PerigeeConversions Class Reference

#include <PerigeeConversions.h>

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

Private Types
typedef FreeTrajectoryState	FTS

Detailed Description

Class provides several methods to transform perigee parameters to and from various other parametrisations.

Definition at line 16 of file PerigeeConversions.h.

Member Typedef Documentation

typedef FreeTrajectoryState PerigeeConversions::FTS

private

Definition at line 18 of file PerigeeConversions.h.

Member Function Documentation

TrackCharge PerigeeConversions::chargeFromPerigee

(

const PerigeeTrajectoryParameters &

perigee

)

const

This method returns the charge.

Definition at line 148 of file PerigeeConversions.cc.

References PerigeeTrajectoryParameters::charge().

{
  return parameters.charge();
}

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

Definition at line 102 of file PerigeeConversions.cc.

References PerigeeTrajectoryError::covarianceMatrix().

Referenced by TrajectoryStateClosestToPoint::calculateFTS().

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

PerigeeTrajectoryError PerigeeConversions::ftsToPerigeeError

(

const FTS &

originalFTS

)

const

Definition at line 63 of file PerigeeConversions.cc.

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

Referenced by 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
	)		const

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

Definition at line 7 of file PerigeeConversions.cc.

References FreeTrajectoryState::charge(), epsilon, edm::hlt::Exception, MagneticField::inInverseGeV(), M_PI, GlobalTrajectoryParameters::magneticField(), FreeTrajectoryState::momentum(), FreeTrajectoryState::parameters(), PV3DBase< T, PVType, FrameType >::perp(), phi, PV3DBase< T, PVType, FrameType >::phi(), FreeTrajectoryState::position(), mathSSE::sqrt(), PV3DBase< T, PVType, FrameType >::theta(), theta(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), detailsBasic3DVector::z, 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().magneticField().inInverseGeV(originalFTS.position()).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) && (fabs(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

)

const

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 199 of file PerigeeConversions.cc.

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

Referenced by 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);
  GlobalPoint x = fts.position();
  GlobalVector B  = fts.parameters().magneticField().inInverseGeV(x);
  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 coslambda = cos(lambda), tanlambda = tan(lambda);

  double TI = 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) = 1/coslambda;
    jac(0,1) = tanlambda/coslambda/fts.parameters().momentum().mag();
  }else{
    double Bz = B.z();
    jac(0,0) = -Bz/coslambda;
    jac(0,1) = -Bz * tanlambda/coslambda*qbp;
    jac(1,3) = alphaQ * NV * UI/TI;
    jac(1,4) = alphaQ * NV * VI/TI;
    jac(0,3) = -jac(0,1) * jac(1,3);
    jac(0,4) = -jac(0,1) * jac(1,4);
    jac(2,3) = -alphaQ/coslambda * NU * UI/TI;
    jac(2,4) = -alphaQ/coslambda * NU * VI/TI;
  }
  jac(1,1) = -1.;
  jac(2,2) = 1.;
  jac(3,3) = VK/TI;
  jac(3,4) = -UK/TI;
  jac(4,3) = -VJ/TI;
  jac(4,4) = UJ/TI;
  
  return jac;
  
}

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

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

Definition at line 171 of file PerigeeConversions.cc.

References ecalTB2006H4_GenSimDigiReco_cfg::bField, DeDxDiscriminatorTools::charge(), funct::cos(), alignCSCRings::e, edm::hlt::Exception, MagneticField::inInverseGeV(), funct::sin(), funct::tan(), and PV3DBase< T, PVType, FrameType >::z().

Referenced by KinematicPerigeeConversions::jacobianParameters2Kinematic().

{
  if (momentum[0]==0.) throw cms::Exception("PerigeeConversions", "Track with rho=0");
  double factor = 1.;
  double bField = field->inInverseGeV(position).z();
  if (charge!=0 && fabs(bField)>1.e-10) {
//     if (bField==0.) throw cms::Exception("PerigeeConversions", "Field is 0");
    factor = -bField*charge;
  }
  AlgebraicMatrix66 frameTransJ;
  frameTransJ(0,0) = 1;
  frameTransJ(1,1) = 1;
  frameTransJ(2,2) = 1;
  frameTransJ(3,3) = - factor * cos(momentum[2]) / (momentum[0]*momentum[0]);
  frameTransJ(4,3) = - factor * sin(momentum[2]) / (momentum[0]*momentum[0]);
  frameTransJ(5,3) = - factor / tan(momentum[1]) / (momentum[0]*momentum[0]);

  frameTransJ(3,5) = - factor * sin(momentum[2])  / (momentum[0]);
  frameTransJ(4,5) = factor * cos(momentum[2]) / (momentum[0]);
  frameTransJ(5,4) = - factor / (momentum[0]*sin(momentum[1])*sin(momentum[1]));

  return frameTransJ;
}

AlgebraicMatrix55 PerigeeConversions::jacobianPerigee2Curvilinear

(

const GlobalTrajectoryParameters &

gtp

)

const

Definition at line 265 of file PerigeeConversions.cc.

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

                                                                                           {

  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);
  GlobalPoint x = gtp.position();
  GlobalVector B  = gtp.magneticField().inInverseGeV(x);
  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 coslambda = cos(lambda), sinlambda = sin(lambda);
  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/coslambda * NU * TJ;
    jac(2,4) = -alphaQ/coslambda * 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
	)		const

This method 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 128 of file PerigeeConversions.cc.

References abs, funct::cos(), alignCSCRings::e, edm::hlt::Exception, MagneticField::inInverseGeV(), funct::sin(), funct::tan(), and PV3DBase< T, PVType, FrameType >::z().

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

{
  double pt;
  if (momentum[0]==0.) throw cms::Exception("PerigeeConversions", "Track with rho=0");

  double bz = fabs(field->inInverseGeV(referencePoint).z());
  if ( charge!=0 && 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(cos(momentum[2]) * pt,
              sin(momentum[2]) * pt,
              pt/tan(momentum[1]));
}

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

This method returns the (Cartesian) momentum from the PerigeeTrajectoryParameters

Definition at line 119 of file PerigeeConversions.cc.

References funct::cos(), PerigeeTrajectoryParameters::phi(), funct::sin(), funct::tan(), and PerigeeTrajectoryParameters::theta().

{
  return GlobalVector(cos(parameters.phi()) * pt,
              sin(parameters.phi()) * pt,
              pt / tan(parameters.theta()));
}

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

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

Definition at line 109 of file PerigeeConversions.cc.

References funct::cos(), funct::sin(), 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]*sin(theVector[2])+referencePoint.x(),
             -theVector[3]*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
	)		const

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 154 of file PerigeeConversions.cc.

Referenced by PerigeeMultiLTS::createRefittedTrackState(), and PerigeeLinearizedTrackState::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);
}