Amg Namespace Reference

Classes
struct	CalculateCompressedSize
struct	CalculateCompressedSize< 1 >
struct	Vector3DComparer
struct	VectorVector3DComparer
Typedefs
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	MatrixX
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	SymMatrixX
typedef Eigen::Matrix< double, Eigen::Dynamic, 1 >	VectorX
typedef Eigen::Quaternion< double >	Rotation3D
typedef Eigen::Translation < double, 3 >	Translation3D
typedef Eigen::AngleAxisd	AngleAxis3D
typedef Eigen::Affine3d	Transform3D
typedef Eigen::Matrix< double, 3, 1 >	Vector3D
typedef Eigen::Matrix< double, 2, 1 >	Vector2D
typedef Eigen::Matrix< double, 3, 3 >	RotationMatrix3D
typedef std::set < Amg::Vector3D, Vector3DComparer >	SetVector3D
typedef std::set< std::vector < Amg::Vector3D > , VectorVector3DComparer >	SetVectorVector3D
Enumerations
enum	AxisDefs {   x = 0, y = 1, z = 2, px = 0,   py = 1, pz = 2 }
Functions
double	error (const Amg::MatrixX &mat, int index)
template<int N>
double	error (const AmgSymMatrix(N)&mat, int index)
template<int N>
void	compress (const AmgSymMatrix(N)&covMatrix, std::vector< float > &vec)
void	compress (const MatrixX &covMatrix, std::vector< float > &vec)
template<int N>
void	expand (std::vector< float >::const_iterator it, std::vector< float >::const_iterator, AmgSymMatrix(N)&covMatrix)
void	expand (std::vector< float >::const_iterator it, std::vector< float >::const_iterator it_end, MatrixX &covMatrix)
template<int N>
double	largestDifference (const AmgSymMatrix(N)&m1, const AmgSymMatrix(N)&m2, bool relative=false)
template<int N>
int	largestDifference (const AmgVector(N)&m1, const AmgVector(N)&m2, bool relative=false)
template<int N>
std::pair< int, int >	compare (const AmgSymMatrix(N)&m1, const AmgSymMatrix(N)&m2, double precision=1e-9, bool relative=false)
template<int N>
int	compare (const AmgVector(N)&m1, const AmgVector(N)&m2, double precision=1e-9, bool relative=false)
template<int N>
bool	isSymMatrix (const AmgSymMatrix(N)&m)
double	roundWithPrecision (double val, int precision)
std::string	toString (const MatrixX &matrix, int precision=4, std::string offset="")
std::string	toString (const CLHEP::HepGenMatrix &matrix, int precision=4, std::string offset="")
template<class T >
std::string	AsString (const T &m)
Amg::Transform3D	CLHEPTransformToEigen (const HepGeom::Transform3D &CLHEPtransf)
RotationMatrix3D	CLHEPRotationToEigen (const CLHEP::HepRotation &CLHEProtation)
Translation3D	CLHEPTranslationToEigen (const CLHEP::Hep3Vector &CLHEPtranslation)
Amg::Transform3D	CLHEPTranslate3DToEigen (const HepGeom::Translate3D &CLHEPtranslate3D)
HepGeom::Transform3D	EigenTransformToCLHEP (const Amg::Transform3D &eigenTransf)
Amg::Vector3D	Hep3VectorToEigen (const CLHEP::Hep3Vector &CLHEPvector)
CLHEP::Hep3Vector	EigenToHep3Vector (const Amg::Vector3D &eigenvector)
Amg::Vector3D	convert_CLHEPPhiThetaPsi_to_EigenEulerAngles (Amg::Vector3D clhep_angles, int convention=0)
Amg::Vector3D	convert_EigenEulerAngles_to_CLHEPPhiThetaPsi (Amg::Vector3D eigen_angles, int convention=0)
Amg::Vector3D	getPhiThetaPsi (Amg::RotationMatrix3D mat, int convention=0)
Amg::RotationMatrix3D	setPhi (Amg::RotationMatrix3D mat, double angle, int convention=0)
double	angle (const Amg::Vector3D &v1, const Amg::Vector3D &v2)
float	distance2 (const Amg::Vector3D &p1, const Amg::Vector3D &p2)
float	distance (const Amg::Vector3D &p1, const Amg::Vector3D &p2)
void	setPhi (Amg::Vector3D &v, double phi)
void	setThetaPhi (Amg::Vector3D &v, double theta, double phi)
void	setRThetaPhi (Amg::Vector3D &v, double r, double theta, double phi)
void	setTheta (Amg::Vector3D &v, double theta)
void	setPerp (Amg::Vector3D &v, double perp)
void	setMag (Amg::Vector3D &v, double mag)
double	deltaPhi (const Amg::Vector3D &v1, const Amg::Vector3D &v2)
double	deltaR (const Amg::Vector3D &v1, const Amg::Vector3D &v2)
void	setVector3DCartesian (Amg::Vector3D &v1, double x1, double y1, double z1)
double	mag2Vector3D (const Amg::Vector3D &v1)
double	magVector3D (const Amg::Vector3D &v1)
double	rVector3D (const Amg::Vector3D &v1)
Amg::Vector3D	transform (Amg::Vector3D &v, Amg::Transform3D &tr)
Amg::Transform3D	getTransformFromRotTransl (Amg::RotationMatrix3D rot, Amg::Vector3D transl_vec)
void	getAngleAxisFromRotation (Amg::RotationMatrix3D &rotation, double &rotationAngle, Amg::Vector3D &rotationAxis)
Amg::Vector3D	getTranslationVectorFromTransform (const Amg::Transform3D &tr)
Amg::Rotation3D	getRotation3DfromAngleAxis (double angle, Amg::Vector3D &axis)
Amg::Transform3D	getRotateX3D (double angle)
Amg::Transform3D	getRotateY3D (double angle)
Amg::Transform3D	getRotateZ3D (double angle)
std::string	toString (const Amg::Translation3D &translation, int precision=4)
std::string	toString (const Amg::Transform3D &transform, int precision=4, std::string offset="")
std::string	toString (const CLHEP::HepRotation &rot, int precision=4, std::string offset="")
std::string	toString (const CLHEP::Hep3Vector &translation, int precision=4)
std::string	toString (const CLHEP::Hep2Vector &translation, int precision=4)
std::string	toString (const HepGeom::Transform3D &transf, int precision=4, std::string offset="")

---

Detailed Description

Event primitives helper functions

Author:

Niels van Eldik

Robert Johannes Langenberg <robert.langenberg@cern.ch>

Andreas Salzburger <Andreas.Salzburger@cern.ch>

Definition of ATLAS Math & Geometry primitives (Amg)

This is based on the Eigen geometry module: http://eigen.tuxfamily.org/dox/group__Geometry__Module.html

Author:

Robert Johannes Langenberg <robert.langenberg@cern.ch>

Andreas Salzburger <Andreas.Salzburger@cern.ch>

Geometry primitives helper functions

Author:

Niels van Eldik

Robert Johannes Langenberg <robert.langenberg@cern.ch>

Andreas Salzburger <Andreas.Salzburger@cern.ch>

---

Typedef Documentation

typedef Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> Amg::MatrixX

Dynamic Matrix - not recommended

typedef Eigen::Matrix<double, Eigen::Dynamic, 1> Amg::VectorX

Dynamic Vector - not recommended

---

Enumeration Type Documentation

enum Amg::AxisDefs

elment for code readability

• please use these for access to the member variables if needed, e.g. double z = position[Amg::z]; double px = momentum[Amg::px];

---

Function Documentation

double Amg::angle	(	const Amg::Vector3D &	v1,
		const Amg::Vector3D &	v2
	)			[inline]

calculates the opening angle between two vectors

template<class T >

std::string Amg::AsString

(

const T &

m

)

[inline]

write an Amg Eigen object to std::string

template<int N>

int Amg::compare	(	const AmgVector(N)&	m1,
		const AmgVector(N)&	m2,
		double	precision = 1e-9,
		bool	relative = false
	)			[inline]

compare two vectors, returns the indices of the first element that fails the condition, returns <-1,-1> if all is ok Users can provide the required precision and whether the difference should be evaluate relative to the values or absolutely

template<int N>

std::pair<int, int> Amg::compare	(	const AmgSymMatrix(N)&	m1,
		const AmgSymMatrix(N)&	m2,
		double	precision = 1e-9,
		bool	relative = false
	)			[inline]

compare two matrices, returns the indices of the first element that fails the condition, returns <-1,-1> if all is ok Users can provide the required precision and whether the difference should be evaluate relative to the values or absolutely

Amg::Vector3D Amg::convert_CLHEPPhiThetaPsi_to_EigenEulerAngles	(	Amg::Vector3D	clhep_angles,
		int	convention = 0
	)			[inline]

Convert CLEHP Phi,Theta,Psi angles to Eigen euler angles using Z-X-Z convention

N.B. if "convention = 0" --> "Z-X-Z" convention ==> DEFAULT!! if "convention = 1" --> "Z-Y-Z"

Amg::Vector3D Amg::convert_EigenEulerAngles_to_CLHEPPhiThetaPsi	(	Amg::Vector3D	eigen_angles,
		int	convention = 0
	)			[inline]

Convert Eigen euler angles to CLEHP Phi,Theta,Psi angles

N.B. if "convention = 0" --> "Z-X-Z" convention ==> DEFAULT!! if "convention = 1" --> "Z-Y-Z" convention

Note: as explained in: eigen / Eigen / src / Geometry / EulerAngles.h the returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi]

(source here: https://bitbucket.org/eigen/eigen/src/42e011583bceb055a43fa688622e828fbbabf818/Eigen/src/Geometry/EulerAngles.h)

N.B.!! CLHEP's Phi, Theta, Psi correspond to eulerAngles[2], [1] and [0] respectively, with the sign inverted.

float Amg::distance	(	const Amg::Vector3D &	p1,
		const Amg::Vector3D &	p2
	)			[inline]

calculates the distance between two point in 3D space

float Amg::distance2	(	const Amg::Vector3D &	p1,
		const Amg::Vector3D &	p2
	)			[inline]

calculates the squared distance between two point in 3D space

double Amg::error	(	const Amg::MatrixX &	mat,
		int	index
	)			[inline]

return diagonal error of the matrix caller should ensure the matrix is symmetric and the index is in range

Amg::Vector3D Amg::getPhiThetaPsi	(	Amg::RotationMatrix3D	mat,
		int	convention = 0
	)			[inline]

Get the equivalents to CLHEP Phi, Theta, Psi Euler angles

phi = vector[0] theta = vector[1] psi = vector[2]

N.B. if "convention = 0" --> "Z-X-Z" convention ==> DEFAULT!! if "convention = 1" --> "Z-Y-Z" convention

N.B.!! for normal usage, use the default notation (simply leave it empty, or use convention=0), or, alternatively, be sure to use the same convention in both setPhi() and getPhiThetaPsi().

we extract the Euler Angles from the Eigen matrix,

Amg::Transform3D Amg::getRotateX3D

(

double

angle

)

[inline]

get a rotation transformation around X-axis

Amg::Transform3D Amg::getRotateY3D

(

double

angle

)

[inline]

get a rotation transformation around Y-axis

Amg::Transform3D Amg::getRotateZ3D

(

double

angle

)

[inline]

get a rotation transformation around Z-axis

Amg::Rotation3D Amg::getRotation3DfromAngleAxis	(	double	angle,
		Amg::Vector3D &	axis
	)			[inline]

get a AngleAxis from an angle and an axis.

to replace the CLHEP constructor: CLHEP::Rotate3D::Rotate3D(double a, cconst Vector3D< double > & v)

Amg::Vector3D Amg::getTranslationVectorFromTransform

(

const Amg::Transform3D &

tr

)

[inline]

Get the Translation vector out of a Transformation

template<int N>

int Amg::largestDifference	(	const AmgVector(N)&	m1,
		const AmgVector(N)&	m2,
		bool	relative = false
	)			[inline]

get largest difference betweem two vectors Users can decide whether the difference should be evaluate relative to the values or absolutely

template<int N>

double Amg::largestDifference	(	const AmgSymMatrix(N)&	m1,
		const AmgSymMatrix(N)&	m2,
		bool	relative = false
	)			[inline]

get largest difference between two matrices Users can decide whether the difference should be evaluate relative to the values or absolutely

double Amg::mag2Vector3D

(

const Amg::Vector3D &

v1

)

[inline]

Gets magnitude squared of the vector.

double Amg::magVector3D

(

const Amg::Vector3D &

v1

)

[inline]

Gets magnitude of the vector.

double Amg::roundWithPrecision	(	double	val,
		int	precision
	)			[inline]

EventPrimitvesToStringConverter

inline methods for conversion of EventPrimitives (Matrix) to std::string.

This is to enhance formatted screen ouput and for ASCII based testing.

The offset can be used to offset the lines (starting from line 2) wrt to the zero position for formatting reasons.

Author:

Niels.Van.Eldik@cern.ch

double Amg::rVector3D

(

const Amg::Vector3D &

v1

)

[inline]

Gets r-component in spherical coordinate system

void Amg::setMag	(	Amg::Vector3D &	v,
		double	mag
	)			[inline]

scales the vector length without changing the angles

void Amg::setPerp	(	Amg::Vector3D &	v,
		double	perp
	)			[inline]

scales the vector in the xy plane without changing the z coordinate nor the angles

void Amg::setPhi	(	Amg::Vector3D &	v,
		double	phi
	)			[inline]

sets the phi angle of a vector without changing theta nor the magnitude

void Amg::setRThetaPhi	(	Amg::Vector3D &	v,
		double	r,
		double	theta,
		double	phi
	)			[inline]

sets radius, the theta and phi angle of a vector. Angles are measured in RADIANS

void Amg::setTheta	(	Amg::Vector3D &	v,
		double	theta
	)			[inline]

sets the theta of a vector without changing phi nor the magnitude

void Amg::setThetaPhi	(	Amg::Vector3D &	v,
		double	theta,
		double	phi
	)			[inline]

sets the theta and phi angle of a vector without changing the magnitude

void Amg::setVector3DCartesian	(	Amg::Vector3D &	v1,
		double	x1,
		double	y1,
		double	z1
	)			[inline]

Sets components in cartesian coordinate system.

std::string Amg::toString	(	const Amg::Translation3D &	translation,
		int	precision = 4
	)			[inline]

GeoPrimitvesToStringConverter

static methods for conversion of GeoPrimitives and will call the EventPrimitives converter (Matrix) to std::string.

This is to enhance formatted screen ouput and for ASCII based testing.

The offset can be used to offset the lines (starting from line 2) wrt to the zero position for formatting reasons.

Author:

Niels.Van.Eldik@cern.ch

Amg::Vector3D Amg::transform	(	Amg::Vector3D &	v,
		Amg::Transform3D &	tr
	)			[inline]

Transform a point from a Trasformation3D

from CLHEP::Point3D::transform: http://proj-clhep.web.cern.ch/proj-clhep/doc/CLHEP_2_0_4_7/doxygen/html/Point3D_8cc-source.html#l00032