PerigeeConversions Namespace Reference

Typedefs
typedef FreeTrajectoryState	FTS

Functions
CurvilinearTrajectoryError	curvilinearError (const PerigeeTrajectoryError &perigeeError, const GlobalTrajectoryParameters &gtp)
PerigeeTrajectoryError	ftsToPerigeeError (const FTS &originalFTS)
PerigeeTrajectoryParameters	ftsToPerigeeParameters (const FTS &originalFTS, const GlobalPoint &referencePoint, double &pt)
AlgebraicMatrix55	jacobianCurvilinear2Perigee (const FreeTrajectoryState &fts)
AlgebraicMatrix66	jacobianParameters2Cartesian (const AlgebraicVector3 &momentum, const GlobalPoint &position, const TrackCharge &charge, const MagneticField *field)
AlgebraicMatrix55	jacobianPerigee2Curvilinear (const GlobalTrajectoryParameters &gtp)
GlobalVector	momentumFromPerigee (const AlgebraicVector3 &momentum, const TrackCharge &charge, const GlobalPoint &referencePoint, const MagneticField *field)
GlobalVector	momentumFromPerigee (const PerigeeTrajectoryParameters &parameters, double pt, const GlobalPoint &referencePoint)
GlobalPoint	positionFromPerigee (const PerigeeTrajectoryParameters &parameters, const GlobalPoint &referencePoint)
TrajectoryStateClosestToPoint	trajectoryStateClosestToPoint (const AlgebraicVector3 &momentum, const GlobalPoint &referencePoint, const TrackCharge &charge, const AlgebraicSymMatrix66 &theCovarianceMatrix, const MagneticField *field)

Detailed Description

namespace provides several functions to transform perigee parameters to and from various other parametrisations.

Typedef Documentation

typedef FreeTrajectoryState PerigeeConversions::FTS

Definition at line 16 of file PerigeeConversions.h.

Function Documentation

CurvilinearTrajectoryError PerigeeConversions::curvilinearError	(	const PerigeeTrajectoryError &	perigeeError,
		const GlobalTrajectoryParameters &	gtp
	)

Definition at line 61 of file PerigeeConversions.cc.

References PerigeeTrajectoryError::covarianceMatrix(), and jacobianPerigee2Curvilinear().

Referenced by TrajectoryStateClosestToPoint::calculateFTS().

{
  AlgebraicMatrix55 perigee2curv = jacobianPerigee2Curvilinear(gtp);
  return CurvilinearTrajectoryError(ROOT::Math::Similarity(perigee2curv, perigeeError.covarianceMatrix()));
}

PerigeeTrajectoryError PerigeeConversions::ftsToPerigeeError

(

const FTS &

originalFTS

)

Definition at line 52 of file PerigeeConversions.cc.

References FreeTrajectoryState::curvilinearError(), jacobianCurvilinear2Perigee(), and CurvilinearTrajectoryError::matrix().

Referenced by TrackerSeedValidator::analyze(), MatcherUsingTracksAlgorithm::getChi2(), MuonTrackingRegionBuilder::region(), and TrajectoryStateClosestToPoint::TrajectoryStateClosestToPoint().

{
  AlgebraicSymMatrix55 errorMatrix = originalFTS.curvilinearError().matrix();
  AlgebraicMatrix55 curv2perigee = jacobianCurvilinear2Perigee(originalFTS);
  return PerigeeTrajectoryError(ROOT::Math::Similarity(curv2perigee,errorMatrix));
}

PerigeeTrajectoryParameters PerigeeConversions::ftsToPerigeeParameters	(	const FTS &	originalFTS,
		const GlobalPoint &	referencePoint,
		double &	pt
	)

calculates the perigee parameters from a given FTS and a reference point.

Definition at line 8 of file PerigeeConversions.cc.

References funct::abs(), FreeTrajectoryState::charge(), epsilon, edm::hlt::Exception, statics::field, M_PI, GlobalTrajectoryParameters::magneticFieldInInverseGeV(), FreeTrajectoryState::momentum(), FreeTrajectoryState::parameters(), PV3DBase< T, PVType, FrameType >::perp(), phi, PV3DBase< T, PVType, FrameType >::phi(), FreeTrajectoryState::position(), RecoTauCleanerPlugins::pt, mathSSE::sqrt(), PV3DBase< T, PVType, FrameType >::theta(), theta(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by MatcherUsingTracksAlgorithm::getChi2(), and TrajectoryStateClosestToPoint::TrajectoryStateClosestToPoint().

{
  GlobalVector impactDistance = originalFTS.position() - referencePoint;

  pt = originalFTS.momentum().perp();
  if (pt==0.) throw cms::Exception("PerigeeConversions", "Track with pt=0");
  
  double theta = originalFTS.momentum().theta();
  double phi = originalFTS.momentum().phi();
  double field  = originalFTS.parameters().magneticFieldInInverseGeV().z();
//   if (field==0.) throw cms::Exception("PerigeeConversions", "Field is 0") << " at " << originalFTS.position() << "\n" ;

  double positiveMomentumPhi = ( (phi>0) ? phi : (2*M_PI+phi) );
  double positionPhi = impactDistance.phi();
  double positivePositionPhi =
   ( (positionPhi>0) ? positionPhi : (2*M_PI+positionPhi) );
  double phiDiff = positiveMomentumPhi - positivePositionPhi;
  if (phiDiff<0.0) phiDiff+= (2*M_PI);
  double signEpsilon = ( (phiDiff > M_PI) ? -1.0 : 1.0);

  double epsilon = signEpsilon *
             sqrt ( impactDistance.x()*impactDistance.x() +
                impactDistance.y()*impactDistance.y() );

  // The track parameters:
  AlgebraicVector5 theTrackParameters;

  double signTC = - originalFTS.charge();
  bool isCharged = (signTC!=0) && (std::abs(field)>1.e-10);
  if (isCharged) {
    theTrackParameters[0] = field / pt*signTC;
  } else {
    theTrackParameters[0] = 1 / pt;
  }
  theTrackParameters[1] = theta;
  theTrackParameters[2] = phi;
  theTrackParameters[3] = epsilon;
  theTrackParameters[4] = impactDistance.z();
  return PerigeeTrajectoryParameters(theTrackParameters, isCharged);
}

AlgebraicMatrix55 PerigeeConversions::jacobianCurvilinear2Perigee

(

const FreeTrajectoryState &

fts

)

Jacobians of tranformations between curvilinear frame at point of closest approach in transverse plane and perigee frame. The fts must therefore be given at exactly this point in order to yield the correct Jacobians.

Definition at line 156 of file PerigeeConversions.cc.

References funct::abs(), alpha, Vector3DBase< T, FrameTag >::cross(), Vector3DBase< T, FrameTag >::dot(), alignCSCRings::e, Exhume::I, M_PI, PV3DBase< T, PVType, FrameType >::mag(), GlobalTrajectoryParameters::magneticFieldInInverseGeV(), FreeTrajectoryState::momentum(), N, AlCaHLTBitMon_ParallelJobs::p, FreeTrajectoryState::parameters(), FreeTrajectoryState::signedInverseMomentum(), PV3DBase< T, PVType, FrameType >::theta(), FreeTrajectoryState::transverseCurvature(), Vector3DBase< T, FrameTag >::unit(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), Gflash::Z, and PV3DBase< T, PVType, FrameType >::z().

Referenced by ftsToPerigeeError(), and PerigeeKinematicState::PerigeeKinematicState().

                                                                             {

  GlobalVector p = fts.momentum();

  GlobalVector Z = GlobalVector(0.,0.,1.);
  GlobalVector T = p.unit();
  GlobalVector U = Z.cross(T).unit();; 
  GlobalVector V = T.cross(U);

  GlobalVector I = GlobalVector(-p.x(), -p.y(), 0.); //opposite to track dir.
  I = I.unit();
  GlobalVector J(-I.y(), I.x(),0.); //counterclockwise rotation
  GlobalVector K(Z);
  GlobalVector B  = fts.parameters().magneticFieldInInverseGeV();
  GlobalVector H = B.unit();
  GlobalVector HxT = H.cross(T);
  GlobalVector N = HxT.unit();
  double alpha = HxT.mag();
  double qbp = fts.signedInverseMomentum();
  double Q = -B.mag() * qbp;
  double alphaQ = alpha * Q;

  double lambda = 0.5 * M_PI - p.theta();
  double sinlambda, coslambda;  vdt::fast_sincos(lambda, sinlambda, coslambda);
  double seclambda = 1./coslambda;

  double ITI = 1./T.dot(I);
  double NU = N.dot(U);
  double NV = N.dot(V);
  double UI = U.dot(I);
  double VI = V.dot(I);
  double UJ = U.dot(J);
  double VJ = V.dot(J);
  double UK = U.dot(K);
  double VK = V.dot(K);

  AlgebraicMatrix55 jac;

  if( fabs(fts.transverseCurvature())<1.e-10 ) {
    jac(0,0) = seclambda;
    jac(0,1) = sinlambda*seclambda*seclambda*std::abs(qbp);
  }else{
    double Bz = B.z();
    jac(0,0) = -Bz * seclambda;
    jac(0,1) = -Bz * sinlambda*seclambda*seclambda*qbp;
    jac(1,3) = alphaQ * NV * UI*ITI;
    jac(1,4) = alphaQ * NV * VI*ITI;
    jac(0,3) = -jac(0,1) * jac(1,3);
    jac(0,4) = -jac(0,1) * jac(1,4);
    jac(2,3) = -alphaQ*seclambda * NU * UI*ITI;
    jac(2,4) = -alphaQ*seclambda * NU * VI*ITI;
  }
  jac(1,1) = -1.;
  jac(2,2) = 1.;
  jac(3,3) = VK*ITI;
  jac(3,4) = -UK*ITI;
  jac(4,3) = -VJ*ITI;
  jac(4,4) = UJ*ITI;
  
  return jac;
  
}

AlgebraicMatrix66 PerigeeConversions::jacobianParameters2Cartesian	(	const AlgebraicVector3 &	momentum,
		const GlobalPoint &	position,
		const TrackCharge &	charge,
		const MagneticField *	field
	)

Jacobians of tranformations between the parametrixation (x, y, z, transverse curvature, theta, phi) to Cartesian

Definition at line 124 of file PerigeeConversions.cc.

References funct::abs(), ecalTB2006H4_GenSimDigiReco_cfg::bField, alignmentValidation::c1, DeDxDiscriminatorTools::charge(), alignCSCRings::e, f, python.connectstrParser::f1, python.connectstrParser::f2, MagneticField::inInverseGeV(), indexGen::s2, and PV3DBase< T, PVType, FrameType >::z().

Referenced by KinematicPerigeeConversions::jacobianParameters2Kinematic(), and trajectoryStateClosestToPoint().

{
  float factor = -1.;
  float bField = field->inInverseGeV(position).z();
  if (charge!=0 && std::abs(bField)>1.e-10f)
    factor = bField*charge;
 

  float s1,c1; vdt::fast_sincosf(momentum[1],s1,c1);
  float s2,c2; vdt::fast_sincosf(momentum[2],s2,c2);
  float f1 = factor/(momentum[0]*momentum[0]);
  float f2 = factor/momentum[0];

  AlgebraicMatrix66 frameTransJ;
  frameTransJ(0,0) = 1;
  frameTransJ(1,1) = 1;
  frameTransJ(2,2) = 1;
  frameTransJ(3,3) =  (f1 * c2); 
  frameTransJ(4,3) =  (f1 * s2);
  frameTransJ(5,3) =  (f1*c1/s1);  

  frameTransJ(3,5) = (f2 * s2);
  frameTransJ(4,5) = -(f2 * c2);
  frameTransJ(5,4) = (f2/(s1*s1));

  return frameTransJ;
}

AlgebraicMatrix55 PerigeeConversions::jacobianPerigee2Curvilinear

(

const GlobalTrajectoryParameters &

gtp

)

Definition at line 222 of file PerigeeConversions.cc.

References alpha, Vector3DBase< T, FrameTag >::cross(), Vector3DBase< T, FrameTag >::dot(), alignCSCRings::e, f, Exhume::I, M_PI, PV3DBase< T, PVType, FrameType >::mag(), GlobalTrajectoryParameters::magneticFieldInInverseGeV(), GlobalTrajectoryParameters::momentum(), N, AlCaHLTBitMon_ParallelJobs::p, GlobalTrajectoryParameters::signedInverseMomentum(), PV3DBase< T, PVType, FrameType >::theta(), GlobalTrajectoryParameters::transverseCurvature(), Vector3DBase< T, FrameTag >::unit(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), Gflash::Z, and PV3DBase< T, PVType, FrameType >::z().

Referenced by curvilinearError().

                                                                                     {

  GlobalVector p = gtp.momentum();

  GlobalVector Z = GlobalVector(0.f,0.f,1.f);
  GlobalVector T = p.unit();
  GlobalVector U = Z.cross(T).unit();; 
  GlobalVector V = T.cross(U);

  GlobalVector I = GlobalVector(-p.x(), -p.y(), 0.f); //opposite to track dir.
  I = I.unit();
  GlobalVector J(-I.y(), I.x(),0.f); //counterclockwise rotation
  GlobalVector K(Z);
   GlobalVector B  = gtp.magneticFieldInInverseGeV();
  GlobalVector H = B.unit();
  GlobalVector HxT = H.cross(T);
  GlobalVector N = HxT.unit();
  double alpha = HxT.mag();
  double qbp = gtp.signedInverseMomentum();
  double Q = -B.mag() * qbp;
  double alphaQ = alpha * Q;


  double lambda = 0.5 * M_PI - p.theta();
  double sinlambda, coslambda;  vdt::fast_sincos(lambda, sinlambda, coslambda);
  double seclambda = 1./coslambda;

  double mqbpt = -1./coslambda * qbp;

  double TJ = T.dot(J);
  double TK = T.dot(K);
  double NU = N.dot(U);
  double NV = N.dot(V);
  double UJ = U.dot(J);
  double VJ = V.dot(J);
  double UK = U.dot(K);
  double VK = V.dot(K);

  AlgebraicMatrix55 jac;

  if( fabs(gtp.transverseCurvature())<1.e-10f ) {
    jac(0,0) = coslambda;
    jac(0,1) = sinlambda/coslambda/gtp.momentum().mag();
  }else{
    jac(0,0) = -coslambda/B.z();
    jac(0,1) = -sinlambda * mqbpt;
    jac(1,3) = -alphaQ * NV * TJ;
    jac(1,4) = -alphaQ * NV * TK;
    jac(2,3) = -alphaQ*seclambda * NU * TJ;
    jac(2,4) = -alphaQ*seclambda * NU * TK;
  }
  jac(1,1) = -1.;
  jac(2,2) = 1.;
  jac(3,3) = UJ;
  jac(3,4) = UK;
  jac(4,3) = VJ;
  jac(4,4) = VK;
  
  return jac;
}

GlobalVector PerigeeConversions::momentumFromPerigee	(	const AlgebraicVector3 &	momentum,
		const TrackCharge &	charge,
		const GlobalPoint &	referencePoint,
		const MagneticField *	field
	)

returns the (Cartesian) momentum. The parameters need not be the full perigee parameters, as long as the first 3 parameters are the transverse curvature, theta and phi.

Definition at line 87 of file PerigeeConversions.cc.

References funct::abs(), MagneticField::inInverseGeV(), RecoTauCleanerPlugins::pt, and PV3DBase< T, PVType, FrameType >::z().

Referenced by TrajectoryStateClosestToPoint::calculateFTS(), TrajectoryStateClosestToPoint::momentum(), and trajectoryStateClosestToPoint().

{
  double pt;

  double bz = fabs(field->inInverseGeV(referencePoint).z());
  if ( charge!=0 && std::abs(bz)>1.e-10 ) {
    pt = std::abs(bz/momentum[0]);
    // if (pt<1.e-10) throw cms::Exception("PerigeeConversions", "pt is 0");
  } else {
    pt = 1 / momentum[0];
  }

  return GlobalVector(vdt::fast_cos(momentum[2]) * pt,
              vdt::fast_sin(momentum[2]) * pt,
              pt/vdt::fast_tan(momentum[1]));
}

GlobalVector PerigeeConversions::momentumFromPerigee	(	const PerigeeTrajectoryParameters &	parameters,
		double	pt,
		const GlobalPoint &	referencePoint
	)

returns the (Cartesian) momentum from the PerigeeTrajectoryParameters

Definition at line 78 of file PerigeeConversions.cc.

References PerigeeTrajectoryParameters::phi(), and PerigeeTrajectoryParameters::theta().

{
  return GlobalVector(vdt::fast_cos(parameters.phi()) * pt,
              vdt::fast_sin(parameters.phi()) * pt,
              pt /vdt::fast_tan(parameters.theta()));
}

GlobalPoint PerigeeConversions::positionFromPerigee	(	const PerigeeTrajectoryParameters &	parameters,
		const GlobalPoint &	referencePoint
	)

returns the position (on the helix) at which the parameters are defined

Definition at line 68 of file PerigeeConversions.cc.

References PerigeeTrajectoryParameters::vector(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by TrajectoryStateClosestToPoint::calculateFTS(), and TrajectoryStateClosestToPoint::position().

{
  AlgebraicVector5 theVector = parameters.vector();
  return GlobalPoint(theVector[3]*vdt::fast_sin(theVector[2])+referencePoint.x(),
             -theVector[3]*vdt::fast_cos(theVector[2])+referencePoint.y(),
             theVector[4]+referencePoint.z());
}

TrajectoryStateClosestToPoint PerigeeConversions::trajectoryStateClosestToPoint	(	const AlgebraicVector3 &	momentum,
		const GlobalPoint &	referencePoint,
		const TrackCharge &	charge,
		const AlgebraicSymMatrix66 &	theCovarianceMatrix,
		const MagneticField *	field
	)

Public constructor. This constructor takes a momentum, with parameters (transverse curvature, theta, phi) and a position, which is both the reference position and the position at which the momentum is defined. The covariance matrix is defined for these 6 parameters, in the order (x, y, z, transverse curvature, theta, phi).

Definition at line 107 of file PerigeeConversions.cc.

References jacobianParameters2Cartesian(), and momentumFromPerigee().

Referenced by PerigeeMultiLTS::createRefittedTrackState().

{
  AlgebraicMatrix66 param2cart = jacobianParameters2Cartesian
    (momentum, referencePoint, charge, field);
  CartesianTrajectoryError cartesianTrajErr(ROOT::Math::Similarity(param2cart, theCovarianceMatrix));

  FTS theFTS(GlobalTrajectoryParameters(referencePoint,
        momentumFromPerigee(momentum, charge, referencePoint, field), charge,
        field), cartesianTrajErr);

  return TrajectoryStateClosestToPoint(theFTS, referencePoint);
}