambdaT(1, 1),
      _lambdaVFit(1, 1),
      _yaVFit(1, 1),
      _constraints(0),
      _measParticles(0),
      _unmeasParticles(0) {
  reset();
}

void TKinFitter::reset() {
  // reset all internal parameters of the fitter

  _status = -1;
  _nbIter = 0;
  _nParA = 0;
  _nParB = 0;
  _verbosity = 1;
  _A.ResizeTo(1, 1);
  _AT.ResizeTo(1, 1);
  _B.ResizeTo(1, 1);
  _BT.ResizeTo(1, 1);
  _V.ResizeTo(1, 1);
  _Vinv.ResizeTo(1, 1);
  _VB.ResizeTo(1, 1);
  _VBinv.ResizeTo(1, 1);
  _VA.ResizeTo(1, 1);
  _VAinv.ResizeTo(1, 1);
  _c.ResizeTo(1, 1);
  _C11.ResizeTo(1, 1);
  _C11T.ResizeTo(1, 1);
  _C21.ResizeTo(1, 1);
  _C21T.ResizeTo(1, 1);
  _C22.ResizeTo(1, 1);
  _C22T.ResizeTo(1, 1);
  _C31.ResizeTo(1, 1);
  _C31T.ResizeTo(1, 1);
  _C32.ResizeTo(1, 1);
  _C32T.ResizeTo(1, 1);
  _C33.ResizeTo(1, 1);
  _C33T.ResizeTo(1, 1);
  _deltaA.ResizeTo(1, 1);
  _deltaY.ResizeTo(1, 1);
  _deltaAstar.ResizeTo(1, 1);
  _deltaYstar.ResizeTo(1, 1);
  _lambda.ResizeTo(1, 1);
  _lambdaT.ResizeTo(1, 1);
  _lambdaVFit.ResizeTo(1, 1);
  _yaVFit.ResizeTo(1, 1);

  _constraints.clear();
  _measParticles.clear();
  _unmeasParticles.clear();

  // Set to default values
  _maxNbIter = 50;
  _maxDeltaS = 5e-3;
  _maxF = 1e-4;
}

void TKinFitter::resetStatus() {
  // reset status of the fit

  _status = -1;
  _nbIter = 0;
}

void TKinFitter::resetParams() {
  // reset all particles to their initial parameters

  for (unsigned int iP = 0; iP < _measParticles.size(); iP++) {
    TAbsFitParticle* particle = _measParticles[iP];
    particle->reset();
  }
  for (unsigned int iP = 0; iP < _unmeasParticles.size(); iP++) {
    TAbsFitParticle* particle = _unmeasParticles[iP];
    particle->reset();
  }
  for (unsigned int iC = 0; iC < _constraints.size(); iC++) {
    TAbsFitConstraint* constraint = _constraints[iC];
    constraint->reset();
  }
}

TKinFitter::~TKinFitter() {}

void TKinFitter::countMeasParams() {
  // count number of measured parameters

  _nParB = 0;
  for (unsigned int indexParticle = 0; indexParticle < _measParticles.size(); indexParticle++) {
    _nParB += _measParticles[indexParticle]->getNPar();
  }
  for (unsigned int indexConstraint = 0; indexConstraint < _constraints.size(); indexConstraint++) {
    _nParB += _constraints[indexConstraint]->getNPar();
  }
}

void TKinFitter::countUnmeasParams() {
  // count number of unmeasured parameters

  _nParA = 0;
  for (unsigned int indexParticle = 0; indexParticle < _unmeasParticles.size(); indexParticle++) {
    _nParA += _unmeasParticles[indexParticle]->getNPar();
  }
}

void TKinFitter::addMeasParticle(TAbsFitParticle* particle) {
  // add one measured particle

  resetStatus();

  if (particle != nullptr) {
    _measParticles.push_back(particle);
  } else {
    edm::LogError("NullPointer") << "Measured particle points to NULL. It will not be added to the KinFitter.";
  }

  countMeasParams();
}

void TKinFitter::addMeasParticles(TAbsFitParticle* p1,
                                  TAbsFitParticle* p2,
                                  TAbsFitParticle* p3,
                                  TAbsFitParticle* p4,
                                  TAbsFitParticle* p5,
                                  TAbsFitParticle* p6,
                                  TAbsFitParticle* p7,
                                  TAbsFitParticle* p8,
                                  TAbsFitParticle* p9) {
  // add many measured particles

  resetStatus();

  if (p1 != nullptr)
    _measParticles.push_back(p1);
  if (p2 != nullptr)
    _measParticles.push_back(p2);
  if (p3 != nullptr)
    _measParticles.push_back(p3);
  if (p4 != nullptr)
    _measParticles.push_back(p4);
  if (p5 != nullptr)
    _measParticles.push_back(p5);
  if (p6 != nullptr)
    _measParticles.push_back(p6);
  if (p7 != nullptr)
    _measParticles.push_back(p7);
  if (p8 != nullptr)
    _measParticles.push_back(p8);
  if (p9 != nullptr)
    _measParticles.push_back(p9);

  countMeasParams();
}

void TKinFitter::addUnmeasParticle(TAbsFitParticle* particle) {
  // add one unmeasured particle

  resetStatus();

  if (particle != nullptr) {
    _unmeasParticles.push_back(particle);
  } else {
    edm::LogError("NullPointer") << "Unmeasured particle points to NULL. It will not be added to the KinFitter.";
  }

  countUnmeasParams();
}

void TKinFitter::addUnmeasParticles(TAbsFitParticle* p1,
                                    TAbsFitParticle* p2,
                                    TAbsFitParticle* p3,
                                    TAbsFitParticle* p4,
                                    TAbsFitParticle* p5,
                                    TAbsFitParticle* p6,
                                    TAbsFitParticle* p7,
                                    TAbsFitParticle* p8,
                                    TAbsFitParticle* p9) {
  // add many unmeasured particles

  resetStatus();

  if (p1 != nullptr)
    _unmeasParticles.push_back(p1);
  if (p2 != nullptr)
    _unmeasParticles.push_back(p2);
  if (p3 != nullptr)
    _unmeasParticles.push_back(p3);
  if (p4 != nullptr)
    _unmeasParticles.push_back(p4);
  if (p5 != nullptr)
    _unmeasParticles.push_back(p5);
  if (p6 != nullptr)
    _unmeasParticles.push_back(p6);
  if (p7 != nullptr)
    _unmeasParticles.push_back(p7);
  if (p8 != nullptr)
    _unmeasParticles.push_back(p8);
  if (p9 != nullptr)
    _unmeasParticles.push_back(p9);

  countUnmeasParams();
}

void TKinFitter::addConstraint(TAbsFitConstraint* constraint) {
  // add a constraint

  resetStatus();

  if (constraint != nullptr) {
    _constraints.push_back(constraint);
  }

  countMeasParams();
}

void TKinFitter::setVerbosity(Int_t verbosity) {
  // Set verbosity of the fitter:
  // 0: quiet
  // 1: print information before and after the fit
  // 2: print output for every iteration of the fit
  // 3: print debug information

  if (verbosity < 0)
    verbosity = 0;
  if (verbosity > 3)
    verbosity = 3;
  _verbosity = verbosity;
}

Int_t TKinFitter::fit() {
  // Perform the fit
  // Returns:
  // 0: converged
  // 1: not converged

  resetParams();
  resetStatus();

  _nbIter = 0;
  Bool_t isConverged = false;
  Double_t prevF;
  Double_t currF = getF();
  Double_t prevS;
  Double_t currS = 0.;

  // Calculate covariance matrix V
  calcV();

  // print status
  if (_verbosity >= 1) {
    print();
  }

  do {
    // Reset status to "RUNNING"
    // (if it was not aborted already due to singular covariance matrix)
    if (_status != -10) {
      _status = 10;
    }

    // Calculate matrices
    calcB();
    calcVB();
    if (_nParA > 0) {
      calcA();
      calcVA();
      calcC32();
    }
    calcC31();
    calcC33();
    calcC();

    // Calculate corretion for a, y, and lambda
    if (_nParA > 0) {
      calcDeltaA();
    }
    calcDeltaY();
    calcLambda();

    if (_verbosity >= 3) {
      printMatrix(_A, "A");
      printMatrix(_B, "B");
      printMatrix(_VBinv, "VBinv");
      printMatrix(_VB, "VB");
      printMatrix(_V, "V");
      printMatrix(_deltaY, "deltaY");
      printMatrix(_deltaA, "deltaA");
      printMatrix(_C32T, "C32T");
      printMatrix(_c, "C");
    }

    if (_verbosity >= 2) {
      print();
    }

    // Apply calculated corrections to measured and unmeasured particles
    if (_nParA > 0) {
      applyDeltaA();
    }
    applyDeltaY();

    _nbIter++;

    //calculate F and S
    prevF = currF;
    currF = getF();
    prevS = currS;
    currS = getS();

    if (TMath::IsNaN(currF)) {
      edm::LogInfo("KinFitter") << "The current value of F is NaN. Fit will be aborted.";
      _status = -10;
    }
    if (TMath::IsNaN(currS)) {
      edm::LogInfo("KinFitter") << "The current value of S is NaN. Fit will be aborted.";
      _status = -10;
    }

    // Reduce step width if F is not getting smaller
    Int_t nstep = 0;
    while (currF >= prevF) {
      nstep++;
      if (nstep == 10)
        break;
      if (_nParA > 0)
        _deltaA -= (0.5) * (_deltaA - _deltaAstar);
      _deltaY -= (0.5) * (_deltaY - _deltaYstar);
      _lambda *= 0.5;
      _lambdaT *= 0.5;
      if (_nParA > 0)
        applyDeltaA();
      applyDeltaY();
      currF = getF();
      currS = getS();
    }

    // Test convergence
    isConverged = converged(currF, prevS, currS);

  } while ((!isConverged) && (_nbIter < _maxNbIter) && (_status != -10));

  // Calculate covariance matrices
  calcB();
  calcVB();

  if (_nParA > 0) {
    calcA();
    calcVA();
    calcC21();
    calcC22();
    calcC32();
  }
  calcC11();
  calcC31();
  calcC33();
  calcVFit();
  applyVFit();

  // Set status information
  if (isConverged) {
    _status = 0;
  } else if (_status != -10) {
    _status = 1;
  }

  // print status
  if (_verbosity >= 1) {
    print();
  }

  return _status;
}

void TKinFitter::setCovMatrix(TMatrixD& V) {
  // Set the covariance matrix of the measured particles

  if ((V.GetNrows() != _nParB) || (V.GetNcols() != _nParB)) {
    edm::LogError("WrongMatrixSize") << "Covariance matrix of measured particles needs to be a " << _nParB << "x"
                                     << _nParB << " matrix.";
  } else {
    _V.ResizeTo(V);
    _V = V;
  }
}

Bool_t TKinFitter::calcV() {
  // Combines the covariance matrices of all measured particles

  _V.ResizeTo(_nParB, _nParB);
  _V.Zero();

  Int_t offsetP = 0;
  for (unsigned int iP = 0; iP < _measParticles.size(); iP++) {
    TAbsFitParticle* particle = _measParticles[iP];
    Int_t nParP = particle->getNPar();
    const TMatrixD* covMatrix = particle->getCovMatrix();

    for (int iX = offsetP; iX < offsetP + nParP; iX++) {
      for (int iY = offsetP; iY < offsetP + nParP; iY++) {
        _V(iX, iY) = (*covMatrix)(iX - offsetP, iY - offsetP);
      }
    }

    offsetP += nParP;
  }

  for (unsigned int iC = 0; iC < _constraints.size(); iC++) {
    TAbsFitConstraint* constraint = _constraints[iC];
    Int_t nParP = constraint->getNPar();
    const TMatrixD* covMatrix = constraint->getCovMatrix();

    for (int iX = offsetP; iX < offsetP + nParP; iX++) {
      for (int iY = offsetP; iY < offsetP + nParP; iY++) {
        _V(iX, iY) = (*covMatrix)(iX - offsetP, iY - offsetP);
      }
    }

    offsetP += nParP;
  }

  _Vinv.ResizeTo(_V);
  _Vinv = _V;
  try {
    _Vinv.Invert();
  } catch (cms::Exception& e) {
    edm::LogInfo("KinFitter") << "Failed to invert covariance matrix V. Fit will be aborted.";
    _status = -10;
  }

  return true;
}

Bool_t TKinFitter::calcA() {
  // Calculate the Jacobi matrix of unmeasured parameters df_i/da_i
  // Row i contains the derivatives of constraint f_i. Column q contains
  // the derivative wrt. a_q.

  _A.ResizeTo(_constraints.size(), _nParA);

  for (unsigned int indexConstr = 0; indexConstr < _constraints.size(); indexConstr++) {
    int offsetParam = 0;
    for (unsigned int indexParticle = 0; indexParticle < _unmeasParticles.size(); indexParticle++) {
      // Calculate matrix product  df/dP * dP/dy = (df/dr, df/dtheta, df/dphi, ...)

      TAbsFitParticle* particle = _unmeasParticles[indexParticle];
      TMatrixD* derivParticle = particle->getDerivative();
      TMatrixD* derivConstr = _constraints[indexConstr]->getDerivative(particle);
      TMatrixD deriv(*derivConstr, TMatrixD::kMult, *derivParticle);

      for (int indexParam = 0; indexParam < deriv.GetNcols(); indexParam++) {
        _A(indexConstr, indexParam + offsetParam) = deriv(0, indexParam);
      }
      offsetParam += deriv.GetNcols();

      delete derivParticle;
      delete derivConstr;
    }
  }

  // Calculate transposed matrix
  TMatrixD AT(TMatrixD::kTransposed, _A);
  _AT.ResizeTo(AT);
  _AT = AT;

  return true;
}

Bool_t TKinFitter::calcB() {
  // Calculate the Jacobi matrix of measured parameters df_i/da_i
  // Row i contains the derivatives of constraint f_i. Column q contains
  // the derivative wrt. a_q.

  _B.ResizeTo(_constraints.size(), _nParB);

  int offsetParam = 0;
  for (unsigned int indexConstr = 0; indexConstr < _constraints.size(); indexConstr++) {
    offsetParam = 0;
    for (unsigned int indexParticle = 0; indexParticle < _measParticles.size(); indexParticle++) {
      // Calculate matrix product  df/dP * dP/dy = (df/dr, df/dtheta, df/dphi, ...)
      TAbsFitParticle* particle = _measParticles[indexParticle];
      TMatrixD* derivParticle = particle->getDerivative();
      TMatrixD* derivConstr = _constraints[indexConstr]->getDerivative(particle);
      TMatrixD deriv(*derivConstr, TMatrixD::kMult, *derivParticle);
      if (_verbosity >= 3) {
        TString matrixName = "B deriv: Particle -> ";
        matrixName += particle->GetName();
        printMatrix(*derivParticle, matrixName);
        matrixName = "B deriv: Constraint -> ";
        matrixName += _constraints[indexConstr]->GetName();
        matrixName += " , Particle -> ";
        matrixName += particle->GetName();
        printMatrix(*derivConstr, matrixName);
      }
      for (int indexParam = 0; indexParam < deriv.GetNcols(); indexParam++) {
        _B(indexConstr, indexParam + offsetParam) = deriv(0, indexParam);
      }
      offsetParam += deriv.GetNcols();

      delete derivParticle;
      delete derivConstr;
    }
  }

  for (unsigned int iC = 0; iC < _constraints.size(); iC++) {
    TAbsFitConstraint* constraint = _constraints[iC];
    TMatrixD* deriv = constraint->getDerivativeAlpha();

    if (deriv != nullptr) {
      if (_verbosity >= 3) {
        TString matrixName = "B deriv alpha: Constraint -> ";
        matrixName += constraint->GetName();
        printMatrix(*deriv, matrixName);
      }
      for (int indexParam = 0; indexParam < deriv->GetNcols(); indexParam++) {
        _B(iC, indexParam + offsetParam) = (*deriv)(0, indexParam);
      }
      offsetParam += deriv->GetNcols();

      delete deriv;
    }
  }

  TMatrixD BT(TMatrixD::kTransposed, _B);
  _BT.ResizeTo(BT);
  _BT = BT;

  return true;
}

Bool_t TKinFitter::calcVB() {
  // Calculate the matrix V_B = (B*V*B^T)^-1

  TMatrixD BV(_B, TMatrixD::kMult, _V);
  TMatrixD VBinv(BV, TMatrixD::kMult, _BT);
  _VBinv.ResizeTo(VBinv);
  _VBinv = VBinv;

  _VB.ResizeTo(_VBinv);
  _VB = _VBinv;
  try {
    _VB.Invert();
  } catch (cms::Exception& e) {
    edm::LogInfo("KinFitter") << "Failed to invert matrix VB. Fit will be aborted.";
    _status = -10;
  }

  return true;
}

Bool_t TKinFitter::calcVA() {
  // Calculate the matrix VA = (A^T*VB*A)

  TMatrixD ATVB(_AT, TMatrixD::kMult, _VB);
  TMatrixD VA(ATVB, TMatrixD::kMult, _A);
  _VA.ResizeTo(VA);
  _VA = VA;

  _VAinv.ResizeTo(_VA);
  _VAinv = _VA;
  try {
    _VAinv.Invert();
  } catch (cms::Exception& e) {
    edm::LogInfo("KinFitter") << "Failed to invert matrix VA. Fit will be aborted.";
    _status = -10;
  }

  return true;
}

Bool_t TKinFitter::calcC11() {
  // Calculate the matrix C11 = V^(-1) - V^(-1)*BT*VB*B*V^(-1) + V^(-1)*BT*VB*A*VA^(-1)*AT*VB*B*V^(-1)

  TMatrixD VBT(_V, TMatrixD::kMult, _BT);
  TMatrixD VBB(_VB, TMatrixD::kMult, _B);
  TMatrixD VBTVBB(VBT, TMatrixD::kMult, VBB);
  TMatrixD m2(VBTVBB, TMatrixD::kMult, _V);

  _C11.ResizeTo(_V);
  _C11 = _V;
  _C11 -= m2;

  if (_nParA > 0) {
    TMatrixD VBA(_VB, TMatrixD::kMult, _A);
    TMatrixD VBTVBA(VBT, TMatrixD::kMult, VBA);
    TMatrixD VAinvAT(_VAinv, TMatrixD::kMult, _AT);
    TMatrixD VBTVBAVAinvAT(VBTVBA, TMatrixD::kMult, VAinvAT);
    TMatrixD VBTVBAVAinvATVBB(VBTVBAVAinvAT, TMatrixD::kMult, VBB);
    TMatrixD m3(VBTVBAVAinvATVBB, TMatrixD::kMult, _V);
    _C11 += m3;
  }

  TMatrixD C11T(TMatrixD::kTransposed, _C11);
  _C11T.ResizeTo(C11T);
  _C11T = C11T;

  return true;
}

Bool_t TKinFitter::calcC21() {
  // Calculate the matrix  C21 = -VA^(-1)*AT*VB*B*V^(-1)

  TMatrixD VAinvAT(_VAinv, TMatrixD::kMult, _AT);
  TMatrixD VBB(_VB, TMatrixD::kMult, _B);
  TMatrixD VAinvATVBB(VAinvAT, TMatrixD::kMult, VBB);
  TMatrixD C21(VAinvATVBB, TMatrixD::kMult, _V);
  C21 *= -1.;
  _C21.ResizeTo(C21);
  _C21 = C21;

  TMatrixD C21T(TMatrixD::kTransposed, _C21);
  _C21T.ResizeTo(C21T);
  _C21T = C21T;

  return true;
}

Bool_t TKinFitter::calcC22() {
  //  Calculate the matrix C22 = VA^(-1)

  _C22.ResizeTo(_VAinv);
  _C22 = _VAinv;

  TMatrixD C22T(TMatrixD::kTransposed, _C22);
  _C22T.ResizeTo(C22T);
  _C22T = C22T;

  return true;
}

Bool_t TKinFitter::calcC31() {
  // Calculate the matrix  C31 = VB*B*V^(-1) - VB*A*VA^(-1)*AT*VB*B*V^(-1)

  TMatrixD VbB(_VB, TMatrixD::kMult, _B);
  TMatrixD m1(VbB, TMatrixD::kMult, _V);

  _C31.ResizeTo(m1);
  _C31 = m1;

  if (_nParA > 0) {
    TMatrixD VbA(_VB, TMatrixD::kMult, _A);
    TMatrixD VAinvAT(_VAinv, TMatrixD::kMult, _AT);
    TMatrixD VbBV(VbB, TMatrixD::kMult, _V);
    TMatrixD VbAVAinvAT(VbA, TMatrixD::kMult, VAinvAT);
    TMatrixD m2(VbAVAinvAT, TMatrixD::kMult, VbBV);

    _C31 -= m2;
  }

  TMatrixD C31T(TMatrixD::kTransposed, _C31);
  _C31T.ResizeTo(C31T);
  _C31T = C31T;

  return true;
}

Bool_t TKinFitter::calcC32() {
  // Calculate the matrix  C32 = VB*A*VA^(-1)

  TMatrixD VbA(_VB, TMatrixD::kMult, _A);
  TMatrixD C32(VbA, TMatrixD::kMult, _VAinv);
  _C32.ResizeTo(C32);
  _C32 = C32;

  TMatrixD C32T(TMatrixD::kTransposed, _C32);
  _C32T.ResizeTo(C32T);
  _C32T = C32T;

  return true;
}

Bool_t TKinFitter::calcC33() {
  // Calculate the matrix C33 = -VB + VB*A*VA^(-1)*AT*VB

  _C33.ResizeTo(_VB);
  _C33 = _VB;
  _C33 *= -1.;

  if (_nParA > 0) {
    TMatrixD VbA(_VB, TMatrixD::kMult, _A);
    TMatrixD VAinvAT(_VAinv, TMatrixD::kMult, _AT);
    TMatrixD VbAVAinvAT(VbA, TMatrixD::kMult, VAinvAT);
    TMatrixD C33(VbAVAinvAT, TMatrixD::kMult, _VB);
    _C33 += C33;
  }

  TMatrixD C33T(TMatrixD::kTransposed, _C33);
  _C33T.ResizeTo(C33T);
  _C33T = C33T;

  return true;
}

Bool_t TKinFitter::calcC() {
  // Calculate the matrix c = A*deltaAStar + B*deltaYStar - fStar

  int offsetParam = 0;

  // calculate delta(a*), = 0 in the first iteration
  TMatrixD deltaastar(1, 1);
  if (_nParA > 0) {
    deltaastar.ResizeTo(_nParA, 1);
    for (unsigned int indexParticle = 0; indexParticle < _unmeasParticles.size(); indexParticle++) {
      TAbsFitParticle* particle = _unmeasParticles[indexParticle];
      const TMatrixD* astar = particle->getParCurr();
      const TMatrixD* a = particle->getParIni();
      TMatrixD deltaastarpart(*astar);
      deltaastarpart -= *a;

      for (int indexParam = 0; indexParam < deltaastarpart.GetNrows(); indexParam++) {
        deltaastar(indexParam + offsetParam, 0) = deltaastarpart(indexParam, 0);
      }
      offsetParam += deltaastarpart.GetNrows();
    }

    if (_verbosity >= 3) {
      printMatrix(deltaastar, "deltaastar");
    }
  }

  // calculate delta(y*), = 0 in the first iteration
  TMatrixD deltaystar(_nParB, 1);
  offsetParam = 0;
  for (unsigned int indexParticle = 0; indexParticle < _measParticles.size(); indexParticle++) {
    TAbsFitParticle* particle = _measParticles[indexParticle];
    const TMatrixD* ystar = particle->getParCurr();
    const TMatrixD* y = particle->getParIni();
    TMatrixD deltaystarpart(*ystar);
    deltaystarpart -= *y;

    for (int indexParam = 0; indexParam < deltaystarpart.GetNrows(); indexParam++) {
      deltaystar(indexParam + offsetParam, 0) = deltaystarpart(indexParam, 0);
    }
    offsetParam += deltaystarpart.GetNrows();
  }

  for (unsigned int iC = 0; iC < _constraints.size(); iC++) {
    TAbsFitConstraint* constraint = _constraints[iC];

    if (constraint->getNPar() > 0) {
      const TMatrixD* alphastar = constraint->getParCurr();
      const TMatrixD* alpha = constraint->getParIni();

      TMatrixD deltaalphastarpart(*alphastar);
      deltaalphastarpart -= *alpha;

      for (int indexParam = 0; indexParam < deltaalphastarpart.GetNrows(); indexParam++) {
        deltaystar(indexParam + offsetParam, 0) = deltaalphastarpart(indexParam, 0);
      }
      offsetParam += deltaalphastarpart.GetNrows();
    }
  }

  if (_verbosity >= 3) {
    printMatrix(deltaystar, "deltaystar");
  }

  // calculate f*
  TMatrixD fstar(_constraints.size(), 1);
  for (unsigned int indexConstr = 0; indexConstr < _constraints.size(); indexConstr++) {
    fstar(indexConstr, 0) = _constraints[indexConstr]->getCurrentValue();
  }

  // calculate c
  _c.ResizeTo(fstar);
  _c = fstar;
  _c *= (-1.);
  TMatrixD Bdeltaystar(_B, TMatrixD::kMult, deltaystar);
  _c += Bdeltaystar;
  if (_nParA) {
    TMatrixD Adeltaastar(_A, TMatrixD::kMult, deltaastar);
    _c += Adeltaastar;
  }

  return true;
}

Bool_t TKinFitter::calcDeltaA() {
  // Calculate the matrix deltaA = C32T * c
  // (corrections to unmeasured parameters)

  TMatrixD deltaA(_C32T, TMatrixD::kMult, _c);
  _deltaA.ResizeTo(deltaA);

  if (_nbIter == 0) {
    _deltaAstar.ResizeTo(deltaA);
    _deltaAstar.Zero();
  } else
    _deltaAstar = _deltaA;

  _deltaA = deltaA;

  return true;
}

Bool_t TKinFitter::calcDeltaY() {
  // Calculate the matrix deltaY = C31T * c
  // (corrections to measured parameters)

  TMatrixD deltaY(_C31T, TMatrixD::kMult, _c);
  _deltaY.ResizeTo(deltaY);

  if (_nbIter == 0) {
    _deltaYstar.ResizeTo(deltaY);
    _deltaYstar.Zero();
  } else
    _deltaYstar = _deltaY;

  _deltaY = deltaY;

  return true;
}

Bool_t TKinFitter::calcLambda() {
  // Calculate the matrix Lambda = C33 * c
  // (Lagrange Multipliers)

  TMatrixD lambda(_C33, TMatrixD::kMult, _c);
  _lambda.ResizeTo(lambda);
  _lambda = lambda;

  TMatrixD lambdaT(TMatrixD::kTransposed, _lambda);
  _lambdaT.ResizeTo(lambdaT);
  _lambdaT = lambdaT;

  return true;
}

Bool_t TKinFitter::calcVFit() {
  // Calculate the covariance matrix of fitted parameters
  //
  // Vfit(y) = ( C11  C21T )
  //     (a)   ( C21  C22  )
  //
  // Vfit(lambda) = (-C33)

  // Calculate covariance matrix of lambda
  _lambdaVFit.ResizeTo(_C33);
  _lambdaVFit = _C33;
  _lambdaVFit *= -1.;

  // Calculate combined covariance matrix of y and a
  Int_t nbRows = _C11.GetNrows();
  Int_t nbCols = _C11.GetNcols();
  if (_nParA > 0) {
    nbRows += _C21.GetNrows();
    nbCols += _C21T.GetNcols();
  }
  _yaVFit.ResizeTo(nbRows, nbCols);

  for (int iRow = 0; iRow < nbRows; iRow++) {
    for (int iCol = 0; iCol < nbCols; iCol++) {
      if (iRow >= _C11.GetNrows()) {
        if (iCol >= _C11.GetNcols()) {
          _yaVFit(iRow, iCol) = _C22(iRow - _C11.GetNrows(), iCol - _C11.GetNcols());
        } else {
          _yaVFit(iRow, iCol) = _C21(iRow - _C11.GetNrows(), iCol);
        }
      } else {
        if (iCol >= _C11.GetNcols()) {
          _yaVFit(iRow, iCol) = _C21T(iRow, iCol - _C11.GetNcols());
        } else {
          _yaVFit(iRow, iCol) = _C11(iRow, iCol);
        }
      }
    }
  }

  return true;
}

void TKinFitter::applyVFit() {
  // apply fit covariance matrix to measured and unmeasured  particles

  int offsetParam = 0;
  for (unsigned int indexParticle = 0; indexParticle < _measParticles.size(); indexParticle++) {
    TAbsFitParticle* particle = _measParticles[indexParticle];
    Int_t nbParams = particle->getNPar();
    TMatrixD vfit(nbParams, nbParams);
    for (Int_t c = 0; c < nbParams; c++) {
      for (Int_t r = 0; r < nbParams; r++) {
        vfit(r, c) = _yaVFit(r + offsetParam, c + offsetParam);
      }
    }
    particle->setCovMatrixFit(&vfit);
    offsetParam += nbParams;
  }

  for (unsigned int indexConstraint = 0; indexConstraint < _constraints.size(); indexConstraint++) {
    TAbsFitConstraint* constraint = _constraints[indexConstraint];
    Int_t nbParams = constraint->getNPar();
    if (nbParams > 0) {
      TMatrixD vfit(nbParams, nbParams);
      for (Int_t c = 0; c < nbParams; c++) {
        for (Int_t r = 0; r < nbParams; r++) {
          vfit(r, c) = _yaVFit(r + offsetParam, c + offsetParam);
        }
      }
      constraint->setCovMatrixFit(&vfit);
      offsetParam += nbParams;
    }
  }

  for (unsigned int indexParticle = 0; indexParticle < _unmeasParticles.size(); indexParticle++) {
    TAbsFitParticle* particle = _unmeasParticles[indexParticle];
    Int_t nbParams = particle->getNPar();
    TMatrixD vfit(nbParams, nbParams);
    for (Int_t c = 0; c < nbParams; c++) {
      for (Int_t r = 0; r < nbParams; r++) {
        vfit(r, c) = _yaVFit(r + offsetParam, c + offsetParam);
      }
    }
    particle->setCovMatrixFit(&vfit);
    offsetParam += nbParams;
  }
}

Bool_t TKinFitter::applyDeltaA() {
  //apply corrections to unmeasured particles

  int offsetParam = 0;
  for (unsigned int indexParticle = 0; indexParticle < _unmeasParticles.size(); indexParticle++) {
    TAbsFitParticle* particle = _unmeasParticles[indexParticle];
    Int_t nbParams = particle->getNPar();
    TMatrixD params(nbParams, 1);
    for (Int_t index = 0; index < nbParams; index++) {
      params(index, 0) = _deltaA(index + offsetParam, 0);
    }
    particle->applycorr(&params);
    offsetParam += nbParams;
  }

  return true;
}

Bool_t TKinFitter::applyDeltaY() {
  //apply corrections to measured particles

  int offsetParam = 0;
  for (unsigned int indexParticle = 0; indexParticle < _measParticles.size(); indexParticle++) {
    TAbsFitParticle* particle = _measParticles[indexParticle];
    Int_t nbParams = particle->getNPar();
    TMatrixD params(nbParams, 1);
    for (Int_t index = 0; index < nbParams; index++) {
      params(index, 0) = _deltaY(index + offsetParam, 0);
    }
    particle->applycorr(&params);
    offsetParam += nbParams;
  }

  for (unsigned int indexConstraint = 0; indexConstraint < _constraints.size(); indexConstraint++) {
    TAbsFitConstraint* constraint = _constraints[indexConstraint];
    Int_t nbParams = constraint->getNPar();
    if (nbParams > 0) {
      TMatrixD params(nbParams, 1);
      for (Int_t index = 0; index < nbParams; index++) {
        params(index, 0) = _deltaY(index + offsetParam, 0);
      }
      constraint->applyDeltaAlpha(&params);
      offsetParam += nbParams;
    }
  }

  return true;
}

Double_t TKinFitter::getF() {
  // calculate current absolut value of constraints
  // F = Sum[ Abs(f_k( aStar, yStar)) ]

  Double_t F = 0.;
  for (unsigned int indexConstr = 0; indexConstr < _constraints.size(); indexConstr++) {
    F += TMath::Abs(_constraints[indexConstr]->getCurrentValue());
  }

  return F;
}

Double_t TKinFitter::getS() {
  // calculate current value of Chi2
  // S = deltaYT * V^-1 * deltaY

  Double_t S = 0.;

  if (_nbIter > 0) {
    TMatrixD deltaYTVinv(_deltaY, TMatrixD::kTransposeMult, _Vinv);
    TMatrixD S2(deltaYTVinv, TMatrixD::kMult, _deltaY);
    S = S2(0, 0);
  }

  return S;
}

Bool_t TKinFitter::converged(Double_t F, Double_t prevS, Double_t currS) {
  // check whether convergence criteria are fulfilled

  Bool_t isConverged = false;

  // calculate F, delta(a) and delta(y) already applied
  isConverged = (F < _maxF);

  // Calculate current Chi^2 and delta(S)
  Double_t deltaS = currS - prevS;
  isConverged = isConverged && (TMath::Abs(deltaS) < _maxDeltaS);

  return isConverged;
}

TString TKinFitter::getStatusString() {
  TString statusstring = "";

  switch (_status) {
    case -1: {
      statusstring = "NO FIT PERFORMED";
      break;
    }
    case 10: {
      statusstring = "RUNNING";
      break;
    }
    case -10: {
      statusstring = "ABORTED";
      break;
    }
    case 0: {
      statusstring = "CONVERGED";
      break;
    }
    case 1: {
      statusstring = "NOT CONVERGED";
      break;
    }
  }

  return statusstring;
}

void TKinFitter::print() {
  edm::LogVerbatim log("KinFitter");
  log << "\n"
      << "\n";
  // Print status of fit
  log << "Status: " << getStatusString() << "   F=" << getF() << "   S=" << getS() << "   N=" << _nbIter
      << "   NDF=" << getNDF() << "\n";
  // Print measured particles
  log << "measured particles: \n";
  Int_t parIndex = 0;
  for (unsigned int iP = 0; iP < _measParticles.size(); iP++) {
    TAbsFitParticle* particle = _measParticles[iP];
    Int_t nParP = particle->getNPar();
    const TMatrixD* par = particle->getParCurr();
    const TMatrixD* covP = particle->getCovMatrix();
    log << std::setw(3) << setiosflags(std::ios::right) << iP;
    log << std::setw(15) << setiosflags(std::ios::right) << particle->GetName();
    log << std::setw(3) << " ";
    for (int iPar = 0; iPar < nParP; iPar++) {
      if (iPar > 0) {
        log << setiosflags(std::ios::right) << std::setw(21) << " ";
      }
      TString colstr = "";
      colstr += parIndex;
      colstr += ":";
      log << std::setw(4) << colstr;
      log << std::setw(2) << " ";
      log << setiosflags(std::ios::left) << setiosflags(std::ios::scientific) << std::setprecision(3);
      log << std::setw(15) << (*par)(iPar, 0);
      if (_nbIter > 0 && _status < 10) {
        log << std::setw(15) << TMath::Sqrt(_yaVFit(iPar, iPar));
      } else {
        log << std::setw(15) << " ";
      }
      log << std::setw(15) << TMath::Sqrt((*covP)(iPar, iPar));
      log << "\n";
      parIndex++;
    }
    log << particle->getInfoString();
  }
  // Print unmeasured particles
  log << "unmeasured particles: \n";
  parIndex = 0;
  for (unsigned int iP = 0; iP < _unmeasParticles.size(); iP++) {
    TAbsFitParticle* particle = _unmeasParticles[iP];
    Int_t nParP = particle->getNPar();
    const TMatrixD* par = particle->getParCurr();
    log << std::setw(3) << setiosflags(std::ios::right) << iP;
    log << std::setw(15) << particle->GetName();
    log << std::setw(3) << " ";
    for (int iPar = 0; iPar < nParP; iPar++) {
      if (iPar > 0) {
        log << setiosflags(std::ios::right) << std::setw(21) << " ";
      }
      TString colstr = "";
      colstr += parIndex;
      colstr += ":";
      log << std::setw(4) << colstr;
      log << std::setw(2) << " ";
      log << setiosflags(std::ios::left) << setiosflags(std::ios::scientific) << std::setprecision(3);
      log << std::setw(15) << (*par)(iPar, 0);
      if (_nbIter > 0 && _status < 10) {
        log << std::setw(15) << TMath::Sqrt(_yaVFit(iPar + _nParB, iPar + _nParB));
      } else {
        log << std::setw(15) << " ";
      }
      log << "\n";
      parIndex++;
    }
    log << particle->getInfoString();
  }
  log << "\n";
  // Print constraints
  log << "constraints: \n";
  for (unsigned int indexConstr = 0; indexConstr < _constraints.size(); indexConstr++) {
    log << _constraints[indexConstr]->getInfoString();
  }
  log << "\n";
}

void TKinFitter::printMatrix(const TMatrixD& matrix, const TString& name) {
  // produce a tabular printout for matrices
  // this function is a modified version of Root's TMatrixTBase<Element>::Print method
  // which could not be used together with the MessageLogger

  if (!matrix.IsValid()) {
    edm::LogWarning("InvalidMatrix") << "Matrix " << name << " is invalid.";
    return;
  }

  edm::LogVerbatim log("KinFitter");

  const Int_t nCols = matrix.GetNcols();
  const Int_t nRows = matrix.GetNrows();
  const Int_t colsPerSheet = 5;
  char topbar[100];
  Int_t nk = 6 + 13 * TMath::Min(colsPerSheet, nCols);
  for (Int_t i = 0; i < nk; i++)
    topbar[i] = '-';
  topbar[nk] = 0;

  Int_t sw = (70 - name.Length()) / 2;

  log << std::setfill('=') << std::setw(sw) << "=  " << name << std::setw(sw) << std::left << "  ="
      << "\n"
      << std::setfill(' ') << std::right << "\n";

  log << nRows << "x" << nCols << " matrix is as follows \n";

  for (Int_t iSheet = 0; iSheet < nCols; iSheet += colsPerSheet) {
    log << "\n"
        << "     |";
    for (Int_t iCol = iSheet; iCol < nCols; iCol++) {
      if (iCol < iSheet + colsPerSheet)
        log << std::setw(8) << iCol << "    |";
    }
    log << "\n" << topbar << " \n";
    for (Int_t iRow = 0; iRow < nRows; iRow++) {
      log << std::setw(4) << iRow << " |";
      for (Int_t iCol = iSheet; iCol < nCols; iCol++) {
        if (iCol < iSheet + colsPerSheet)
          log << std::setw(12) << matrix(iRow, iCol) << " ";
      }
      log << "\n";
    }
  }
}