Belle2::DistanceTools Namespace Reference

This namespace contains a collection of function that are useful to compute distances between tracks and vertices. More...

Functions
ROOT::Math::XYZVector	poca (ROOT::Math::XYZVector const &trackPos, ROOT::Math::XYZVector const &trackP, ROOT::Math::XYZVector const &vtxPos)
	Returns the Point Of Closest Approach of a track to a vertex.
B2Vector3D	trackToVtxVec (B2Vector3D const &trackPos, B2Vector3D const &trackP, B2Vector3D const &vtxPos)
	Returns the 3D vector between a vertex and a track's point of closest approach to that vertex.
double	trackToVtxDist (B2Vector3D const &trackPos, B2Vector3D const &trackP, B2Vector3D const &vtxPos)
	Returns the distance between a vertex and a track's point of closest approach to that vertex.
TMatrixDSym	trackToVtxCovmat (B2Vector3D const &trackP, TMatrixDSym const &trackPosCovMat, TMatrixDSym const &vtxPosCovMat)
	Returns the covariance (error) matrix of the 3D vector between a vertex and a track's point of closest approach to that vertex.
double	trackToVtxDistErr (B2Vector3D const &trackPos, B2Vector3D const &trackP, B2Vector3D const &vtxPos, TMatrixDSym const &trackPosCovMat, TMatrixDSym const &vtxPosCovMat)
	Returns the estimated uncertainty between a vertex and a track's point of closest approach to that vertex.
B2Vector3D	vtxToVtxVec (B2Vector3D const &vtx1Pos, B2Vector3D const &vtx2Pos)
	Returns the 3D vector between two vertices, ie vtxPos2 - vtxPos1.
double	vtxToVtxDist (B2Vector3D const &vtx1Pos, B2Vector3D const &vtx2Pos)
	Returns the distance between two vertices.
TMatrixDSym	vtxToVtxCovMat (TMatrixDSym const &vtx1CovMat, TMatrixDSym const &vtx2CovMat)
	Returns the covariance (error) matrix related to the vector linking two vertices.
double	vtxToVtxDistErr (B2Vector3D const &vtx1Pos, B2Vector3D const &vtx2Pos, TMatrixDSym const &vtx1CovMat, TMatrixDSym const &vtx2CovMat)
	Returns the estimated uncertainty on the distance between two vertices.

Detailed Description

This namespace contains a collection of function that are useful to compute distances between tracks and vertices.

All tracks are assumed to be straight in the current implementation.

Function Documentation

poca()

ROOT::Math::XYZVector poca	(	ROOT::Math::XYZVector const &	trackPos,
		ROOT::Math::XYZVector const &	trackP,
		ROOT::Math::XYZVector const &	vtxPos
	)

Returns the Point Of Closest Approach of a track to a vertex.

Definition at line 17 of file DistanceTools.cc.

{
  ROOT::Math::XYZVector trackDir(trackP.Unit());
  ROOT::Math::XYZVector r(vtxPos - trackPos);
  return trackPos + r.Dot(trackDir) * trackDir;
}

trackToVtxCovmat()

TMatrixDSym trackToVtxCovmat	(	B2Vector3D const &	trackP,
		TMatrixDSym const &	trackPosCovMat,
		TMatrixDSym const &	vtxPosCovMat
	)

Returns the covariance (error) matrix of the 3D vector between a vertex and a track's point of closest approach to that vertex.

Definition at line 37 of file DistanceTools.cc.

{
  if (trackPosCovMat.GetNcols() != 3 || vtxPosCovMat.GetNcols() != 3) {
    B2ERROR("in DistanceTools::trackToVtxCovmat, matrices must be of size 3");
    return TMatrixDSym(3);
  }
 
  TMatrixDSym rCovMat(trackPosCovMat + vtxPosCovMat);
  B2Vector3D trackDir(trackP.Unit());
  //d_j = r_j - v_j * v_k r_k
  //Jij = del_i d_j = delta_ij - v_i * v_j
  //Since the vector of closest approach is a linear function of r, its
  //propagation of errors is exact
  TMatrixDSym Jacobian(3);
  // Jacobian_ij = delta_ij -v(i)v(j)
  for (int i(0); i < 3; ++i)
    for (int j(0); j < 3; ++j)
      Jacobian(i, j) = -trackDir(i) * trackDir(j);
  for (int i(0); i < 3; ++i)
    Jacobian(i, i) += 1;
 
  return rCovMat.Similarity(Jacobian);  //calculates J * rCovMat * J^T, and returns it
 
}

trackToVtxDist()

double trackToVtxDist	(	B2Vector3D const &	trackPos,
		B2Vector3D const &	trackP,
		B2Vector3D const &	vtxPos
	)

Returns the distance between a vertex and a track's point of closest approach to that vertex.

Definition at line 32 of file DistanceTools.cc.

{
  return trackToVtxVec(trackPos, trackP, vtxPos).Mag();
}

trackToVtxDistErr()

double trackToVtxDistErr	(	B2Vector3D const &	trackPos,
		B2Vector3D const &	trackP,
		B2Vector3D const &	vtxPos,
		TMatrixDSym const &	trackPosCovMat,
		TMatrixDSym const &	vtxPosCovMat
	)

Returns the estimated uncertainty between a vertex and a track's point of closest approach to that vertex.

Definition at line 63 of file DistanceTools.cc.

{
  TMatrixDSym covMat(trackToVtxCovmat(trackP, trackPosCovMat, vtxPosCovMat));
  B2Vector3D dVec(trackToVtxVec(trackPos, trackP, vtxPos));
  // n is the normalise vector in the direction of the POCA between the track and the vtx
  B2Vector3D n((1. / dVec.Mag()) * dVec);
 
  double ret(0);
 
  //error on the distance computed as d^T * covMat * d
  for (int i(0); i < 3; ++i)
    for (int j(0); j < 3; ++j)
      ret += n(i) * covMat(i, j) * n(j);
 
  return TMath::Sqrt(ret);
}

trackToVtxVec()

B2Vector3D trackToVtxVec	(	B2Vector3D const &	trackPos,
		B2Vector3D const &	trackP,
		B2Vector3D const &	vtxPos
	)

Returns the 3D vector between a vertex and a track's point of closest approach to that vertex.

Definition at line 25 of file DistanceTools.cc.

{
  B2Vector3D trackDir(trackP.Unit());
  B2Vector3D r(vtxPos - trackPos);
  return r - (r.Dot(trackDir)) * trackDir;
}

vtxToVtxCovMat()

TMatrixDSym vtxToVtxCovMat	(	TMatrixDSym const &	vtx1CovMat,
		TMatrixDSym const &	vtx2CovMat
	)

Returns the covariance (error) matrix related to the vector linking two vertices.

Definition at line 92 of file DistanceTools.cc.

{
  if (vtx1CovMat.GetNcols() != 3 || vtx2CovMat.GetNcols() != 3) {
    B2ERROR("in DistanceTools::vtxToVtxCovMat, matrices must be of size 3");
    return TMatrixDSym(3);
  }
 
  return vtx1CovMat + vtx2CovMat;
}

vtxToVtxDist()

double vtxToVtxDist	(	B2Vector3D const &	vtx1Pos,
		B2Vector3D const &	vtx2Pos
	)

Returns the distance between two vertices.

Definition at line 87 of file DistanceTools.cc.

{
  return vtxToVtxVec(vtx1Pos, vtx2Pos).Mag();
}

vtxToVtxDistErr()

double vtxToVtxDistErr	(	B2Vector3D const &	vtx1Pos,
		B2Vector3D const &	vtx2Pos,
		TMatrixDSym const &	vtx1CovMat,
		TMatrixDSym const &	vtx2CovMat
	)

Returns the estimated uncertainty on the distance between two vertices.

Definition at line 102 of file DistanceTools.cc.

{
  TMatrixDSym covMat(vtxToVtxCovMat(vtx1CovMat, vtx2CovMat));
  B2Vector3D dVec(vtxToVtxVec(vtx1Pos, vtx2Pos));
  B2Vector3D n((1. / dVec.Mag()) * dVec);
 
  double ret(0);
 
  //error on the distance computed as d^T * covMat * d
  for (int i(0); i < 3; ++i)
    for (int j(0); j < 3; ++j)
      ret += n(i) * covMat(i, j) * n(j);
 
  return TMath::Sqrt(ret);
}

vtxToVtxVec()

B2Vector3D vtxToVtxVec	(	B2Vector3D const &	vtx1Pos,
		B2Vector3D const &	vtx2Pos
	)

Returns the 3D vector between two vertices, ie vtxPos2 - vtxPos1.

Definition at line 82 of file DistanceTools.cc.

{
  return vtx2Pos - vtx1Pos;
}