Utility struct for functions and types related to the helix parameters. More...

#include <HelixParameters.h>

Inheritance diagram for HelixUtil:

Public Types
using	PerigeeAmbiguity = TrackFindingCDC::JacobianMatrix< 3, 5 >
	Matrix type for the ambiguity to the perigee parameters, e.g. under the stereo projection.

using	EParamaters = EHelixParameter
	Indices of the parameters.

using	ParameterVector = TrackFindingCDC::ParameterVector< c_N >
	The vector type representing the n related parameters.

using	CovarianceMatrix = TrackFindingCDC::CovarianceMatrix< c_N >
	The matrix type representing the covariance of the n related parameters.

using	PrecisionMatrix = TrackFindingCDC::PrecisionMatrix< c_N >
	The matrix type representing the precision of the n related parameters.

using	JacobianMatrix = TrackFindingCDC::JacobianMatrix< c_N >
	The matrix type used to translate covariances and precisions im auto mapping of the parameter space.

Static Public Member Functions
static HelixUtil::ParameterVector	reversalSigns ()
	Getter for the signs which have to be applied to reverse the parameters.

static PerigeeUtil::ParameterVector	getPerigeeParameters (const ParameterVector &helixPar)
	Get helix parameters related to the xy space.

static SZUtil::ParameterVector	getSZParameters (const ParameterVector &helixPar)
	Get sz parameters.

static HelixUtil::ParameterVector	stack (const PerigeeUtil::ParameterVector &perigeePar, const SZUtil::ParameterVector &szPar)
	Combine parameters from the xy space and the sz space.

static PerigeeUtil::CovarianceMatrix	getPerigeeCovariance (const CovarianceMatrix &helixCov)
	Get perigee covariance matrix related to the xy space.

static SZUtil::CovarianceMatrix	getSZCovariance (const CovarianceMatrix &helixCov)
	Get sz covariance matrix.

static HelixUtil::CovarianceMatrix	stackBlocks (const PerigeeUtil::CovarianceMatrix &perigeeCov, const SZUtil::CovarianceMatrix &szCov)
	Combine covariance matrices from the xy space and the sz space in their respective blocks.

static PerigeeAmbiguity	defaultPerigeeAmbiguity ()
	Initialise a default covariance matrix to zero.

static double	average (const HelixUtil::ParameterVector &fromPar, const HelixUtil::CovarianceMatrix &fromCov, const HelixUtil::ParameterVector &toPar, const HelixUtil::CovarianceMatrix &toCov, HelixUtil::ParameterVector &avgPar, HelixUtil::CovarianceMatrix &avgCov)
	Calculates the weighted average between two helix parameter sets with their respective covariance matrix.

static double	average (const PerigeeUtil::ParameterVector &fromPar, const PerigeeUtil::CovarianceMatrix &fromCov, const HelixUtil::PerigeeAmbiguity &fromAmbiguity, const HelixUtil::ParameterVector &toPar, const HelixUtil::CovarianceMatrix &toCov, HelixUtil::ParameterVector &avgPar, HelixUtil::CovarianceMatrix &avgCov)
	Calculates the weighted average between a perigee parameter sets and helix parameter sets with their respective covariance matrix under consideration of the relative ambiguity between the helix and the given perigee parameters.

static double	average (const PerigeeUtil::ParameterVector &fromPar, const PerigeeUtil::CovarianceMatrix &fromCov, const HelixUtil::PerigeeAmbiguity &fromAmbiguity, const PerigeeUtil::ParameterVector &toPar, const PerigeeUtil::CovarianceMatrix &toCov, const HelixUtil::PerigeeAmbiguity &toAmbiguity, const SZUtil::ParameterVector &szParameters, HelixUtil::ParameterVector &avgPar, HelixUtil::CovarianceMatrix &avgCov)
	Calculates the weighted average between two perigee parameter sets with their respective covariance matrix under consideration of their relative ambiguity to a helix near the sz parameters given as a reference.

static void	transport (const JacobianMatrix &jacobian, CovarianceMatrix &cov)
	Transport the covariance matrix inplace with the given jacobian matrix.

static CovarianceMatrix	transported (const JacobianMatrix &jacobian, const CovarianceMatrix &cov)
	Return a copy of the covariance matrix transported with the given jacobian matrix.

static JacobianMatrix	reversalJacobian ()
	Jacobian matrix needed in the reversal operation of the parameter vector.

static void	reverse (CovarianceMatrix &cov)
	Reverse the covariance matrix inplace.

static CovarianceMatrix	reversed (const CovarianceMatrix &cov)
	Return a copy of the reversed covariance matrix.

static CovarianceMatrix	identity ()
	Returns an identity matrix.

static CovarianceMatrix	covarianceFromPrecision (const PrecisionMatrix &prec)
	Convert the precision matrix to the corresponding covariance matrix.

static PrecisionMatrix	precisionFromCovariance (const CovarianceMatrix &cov)
	Convert the covariance matrix to the corresponding precision matrix.

static CovarianceMatrix	covarianceFromFullPrecision (const PrecisionMatrix &prec)
	Convert the precision matrix to the corresponding covariance matrix.

static PrecisionMatrix	precisionFromFullCovariance (const CovarianceMatrix &cov)
	Convert the covariance matrix to the corresponding precision matrix.

static AParameterVector	getSubParameterVector (const ParameterVector &par)
	Getter for a sub part of the covariance matrix.

static ACovarianceMatrix	getSubCovarianceMatrix (const CovarianceMatrix &cov)
	Getter for a sub part of the covariance matrix.

Static Public Attributes
static const size_t	c_N
	Number of elements.

Detailed Description

Utility struct for functions and types related to the helix parameters.

Definition at line 56 of file HelixParameters.h.

Member Typedef Documentation

◆ CovarianceMatrix

using CovarianceMatrix = TrackFindingCDC::CovarianceMatrix<c_N>

inherited

The matrix type representing the covariance of the n related parameters.

Definition at line 36 of file UncertainParameters.h.

◆ EParamaters

using EParamaters = EHelixParameter

inherited

Indices of the parameters.

Definition at line 27 of file UncertainParameters.h.

◆ JacobianMatrix

using JacobianMatrix = TrackFindingCDC::JacobianMatrix<c_N>

inherited

The matrix type used to translate covariances and precisions im auto mapping of the parameter space.

Definition at line 42 of file UncertainParameters.h.

◆ ParameterVector

using ParameterVector = TrackFindingCDC::ParameterVector<c_N>

inherited

The vector type representing the n related parameters.

Definition at line 33 of file UncertainParameters.h.

◆ PerigeeAmbiguity

using PerigeeAmbiguity = TrackFindingCDC::JacobianMatrix<3, 5>

Matrix type for the ambiguity to the perigee parameters, e.g. under the stereo projection.

Definition at line 82 of file HelixParameters.h.

◆ PrecisionMatrix

using PrecisionMatrix = TrackFindingCDC::PrecisionMatrix<c_N>

inherited

The matrix type representing the precision of the n related parameters.

Definition at line 39 of file UncertainParameters.h.

Member Function Documentation

◆ average() [1/3]

double average	(	const HelixUtil::ParameterVector &	fromPar,
		const HelixUtil::CovarianceMatrix &	fromCov,
		const HelixUtil::ParameterVector &	toPar,
		const HelixUtil::CovarianceMatrix &	toCov,
		HelixUtil::ParameterVector &	avgPar,
		HelixUtil::CovarianceMatrix &	avgCov
	)

static

Calculates the weighted average between two helix parameter sets with their respective covariance matrix.

Returns the chi2 value of the average.

Definition at line 70 of file HelixParameters.cc.

{
  using namespace NHelixParameterIndices;
  HelixParameters refPar = (fromPar + toPar) / 2.0;
  refPar[c_Phi0] = AngleUtil::average(fromPar[c_Phi0], toPar[c_Phi0]);
 
  HelixParameters relFromPar = fromPar - refPar;
  AngleUtil::normalise(relFromPar[c_Phi0]);
 
  HelixParameters relToPar = toPar - refPar;
  AngleUtil::normalise(relToPar[c_Phi0]);
 
  HelixParameters relAvgPar;
  double chi2 =
    CovarianceMatrixUtil::average(relFromPar, fromCov, relToPar, toCov, relAvgPar, avgCov);
 
  avgPar = relAvgPar + refPar;
  AngleUtil::normalise(avgPar[c_Phi0]);
 
  return chi2;
}

◆ average() [2/3]

double average	(	const PerigeeUtil::ParameterVector &	fromPar,
		const PerigeeUtil::CovarianceMatrix &	fromCov,
		const HelixUtil::PerigeeAmbiguity &	fromAmbiguity,
		const HelixUtil::ParameterVector &	toPar,
		const HelixUtil::CovarianceMatrix &	toCov,
		HelixUtil::ParameterVector &	avgPar,
		HelixUtil::CovarianceMatrix &	avgCov
	)

static

Calculates the weighted average between a perigee parameter sets and helix parameter sets with their respective covariance matrix under consideration of the relative ambiguity between the helix and the given perigee parameters.

Returns the chi2 value of the average.

Definition at line 97 of file HelixParameters.cc.

{
  auto toAmbiguity = JacobianMatrixUtil::identity<5>();
 
  using namespace NPerigeeParameterIndices;
  PerigeeParameters refPar = (fromPar + toPar.head<3>()) / 2.0;
  refPar[c_Phi0] = AngleUtil::average(fromPar[c_Phi0], toPar[c_Phi0]);
 
  HelixParameters refHelixPar = stack(refPar, toPar.tail<2>());
 
  PerigeeParameters relFromPar = fromPar - refPar;
  AngleUtil::normalise(relFromPar[c_Phi0]);
 
  HelixParameters relToPar = toPar - refHelixPar;
  AngleUtil::normalise(relToPar[c_Phi0]);
 
  HelixParameters relAvgPar;
 
  // Chi2 value
  double chi2 = CovarianceMatrixUtil::average(relFromPar,
                                              fromCov,
                                              fromAmbiguity,
                                              relToPar,
                                              toCov,
                                              toAmbiguity,
                                              relAvgPar,
                                              avgCov);
 
  avgPar = relAvgPar + refHelixPar;
  AngleUtil::normalise(avgPar[c_Phi0]);
 
  return chi2;
}

◆ average() [3/3]

double average	(	const PerigeeUtil::ParameterVector &	fromPar,
		const PerigeeUtil::CovarianceMatrix &	fromCov,
		const HelixUtil::PerigeeAmbiguity &	fromAmbiguity,
		const PerigeeUtil::ParameterVector &	toPar,
		const PerigeeUtil::CovarianceMatrix &	toCov,
		const HelixUtil::PerigeeAmbiguity &	toAmbiguity,
		const SZUtil::ParameterVector &	szParameters,
		HelixUtil::ParameterVector &	avgPar,
		HelixUtil::CovarianceMatrix &	avgCov
	)

static

Calculates the weighted average between two perigee parameter sets with their respective covariance matrix under consideration of their relative ambiguity to a helix near the sz parameters given as a reference.

Returns the chi2 value of the average.

Definition at line 137 of file HelixParameters.cc.

{
  using namespace NPerigeeParameterIndices;
  PerigeeParameters refPar = (fromPar + toPar) / 2.0;
  refPar[c_Phi0] = AngleUtil::average(fromPar[c_Phi0], toPar[c_Phi0]);
 
  HelixParameters refHelixPar = stack(refPar, szParameters);
 
  PerigeeParameters relFromPar = fromPar - refPar;
  AngleUtil::normalise(relFromPar[c_Phi0]);
 
  PerigeeParameters relToPar = toPar - refPar;
  AngleUtil::normalise(relToPar[c_Phi0]);
 
  HelixParameters relAvgPar;
 
  // Chi2 value
  double chi2 = CovarianceMatrixUtil::average(relFromPar,
                                              fromCov,
                                              fromAmbiguity,
                                              relToPar,
                                              toCov,
                                              toAmbiguity,
                                              relAvgPar,
                                              avgCov);
 
  avgPar = relAvgPar + refHelixPar;
  AngleUtil::normalise(avgPar[c_Phi0]);
 
  return chi2;
}

◆ covarianceFromFullPrecision()

auto covarianceFromFullPrecision ( const PrecisionMatrix & prec )

staticinherited

Convert the precision matrix to the corresponding covariance matrix.

Faster version with foreknowledge that the precision is of full rank.

Definition at line 73 of file UncertainParameters.icc.h.

                        {
      return CovarianceMatrixUtil::fromFullPrecision(prec);
    }

◆ covarianceFromPrecision()

auto covarianceFromPrecision ( const PrecisionMatrix & prec )

staticinherited

Convert the precision matrix to the corresponding covariance matrix.

Definition at line 64 of file UncertainParameters.icc.h.

                        {
      return CovarianceMatrixUtil::fromPrecision(prec);
    }

◆ defaultPerigeeAmbiguity()

HelixUtil::PerigeeAmbiguity defaultPerigeeAmbiguity ( )

static

Initialise a default covariance matrix to zero.

Definition at line 65 of file HelixParameters.cc.

{
  return PerigeeAmbiguity::Zero();
}

◆ getPerigeeCovariance()

PerigeeUtil::CovarianceMatrix getPerigeeCovariance ( const CovarianceMatrix & helixCov )

static

Get perigee covariance matrix related to the xy space.

Definition at line 46 of file HelixParameters.cc.

{
  using namespace NHelixParameterIndices;
  return getSubCovarianceMatrix<PerigeeUtil::CovarianceMatrix, c_Curv>(helixCov);
}

◆ getPerigeeParameters()

PerigeeUtil::ParameterVector getPerigeeParameters ( const ParameterVector & helixPar )

static

Get helix parameters related to the xy space.

Definition at line 27 of file HelixParameters.cc.

{
  using namespace NHelixParameterIndices;
  return getSubParameterVector<PerigeeUtil::ParameterVector, c_Curv>(helixPar);
}

◆ getSubCovarianceMatrix()

ACovarianceMatrix getSubCovarianceMatrix ( const CovarianceMatrix & cov )

staticinherited

Getter for a sub part of the covariance matrix.

Definition at line 87 of file UncertainParameters.icc.h.

    {
      return CovarianceMatrixUtil::getSub<ACovarianceMatrix, I>(cov);
    }

◆ getSubParameterVector()

AParameterVector getSubParameterVector ( const ParameterVector & par )

staticinherited

Getter for a sub part of the covariance matrix.

Definition at line 83 of file UncertainParameters.icc.h.

    {
      return ParameterVectorUtil::getSub<AParameterVector, I>(par);
    }

◆ getSZCovariance()

SZUtil::CovarianceMatrix getSZCovariance ( const CovarianceMatrix & helixCov )

static

Get sz covariance matrix.

Definition at line 52 of file HelixParameters.cc.

{
  using namespace NHelixParameterIndices;
  return getSubCovarianceMatrix<SZUtil::CovarianceMatrix, c_TanL>(helixCov);
}

◆ getSZParameters()

SZUtil::ParameterVector getSZParameters ( const ParameterVector & helixPar )

static

Get sz parameters.

Definition at line 33 of file HelixParameters.cc.

{
  using namespace NHelixParameterIndices;
  return getSubParameterVector<SZUtil::ParameterVector, c_TanL>(helixPar);
}

◆ identity()

auto identity

staticinherited

Returns an identity matrix.

Definition at line 61 of file UncertainParameters.icc.h.

                                                                                {
      return CovarianceMatrixUtil::identity<c_N>();
    }

◆ precisionFromCovariance()

auto precisionFromCovariance ( const CovarianceMatrix & cov )

staticinherited

Convert the covariance matrix to the corresponding precision matrix.

Definition at line 67 of file UncertainParameters.icc.h.

                       {
      return CovarianceMatrixUtil::toPrecision(cov);
    }

◆ precisionFromFullCovariance()

auto precisionFromFullCovariance ( const CovarianceMatrix & cov )

staticinherited

Convert the covariance matrix to the corresponding precision matrix.

Faster version with foreknowledge that the precision is of full rank.

Definition at line 79 of file UncertainParameters.icc.h.

                       {
      return CovarianceMatrixUtil::fullToPrecision(cov);
    }

◆ reversalJacobian()

auto reversalJacobian

staticinherited

Jacobian matrix needed in the reversal operation of the parameter vector.

Definition at line 52 of file UncertainParameters.icc.h.

                                                                                      {
      return JacobianMatrixUtil::scale(T::reversalSigns());
    }

◆ reversalSigns()

HelixUtil::ParameterVector reversalSigns ( )

static

Getter for the signs which have to be applied to reverse the parameters.

Definition at line 22 of file HelixParameters.cc.

{
  return ParameterVectorUtil::stack(PerigeeUtil::reversalSigns(), SZUtil::reversalSigns());
}

◆ reverse()

void reverse ( CovarianceMatrix & cov )

staticinherited

Reverse the covariance matrix inplace.

Definition at line 55 of file UncertainParameters.icc.h.

    {
      return transport(reversalJacobian(), cov);
    }

◆ reversed()

auto reversed ( const CovarianceMatrix & cov )

staticinherited

Return a copy of the reversed covariance matrix.

Definition at line 58 of file UncertainParameters.icc.h.

                        {
      return transported(reversalJacobian(), cov);
    }

◆ stack()

HelixUtil::ParameterVector stack	(	const PerigeeUtil::ParameterVector &	perigeePar,
		const SZUtil::ParameterVector &	szPar
	)

static

Combine parameters from the xy space and the sz space.

Definition at line 39 of file HelixParameters.cc.

{
  ParameterVector result = ParameterVectorUtil::stack(perigeePar, szPar);
  return result;
}

◆ stackBlocks()

HelixUtil::CovarianceMatrix stackBlocks	(	const PerigeeUtil::CovarianceMatrix &	perigeeCov,
		const SZUtil::CovarianceMatrix &	szCov
	)

static

Combine covariance matrices from the xy space and the sz space in their respective blocks.

Definition at line 58 of file HelixParameters.cc.

{
  CovarianceMatrix result = CovarianceMatrixUtil::stackBlocks(perigeeCov, szCov);
  return result;
}

◆ transport()

void transport	(	const JacobianMatrix &	jacobian,
		CovarianceMatrix &	cov
	)

staticinherited

Transport the covariance matrix inplace with the given jacobian matrix.

Definition at line 45 of file UncertainParameters.icc.h.

    {
      CovarianceMatrixUtil::transport(jacobian, cov);
    }

◆ transported()

auto transported	(	const JacobianMatrix &	jacobian,
		const CovarianceMatrix &	cov
	)

staticinherited

Return a copy of the covariance matrix transported with the given jacobian matrix.

Definition at line 48 of file UncertainParameters.icc.h.

                        {
      return CovarianceMatrixUtil::transported(jacobian, cov);
    }

Member Data Documentation

◆ c_N

const size_t c_N

staticinherited

Number of elements.

Definition at line 30 of file UncertainParameters.h.

The documentation for this struct was generated from the following files:

tracking/trackFindingCDC/geometry/include/HelixParameters.h
tracking/trackFindingCDC/geometry/src/HelixParameters.cc

Public Types

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ CovarianceMatrix

◆ EParamaters

◆ JacobianMatrix

◆ ParameterVector

◆ PerigeeAmbiguity

◆ PrecisionMatrix

Member Function Documentation

◆ average() [1/3]

◆ average() [2/3]

◆ average() [3/3]

◆ covarianceFromFullPrecision()

◆ covarianceFromPrecision()

◆ defaultPerigeeAmbiguity()

◆ getPerigeeCovariance()

◆ getPerigeeParameters()

◆ getSubCovarianceMatrix()

◆ getSubParameterVector()

◆ getSZCovariance()

◆ getSZParameters()

◆ identity()

◆ precisionFromCovariance()

◆ precisionFromFullCovariance()

◆ reversalJacobian()

◆ reversalSigns()

◆ reverse()

◆ reversed()

◆ stack()

◆ stackBlocks()

◆ transport()

◆ transported()

Member Data Documentation

◆ c_N