#include <LagrangeMultipliersFitter.h>

Public Types
enum	ConvergeProc { ConstraintMin = 0, Chi2Min, Chi2AndConstaintMin }

enum	Parameters { par_vx = 0, par_vy, par_vz, par_px, par_py, par_pz, par_m, npardim }

enum	Position { pos_x = 0, pos_y, pos_z, nposdim }

Public Member Functions
virtual double	chiSquare ()

virtual double	cSum ()

virtual bool	fit ()

virtual LorentzVectorParticle	getMother ()=0

virtual std::vector< LorentzVectorParticle >	getRefitDaughters ()=0

virtual bool	isConfigured ()

virtual bool	isConverged ()

	LagrangeMultipliersFitter ()

virtual double	nConstraints ()=0

virtual int	nDaughters ()=0

virtual double	ndf ()=0

virtual double	nIter ()

virtual void	setMaxDelta (double MaxDelta)

virtual void	setNIterMax (int Nitermax)

virtual void	setWeight (double weight)

virtual	~LagrangeMultipliersFitter ()

Protected Member Functions
virtual TVectorD	value (const TVectorD &v)=0

Protected Attributes
TMatrixTSym< double >	cov_

TMatrixTSym< double >	cov_0_

bool	isConfigured_

bool	isFit_

TVectorD	par_

TVectorD	par_0_

Private Member Functions
bool	applyLagrangianConstraints ()

double	chiSquare (const TVectorT< double > &delta_alpha, const TVectorT< double > &lambda, const TMatrixT< double > &D, const TVectorT< double > &d)

double	chiSquareUsingInitalPoint (const TVectorT< double > &alpha, const TVectorT< double > &lambda)

TMatrixT< double >	computeVariance ()

double	constraintDelta (const TVectorT< double > &par)

TMatrixT< double >	derivative ()

Private Attributes
double	chi2_

double	chi2prev_

TMatrixT< double >	D_

double	delta_

double	epsilon_

double	maxDelta_

double	niter_

double	nitermax_

double	ScaleFactor_

TMatrixTSym< double >	V_alpha0_inv_

TMatrixT< double >	V_corr_prev_

TMatrixTSym< double >	V_D_

double	weight_

Detailed Description

Definition at line 18 of file LagrangeMultipliersFitter.h.

Member Enumeration Documentation

◆ ConvergeProc

enum tauImpactParameter::LagrangeMultipliersFitter::ConvergeProc

Enumerator
ConstraintMin
Chi2Min
Chi2AndConstaintMin

Definition at line 22 of file LagrangeMultipliersFitter.h.

22 { ConstraintMin = 0, Chi2Min, Chi2AndConstaintMin };

◆ Parameters

enum tauImpactParameter::LagrangeMultipliersFitter::Parameters

Enumerator
par_vx
par_vy
par_vz
par_px
par_py
par_pz
par_m
npardim

Definition at line 21 of file LagrangeMultipliersFitter.h.

21 { par_vx = 0, par_vy, par_vz, par_px, par_py, par_pz, par_m, npardim };

◆ Position

enum tauImpactParameter::LagrangeMultipliersFitter::Position

Enumerator
pos_x
pos_y
pos_z
nposdim

Definition at line 20 of file LagrangeMultipliersFitter.h.

20 { pos_x = 0, pos_y, pos_z, nposdim };

Constructor & Destructor Documentation

◆ LagrangeMultipliersFitter()

LagrangeMultipliersFitter::LagrangeMultipliersFitter ( )

Definition at line 13 of file LagrangeMultipliersFitter.cc.

     : isConfigured_(false),
       isFit_(false),
       epsilon_(0.00001),
       weight_(1.0),
       maxDelta_(0.1),
       nitermax_(100),
       chi2_(1e10),
       D_(1, 1),
       V_D_(1, 1) {}

◆ ~LagrangeMultipliersFitter()

virtual tauImpactParameter::LagrangeMultipliersFitter::~LagrangeMultipliersFitter ( )

inlinevirtual

Definition at line 25 of file LagrangeMultipliersFitter.h.

25 {};

Member Function Documentation

◆ applyLagrangianConstraints()

bool LagrangeMultipliersFitter::applyLagrangianConstraints ( )

private

Definition at line 50 of file LagrangeMultipliersFitter.cc.

                                                            {
   if (V_D_.GetNrows() != nConstraints())
     V_D_.ResizeTo(nConstraints(), nConstraints());
   if (D_.GetNrows() != nConstraints() || D_.GetNcols() != par_.GetNrows())
     D_.ResizeTo(nConstraints(), par_.GetNrows());
  
   // Setup intial values
   TVectorT<double> alpha_A = par_;
   TVectorT<double> alpha_0 = par_0_;
   TVectorT<double> delta_alpha_A = alpha_A - alpha_0;
   D_ = derivative();
   TVectorT<double> d = value(par_);
   TVectorT<double> C = D_ * delta_alpha_A - d;
   TMatrixTSym<double> V_alpha0 = cov_0_;
   TMatrixTSym<double> V_D_inv = V_alpha0;
   V_D_inv.Similarity(D_);
   double det = V_D_inv.Determinant();
   TDecompBK Inverter(V_D_inv);
   if (fabs(det) > 1e40) {
     edm::LogWarning("LagrangeMultipliersFitter::Fit")
         << "Fit failed: unable to invert SYM gain matrix LARGE Determinant" << det << " \n"
         << std::endl;
     return false;
   }
   if (!Inverter.Decompose()) {
     edm::LogWarning("LagrangeMultipliersFitter::Fit") << "Fit failed: unable to invert SYM gain matrix " << det << " \n"
                                                       << std::endl;
     return false;
   }
   V_D_ = Inverter.Invert();
  
   // solve equations
   TVectorT<double> lambda = -1.0 * V_D_ * C;
   TMatrixT<double> DT = D_;
   DT.T();
   TVectorT<double> alpha = alpha_0 - V_alpha0 * DT * lambda;
  
   // do while loop to see if the convergance criteria are satisfied
   double s(1), stepscale(0.01);
   chi2prev_ = chi2_;
   double currentchi2(chiSquareUsingInitalPoint(alpha_A, lambda)), currentdelta(constraintDelta(par_));
   TVectorT<double> alpha_s = alpha;
   // convergence in 2 step procedure to minimize chi2 within MaxDelta_ of the constriants
   // 1) Get within 5x MaxDelta_
   // 2) converge based on improving chi2 and constrianed delta
   unsigned int Proc = ConstraintMin;
   if (constraintDelta(par_) < 5 * maxDelta_)
     Proc = Chi2AndConstaintMin;
   int NIter = (int)(1.0 / stepscale);
   for (int iter = 0; iter < NIter; iter++) {
     // compute safty cutoff for numberical constraint
     double diff = 0;
     for (int l = 0; l < alpha_s.GetNrows(); l++) {
       if (diff < alpha_s(l) - alpha_A(l))
         diff = alpha_s(l) - alpha_A(l);
     }
     double delta_alpha_s = constraintDelta(alpha_s);
     if (Proc == ConstraintMin) {
       if (delta_alpha_s < currentdelta || iter == NIter || diff < 100 * epsilon_) {
         currentchi2 = chiSquareUsingInitalPoint(alpha_s, lambda);
         currentdelta = delta_alpha_s;
         ScaleFactor_ = s;
         break;
       }
     } else if (Proc == Chi2AndConstaintMin) {
       double chi2_s = chiSquareUsingInitalPoint(alpha_s, lambda);
       if ((delta_alpha_s < currentdelta /*+maxDelta_*/ && chi2_s < currentchi2) || iter == NIter ||
           diff < 100 * epsilon_) {
         currentchi2 = chi2_s;
         currentdelta = delta_alpha_s;
         ScaleFactor_ = s;
         break;
       }
     }
     s -= stepscale;
     alpha_s = alpha_A + s * (alpha - alpha_A);
   }
   // set chi2
   chi2_ = currentchi2;
   //set delta
   delta_ = currentdelta;
   par_ = alpha_s;
   return true;
 }

References zMuMuMuonUserData::alpha, gen::C, chi2_, Chi2AndConstaintMin, chi2prev_, chiSquareUsingInitalPoint(), constraintDelta(), ConstraintMin, cov_0_, ztail::d, D_, delta_, derivative(), change_name::diff, GeomDetEnumerators::DT, epsilon_, createfilelist::int, cmsLHEtoEOSManager::l, maxDelta_, nConstraints(), par_, par_0_, alignCSCRings::s, ScaleFactor_, V_D_, and value().

Referenced by fit().

◆ chiSquare() [1/2]

virtual double tauImpactParameter::LagrangeMultipliersFitter::chiSquare ( )

inlinevirtual

Definition at line 34 of file LagrangeMultipliersFitter.h.

34 { return chi2_; }

References chi2_.

◆ chiSquare() [2/2]

double LagrangeMultipliersFitter::chiSquare	(	const TVectorT< double > &	delta_alpha,
		const TVectorT< double > &	lambda,
		const TMatrixT< double > &	D,
		const TVectorT< double > &	d
	)

private

Definition at line 162 of file LagrangeMultipliersFitter.cc.

                                                                        {
   double c2 = lambda * (D * delta_alpha + d);
   return c2;
 }

References ztail::d.

◆ chiSquareUsingInitalPoint()

double LagrangeMultipliersFitter::chiSquareUsingInitalPoint	(	const TVectorT< double > &	alpha,
		const TVectorT< double > &	lambda
	)

private

Definition at line 170 of file LagrangeMultipliersFitter.cc.

                                                                                             {
   if (cov_0_.GetNrows() != V_alpha0_inv_.GetNrows()) {
     TMatrixTSym<double> V_alpha0 = cov_0_;
     V_alpha0_inv_.ResizeTo(cov_0_.GetNrows(), cov_0_.GetNrows());
     TDecompBK Inverter(V_alpha0);
     if (!Inverter.Decompose()) {  // handle rare case where inversion is not possible (ie assume diagonal)
       edm::LogWarning("LagrangeMultipliersFitter::chiSquareUsingInitalPoint")
           << "Error non-invertable Matrix... Calculating under assumption that correlations can be neglected!!!"
           << std::endl;
       for (int j = 0; j < par_.GetNrows(); j++) {
         for (int i = 0; i < par_.GetNrows(); i++) {
           if (i == j)
             V_alpha0_inv_(i, j) = 1.0 / V_alpha0(i, j);
           else
             V_alpha0_inv_(i, j) = 0.0;
         }
       }
     } else {
       V_alpha0_inv_ = Inverter.Invert();
     }
   }
  
   TVectorT<double> alpha_0 = par_0_;
   TVectorT<double> dalpha = alpha - alpha_0;
   double c2_var = dalpha * (V_alpha0_inv_ * dalpha);
   const TVectorT<double>& alpha_v = alpha;
   double c2_constraints = lambda * value(alpha_v);
   double c2 = c2_var + c2_constraints;
   return c2;
 }

References zMuMuMuonUserData::alpha, cov_0_, mps_fire::i, dqmiolumiharvest::j, par_, par_0_, V_alpha0_inv_, and value().

Referenced by applyLagrangianConstraints().

◆ computeVariance()

TMatrixT< double > LagrangeMultipliersFitter::computeVariance ( )

private

Definition at line 211 of file LagrangeMultipliersFitter.cc.

                                                             {
   TMatrixTSym<double> V_alpha0 = cov_0_;
   TMatrixTSym<double> DTV_DD = V_D_.SimilarityT(D_);
   TMatrixT<double> DTV_DDV = DTV_DD * V_alpha0;
   TMatrixT<double> VDTV_DDV = V_alpha0 * DTV_DDV;
   TMatrixT<double> CovCor = VDTV_DDV;
   //CovCor*=ScaleFactor_;
   if (V_corr_prev_.GetNrows() != V_alpha0.GetNrows()) {
     V_corr_prev_.ResizeTo(V_alpha0.GetNrows(), V_alpha0.GetNrows());
     V_corr_prev_ = CovCor;
   } else {
     V_corr_prev_ *= (1 - ScaleFactor_);
     CovCor += V_corr_prev_;
     V_corr_prev_ = CovCor;
   }
  
   TMatrixT<double> V_alpha = V_alpha0 - CovCor;
   for (int i = 0; i < cov_.GetNrows(); i++) {
     for (int j = 0; j <= i; j++) {
       cov_(i, j) = V_alpha(i, j);
     }
   }
   return cov_;
 }

References cov_, cov_0_, D_, mps_fire::i, dqmiolumiharvest::j, ScaleFactor_, V_corr_prev_, and V_D_.

Referenced by fit().

◆ constraintDelta()

double LagrangeMultipliersFitter::constraintDelta ( const TVectorT< double > & par )

private

Definition at line 202 of file LagrangeMultipliersFitter.cc.

                                                                              {
   TVectorD d_par = value(par);
   double delta_d(0);
   for (int i = 0; i < d_par.GetNrows(); i++) {
     delta_d += fabs(d_par(i));
   }
   return delta_d;
 }

References mps_fire::i, and value().

Referenced by applyLagrangianConstraints().

◆ cSum()

virtual double tauImpactParameter::LagrangeMultipliersFitter::cSum ( )

inlinevirtual

Definition at line 35 of file LagrangeMultipliersFitter.h.

35 { return delta_; };

References delta_.

◆ derivative()

TMatrixD LagrangeMultipliersFitter::derivative ( )

private

Definition at line 135 of file LagrangeMultipliersFitter.cc.

                                                {  // alway evaluated at current par
   TMatrixD Derivatives(nConstraints(), par_.GetNrows());
   TVectorD par_plus(par_.GetNrows());
   TVectorD value_par(nConstraints());
   TVectorD value_par_plus(nConstraints());
   for (int j = 0; j < par_.GetNrows(); j++) {
     for (int i = 0; i < par_.GetNrows(); i++) {
       par_plus(i) = par_(i);
       if (i == j)
         par_plus(i) = par_(i) + epsilon_;
     }
     value_par = value(par_);
     value_par_plus = value(par_plus);
     for (int i = 0; i < nConstraints(); i++) {
       Derivatives(i, j) = (value_par_plus(i) - value_par(i)) / epsilon_;
     }
   }
   return Derivatives;
 }

References epsilon_, mps_fire::i, dqmiolumiharvest::j, nConstraints(), par_, and value().

Referenced by applyLagrangianConstraints().

◆ fit()

bool LagrangeMultipliersFitter::fit ( void )

virtual

Definition at line 24 of file LagrangeMultipliersFitter.cc.

                                     {
   if (cov_.GetNrows() != par_0_.GetNrows()) {
     // set cov to cov_0 until value is computed
     cov_.ResizeTo(par_0_.GetNrows(), par_0_.GetNrows());
     cov_ = cov_0_;
   }
   if (!isConfigured_)
     return false;
   if (isFit_)
     return isConverged();
   isFit_ = true;
   niter_ = 0;
   for (niter_ = 0; niter_ <= nitermax_; niter_++) {
     bool passed = applyLagrangianConstraints();
     if (!passed || (niter_ == nitermax_ && delta_ >= 4.0 * maxDelta_)) {
       edm::LogWarning("LagrangeMultipliersFitter::Fit")
           << "Reached Maximum number of iterations..." << niter_ << std::endl;
       return false;
     }
     if (isConverged())
       break;
   }
   computeVariance();
   return true;
 }

References applyLagrangianConstraints(), computeVariance(), cov_, cov_0_, delta_, isConfigured_, isConverged(), isFit_, maxDelta_, niter_, nitermax_, par_0_, and TriggerAnalyzer::passed.

Referenced by trackingPlots.Iteration::modules().

◆ getMother()

virtual LorentzVectorParticle tauImpactParameter::LagrangeMultipliersFitter::getMother ( )

pure virtual

◆ getRefitDaughters()

virtual std::vector<LorentzVectorParticle> tauImpactParameter::LagrangeMultipliersFitter::getRefitDaughters ( )

pure virtual

◆ isConfigured()

virtual bool tauImpactParameter::LagrangeMultipliersFitter::isConfigured ( )

inlinevirtual

Definition at line 33 of file LagrangeMultipliersFitter.h.

33 { return isConfigured_; }

References isConfigured_.

◆ isConverged()

bool LagrangeMultipliersFitter::isConverged ( )

virtual

Definition at line 155 of file LagrangeMultipliersFitter.cc.

                                             {
   if (delta_ < maxDelta_) {
     return true;
   }
   return false;
 }

References delta_, and maxDelta_.

Referenced by fit().

◆ nConstraints()

virtual double tauImpactParameter::LagrangeMultipliersFitter::nConstraints ( )

pure virtual

Referenced by applyLagrangianConstraints(), and derivative().

◆ nDaughters()

virtual int tauImpactParameter::LagrangeMultipliersFitter::nDaughters ( )

pure virtual

◆ ndf()

virtual double tauImpactParameter::LagrangeMultipliersFitter::ndf ( )

pure virtual

◆ nIter()

virtual double tauImpactParameter::LagrangeMultipliersFitter::nIter ( )

inlinevirtual

Definition at line 36 of file LagrangeMultipliersFitter.h.

36 { return niter_; };

References niter_.

◆ setMaxDelta()

virtual void tauImpactParameter::LagrangeMultipliersFitter::setMaxDelta ( double MaxDelta )

inlinevirtual

Definition at line 28 of file LagrangeMultipliersFitter.h.

28 { maxDelta_ = MaxDelta; }

References maxDelta_.

◆ setNIterMax()

virtual void tauImpactParameter::LagrangeMultipliersFitter::setNIterMax ( int Nitermax )

inlinevirtual

Definition at line 29 of file LagrangeMultipliersFitter.h.

29 { nitermax_ = Nitermax; }

References nitermax_.

◆ setWeight()

virtual void tauImpactParameter::LagrangeMultipliersFitter::setWeight ( double weight )

inlinevirtual

Definition at line 27 of file LagrangeMultipliersFitter.h.

27 { weight_ = weight; }

References mps_merge::weight, and weight_.

◆ value()

virtual TVectorD tauImpactParameter::LagrangeMultipliersFitter::value ( const TVectorD & v )

protectedpure virtual

Referenced by applyLagrangianConstraints(), chiSquareUsingInitalPoint(), constraintDelta(), and derivative().

Member Data Documentation

◆ chi2_

double tauImpactParameter::LagrangeMultipliersFitter::chi2_

private

Definition at line 69 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), and chiSquare().

◆ chi2prev_

double tauImpactParameter::LagrangeMultipliersFitter::chi2prev_

private

Definition at line 69 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints().

◆ cov_

TMatrixTSym<double> tauImpactParameter::LagrangeMultipliersFitter::cov_

protected

Definition at line 50 of file LagrangeMultipliersFitter.h.

Referenced by computeVariance(), and fit().

◆ cov_0_

TMatrixTSym<double> tauImpactParameter::LagrangeMultipliersFitter::cov_0_

protected

Definition at line 49 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), chiSquareUsingInitalPoint(), computeVariance(), and fit().

◆ D_

TMatrixT<double> tauImpactParameter::LagrangeMultipliersFitter::D_

private

Definition at line 73 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), and computeVariance().

◆ delta_

double tauImpactParameter::LagrangeMultipliersFitter::delta_

private

Definition at line 69 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), cSum(), fit(), and isConverged().

◆ epsilon_

double tauImpactParameter::LagrangeMultipliersFitter::epsilon_

private

Definition at line 66 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), and derivative().

◆ isConfigured_

bool tauImpactParameter::LagrangeMultipliersFitter::isConfigured_

protected

Definition at line 51 of file LagrangeMultipliersFitter.h.

Referenced by fit(), and isConfigured().

◆ isFit_

bool tauImpactParameter::LagrangeMultipliersFitter::isFit_

protected

Definition at line 52 of file LagrangeMultipliersFitter.h.

Referenced by fit().

◆ maxDelta_

double tauImpactParameter::LagrangeMultipliersFitter::maxDelta_

private

Definition at line 66 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), fit(), isConverged(), and setMaxDelta().

◆ niter_

double tauImpactParameter::LagrangeMultipliersFitter::niter_

private

Definition at line 69 of file LagrangeMultipliersFitter.h.

Referenced by fit(), and nIter().

◆ nitermax_

double tauImpactParameter::LagrangeMultipliersFitter::nitermax_

private

Definition at line 66 of file LagrangeMultipliersFitter.h.

Referenced by fit(), and setNIterMax().

◆ par_

TVectorD tauImpactParameter::LagrangeMultipliersFitter::par_

protected

Definition at line 48 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), chiSquareUsingInitalPoint(), and derivative().

◆ par_0_

TVectorD tauImpactParameter::LagrangeMultipliersFitter::par_0_

protected

Definition at line 47 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), chiSquareUsingInitalPoint(), and fit().

◆ ScaleFactor_

double tauImpactParameter::LagrangeMultipliersFitter::ScaleFactor_

private

Definition at line 75 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), and computeVariance().

◆ V_alpha0_inv_

TMatrixTSym<double> tauImpactParameter::LagrangeMultipliersFitter::V_alpha0_inv_

private

Definition at line 72 of file LagrangeMultipliersFitter.h.

Referenced by chiSquareUsingInitalPoint().

◆ V_corr_prev_

TMatrixT<double> tauImpactParameter::LagrangeMultipliersFitter::V_corr_prev_

private

Definition at line 76 of file LagrangeMultipliersFitter.h.

Referenced by computeVariance().

◆ V_D_

TMatrixTSym<double> tauImpactParameter::LagrangeMultipliersFitter::V_D_

private

Definition at line 74 of file LagrangeMultipliersFitter.h.

Referenced by applyLagrangianConstraints(), and computeVariance().

◆ weight_

double tauImpactParameter::LagrangeMultipliersFitter::weight_

private

Definition at line 66 of file LagrangeMultipliersFitter.h.

Referenced by setWeight().

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

◆ ConvergeProc

◆ Parameters

◆ Position

Constructor & Destructor Documentation

◆ LagrangeMultipliersFitter()

◆ ~LagrangeMultipliersFitter()

Member Function Documentation

◆ applyLagrangianConstraints()

◆ chiSquare() [1/2]

◆ chiSquare() [2/2]

◆ chiSquareUsingInitalPoint()

◆ computeVariance()

◆ constraintDelta()

◆ cSum()

◆ derivative()

◆ fit()

◆ getMother()

◆ getRefitDaughters()

◆ isConfigured()

◆ isConverged()

◆ nConstraints()

◆ nDaughters()

◆ ndf()

◆ nIter()

◆ setMaxDelta()

◆ setNIterMax()

◆ setWeight()

◆ value()

Member Data Documentation

◆ chi2_

◆ chi2prev_

◆ cov_

◆ cov_0_

◆ D_

◆ delta_

◆ epsilon_

◆ isConfigured_

◆ isFit_

◆ maxDelta_

◆ niter_

◆ nitermax_

◆ par_

◆ par_0_

◆ ScaleFactor_

◆ V_alpha0_inv_

◆ V_corr_prev_

◆ V_D_

◆ weight_