CDCTrajectory3D.cc

/**************************************************************************
 * BASF2 (Belle Analysis Framework 2)                                     *
 * Copyright(C) 2014 - Belle II Collaboration                             *
 *                                                                        *
 * Author: The Belle II Collaboration                                     *
 * Contributors: Oliver Frost                                             *
 *                                                                        *
 * This software is provided "as is" without any warranty.                *
 **************************************************************************/
#include <tracking/trackFindingCDC/eventdata/trajectories/CDCTrajectory3D.h>
 
#include <tracking/trackFindingCDC/eventdata/trajectories/CDCTrajectory2D.h>
#include <tracking/trackFindingCDC/eventdata/trajectories/CDCTrajectorySZ.h>
 
#include <tracking/trackFindingCDC/eventdata/trajectories/CDCBFieldUtil.h>
 
#include <tracking/trackFindingCDC/topology/CDCWireTopology.h>
 
#include <tracking/trackFindingCDC/geometry/UncertainHelix.h>
#include <tracking/trackFindingCDC/geometry/Helix.h>
#include <tracking/trackFindingCDC/geometry/HelixParameters.h>
#include <tracking/trackFindingCDC/geometry/UncertainPerigeeCircle.h>
#include <tracking/trackFindingCDC/geometry/UncertainSZLine.h>
#include <tracking/trackFindingCDC/geometry/PerigeeCircle.h>
 
#include <tracking/trackFindingCDC/geometry/Vector3D.h>
#include <tracking/trackFindingCDC/geometry/Vector2D.h>
 
#include <tracking/trackFindingCDC/numerics/ESign.h>
#include <tracking/trackFindingCDC/numerics/Quadratic.h>
 
#include <tracking/trackFindingCDC/numerics/CovarianceMatrixUtil.h>
#include <tracking/trackFindingCDC/numerics/JacobianMatrixUtil.h>
#include <tracking/trackFindingCDC/numerics/TMatrixConversion.h>
 
#include <genfit/TrackCand.h>
 
#include <mdst/dataobjects/MCParticle.h>
 
#include <framework/gearbox/Const.h>
 
#include <TMatrixDSym.h>
#include <TVector3.h>
 
#include <ostream>
 
using namespace Belle2;
using namespace TrackFindingCDC;
 
CDCTrajectory3D::CDCTrajectory3D(const CDCTrajectory2D& trajectory2D,
                                 const CDCTrajectorySZ& trajectorySZ)
  : m_localOrigin(trajectory2D.getLocalOrigin())
  , m_localHelix(trajectory2D.getLocalCircle(), trajectorySZ.getSZLine())
  , m_flightTime(trajectory2D.getFlightTime())
{
}
 
CDCTrajectory3D::CDCTrajectory3D(const CDCTrajectory2D& trajectory2D)
  : CDCTrajectory3D(trajectory2D, CDCTrajectorySZ::basicAssumption())
{
}
 
CDCTrajectory3D::CDCTrajectory3D(const Vector3D& pos3D,
                                 const double time,
                                 const Vector3D& mom3D,
                                 const double charge,
                                 const double bZ)
  : m_localOrigin(pos3D)
  , m_localHelix(CDCBFieldUtil::absMom2DToCurvature(mom3D.xy().norm(), charge, bZ),
                 mom3D.xy().unit(),
                 0.0,
                 mom3D.cotTheta(),
                 0.0)
  , m_flightTime(time)
{
}
 
CDCTrajectory3D::CDCTrajectory3D(const Vector3D& pos3D,
                                 const double time,
                                 const Vector3D& mom3D,
                                 const double charge)
  : CDCTrajectory3D(pos3D, time, mom3D, charge, CDCBFieldUtil::getBFieldZ(pos3D))
{
}
 
CDCTrajectory3D::CDCTrajectory3D(const MCParticle& mcParticle, const double bZ)
  : CDCTrajectory3D(Vector3D{mcParticle.getProductionVertex()},
                    mcParticle.getProductionTime(),
                    Vector3D{mcParticle.getMomentum()},
                    mcParticle.getCharge(),
                    bZ)
{
}
 
CDCTrajectory3D::CDCTrajectory3D(const MCParticle& mcParticle)
  : CDCTrajectory3D(Vector3D{mcParticle.getProductionVertex()},
                    mcParticle.getProductionTime(),
                    Vector3D{mcParticle.getMomentum()},
                    mcParticle.getCharge())
{
}
 
CDCTrajectory3D::CDCTrajectory3D(const genfit::TrackCand& gfTrackCand, const double bZ)
  : CDCTrajectory3D(Vector3D{gfTrackCand.getPosSeed()},
                    gfTrackCand.getTimeSeed(),
                    Vector3D{gfTrackCand.getMomSeed()},
                    gfTrackCand.getChargeSeed(),
                    bZ)
{
  // Maybe push these out of this function:
  // Indices of the cartesian coordinates
  const int iX = 0;
  const int iY = 1;
  const int iZ = 2;
  const int iPx = 3;
  const int iPy = 4;
  const int iPz = 5;
 
  const TMatrixDSym& seedCov = gfTrackCand.getCovSeed();
  CovarianceMatrix<6> cov6 = TMatrixConversion::fromTMatrix<6>(seedCov);
 
  // 1. Rotate to a system where phi0 = 0
  JacobianMatrix<6, 6> jacobianRot = JacobianMatrixUtil::zero<6, 6>();
 
  const double px = gfTrackCand.getStateSeed()[iPx];
  const double py = gfTrackCand.getStateSeed()[iPy];
  const double pt = hypot2(px, py);
 
  const double cosPhi0 = px / pt;
  const double sinPhi0 = py / pt;
 
  // Passive rotation matrix by phi0:
  jacobianRot(iX, iX) = cosPhi0;
  jacobianRot(iX, iY) = sinPhi0;
  jacobianRot(iY, iX) = -sinPhi0;
  jacobianRot(iY, iY) = cosPhi0;
  jacobianRot(iZ, iZ) = 1.0;
 
  jacobianRot(iPx, iPx) = cosPhi0;
  jacobianRot(iPx, iPy) = sinPhi0;
  jacobianRot(iPy, iPx) = -sinPhi0;
  jacobianRot(iPy, iPy) = cosPhi0;
  jacobianRot(iPz, iPz) = 1.0;
 
  // Apply transformation inplace
  CovarianceMatrixUtil::transport(jacobianRot, cov6);
 
  // 2. Translate to perigee parameters
  JacobianMatrix<5, 6> jacobianReduce = JacobianMatrixUtil::zero<5, 6>();
 
  const double invPt = 1 / pt;
  const double invPtSquared = invPt * invPt;
  const double pz = gfTrackCand.getStateSeed()[iPz];
  const double alpha = CDCBFieldUtil::getAlphaFromBField(bZ);
  const double charge = gfTrackCand.getChargeSeed();
 
  using namespace NHelixParameterIndices;
  jacobianReduce(c_Curv, iPx) = charge * invPtSquared / alpha ;
  jacobianReduce(c_Phi0, iPy) = invPt;
  jacobianReduce(c_I, iY) = 1;
  jacobianReduce(c_TanL, iPx) = - pz * invPtSquared;
  jacobianReduce(c_TanL, iPz) = invPt;
  jacobianReduce(c_Z0, iZ) = 1;
  // Note the column corresponding to iX is completely zero as expectable.
 
  CovarianceMatrix<5> cov5 = CovarianceMatrixUtil::transported(jacobianReduce, cov6);
  const HelixCovariance& helixCovariance = cov5;
 
  // The covariance should now be the correct 5x5 covariance matrix.
  m_localHelix.setHelixCovariance(helixCovariance);
}
 
CDCTrajectory3D::CDCTrajectory3D(const genfit::TrackCand& gfTrackCand)
  : CDCTrajectory3D(gfTrackCand, CDCBFieldUtil::getBFieldZ(Vector3D{gfTrackCand.getPosSeed()}))
{
}
 
namespace {
  CovarianceMatrix<6> calculateCovarianceMatrix(const UncertainHelix& localHelix,
                                                const Vector3D& momentum,
                                                const ESign charge,
                                                const double bZ)
  {
    const double impactXY = localHelix->impactXY();
    const Vector2D& phi0Vec = localHelix->phi0Vec();
 
    const double cosPhi0 = phi0Vec.x();
    const double sinPhi0 = phi0Vec.y();
 
    const double curvatureXY = localHelix->curvatureXY();
    const double tanLambda = localHelix->tanLambda();
 
    // 0. Define indices
    // Maybe push these out of this function:
    // Indices of the cartesian coordinates
    const int iX = 0;
    const int iY = 1;
    const int iZ = 2;
    const int iPx = 3;
    const int iPy = 4;
    const int iPz = 5;
 
    CovarianceMatrix<5> cov5 = localHelix.helixCovariance();
 
    // 1. Inflat the perigee covariance to a cartesian covariance where phi0 = 0 is assumed
    // Jacobian matrix for the translation
    JacobianMatrix<6, 5> jacobianInflate = JacobianMatrixUtil::zero<6, 5>();
 
    const double alpha = CDCBFieldUtil::getAlphaFromBField(bZ);
    const double chargeAlphaCurv = charge * alpha * curvatureXY;
    const double chargeAlphaCurv2 = charge * alpha * std::pow(curvatureXY, 2);
 
    const double invChargeAlphaCurv = 1.0 / chargeAlphaCurv;
    const double invChargeAlphaCurv2 = 1.0 / chargeAlphaCurv2;
 
    using namespace NHelixParameterIndices;
    // Position
    jacobianInflate(iX, c_Phi0) = -impactXY;
    jacobianInflate(iY, c_I)    = 1.0;
    jacobianInflate(iZ, c_Z0)   = 1.0;
 
    // Momentum
    if (bZ == 0) {
      jacobianInflate(iPx, c_Curv) = 0;
      jacobianInflate(iPy, c_Phi0) = momentum.cylindricalR();
      jacobianInflate(iPz, c_Curv) = 0;
      jacobianInflate(iPz, c_TanL) = momentum.cylindricalR();
    } else {
      jacobianInflate(iPx, c_Curv) = invChargeAlphaCurv2;
      jacobianInflate(iPy, c_Phi0) = - invChargeAlphaCurv;
      jacobianInflate(iPz, c_Curv) = tanLambda * invChargeAlphaCurv2;
      jacobianInflate(iPz, c_TanL) = - invChargeAlphaCurv;
    }
 
    // Transform
    CovarianceMatrix<6> cov6 = CovarianceMatrixUtil::transported(jacobianInflate, cov5);
 
    JacobianMatrix<6, 6> jacobianRot = JacobianMatrixUtil::zero<6, 6>();
 
    // Active rotation matrix by phi0:
    jacobianRot(iX, iX) = cosPhi0;
    jacobianRot(iX, iY) = -sinPhi0;
    jacobianRot(iY, iX) = sinPhi0;
    jacobianRot(iY, iY) = cosPhi0;
    jacobianRot(iZ, iZ) = 1.0;
 
    jacobianRot(iPx, iPx) = cosPhi0;
    jacobianRot(iPx, iPy) = -sinPhi0;
    jacobianRot(iPy, iPx) = sinPhi0;
    jacobianRot(iPy, iPy) = cosPhi0;
    jacobianRot(iPz, iPz) = 1.0;
 
    // Apply transformation inplace
    CovarianceMatrixUtil::transport(jacobianRot, cov6);
 
    // 3. Forward the covariance matrix.
    return cov6;
  }
}
 
 
bool CDCTrajectory3D::fillInto(genfit::TrackCand& trackCand) const
{
  Vector3D position = getSupport();
  return fillInto(trackCand, CDCBFieldUtil::getBFieldZ(position));
}
 
bool CDCTrajectory3D::fillInto(genfit::TrackCand& gfTrackCand, const double bZ) const
{
  // Set the start parameters
  Vector3D position = getSupport();
  Vector3D momentum = bZ == 0 ? getFlightDirection3DAtSupport() : getMom3DAtSupport(bZ);
  ESign charge = getChargeSign();
 
  // Do not propagate invalid fits, signal that the fit is invalid to the caller.
  if (not ESignUtil::isValid(charge) or momentum.hasNAN() or position.hasNAN()) {
    return false;
  }
 
  gfTrackCand.setPosMomSeed(position, momentum, charge);
 
  const CovarianceMatrix<6> cov6 = calculateCovarianceMatrix(getLocalHelix(), momentum, charge, bZ);
  TMatrixDSym covSeed = TMatrixConversion::toTMatrix(cov6);
 
  gfTrackCand.setCovSeed(covSeed);
 
  return true;
}
 
CovarianceMatrix<6> CDCTrajectory3D::getCartesianCovariance(double bZ) const
{
  // Set the start parameters
  Vector3D momentum = bZ == 0 ? getFlightDirection3DAtSupport() : getMom3DAtSupport(bZ);
  ESign charge = getChargeSign();
  return calculateCovarianceMatrix(getLocalHelix(), momentum, charge, bZ);
}
 
bool CDCTrajectory3D::isCurler(double factor) const
{
  const CDCWireTopology& topology = CDCWireTopology::getInstance();
  return getMaximalCylindricalR() < factor * topology.getOuterCylindricalR();
}
 
ESign CDCTrajectory3D::getChargeSign() const
{
  return CDCBFieldUtil::ccwInfoToChargeSign(getLocalHelix()->circleXY().orientation());
}
 
double CDCTrajectory3D::getAbsMom3D(const double bZ) const
{
  double tanLambda = getLocalHelix()->tanLambda();
  double factor2DTo3D = hypot2(1, tanLambda);
  double curvatureXY = getLocalHelix()->curvatureXY();
  double absMom2D = CDCBFieldUtil::curvatureToAbsMom2D(curvatureXY, bZ);
  return factor2DTo3D * absMom2D;
}
 
double CDCTrajectory3D::getAbsMom3D() const
{
  Vector3D position = getSupport();
  double tanLambda = getLocalHelix()->tanLambda();
  double factor2DTo3D = hypot2(1, tanLambda);
  double curvatureXY = getLocalHelix()->curvatureXY();
  double absMom2D = CDCBFieldUtil::curvatureToAbsMom2D(curvatureXY, position);
  return factor2DTo3D * absMom2D;
}
 
double CDCTrajectory3D::shiftPeriod(int nPeriods)
{
  double arcLength2D = m_localHelix.shiftPeriod(nPeriods);
  m_flightTime += arcLength2D / Const::speedOfLight;
  return arcLength2D;
}
 
CDCTrajectory2D CDCTrajectory3D::getTrajectory2D() const
{
  return CDCTrajectory2D(getLocalOrigin().xy(),
                         getLocalHelix().uncertainCircleXY(),
                         getFlightTime());
}
 
CDCTrajectorySZ CDCTrajectory3D::getTrajectorySZ() const
{
  UncertainSZLine globalSZLine = getLocalHelix().uncertainSZLine();
  globalSZLine.passiveMoveBy(Vector2D(0, -getLocalOrigin().z()));
  return CDCTrajectorySZ(globalSZLine);
}
 
 
PerigeeCircle CDCTrajectory3D::getGlobalCircle() const
{
  // Down cast since we do not necessarily wont the covariance matrix transformed as well
  PerigeeCircle result(getLocalHelix()->circleXY());
  result.passiveMoveBy(-getLocalOrigin().xy());
  return result;
}
 
UncertainPerigeeCircle CDCTrajectory3D::getLocalCircle() const
{
  return getLocalHelix().uncertainCircleXY();
}
 
UncertainSZLine CDCTrajectory3D::getLocalSZLine() const
{
  return getLocalHelix().uncertainSZLine();
}
 
double CDCTrajectory3D::setLocalOrigin(const Vector3D& localOrigin)
{
  double arcLength2D = calcArcLength2D(localOrigin);
  double factor2DTo3D = hypot2(1, getTanLambda());
  double arcLength3D = arcLength2D * factor2DTo3D;
  m_flightTime += arcLength3D / Const::speedOfLight;
  m_localHelix.passiveMoveBy(localOrigin - m_localOrigin);
  m_localOrigin = localOrigin;
  return arcLength2D;
}
 
std::ostream& TrackFindingCDC::operator<<(std::ostream& output, const CDCTrajectory3D& trajectory3D)
{
  return output << "Local origin : " << trajectory3D.getLocalOrigin() << ", "
         << "local helix : " << trajectory3D.getLocalHelix();
}