DTRecSegment4D.cc

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/* This Class Header */
#include "DataFormats/DTRecHit/interface/DTRecSegment4D.h"

/* Collaborating Class Header */
#include "DataFormats/MuonDetId/interface/DTChamberId.h"
#include "FWCore/Utilities/interface/Exception.h"
/* C++ Headers */

DTRecSegment4D::DTRecSegment4D(const DTChamberRecSegment2D& phiSeg,
                               const DTSLRecSegment2D& zedSeg,
                               const LocalPoint& posZInCh,
                               const LocalVector& dirZInCh)
    : RecSegment(phiSeg.chamberId()), theProjection(full), thePhiSeg(phiSeg), theZedSeg(zedSeg), theDimension(4) {
  // Check consistency of 2 sub-segments
  if (DTChamberId(phiSeg.geographicalId().rawId()) != DTChamberId(zedSeg.geographicalId().rawId()))
    throw cms::Exception("DTRecSegment4D")
        << "the z Segment and the phi segment have different chamber id" << std::endl;

  // The position of 2D segments are defined in the SL frame: I must first
  // extrapolate that position at the Chamber reference plane
  LocalPoint posZAt0 = posZInCh + dirZInCh * (-posZInCh.z()) / cos(dirZInCh.theta());

  thePosition = LocalPoint(phiSeg.localPosition().x(), posZAt0.y(), 0.);
  LocalVector dirPhiInCh = phiSeg.localDirection();

  // given the actual definition of chamber refFrame, (with z poiniting to IP),
  // the zed component of direction is negative.
  theDirection = LocalVector(dirPhiInCh.x() / fabs(dirPhiInCh.z()), dirZInCh.y() / fabs(dirZInCh.z()), -1.);
  theDirection = theDirection.unit();

  // set cov matrix
  theCovMatrix = AlgebraicSymMatrix(4);
  theCovMatrix[0][0] = phiSeg.covMatrix()[0][0];  //sigma (dx/dz)
  theCovMatrix[0][2] = phiSeg.covMatrix()[0][1];  //cov(dx/dz,x)
  theCovMatrix[2][2] = phiSeg.covMatrix()[1][1];  //sigma (x)
  setCovMatrixForZed(posZInCh);
}

DTRecSegment4D::DTRecSegment4D(const DTChamberRecSegment2D& phiSeg)
    : RecSegment(phiSeg.chamberId()),
      theProjection(phi),
      thePhiSeg(phiSeg),
      theZedSeg(DTSLRecSegment2D()),
      theDimension(2) {
  thePosition = thePhiSeg.localPosition();

  theDirection = thePhiSeg.localDirection();

  // set cov matrix
  theCovMatrix = AlgebraicSymMatrix(4);
  theCovMatrix[0][0] = phiSeg.covMatrix()[0][0];  //sigma (dx/dz)
  theCovMatrix[0][2] = phiSeg.covMatrix()[0][1];  //cov(dx/dz,x)
  theCovMatrix[2][2] = phiSeg.covMatrix()[1][1];  //sigma (x)
}

DTRecSegment4D::DTRecSegment4D(const DTSLRecSegment2D& zedSeg, const LocalPoint& posZInCh, const LocalVector& dirZInCh)
    : RecSegment(zedSeg.superLayerId().chamberId()),
      theProjection(Z),
      thePhiSeg(DTChamberRecSegment2D()),
      theZedSeg(zedSeg),
      theDimension(2) {
  LocalPoint posZAt0 = posZInCh + dirZInCh * (-posZInCh.z() / cos(dirZInCh.theta()));

  thePosition = posZAt0;
  theDirection = dirZInCh;

  // set cov matrix
  theCovMatrix = AlgebraicSymMatrix(4);
  setCovMatrixForZed(posZInCh);
}

DTRecSegment4D::~DTRecSegment4D() {}

AlgebraicVector DTRecSegment4D::parameters() const {
  if (dimension() == 4) {
    // (dx/dz,dy/dz,x,y)
    AlgebraicVector result(4);
    result[2] = thePosition.x();
    result[3] = thePosition.y();
    result[0] = theDirection.x() / theDirection.z();
    result[1] = theDirection.y() / theDirection.z();
    return result;
  }

  AlgebraicVector result(2);
  if (theProjection == phi) {
    // (dx/dz,x)
    result[1] = thePosition.x();
    result[0] = theDirection.x() / theDirection.z();
  } else if (theProjection == Z) {
    // (dy/dz,y) (note we are in the chamber r.f.)
    result[1] = thePosition.y();
    result[0] = theDirection.y() / theDirection.z();
  }
  return result;
}

AlgebraicSymMatrix DTRecSegment4D::parametersError() const {
  if (dimension() == 4) {
    return theCovMatrix;
  }

  AlgebraicSymMatrix result(2);
  if (theProjection == phi) {
    result[0][0] = theCovMatrix[0][0];  //S(dx/dz)
    result[0][1] = theCovMatrix[0][2];  //Cov(dx/dz,x)
    result[1][1] = theCovMatrix[2][2];  //S(x)
  } else if (theProjection == Z) {
    result[0][0] = theCovMatrix[1][1];  //S(dy/dz)
    result[0][1] = theCovMatrix[1][3];  //Cov(dy/dz,y)
    result[1][1] = theCovMatrix[3][3];  //S(y)
  }
  return result;
}

//These methods are only used to initialize the const static values
// used by projectionMatrix().
static AlgebraicMatrix initThe4DProjectionMatrix() {
  AlgebraicMatrix the4DProjectionMatrix(4, 5, 0);
  the4DProjectionMatrix[0][1] = 1;
  the4DProjectionMatrix[1][2] = 1;
  the4DProjectionMatrix[2][3] = 1;
  the4DProjectionMatrix[3][4] = 1;
  return the4DProjectionMatrix;
}
static const AlgebraicMatrix the4DProjectionMatrix{initThe4DProjectionMatrix()};

static AlgebraicMatrix initThe2DPhiProjMatrix() {
  AlgebraicMatrix the2DPhiProjMatrix(2, 5, 0);
  the2DPhiProjMatrix[0][1] = 1;
  the2DPhiProjMatrix[1][3] = 1;
  return the2DPhiProjMatrix;
}
static const AlgebraicMatrix the2DPhiProjMatrix{initThe2DPhiProjMatrix()};

static AlgebraicMatrix initThe2DZProjMatrix() {
  AlgebraicMatrix the2DZProjMatrix(2, 5, 0);
  the2DZProjMatrix[0][2] = 1;
  the2DZProjMatrix[1][4] = 1;
  return the2DZProjMatrix;
}
static const AlgebraicMatrix the2DZProjMatrix{initThe2DZProjMatrix()};

AlgebraicMatrix DTRecSegment4D::projectionMatrix() const {
  if (dimension() == 4) {
    return the4DProjectionMatrix;
  } else if (theProjection == phi) {
    return the2DPhiProjMatrix;
  } else if (theProjection == Z) {
    return the2DZProjMatrix;
  } else {
    return AlgebraicMatrix();
  }
}

LocalError DTRecSegment4D::localPositionError() const {
  return LocalError(theCovMatrix[2][2], theCovMatrix[2][3], theCovMatrix[3][3]);
}

LocalError DTRecSegment4D::localDirectionError() const {
  return LocalError(theCovMatrix[0][0], theCovMatrix[0][1], theCovMatrix[1][1]);
}

double DTRecSegment4D::chi2() const {
  double result = 0;
  if (hasPhi())
    result += thePhiSeg.chi2();
  if (hasZed())
    result += theZedSeg.chi2();
  return result;
}

int DTRecSegment4D::degreesOfFreedom() const {
  int result = 0;
  if (hasPhi())
    result += thePhiSeg.degreesOfFreedom();
  if (hasZed())
    result += theZedSeg.degreesOfFreedom();
  return result;
}

void DTRecSegment4D::setCovMatrixForZed(const LocalPoint& posZInCh) {
  // Warning!!! the covariance matrix for Theta SL segment is defined in the SL
  // reference frame, here that in the Chamber ref frame must be used.
  // For direction, no problem, but the position is extrapolated, so we must
  // propagate the error properly.

  // many thanks to Paolo Ronchese for the help in deriving the formulas!

  // y=m*z+q in SL frame
  // y=m'*z+q' in CH frame

  // var(m') = var(m)
  theCovMatrix[1][1] = theZedSeg.parametersError()[0][0];  //sigma (dy/dz)

  // cov(m',q') = DeltaZ*Var(m) + Cov(m,q)
  theCovMatrix[1][3] =
      posZInCh.z() * theZedSeg.parametersError()[0][0] + theZedSeg.parametersError()[0][1];  //cov(dy/dz,y)

  // Var(q') = DeltaZ^2*Var(m) + Var(q) + 2*DeltaZ*Cov(m,q)
  // cout << "Var(q') = DeltaZ^2*Var(m) + Var(q) + 2*DeltaZ*Cov(m,q)" << endl;
  // cout << "Var(q')= " << posZInCh.z()*posZInCh.z() << "*" <<
  //   theZedSeg.parametersError()[0][0] << " + " <<
  //   theZedSeg.parametersError()[1][1] << " + " <<
  //   2*posZInCh.z() << "*" << theZedSeg.parametersError()[0][1] ;
  theCovMatrix[3][3] = 2. * (posZInCh.z() * posZInCh.z()) * theZedSeg.parametersError()[0][0] +
                       theZedSeg.parametersError()[1][1] + 2. * posZInCh.z() * theZedSeg.parametersError()[0][1];
  // cout << " = " << theCovMatrix[3][3] << endl;
}

std::ostream& operator<<(std::ostream& os, const DTRecSegment4D& seg) {
  os << "Pos " << seg.localPosition() << " Dir: " << seg.localDirection() << " dim: " << seg.dimension()
     << " chi2/ndof: " << seg.chi2() << "/" << seg.degreesOfFreedom() << " :";
  if (seg.hasPhi())
    os << seg.phiSegment()->recHits().size();
  else
    os << 0;
  os << ":";
  if (seg.hasZed())
    os << seg.zSegment()->recHits().size();
  else
    os << 0;
  return os;
}

std::vector<const TrackingRecHit*> DTRecSegment4D::recHits() const {
  std::vector<const TrackingRecHit*> pointersOfRecHits;

  if (hasPhi())
    pointersOfRecHits.push_back(phiSegment());
  if (hasZed())
    pointersOfRecHits.push_back(zSegment());

  return pointersOfRecHits;
}

std::vector<TrackingRecHit*> DTRecSegment4D::recHits() {
  std::vector<TrackingRecHit*> pointersOfRecHits;

  if (hasPhi())
    pointersOfRecHits.push_back(phiSegment());
  if (hasZed())
    pointersOfRecHits.push_back(zSegment());

  return pointersOfRecHits;
}

DTChamberId DTRecSegment4D::chamberId() const { return DTChamberId(geographicalId()); }