A general helix class including a covariance matrix. More...

#include <UncertainHelix.h>

Public Member Functions
	UncertainHelix ()
	Default constructor for ROOT compatibility.

	UncertainHelix (const double curvature, const double phi0, const double impact, const double tanLambda, const double z0, const HelixCovariance &helixCovariance=HelixUtil::identity(), const double chi2=0.0, std::size_t ndf=0)
	Composes an uncertain perigee circle from the perigee parameters and a 3x3 covariance matrix.

	UncertainHelix (const HelixParameters &parameters, const HelixCovariance &helixCovariance=HelixUtil::identity(), const double chi2=0.0, std::size_t ndf=0)
	Constructor taking all stored parameters.

	UncertainHelix (const double curvature, const Vector2D &phi0Vec, const double impact, const double tanLambda, const double z0, const HelixCovariance &helixCovariance=HelixUtil::identity(), const double chi2=0.0, std::size_t ndf=0)
	Composes an uncertain perigee circle from the perigee parameters and a 3x3 covariance matrix.

	UncertainHelix (const Helix &helix, const HelixCovariance &helixCovariance=HelixUtil::identity(), const double chi2=0.0, std::size_t ndf=0)
	Augments a plain helix with a covariance matrix. Covariance defaults to zero.

	UncertainHelix (const UncertainPerigeeCircle &uncertainPerigeeCircle, const UncertainSZLine &uncertainSZLine)
	Augments a plain helix with a covariance matrix. Covariance defaults to zero.

const Helix *	operator-> () const
	Access to the constant interface of the underlying parameter line Allows the user of this "super" class to use the getters and other methods to get information about the line but disallows mutation of internal state.

	operator const Helix & () const
	Downcast to the "super" class.

const Helix &	helix () const
	Getter for the underlying helix.

HelixParameters	helixParameters () const
	Getter for the perigee parameters in the order defined by EPerigeeParameter.h.

UncertainPerigeeCircle	uncertainCircleXY () const
	Projects the helix into the xy plain carrying over the relevant parts of the convariance matrix.

UncertainSZLine	uncertainSZLine () const
	Reduces the helix to an sz line carrying over the relevant parts of the convariance matrix.

void	setHelixCovariance (const HelixCovariance &helixCovariance)
	Setter for the whole covariance matrix of the perigee parameters.

const HelixCovariance &	helixCovariance () const
	Getter for the whole covariance matrix of the perigee parameters.

double	covariance (const EHelixParameter &iRow, const EHelixParameter &iCol) const
	Getter for individual elements of the covariance matrix.

double	variance (const EHelixParameter &i) const
	Getter for individual diagonal elements of the covariance matrix.

double	chi2 () const
	Getter for the chi square value of the helix fit.

void	setChi2 (const double chi2)
	Setter for the chi square value of the helix fit.

std::size_t	ndf () const
	Getter for the number of degrees of freediom used in the helix fit.

void	setNDF (std::size_t ndf)
	Setter for the number of degrees of freediom used in the helix fit.

void	invalidate ()
	Sets all circle parameters to zero and the covariance matrix to something noninformative.

void	reverse ()
	Flips the orientation of the circle in place.

UncertainHelix	reversed () const
	Returns a copy of the circle with opposite orientation.

void	passiveMoveBy (const Vector3D &by)
	Moves the coordinate system by the vector by and calculates the new perigee and its covariance matrix.

double	shiftPeriod (int nPeriods)
	Adjust the arclength measure to start n periods later.

Static Public Member Functions
static UncertainHelix	average (const UncertainHelix &fromHelix, const UncertainHelix &toHelix)
	Construct the averages of the two given helices by properly considering their covariance matrix.

static UncertainHelix	average (const UncertainPerigeeCircle &fromPerigeeCircle, const PerigeeHelixAmbiguity &fromAmbiguity, const UncertainPerigeeCircle &toPerigeeCircle, const PerigeeHelixAmbiguity &toAmbiguity, const SZParameters &szParameters)
	Construct the average helix including its covariance matrix from two different stereo angle projections.

static UncertainHelix	average (const UncertainHelix &helix, const UncertainPerigeeCircle &perigeeCircle, const PerigeeHelixAmbiguity &ambiguityMatrix)
	Construct the average helix including its covariance matrix incoorporating additional information from a stereo projection.

static UncertainHelix	average (const UncertainPerigeeCircle &fromPerigeeCircle, const PerigeeHelixAmbiguity &fromAmbiguity, const UncertainHelix &toHelix)
	Construct the average helix including its covariance matrix incoorporating additional information from a stereo projection.

Private Attributes
Helix	m_helix
	Memory for the underlying helix.

HelixCovariance	m_helixCovariance = HelixUtil::identity()
	Memory for the 5x5 covariance matrix of the helix parameters.

double	m_chi2 = 0.0
	Memory for the chi square value of the fit of this helix.

size_t	m_ndf = 0.0
	Memory for the number of degrees of freedom of the fit of this helix.

Detailed Description

A general helix class including a covariance matrix.

Definition at line 34 of file UncertainHelix.h.

Constructor & Destructor Documentation

◆ UncertainHelix() [1/6]

UncertainHelix ( )

inline

Default constructor for ROOT compatibility.

Definition at line 38 of file UncertainHelix.h.

39 {

40 }

◆ UncertainHelix() [2/6]

UncertainHelix	(	const double	curvature,
		const double	phi0,
		const double	impact,
		const double	tanLambda,
		const double	z0,
		const HelixCovariance &	helixCovariance = `HelixUtil::identity()`,
		const double	chi2 = `0.0`,
		std::size_t	ndf = `0`
	)

inline

Composes an uncertain perigee circle from the perigee parameters and a 3x3 covariance matrix.

Definition at line 44 of file UncertainHelix.h.

        : m_helix(curvature, phi0, impact, tanLambda, z0)
        , m_helixCovariance(helixCovariance)
        , m_chi2(chi2)
        , m_ndf(ndf)
      {
      }

◆ UncertainHelix() [3/6]

UncertainHelix	(	const HelixParameters &	parameters,
		const HelixCovariance &	helixCovariance = `HelixUtil::identity()`,
		const double	chi2 = `0.0`,
		std::size_t	ndf = `0`
	)

inlineexplicit

Constructor taking all stored parameters.

Definition at line 60 of file UncertainHelix.h.

        : m_helix(parameters)
        , m_helixCovariance(helixCovariance)
        , m_chi2(chi2)
        , m_ndf(ndf)
      {
      }

◆ UncertainHelix() [4/6]

UncertainHelix	(	const double	curvature,
		const Vector2D &	phi0Vec,
		const double	impact,
		const double	tanLambda,
		const double	z0,
		const HelixCovariance &	helixCovariance = `HelixUtil::identity()`,
		const double	chi2 = `0.0`,
		std::size_t	ndf = `0`
	)

inline

Composes an uncertain perigee circle from the perigee parameters and a 3x3 covariance matrix.

Definition at line 73 of file UncertainHelix.h.

        : m_helix(curvature, phi0Vec, impact, tanLambda, z0)
        , m_helixCovariance(helixCovariance)
        , m_chi2(chi2)
        , m_ndf(ndf)
      {
      }

◆ UncertainHelix() [5/6]

UncertainHelix	(	const Helix &	helix,
		const HelixCovariance &	helixCovariance = `HelixUtil::identity()`,
		const double	chi2 = `0.0`,
		std::size_t	ndf = `0`
	)

inlineexplicit

Augments a plain helix with a covariance matrix. Covariance defaults to zero.

Definition at line 89 of file UncertainHelix.h.

        : m_helix(helix)
        , m_helixCovariance(helixCovariance)
        , m_chi2(chi2)
        , m_ndf(ndf)
      {
      }

◆ UncertainHelix() [6/6]

UncertainHelix	(	const UncertainPerigeeCircle &	uncertainPerigeeCircle,
		const UncertainSZLine &	uncertainSZLine
	)

inline

Augments a plain helix with a covariance matrix. Covariance defaults to zero.

Definition at line 101 of file UncertainHelix.h.

        : m_helix(uncertainPerigeeCircle, uncertainSZLine)
        , m_helixCovariance(HelixUtil::stackBlocks(uncertainPerigeeCircle.perigeeCovariance(),
                                                   uncertainSZLine.szCovariance()))
        , m_chi2(uncertainPerigeeCircle.chi2() + uncertainSZLine.chi2())
        , m_ndf(uncertainPerigeeCircle.ndf() + uncertainSZLine.ndf())
      {
      }

Member Function Documentation

◆ average() [1/4]

UncertainHelix average	(	const UncertainHelix &	fromHelix,
		const UncertainHelix &	toHelix
	)

static

Construct the averages of the two given helices by properly considering their covariance matrix.

Definition at line 23 of file UncertainHelix.cc.

{
  HelixParameters fromPar = fromHelix.helixParameters();
  HelixCovariance fromCov = fromHelix.helixCovariance();
 
  HelixParameters toPar = toHelix.helixParameters();
  HelixCovariance toCov = toHelix.helixCovariance();
 
  HelixParameters avgPar;
  HelixCovariance avgCov;
 
  double chi2 = HelixUtil::average(fromPar, fromCov, toPar, toCov, avgPar, avgCov);
 
  // Calculating 5 parameters from 10 input parameters. 5 NDF remaining.
  size_t ndf = 5;
 
  return UncertainHelix(avgPar, avgCov, chi2, ndf);
}

◆ average() [2/4]

static UncertainHelix average	(	const UncertainHelix &	helix,
		const UncertainPerigeeCircle &	perigeeCircle,
		const PerigeeHelixAmbiguity &	ambiguityMatrix
	)

inlinestatic

Construct the average helix including its covariance matrix incoorporating additional information from a stereo projection.

The averaging in the higher dimensional helix parameter space from the lower dimensional projectsions is accomplished by considering the ambiguity matrix of the projection.

Both circle and helix parameters and their covariance matrix are considered to be passed on the same origin. The circle is considered to be fitted in the sz space defined by the given helix.

Parameters

helix	Second perigee circle
perigeeCircle	Perigee circle to be incoorporated
ambiguityMatrix	Ambiguity matrix of the perigee parameters with respect to the helix parameters

Definition at line 161 of file UncertainHelix.h.

      {
        return average(perigeeCircle, ambiguityMatrix, helix);
      }

◆ average() [3/4]

UncertainHelix average	(	const UncertainPerigeeCircle &	fromPerigeeCircle,
		const PerigeeHelixAmbiguity &	fromAmbiguity,
		const UncertainHelix &	toHelix
	)

static

Construct the average helix including its covariance matrix incoorporating additional information from a stereo projection.

The averaging in the higher dimensional helix parameter space from the lower dimensional projectsions is accomplished by considering the ambiguity matrix of the projection.

Both circle and helix parameters and their covariance matrix are considered to be passed on the same origin. The circle is considered to be fitted in the sz space defined by the given helix.

Parameters

fromPerigeeCircle	Perigee circle to be incorporated
fromAmbiguity	Ambiguity matrix of the perigee parameters with respect to the helix parameters
toHelix	Second perigee circle

Definition at line 43 of file UncertainHelix.cc.

{
  PerigeeParameters fromPar = fromPerigeeCircle.perigeeParameters();
  PerigeeCovariance fromCov = fromPerigeeCircle.perigeeCovariance();
 
  HelixParameters toPar = toHelix.helixParameters();
  HelixCovariance toCov = toHelix.helixCovariance();
 
  HelixParameters avgPar;
  HelixCovariance avgCov;
 
  double chi2 = HelixUtil::average(fromPar, fromCov, fromAmbiguity, toPar, toCov, avgPar, avgCov);
 
  // Calculating 5 parameters from 8 input parameters. 3 NDF remaining.
  size_t ndf = 3;
 
  return UncertainHelix(avgPar, avgCov, chi2, ndf);
}

◆ average() [4/4]

UncertainHelix average	(	const UncertainPerigeeCircle &	fromPerigeeCircle,
		const PerigeeHelixAmbiguity &	fromAmbiguity,
		const UncertainPerigeeCircle &	toPerigeeCircle,
		const PerigeeHelixAmbiguity &	toAmbiguity,
		const SZParameters &	szParameters
	)

static

Construct the average helix including its covariance matrix from two different stereo angle projections.

The averaging in the higher dimensional helix parameter space from the lower dimensional projections is accomplished by considering the ambiguity matrix of the projections. The average only succeeds when the projections are not parallel two each other which is generally the case for two different super layers of different stereo kind.

Both circle and helix parameters and their covariance matrix are considered to be passed on the same origin.

Parameters

fromPerigeeCircle	First perigee circle
fromAmbiguity	Ambiguity matrix of the first perigee parameters with respect to the helix parameters
toPerigeeCircle	Second perigee circle
toAmbiguity	Ambiguity matrix of the second perigee parameters with respect to the helix parameters
szParameters	Reference sz parameters where the perigee circles have been fitted.

Definition at line 64 of file UncertainHelix.cc.

{
  const PerigeeParameters& fromPar = fromPerigeeCircle.perigeeParameters();
  const PerigeeCovariance& fromCov = fromPerigeeCircle.perigeeCovariance();
 
  const PerigeeParameters& toPar = toPerigeeCircle.perigeeParameters();
  const PerigeeCovariance& toCov = toPerigeeCircle.perigeeCovariance();
 
  HelixParameters avgPar;
  HelixCovariance avgCov;
 
  double chi2 = HelixUtil::average(fromPar,
                                   fromCov,
                                   fromAmbiguity,
                                   toPar,
                                   toCov,
                                   toAmbiguity,
                                   szParameters,
                                   avgPar,
                                   avgCov);
 
  // Calculating 5 parameters from 6 input parameters. 1 NDF remaining.
  size_t ndf = 1;
 
  return UncertainHelix(avgPar, avgCov, chi2, ndf);
}

◆ chi2()

double chi2 ( ) const

inline

Getter for the chi square value of the helix fit.

Definition at line 263 of file UncertainHelix.h.

      {
        return m_chi2;
      }

◆ covariance()

double covariance	(	const EHelixParameter &	iRow,
		const EHelixParameter &	iCol
	)		const

inline

Getter for individual elements of the covariance matrix.

Definition at line 251 of file UncertainHelix.h.

      {
        return helixCovariance()(iRow, iCol);
      }

◆ helix()

const Helix & helix ( ) const

inline

Getter for the underlying helix.

Definition at line 211 of file UncertainHelix.h.

      {
        return m_helix;
      }

◆ helixCovariance()

const HelixCovariance & helixCovariance ( ) const

inline

Getter for the whole covariance matrix of the perigee parameters.

Definition at line 245 of file UncertainHelix.h.

      {
        return m_helixCovariance;
      }

◆ helixParameters()

HelixParameters helixParameters ( ) const

inline

Getter for the perigee parameters in the order defined by EPerigeeParameter.h.

Definition at line 217 of file UncertainHelix.h.

      {
        return m_helix.helixParameters();
      }

◆ invalidate()

void invalidate ( )

inline

Sets all circle parameters to zero and the covariance matrix to something noninformative.

Definition at line 287 of file UncertainHelix.h.

      {
        m_helix.invalidate();
        m_helixCovariance = HelixUtil::identity();
        m_chi2 = 0.0;
        m_ndf = 0;
      }

◆ ndf()

std::size_t ndf ( ) const

inline

Getter for the number of degrees of freediom used in the helix fit.

Definition at line 275 of file UncertainHelix.h.

      {
        return m_ndf;
      }

◆ operator const Helix &()

operator const Helix & ( ) const

inline

Downcast to the "super" class.

Definition at line 205 of file UncertainHelix.h.

      {
        return m_helix;
      }

◆ operator->()

const Helix * operator-> ( ) const

inline

Access to the constant interface of the underlying parameter line Allows the user of this "super" class to use the getters and other methods to get information about the line but disallows mutation of internal state.

This ensures that the parameters are not changed without proper adjustment to the covariance matrix in this class, which can be achieved by the more limited set of methods in this class accessible by normal . method calls

Definition at line 199 of file UncertainHelix.h.

      {
        return &m_helix;
      }

◆ passiveMoveBy()

void passiveMoveBy ( const Vector3D & by )

inline

Moves the coordinate system by the vector by and calculates the new perigee and its covariance matrix.

Change is inplace.

Definition at line 315 of file UncertainHelix.h.

      {
        // Move the covariance matrix first to have access to the original parameters
        HelixJacobian jacobian = m_helix.passiveMoveByJacobian(by);
        HelixUtil::transport(jacobian, m_helixCovariance);
        m_helix.passiveMoveBy(by);
      }

◆ reverse()

void reverse ( )

inline

Flips the orientation of the circle in place.

Definition at line 297 of file UncertainHelix.h.

      {
        m_helix.reverse();
        HelixUtil::reverse(m_helixCovariance);
      }

◆ reversed()

UncertainHelix reversed ( ) const

inline

Returns a copy of the circle with opposite orientation.

Definition at line 304 of file UncertainHelix.h.

      {
        return UncertainHelix(m_helix.reversed(),
                              HelixUtil::reversed(m_helixCovariance),
                              chi2(),
                              ndf());
      }

◆ setChi2()

void setChi2 ( const double chi2 )

inline

Setter for the chi square value of the helix fit.

Definition at line 269 of file UncertainHelix.h.

      {
        m_chi2 = chi2;
      }

◆ setHelixCovariance()

void setHelixCovariance ( const HelixCovariance & helixCovariance )

inline

Setter for the whole covariance matrix of the perigee parameters.

Definition at line 239 of file UncertainHelix.h.

      {
        m_helixCovariance = helixCovariance;
      }

◆ setNDF()

void setNDF ( std::size_t ndf )

inline

Setter for the number of degrees of freediom used in the helix fit.

Definition at line 281 of file UncertainHelix.h.

      {
        m_ndf = ndf;
      }

◆ shiftPeriod()

double shiftPeriod ( int nPeriods )

inline

Adjust the arclength measure to start n periods later.

Returns: The arc length needed to travel n periods.

Definition at line 327 of file UncertainHelix.h.

      {
        double arcLength2D = m_helix.shiftPeriod(nPeriods);
        SZJacobian szJacobian = m_helix.szLine().passiveMoveByJacobian(Vector2D(arcLength2D, 0));
        PerigeeJacobian perigeeJacobian = PerigeeUtil::identity();
        HelixJacobian jacobian = HelixUtil::stackBlocks(perigeeJacobian, szJacobian);
        HelixUtil::transport(jacobian, m_helixCovariance);
        return arcLength2D;
      }

◆ uncertainCircleXY()

UncertainPerigeeCircle uncertainCircleXY ( ) const

inline

Projects the helix into the xy plain carrying over the relevant parts of the convariance matrix.

Definition at line 225 of file UncertainHelix.h.

      {
        return UncertainPerigeeCircle(helix().circleXY(),
                                      HelixUtil::getPerigeeCovariance(helixCovariance()));
      }

◆ uncertainSZLine()

UncertainSZLine uncertainSZLine ( ) const

inline

Reduces the helix to an sz line carrying over the relevant parts of the convariance matrix.

Definition at line 233 of file UncertainHelix.h.

      {
        return UncertainSZLine(helix().szLine(), HelixUtil::getSZCovariance(helixCovariance()));
      }

◆ variance()

double variance ( const EHelixParameter & i ) const

inline

Getter for individual diagonal elements of the covariance matrix.

Definition at line 257 of file UncertainHelix.h.

      {
        return helixCovariance()(i, i);
      }

Member Data Documentation

◆ m_chi2

double m_chi2 = 0.0

private

Memory for the chi square value of the fit of this helix.

Definition at line 345 of file UncertainHelix.h.

◆ m_helix

Helix m_helix

private

Memory for the underlying helix.

Definition at line 339 of file UncertainHelix.h.

◆ m_helixCovariance

HelixCovariance m_helixCovariance = HelixUtil::identity()

private

Memory for the 5x5 covariance matrix of the helix parameters.

Definition at line 342 of file UncertainHelix.h.

◆ m_ndf

size_t m_ndf = 0.0

private

Memory for the number of degrees of freedom of the fit of this helix.

Definition at line 348 of file UncertainHelix.h.

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

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

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ UncertainHelix() [1/6]

◆ UncertainHelix() [2/6]

◆ UncertainHelix() [3/6]

◆ UncertainHelix() [4/6]

◆ UncertainHelix() [5/6]

◆ UncertainHelix() [6/6]

Member Function Documentation

◆ average() [1/4]

◆ average() [2/4]

◆ average() [3/4]

◆ average() [4/4]

◆ chi2()

◆ covariance()

◆ helix()

◆ helixCovariance()

◆ helixParameters()

◆ invalidate()

◆ ndf()

◆ operator const Helix &()

◆ operator->()

◆ passiveMoveBy()

◆ reverse()

◆ reversed()

◆ setChi2()

◆ setHelixCovariance()

◆ setNDF()

◆ shiftPeriod()

◆ uncertainCircleXY()

◆ uncertainSZLine()

◆ variance()

Member Data Documentation

◆ m_chi2

◆ m_helix

◆ m_helixCovariance

◆ m_ndf