#include <CSCSegAlgoSK.h>

Inheritance diagram for CSCSegAlgoSK:

Public Types
typedef std::deque< bool >	BoolContainer

typedef std::vector< const CSCRecHit2D * >	ChamberHitContainer

typedef std::vector< const CSCRecHit2D * > ::const_iterator	ChamberHitContainerCIt

typedef std::vector< int >	LayerIndex
	Typedefs. More...

Public Member Functions
std::vector< CSCSegment >	buildSegments (const ChamberHitContainer &rechits)

	CSCSegAlgoSK (const edm::ParameterSet &ps)
	Constructor. More...

std::vector< CSCSegment >	run (const CSCChamber *aChamber, const ChamberHitContainer &rechits)

virtual	~CSCSegAlgoSK ()
	Destructor. More...

Public Member Functions inherited from CSCSegmentAlgorithm
	CSCSegmentAlgorithm (const edm::ParameterSet &)
	Constructor. More...

virtual std::vector< CSCSegment >	run (const CSCChamber chamber, const std::vector< const CSCRecHit2D > &rechits)=0

virtual	~CSCSegmentAlgorithm ()
	Destructor. More...

Private Member Functions
bool	addHit (const CSCRecHit2D *hit, int layer)
	Utility functions. More...

bool	areHitsCloseInGlobalPhi (const CSCRecHit2D h1, const CSCRecHit2D h2) const

bool	areHitsCloseInLocalX (const CSCRecHit2D h1, const CSCRecHit2D h2) const
	Utility functions. More...

AlgebraicSymMatrix	calculateError (void) const

void	compareProtoSegment (const CSCRecHit2D *h, int layer)

CLHEP::HepMatrix	derivativeMatrix (void) const

void	dumpHits (const ChamberHitContainer &rechits) const

void	fillChiSquared (void)

void	fillLocalDirection (void)

void	fitSlopes (void)

void	flagHitsAsUsed (const ChamberHitContainer &rechitsInChamber, BoolContainer &used) const

void	flipErrors (AlgebraicSymMatrix &) const

bool	hasHitOnLayer (int layer) const

void	increaseProtoSegment (const CSCRecHit2D *h, int layer)

bool	isHitNearSegment (const CSCRecHit2D *h) const

bool	isSegmentGood (const ChamberHitContainer &rechitsInChamber) const

float	phiAtZ (float z) const

bool	replaceHit (const CSCRecHit2D *h, int layer)

void	tryAddingHitsToSegment (const ChamberHitContainer &rechitsInChamber, const BoolContainer &used, const LayerIndex &layerIndex, const ChamberHitContainerCIt i1, const ChamberHitContainerCIt i2)

void	updateParameters (void)

AlgebraicSymMatrix	weightMatrix (void) const

Private Attributes
float	chi2Max

bool	debugInfo

float	dPhiFineMax

float	dPhiMax

float	dRPhiFineMax

float	dRPhiMax

int	minLayersApart

const std::string	myName

ChamberHitContainer	proto_segment

const CSCChamber *	theChamber

double	theChi2

LocalVector	theDirection

LocalPoint	theOrigin

float	uz

float	vz

float	wideSeg

float	windowScale

Detailed Description

This is the original algorithm for building endcap muon track segments out of the rechit's in a CSCChamber. cf. CSCSegmentizerTC.
'SK' = 'Sasha Khanov' = Speed King

A CSCSegment is a RecSegment4D, and is built from CSCRecHit2D objects, each of which is a RecHit2DLocalPos.

This class is used by the CSCSegmentAlgorithm.
Alternative algorithms can be used for the segment building by writing classes like this, and then selecting which one is actually used via the CSCSegmentBuilder.

Original (in FORTRAN): Alexa.nosp@m.ndre.nosp@m..Khan.nosp@m.ov@c.nosp@m.ern.c.nosp@m.h
Ported to C++ and improved: Rick..nosp@m.Wilk.nosp@m.inson.nosp@m.@cer.nosp@m.n.ch
Reimplemented in terms of layer index, and bug fix: Tim.C.nosp@m.ox@c.nosp@m.ern.c.nosp@m.h
Ported to CMSSW 2006-04-03: Matte.nosp@m.o.Sa.nosp@m.ni@ce.nosp@m.rn.c.nosp@m.h

Author: M. Sani

Definition at line 35 of file CSCSegAlgoSK.h.

Member Typedef Documentation

typedef std::deque<bool> CSCSegAlgoSK::BoolContainer

Definition at line 58 of file CSCSegAlgoSK.h.

typedef std::vector<const CSCRecHit2D*> CSCSegAlgoSK::ChamberHitContainer

Definition at line 50 of file CSCSegAlgoSK.h.

typedef std::vector<const CSCRecHit2D*>::const_iterator CSCSegAlgoSK::ChamberHitContainerCIt

Definition at line 51 of file CSCSegAlgoSK.h.

typedef std::vector<int> CSCSegAlgoSK::LayerIndex

Typedefs.

Definition at line 49 of file CSCSegAlgoSK.h.

Constructor & Destructor Documentation

CSCSegAlgoSK::CSCSegAlgoSK ( const edm::ParameterSet & ps )

explicit

Constructor.

Definition at line 21 of file CSCSegAlgoSK.cc.

References chi2Max, debugInfo, dPhiFineMax, dPhiMax, dRPhiFineMax, dRPhiMax, edm::ParameterSet::getParameter(), edm::ParameterSet::getUntrackedParameter(), LogDebug, minLayersApart, myName, and wideSeg.

                                                     : CSCSegmentAlgorithm(ps),
     myName("CSCSegAlgoSK") {
     
   debugInfo = ps.getUntrackedParameter<bool>("verboseInfo");
     
   dRPhiMax       = ps.getParameter<double>("dRPhiMax");
   dPhiMax        = ps.getParameter<double>("dPhiMax");
   dRPhiFineMax   = ps.getParameter<double>("dRPhiFineMax");
   dPhiFineMax    = ps.getParameter<double>("dPhiFineMax");
   chi2Max        = ps.getParameter<double>("chi2Max");
   wideSeg        = ps.getParameter<double>("wideSeg");
   minLayersApart = ps.getParameter<int>("minLayersApart");
     
   LogDebug("CSC") << myName << " has algorithm cuts set to: \n"
           << "--------------------------------------------------------------------\n"
           << "dRPhiMax     = " << dRPhiMax << '\n'
           << "dPhiMax      = " << dPhiMax << '\n'
           << "dRPhiFineMax = " << dRPhiFineMax << '\n'
           << "dPhiFineMax  = " << dPhiFineMax << '\n'
           << "chi2Max      = " << chi2Max << '\n'
           << "wideSeg      = " << wideSeg << '\n'
           << "minLayersApart = " << minLayersApart << std::endl;
 }

virtual CSCSegAlgoSK::~CSCSegAlgoSK ( )

inlinevirtual

Destructor.

Definition at line 63 of file CSCSegAlgoSK.h.

63 {};

Member Function Documentation

bool CSCSegAlgoSK::addHit	(	const CSCRecHit2D *	hit,
		int	layer
	)

private

Utility functions.

Definition at line 375 of file CSCSegAlgoSK.cc.

References proto_segment, and updateParameters().

Referenced by buildSegments(), increaseProtoSegment(), and replaceHit().

                                                             {
   
   // Return true if hit was added successfully 
   // (and then parameters are updated).
   // Return false if there is already a hit on the same layer, or insert failed.
   
   ChamberHitContainer::const_iterator it;
   
   for(it = proto_segment.begin(); it != proto_segment.end(); it++)
     if (((*it)->cscDetId().layer() == layer) && (aHit != (*it)))
       return false; 
   
   proto_segment.push_back(aHit);
   updateParameters();
   
   return true;
 }

bool CSCSegAlgoSK::areHitsCloseInGlobalPhi	(	const CSCRecHit2D *	h1,
		const CSCRecHit2D *	h2
	)		const

private

Definition at line 258 of file CSCSegAlgoSK.cc.

References dPhiMax, CSCChamber::layer(), LogDebug, M_PI, PV3DBase< T, PVType, FrameType >::phi(), theChamber, GeomDet::toGlobal(), and windowScale.

Referenced by buildSegments().

                                                                                              {
   
   const CSCLayer* l1 = theChamber->layer(h1->cscDetId().layer());
   GlobalPoint gp1 = l1->toGlobal(h1->localPosition());  
   const CSCLayer* l2 = theChamber->layer(h2->cscDetId().layer());
   GlobalPoint gp2 = l2->toGlobal(h2->localPosition());  
   
   float h1p = gp1.phi();
   float h2p = gp2.phi();
   float dphi12 = h1p - h2p;
   
   // Into range [-pi, pi) (phi() returns values in this range)
   if (dphi12 < -M_PI) 
     dphi12 += 2.*M_PI;  
   if (dphi12 >  M_PI) 
     dphi12 -= 2.*M_PI;
   LogDebug("CSC") << "    Hits at global phi= " << h1p << ", " 
           << h2p << " have separation= " << dphi12;
   return (fabs(dphi12) < (dPhiMax * windowScale))? true:false;  // +v
 }

bool CSCSegAlgoSK::areHitsCloseInLocalX	(	const CSCRecHit2D *	h1,
		const CSCRecHit2D *	h2
	)		const

private

Utility functions.

Definition at line 249 of file CSCSegAlgoSK.cc.

References dRPhiMax, LogDebug, windowScale, and x.

Referenced by buildSegments().

                                                                                           {
   float h1x = h1->localPosition().x();
   float h2x = h2->localPosition().x();
   float deltaX = (h1->localPosition()-h2->localPosition()).x();
   LogDebug("CSC") << "    Hits at local x= " << h1x << ", " 
           << h2x << " have separation= " << deltaX;
   return (fabs(deltaX) < (dRPhiMax * windowScale))? true:false;   // +v
 }

std::vector< CSCSegment > CSCSegAlgoSK::buildSegments ( const ChamberHitContainer & rechits )

Build track segments in this chamber (this is where the actual segment-building algorithm hides.)

Definition at line 50 of file CSCSegAlgoSK.cc.

References funct::abs(), addHit(), areHitsCloseInGlobalPhi(), areHitsCloseInLocalX(), calculateError(), CSCChamberSpecs::chamberTypeName(), debugInfo, dumpHits(), benchmark_cfg::errors, flagHitsAsUsed(), flipErrors(), i, cuy::ib, isSegmentGood(), CSCChamber::layer(), LogDebug, minLayersApart, myName, GeomDet::position(), proto_segment, HI_PhotonSkim_cff::rechits, CSCChamber::specs(), groupFilesInBlocks::temp, theChamber, theChi2, theDirection, theOrigin, GeomDet::toGlobal(), tryAddingHitsToSegment(), wideSeg, windowScale, and PV3DBase< T, PVType, FrameType >::z().

Referenced by run().

                                                                                      {
     
   LogDebug("CSC") << "*********************************************";
   LogDebug("CSC") << "Start segment building in the new chamber: " << theChamber->specs()->chamberTypeName();
   LogDebug("CSC") << "*********************************************";
   
   ChamberHitContainer rechits = urechits;
   LayerIndex layerIndex(rechits.size());
   
   for(unsigned int i = 0; i < rechits.size(); i++) {
     
     layerIndex[i] = rechits[i]->cscDetId().layer();
   }
   
   double z1 = theChamber->layer(1)->position().z();
   double z6 = theChamber->layer(6)->position().z();
   
   if ( z1 > 0. ) {
     if ( z1 > z6 ) { 
       reverse(layerIndex.begin(), layerIndex.end());
       reverse(rechits.begin(), rechits.end());
     }    
   }
   else if ( z1 < 0. ) {
     if ( z1 < z6 ) {
       reverse(layerIndex.begin(), layerIndex.end());
       reverse(rechits.begin(), rechits.end());
     }    
   }
   
   if (debugInfo) {
     // dump after sorting
     dumpHits(rechits);
   }
   
   if (rechits.size() < 2) {
     LogDebug("CSC") << myName << ": " << rechits.size() << 
       "  hit(s) in chamber is not enough to build a segment.\n";
     return std::vector<CSCSegment>(); 
   }
     
   // We have at least 2 hits. We intend to try all possible pairs of hits to start 
   // segment building. 'All possible' means each hit lies on different layers in the chamber.
   // BUT... once a hit has been assigned to a segment, we don't consider
   // it again.
   
   // Choose first hit (as close to IP as possible) h1 and 
   // second hit (as far from IP as possible) h2
   // To do this we iterate over hits in the chamber by layer - pick two layers.
   // @@ Require the two layers are at least 3 layers apart. May need tuning?
   // Then we iterate over hits within each of these layers and pick h1 and h2 from these.
   // If they are 'close enough' we build an empty segment.
   // Then try adding hits to this segment.
   
   // Initialize flags that a given hit has been allocated to a segment
   BoolContainer used(rechits.size(), false);
   
   // Define buffer for segments we build 
   std::vector<CSCSegment> segments;
   
   ChamberHitContainerCIt ib = rechits.begin();
   ChamberHitContainerCIt ie = rechits.end();
   
   // Possibly allow 2 passes, second widening scale factor for cuts
   windowScale = 1.; // scale factor for cuts
   
   int npass = (wideSeg > 1.)? 2 : 1;
   
   for (int ipass = 0; ipass < npass; ++ipass) {
     for (ChamberHitContainerCIt i1 = ib; i1 != ie; ++i1) {
       bool segok = false;
       if(used[i1-ib]) 
         continue;
       
       int layer1 = layerIndex[i1-ib]; //(*i1)->cscDetId().layer();
       const CSCRecHit2D* h1 = *i1;
       
       for (ChamberHitContainerCIt i2 = ie-1; i2 != i1; --i2) {
         if(used[i2-ib]) 
           continue;
         
         int layer2 = layerIndex[i2-ib]; //(*i2)->cscDetId().layer();
                 
         if (abs(layer2 - layer1) < minLayersApart) 
           break;
         const CSCRecHit2D* h2 = *i2;
         
         if (areHitsCloseInLocalX(h1, h2) && areHitsCloseInGlobalPhi(h1, h2)) {
           
           proto_segment.clear();
           
           const CSCLayer* l1 = theChamber->layer(layer1);
           GlobalPoint gp1 = l1->toGlobal(h1->localPosition());                  
           const CSCLayer* l2 = theChamber->layer(layer2);
           GlobalPoint gp2 = l2->toGlobal(h2->localPosition());                  
           LogDebug("CSC") << "start new segment from hits " << "h1: " 
                           << gp1 << " - h2: " << gp2 << "\n";
           
           if (!addHit(h1, layer1)) { 
             LogDebug("CSC") << "  failed to add hit h1\n";
             continue;
           }
           
           if (!addHit(h2, layer2)) { 
             LogDebug("CSC") << "  failed to add hit h2\n";
             continue;
           }
           
           tryAddingHitsToSegment(rechits, used, layerIndex, i1, i2); 
           
           // Check no. of hits on segment, and if enough flag them as used
           // and store the segment
           segok = isSegmentGood(rechits);
           if (segok) {
             flagHitsAsUsed(rechits, used);
             // Copy the proto_segment and its properties inside a CSCSegment.
             // Then fill the segment vector..
             
             if (proto_segment.empty()) {
               LogDebug("CSC") << "No segment has been found !!!\n";
             }   
             else {
               
               // calculate error matrix...
               AlgebraicSymMatrix errors = calculateError();
 
           // but reorder components to match what's required by TrackingRecHit interface
           // i.e. slopes first, then positions
 
               flipErrors( errors );
 
               CSCSegment temp(proto_segment, theOrigin, theDirection, errors, theChi2); 
               
               LogDebug("CSC") << "Found a segment !!!\n";
               segments.push_back(temp); 
             }
           }
         }  //   h1 & h2 close
         
         if (segok) 
           break;
       }  //  i2
     }  //  i1
     
     if (segments.size() > 1)  
       break;  // only change window if no segments found
     
     // Increase cut windows by factor of wideSeg
     windowScale = wideSeg;
     
   }  //  ipass
   
   // Give the segments to the CSCChamber
   return segments;
 }

AlgebraicSymMatrix CSCSegAlgoSK::calculateError ( void ) const

private

Definition at line 799 of file CSCSegAlgoSK.cc.

References funct::A, derivativeMatrix(), query::result, weightMatrix(), and create_public_pileup_plots::weights.

Referenced by buildSegments().

                                                       {
   
   AlgebraicSymMatrix weights = weightMatrix();
   AlgebraicMatrix A = derivativeMatrix();
   
   // (AT W A)^-1
   // from http://www.phys.ufl.edu/~avery/fitting.html, part I
   int ierr;
   AlgebraicSymMatrix result = weights.similarityT(A);
   result.invert(ierr);
   
   // blithely assuming the inverting never fails...
   return result;
 }

void CSCSegAlgoSK::compareProtoSegment	(	const CSCRecHit2D *	h,
		int	layer
	)

private

Definition at line 699 of file CSCSegAlgoSK.cc.

References LogDebug, convertSQLiteXML::ok, proto_segment, replaceHit(), theChi2, theDirection, and theOrigin.

Referenced by tryAddingHitsToSegment().

                                                                       {
   
   // compare the chi2 of two segments
   double oldChi2 = theChi2;
   LocalPoint oldOrigin = theOrigin;
   LocalVector oldDirection = theDirection;
   ChamberHitContainer oldSegment = proto_segment;
   
   bool ok = replaceHit(h, layer);
   
   if (ok) {
     LogDebug("CSC") << "    hit in same layer as a hit on segment; try replacing old one..." 
             << " chi2 new: " << theChi2 << " old: " << oldChi2 << "\n";
   }
   
   if ((theChi2 < oldChi2) && (ok)) {
     LogDebug("CSC")  << "    segment with replaced hit is better.\n";
   }
   else {
     proto_segment = oldSegment;
     theChi2 = oldChi2;
     theOrigin = oldOrigin;
     theDirection = oldDirection;
   }
 }

CLHEP::HepMatrix CSCSegAlgoSK::derivativeMatrix ( void ) const

private

Definition at line 752 of file CSCSegAlgoSK.cc.

References CSCChamber::layer(), makeMuonMisalignmentScenario::matrix, proto_segment, theChamber, GeomDet::toGlobal(), GeomDet::toLocal(), detailsBasic3DVector::z, and PV3DBase< T, PVType, FrameType >::z().

Referenced by calculateError().

                                                     {
   
   ChamberHitContainer::const_iterator it;
   int nhits = proto_segment.size();
   CLHEP::HepMatrix matrix(2*nhits, 4);
   int row = 0;
   
   for(it = proto_segment.begin(); it != proto_segment.end(); ++it) {
     
     const CSCRecHit2D& hit = (**it);
     const CSCLayer* layer = theChamber->layer(hit.cscDetId().layer());
     GlobalPoint gp = layer->toGlobal(hit.localPosition());      
     LocalPoint lp = theChamber->toLocal(gp); 
     float z = lp.z();
     ++row;
     matrix(row, 1) = 1.;
     matrix(row, 3) = z;
     ++row;
     matrix(row, 2) = 1.;
     matrix(row, 4) = z;
   }
   return matrix;
 }

void CSCSegAlgoSK::dumpHits ( const ChamberHitContainer & rechits ) const

private

Dump position and phi of each rechit in chamber after sort in z

Definition at line 325 of file CSCSegAlgoSK.cc.

References CSCChamber::layer(), Geom::Phi< T >::phi(), PV3DBase< T, PVType, FrameType >::phi(), theChamber, and GeomDet::toGlobal().

Referenced by buildSegments().

                                                                     {
   
   // Dump positions of RecHit's in each CSCChamber
   ChamberHitContainerCIt it;
   edm::LogInfo("CSC") << "CSCChamber rechit dump.\n";   
   for(it=rechits.begin(); it!=rechits.end(); it++) {
     
     const CSCLayer* l1 = theChamber->layer((*it)->cscDetId().layer());
     GlobalPoint gp1 = l1->toGlobal((*it)->localPosition()); 
     
     edm::LogInfo("CSC") << "Global pos.: " << gp1 << ", phi: " << gp1.phi() << ". Local position: "
             << (*it)->localPosition() << ", phi: "
             << (*it)->localPosition().phi() << ". Layer: "
             << (*it)->cscDetId().layer() << "\n";
   } 
 }

void CSCSegAlgoSK::fillChiSquared ( void )

private

Definition at line 605 of file CSCSegAlgoSK.cc.

References AnalysisDataFormats_SUSYBSMObjects::hv, CSCChamber::layer(), LogDebug, proto_segment, theChamber, theChi2, theOrigin, GeomDet::toGlobal(), GeomDet::toLocal(), uz, vz, PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by updateParameters().

                                   {
   
   // The chi-squared is (m-Ap)T E (m-Ap)
   // where T denotes transpose.
   // This collapses to a simple sum over contributions from each
   // pair of measurements.
   float u0 = theOrigin.x();
   float v0 = theOrigin.y();
   double chsq = 0.;
   
   ChamberHitContainer::const_iterator ih;
   for (ih = proto_segment.begin(); ih != proto_segment.end(); ++ih) {
     
     const CSCRecHit2D& hit = (**ih);
     const CSCLayer* layer = theChamber->layer(hit.cscDetId().layer());
     GlobalPoint gp = layer->toGlobal(hit.localPosition());
     LocalPoint lp = theChamber->toLocal(gp);  // FIX !!
     
     double hu = lp.x();
     double hv = lp.y();
     double hz = lp.z();
     
     double du = u0 + uz * hz - hu;
     double dv = v0 + vz * hz - hv;
     
     CLHEP::HepMatrix IC(2,2);
     IC(1,1) = hit.localPositionError().xx();
     IC(1,2) = hit.localPositionError().xy();
     IC(2,1) = IC(1,2);
     IC(2,2) = hit.localPositionError().yy();
     
     // Invert covariance matrix
     int ierr = 0;
     IC.invert(ierr);
     if (ierr != 0) {
       LogDebug("CSC") << "CSCSegment::fillChiSquared: failed to invert covariance matrix=\n" << IC << "\n";
       
       // @@ NOW WHAT TO DO? Exception? Return? Ignore?
     }
     
     chsq += du*du*IC(1,1) + 2.*du*dv*IC(1,2) + dv*dv*IC(2,2);
   }
   theChi2 = chsq;
 }

void CSCSegAlgoSK::fillLocalDirection ( void )

private

Always enforce direction of segment to point from IP outwards (Incorrect for particles not coming from IP, of course.)

Definition at line 650 of file CSCSegAlgoSK.cc.

References mathSSE::sqrt(), theChamber, theDirection, theOrigin, GeomDet::toGlobal(), csvLumiCalc::unit, uz, vz, and detailsBasic3DVector::z.

Referenced by updateParameters().

                                       {
   // Always enforce direction of segment to point from IP outwards
   // (Incorrect for particles not coming from IP, of course.)
   
   double dxdz = uz;
   double dydz = vz;
   double dz = 1./sqrt(1. + dxdz*dxdz + dydz*dydz);
   double dx = dz*dxdz;
   double dy = dz*dydz;
   LocalVector localDir(dx,dy,dz);
   
   // localDir may need sign flip to ensure it points outward from IP
   // ptc: Examine its direction and origin in global z: to point outward
   // the localDir should always have same sign as global z...
   
   double globalZpos = ( theChamber->toGlobal( theOrigin ) ).z();
   double globalZdir = ( theChamber->toGlobal( localDir ) ).z();
   double directionSign = globalZpos * globalZdir;
   
   theDirection = (directionSign * localDir).unit();
   
 }

void CSCSegAlgoSK::fitSlopes ( void )

private

Definition at line 453 of file CSCSegAlgoSK.cc.

References CSCChamber::layer(), LogDebug, AlCaHLTBitMon_ParallelJobs::p, proto_segment, theChamber, theOrigin, GeomDet::toGlobal(), GeomDet::toLocal(), uz, findQualityFiles::v, vz, PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), detailsBasic3DVector::z, and PV3DBase< T, PVType, FrameType >::z().

Referenced by updateParameters().

                              {
   
   // Update parameters of fit
   // ptc 13-Aug-02: This does a linear least-squares fit
   // to the hits associated with the segment, in the z projection.
   
   // In principle perhaps one could fit the strip and wire
   // measurements (u, v respectively), to
   // u = u0 + uz * z
   // v = v0 + vz * z
   // where u0, uz, v0, vz are the parameters resulting from the fit.
   // But what is actually done is fit to the local x, y coordinates 
   // of the RecHits. However the strip measurement controls the precision
   // of x, and the wire measurement controls that of y.
   // Precision in local coordinate:
   //       u (strip, sigma~200um), v (wire, sigma~1cm)
   
   // I have verified that this code agrees with the formulation given
   // on p246-247 of 'Data analysis techniques for high-energy physics
   // experiments' by Bock, Grote, Notz & Regler, and that on p111-113
   // of 'Statistics' by Barlow.
   
   // Formulate the matrix equation representing the least-squares fit
   // We have a vector of measurements m, which is a 2n x 1 dim matrix
   // The transpose mT is (u1, v1, u2, v2, ..., un, vn)
   // where ui is the strip-associated measurement and vi is the
   // wire-associated measurement for a given RecHit i.
   // The fit is to
   // u = u0 + uz * z
   // v = v0 + vz * z
   // where u0, uz, v0, vz are the parameters to be obtained from the fit.
   // These are contained in a vector p which is a 4x1 dim matrix, and
   // its transpose pT is (u0, v0, uz, vz). Note the ordering!
   // The covariance matrix for each pair of measurements is 2 x 2 and
   // the inverse of this is the error matrix E.
   // The error matrix for the whole set of n measurements is a diagonal
   // matrix with diagonal elements the individual 2 x 2 error matrices
   // (because the inverse of a diagonal matrix is a diagonal matrix
   // with each element the inverse of the original.)
   
   // The matrix 'matrix' in method 'CSCSegment::weightMatrix()' is this 
   // block-diagonal overall covariance matrix. It is inverted to the 
   // block-diagonal error matrix right before it is returned.
   
   // Use the matrix A defined by
   //    1   0   z1  0
   //    0   1   0   z1
   //    1   0   z2  0
   //    0   1   0   z2
   //    ..  ..  ..  ..
   //    1   0   zn  0
   //    0   1   0   zn
   
   // The matrix A is returned by 'CSCSegment::derivativeMatrix()'.
   
   // Then the normal equations are encapsulated in the matrix equation
   //
   //    (AT E A)p = (AT E)m
   //
   // where AT is the transpose of A.
   // We'll call the combined matrix on the LHS, M, and that on the RHS, B:
   //     M p = B
   
   // We solve this for the parameter vector, p.
   // The elements of M and B then involve sums over the hits
   
   // The error matrix of the parameters is obtained by 
   // (AT E A)^-1 calculated in 'calculateError()'.
   
   // The 4 values in p can be accessed from 'CSCSegment::parameters()'
   // in the order uz, vz, u0, v0.
   
   // NOTE 1
   // Do the #hits = 2 case separately.
   // (I hope they're not on the same layer! They should not be, by construction.)
   
   // NOTE 2
   // We need local position of a RecHit w.r.t. the CHAMBER
   // and the RecHit itself only knows its local position w.r.t.
   // the LAYER, so we must explicitly transform global position.
   
   CLHEP::HepMatrix M(4,4,0);
   CLHEP::HepVector B(4,0);
   
   ChamberHitContainer::const_iterator ih = proto_segment.begin();
   
   for (ih = proto_segment.begin(); ih != proto_segment.end(); ++ih) {
     
     const CSCRecHit2D& hit = (**ih);
     const CSCLayer* layer = theChamber->layer(hit.cscDetId().layer());
     GlobalPoint gp = layer->toGlobal(hit.localPosition());
     LocalPoint  lp  = theChamber->toLocal(gp); 
     
     // ptc: Local position of hit w.r.t. chamber
     double u = lp.x();
     double v = lp.y();
     double z = lp.z();
     
     // ptc: Covariance matrix of local errors 
     CLHEP::HepMatrix IC(2,2);
     IC(1,1) = hit.localPositionError().xx();
     IC(1,2) = hit.localPositionError().xy();
     IC(2,1) = IC(1,2); // since Cov is symmetric
     IC(2,2) = hit.localPositionError().yy();
     
     // ptc: Invert covariance matrix (and trap if it fails!)
     int ierr = 0;
     IC.invert(ierr); // inverts in place
     if (ierr != 0) {
       LogDebug("CSC") << "CSCSegment::fitSlopes: failed to invert covariance matrix=\n" << IC << "\n";
       
       //@@ NOW WHAT TO DO? Exception? Return? Ignore?
       //@@ Implement throw
     }
     
     // ptc: Note that IC is no longer Cov but Cov^-1
     M(1,1) += IC(1,1);
     M(1,2) += IC(1,2);
     M(1,3) += IC(1,1) * z;
     M(1,4) += IC(1,2) * z;
     B(1) += u * IC(1,1) + v * IC(1,2);
     
     M(2,1) += IC(2,1);
     M(2,2) += IC(2,2);
     M(2,3) += IC(2,1) * z;
     M(2,4) += IC(2,2) * z;
     B(2) += u * IC(2,1) + v * IC(2,2);
     
     M(3,1) += IC(1,1) * z;
     M(3,2) += IC(1,2) * z;
     M(3,3) += IC(1,1) * z * z;
     M(3,4) += IC(1,2) * z * z;
     B(3) += ( u * IC(1,1) + v * IC(1,2) ) * z;
     
     M(4,1) += IC(2,1) * z;
     M(4,2) += IC(2,2) * z;
     M(4,3) += IC(2,1) * z * z;
     M(4,4) += IC(2,2) * z * z;
     B(4) += ( u * IC(2,1) + v * IC(2,2) ) * z;
   }
   
   // Solve the matrix equation using CLHEP's 'solve'
   //@@ ptc: CAN solve FAIL?? UNCLEAR FROM (LACK OF) CLHEP DOC
   CLHEP::HepVector p = solve(M, B);
   
   // Update member variables uz, vz, theOrigin
   // Note it has local z = 0
   theOrigin = LocalPoint(p(1), p(2), 0.);
   uz = p(3);
   vz = p(4);
 }

void CSCSegAlgoSK::flagHitsAsUsed	(	const ChamberHitContainer &	rechitsInChamber,
		BoolContainer &	used
	)		const

private

Flag hits on segment as used

Definition at line 360 of file CSCSegAlgoSK.cc.

References cuy::ib, and proto_segment.

Referenced by buildSegments().

                                               {
   
   // Flag hits on segment as used
   ChamberHitContainerCIt ib = rechitsInChamber.begin();
   ChamberHitContainerCIt hi, iu;
   
   for(hi = proto_segment.begin(); hi != proto_segment.end(); ++hi) {
     for(iu = ib; iu != rechitsInChamber.end(); ++iu) {
       if(*hi == *iu)
     used[iu-ib] = true;
     }
   }
 }

void CSCSegAlgoSK::flipErrors ( AlgebraicSymMatrix & a ) const

private

Definition at line 814 of file CSCSegAlgoSK.cc.

References a.

Referenced by buildSegments().

                                                            {
 
   // The CSCSegment needs the error matrix re-arranged
 
   AlgebraicSymMatrix hold( a );
 
   // errors on slopes into upper left
   a(1,1) = hold(3,3);
   a(1,2) = hold(3,4);
   a(2,1) = hold(4,3);
   a(2,2) = hold(4,4);
   
   // errors on positions into lower right
   a(3,3) = hold(1,1);
   a(3,4) = hold(1,2);
   a(4,3) = hold(2,1);
   a(4,4) = hold(2,2);
 
   // off-diagonal elements remain unchanged
 
 }

bool CSCSegAlgoSK::hasHitOnLayer ( int layer ) const

private

Definition at line 673 of file CSCSegAlgoSK.cc.

References proto_segment.

Referenced by tryAddingHitsToSegment().

                                                 {
   
   // Is there is already a hit on this layer?
   ChamberHitContainerCIt it;
   
   for(it = proto_segment.begin(); it != proto_segment.end(); it++)
     if ((*it)->cscDetId().layer() == layer)
       return true; 
   
   return false;
 }

void CSCSegAlgoSK::increaseProtoSegment	(	const CSCRecHit2D *	h,
		int	layer
	)

private

Definition at line 725 of file CSCSegAlgoSK.cc.

References addHit(), chi2Max, LogDebug, convertSQLiteXML::ok, proto_segment, theChi2, theDirection, and theOrigin.

Referenced by tryAddingHitsToSegment().

                                                                        {
   
   double oldChi2 = theChi2;
   LocalPoint oldOrigin = theOrigin;
   LocalVector oldDirection = theDirection;
   ChamberHitContainer oldSegment = proto_segment;
   
   bool ok = addHit(h, layer);
   
   if (ok) {
     LogDebug("CSC") << "    hit in new layer: added to segment, new chi2: " 
             << theChi2 << "\n";
   }
   
   int ndf = 2*proto_segment.size() - 4;
   
   if (ok && ((ndf <= 0) || (theChi2/ndf < chi2Max))) {
     LogDebug("CSC") << "    segment with added hit is good.\n" ;        // FIX
   } 
   else {
     proto_segment = oldSegment;
     theChi2 = oldChi2;
     theOrigin = oldOrigin;
     theDirection = oldDirection;
   }         
 }       

bool CSCSegAlgoSK::isHitNearSegment ( const CSCRecHit2D * h ) const

private

Definition at line 279 of file CSCSegAlgoSK.cc.

References dPhiFineMax, dRPhiFineMax, AnalysisDataFormats_SUSYBSMObjects::hp, CSCChamber::layer(), LogDebug, M_PI, PV3DBase< T, PVType, FrameType >::perp(), PV3DBase< T, PVType, FrameType >::phi(), phiAtZ(), theChamber, GeomDet::toGlobal(), windowScale, and PV3DBase< T, PVType, FrameType >::z().

Referenced by tryAddingHitsToSegment().

                                                               {
   
   // Is hit near segment? 
   // Requires deltaphi and rxy*deltaphi within ranges specified
   // in parameter set, where rxy=sqrt(x**2+y**2) of hit itself.
   // Note that to make intuitive cuts on delta(phi) one must work in
   // phi range (-pi, +pi] not [0, 2pi)
   
   const CSCLayer* l1 = theChamber->layer(h->cscDetId().layer());
   GlobalPoint hp = l1->toGlobal(h->localPosition());    
   
   float hphi = hp.phi();          // in (-pi, +pi]
   if (hphi < 0.) 
     hphi += 2.*M_PI;            // into range [0, 2pi)
   float sphi = phiAtZ(hp.z());    // in [0, 2*pi)
   float phidif = sphi-hphi;
   if (phidif < 0.) 
     phidif += 2.*M_PI;          // into range [0, 2pi)
   if (phidif > M_PI) 
     phidif -= 2.*M_PI;          // into range (-pi, pi]
   
   float dRPhi = fabs(phidif)*hp.perp();
   LogDebug("CSC") << "    is hit at phi_h= " << hphi << " near segment phi_seg= " << sphi 
           << "? is " << dRPhi << "<" << dRPhiFineMax*windowScale << " ? " 
           << " and is |" << phidif << "|<" << dPhiFineMax*windowScale << " ?";
   
   return ((dRPhi < dRPhiFineMax*windowScale) && 
       (fabs(phidif) < dPhiFineMax*windowScale))? true:false;  // +v
 }

bool CSCSegAlgoSK::isSegmentGood ( const ChamberHitContainer & rechitsInChamber ) const

private

Return true if segment is 'good'. In this algorithm, 'good' means has sufficient hits

Definition at line 342 of file CSCSegAlgoSK.cc.

References convertSQLiteXML::ok, proto_segment, and windowScale.

Referenced by buildSegments().

                                                                                   {
   
   // If the chamber has 20 hits or fewer, require at least 3 hits on segment
   // If the chamber has >20 hits require at least 4 hits
   //@@ THESE VALUES SHOULD BECOME PARAMETERS?
   bool ok = false;
   
   unsigned int iadd = ( rechitsInChamber.size() > 20 )?  1 : 0;  
   
   if (windowScale > 1.)
     iadd = 1;
   
   if (proto_segment.size() >= 3+iadd)
     ok = true;
   
   return ok;
 }

float CSCSegAlgoSK::phiAtZ ( float z ) const

private

Definition at line 309 of file CSCSegAlgoSK.cc.

References f, CSCChamber::layer(), M_PI, phi, proto_segment, theChamber, theDirection, theOrigin, GeomDet::toGlobal(), x, PV3DBase< T, PVType, FrameType >::x(), detailsBasic3DVector::y, PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by isHitNearSegment().

                                         {
   
   // Returns a phi in [ 0, 2*pi )
   const CSCLayer* l1 = theChamber->layer((*(proto_segment.begin()))->cscDetId().layer());
   GlobalPoint gp = l1->toGlobal(theOrigin); 
   GlobalVector gv = l1->toGlobal(theDirection); 
   
   float x = gp.x() + (gv.x()/gv.z())*(z - gp.z());
   float y = gp.y() + (gv.y()/gv.z())*(z - gp.z());
   float phi = atan2(y, x);
   if (phi < 0.f ) 
     phi += 2. * M_PI;
   
   return phi ;
 }

bool CSCSegAlgoSK::replaceHit	(	const CSCRecHit2D *	h,
		int	layer
	)

private

Definition at line 685 of file CSCSegAlgoSK.cc.

References addHit(), and proto_segment.

Referenced by compareProtoSegment().

                                                              {
   
   // replace a hit from a layer 
   ChamberHitContainer::iterator it;
   for (it = proto_segment.begin(); it != proto_segment.end();) {
     if ((*it)->cscDetId().layer() == layer)
       it = proto_segment.erase(it);
     else
       ++it;   
   }
   
   return addHit(h, layer);                  
 }

std::vector< CSCSegment > CSCSegAlgoSK::run	(	const CSCChamber *	aChamber,
		const ChamberHitContainer &	rechits
	)

Here we must implement the algorithm

Definition at line 45 of file CSCSegAlgoSK.cc.

References buildSegments(), and theChamber.

                                                                                                       {
     theChamber = aChamber; 
     return buildSegments(rechits); 
 }

void CSCSegAlgoSK::tryAddingHitsToSegment	(	const ChamberHitContainer &	rechitsInChamber,
		const BoolContainer &	used,
		const LayerIndex &	layerIndex,
		const ChamberHitContainerCIt	i1,
		const ChamberHitContainerCIt	i2
	)

private

Try adding non-used hits to segment

Definition at line 206 of file CSCSegAlgoSK.cc.

References compareProtoSegment(), h, hasHitOnLayer(), i, cuy::ib, increaseProtoSegment(), isHitNearSegment(), CSCChamber::layer(), LogDebug, proto_segment, theChamber, and GeomDet::toGlobal().

Referenced by buildSegments().

                                                                                         {
 
   // Iterate over the layers with hits in the chamber
   // Skip the layers containing the segment endpoints
   // Test each hit on the other layers to see if it is near the segment
   // If it is, see whether there is already a hit on the segment from the same layer
   //    - if so, and there are more than 2 hits on the segment, copy the segment,
   //      replace the old hit with the new hit. If the new segment chi2 is better
   //      then replace the original segment with the new one (by swap)
   //    - if not, copy the segment, add the hit. If the new chi2/dof is still satisfactory
   //      then replace the original segment with the new one (by swap)
   
   ChamberHitContainerCIt ib = rechits.begin();
   ChamberHitContainerCIt ie = rechits.end();
   
   for (ChamberHitContainerCIt i = ib; i != ie; ++i) {
     if (i == i1 || i == i2 || used[i-ib]) 
       continue; 
     
     int layer = layerIndex[i-ib]; 
     const CSCRecHit2D* h = *i;
     if (isHitNearSegment(h)) {
       
       GlobalPoint gp1 = theChamber->layer(layer)->toGlobal(h->localPosition());     
       LogDebug("CSC") << "    hit at global " << gp1 << " is near segment\n.";
       
       // Don't consider alternate hits on layers holding the two starting points
       if (hasHitOnLayer(layer)) {
     if (proto_segment.size() <= 2) {
       LogDebug("CSC") << "    " << proto_segment.size() 
               << " hits on segment...skip hit on same layer.\n";
       continue;
     }
     compareProtoSegment(h, layer);
       } 
       else                  
     increaseProtoSegment(h, layer);
     }   // h & seg close
   }   // i
 }

void CSCSegAlgoSK::updateParameters ( void )

private

Definition at line 393 of file CSCSegAlgoSK.cc.

References fillChiSquared(), fillLocalDirection(), fitSlopes(), CSCChamber::layer(), proto_segment, theChamber, theChi2, theOrigin, GeomDet::toGlobal(), GeomDet::toLocal(), uz, vz, PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by addHit().

                                     {
   
   // Note that we need local position of a RecHit w.r.t. the CHAMBER
   // and the RecHit itself only knows its local position w.r.t.
   // the LAYER, so need to explicitly transform to global position.
   
   //  no. of hits in the RecHitsOnSegment
   //  By construction this is the no. of layers with hits
   //  since we allow just one hit per layer in a segment.
   
   int nh = proto_segment.size();
   
   // First hit added to a segment must always fail here
   if (nh < 2) 
     return;
   
   if (nh == 2) {
     
     // Once we have two hits we can calculate a straight line 
     // (or rather, a straight line for each projection in xz and yz.)
     ChamberHitContainer::const_iterator ih = proto_segment.begin();
     int il1 = (*ih)->cscDetId().layer();
     const CSCRecHit2D& h1 = (**ih);
     ++ih;    
     int il2 = (*ih)->cscDetId().layer();
     const CSCRecHit2D& h2 = (**ih);
     
     //@@ Skip if on same layer, but should be impossible
     if (il1 == il2) 
       return;
     
     const CSCLayer* layer1 = theChamber->layer(il1);
     const CSCLayer* layer2 = theChamber->layer(il2);
     
     GlobalPoint h1glopos = layer1->toGlobal(h1.localPosition());
     GlobalPoint h2glopos = layer2->toGlobal(h2.localPosition());
     
     // localPosition is position of hit wrt layer (so local z = 0)
     theOrigin = h1.localPosition();
     
     // We want hit wrt chamber (and local z will be != 0)
     LocalPoint h1pos = theChamber->toLocal(h1glopos);  
     LocalPoint h2pos = theChamber->toLocal(h2glopos);  
     
     float dz = h2pos.z()-h1pos.z();
     uz = (h2pos.x()-h1pos.x())/dz ;
     vz = (h2pos.y()-h1pos.y())/dz ;
     
     theChi2 = 0.;
   }
   else if (nh > 2) {
     
     // When we have more than two hits then we can fit projections to straight lines
     fitSlopes();  
     fillChiSquared();
   } // end of 'if' testing no. of hits
   
   fillLocalDirection(); 
 }

AlgebraicSymMatrix CSCSegAlgoSK::weightMatrix ( void ) const

private

Definition at line 777 of file CSCSegAlgoSK.cc.

References makeMuonMisalignmentScenario::matrix, and proto_segment.

Referenced by calculateError().

                                                     {
   
   std::vector<const CSCRecHit2D*>::const_iterator it;
   int nhits = proto_segment.size();
   AlgebraicSymMatrix matrix(2*nhits, 0);
   int row = 0;
   
   for (it = proto_segment.begin(); it != proto_segment.end(); ++it) {
     
     const CSCRecHit2D& hit = (**it);
     ++row;
     matrix(row, row)   = hit.localPositionError().xx();
     matrix(row, row+1) = hit.localPositionError().xy();
     ++row;
     matrix(row, row-1) = hit.localPositionError().xy();
     matrix(row, row)   = hit.localPositionError().yy();
   }
   int ierr;
   matrix.invert(ierr);
   return matrix;
 }