ROOT::Math::LorentzRotation Class Reference

Lorentz transformation class with the (4D) transformation represented by a 4x4 orthosymplectic matrix.

See also Boost, BoostX, BoostY and BoostZ for classes representing specialized Lorentz transformations. Also, the 3-D rotation classes can be considered to be special Lorentz transformations which do not mix space and time components.

Definition at line 54 of file LorentzRotation.h.

Public Types
enum	ELorentzRotationMatrixIndex {   kXX = 0 , kXY = 1 , kXZ = 2 , kXT = 3 ,   kYX = 4 , kYY = 5 , kYZ = 6 , kYT = 7 ,   kZX = 8 , kZY = 9 , kZZ = 10 , kZT = 11 ,   kTX = 12 , kTY = 13 , kTZ = 14 , kTT = 15 }
typedef double	Scalar

Public Member Functions
	LorentzRotation ()
	Default constructor (identity transformation) More...
	LorentzRotation (AxisAngle const &a)
	LorentzRotation (Boost const &b)
	Construct from a pure boost. More...
	LorentzRotation (BoostX const &bx)
	LorentzRotation (BoostY const &by)
	LorentzRotation (BoostZ const &bz)
template<class Foreign4Vector >
	LorentzRotation (const Foreign4Vector &v1, const Foreign4Vector &v2, const Foreign4Vector &v3, const Foreign4Vector &v4)
	Construct from four orthosymplectic vectors (which must have methods x(), y(), z() and t()) which will be used as the columns of the Lorentz rotation matrix. More...
template<class ForeignMatrix >
	LorentzRotation (const ForeignMatrix &m)
	Construct from a linear algebra matrix of size at least 4x4, which must support operator()(i,j) to obtain elements (0,3) thru (3,3). More...
	LorentzRotation (EulerAngles const &e)
template<class IT >
	LorentzRotation (IT begin, IT end)
	Construct given a pair of pointers or iterators defining the beginning and end of an array of sixteen Scalars. More...
	LorentzRotation (LorentzRotation const &r)
	Copy constructor. More...
	LorentzRotation (Quaternion const &q)
	LorentzRotation (Rotation3D const &r)
	Construct from a 3-D rotation (no space-time mixing) More...
	LorentzRotation (RotationX const &r)
	LorentzRotation (RotationY const &r)
	LorentzRotation (RotationZ const &r)
	LorentzRotation (Scalar xx, Scalar xy, Scalar xz, Scalar xt, Scalar yx, Scalar yy, Scalar yz, Scalar yt, Scalar zx, Scalar zy, Scalar zz, Scalar zt, Scalar tx, Scalar ty, Scalar tz, Scalar tt)
	Raw constructor from sixteen Scalar components (without any checking) More...
template<class Foreign4Vector >
void	GetComponents (Foreign4Vector &v1, Foreign4Vector &v2, Foreign4Vector &v3, Foreign4Vector &v4) const
	Get components into four 4-vectors which will be the (orthosymplectic) columns of the rotation matrix. More...
template<class IT >
void	GetComponents (IT begin) const
	Get the 16 matrix components into data specified by an iterator begin. More...
template<class IT >
void	GetComponents (IT begin, IT end) const
	Get the 16 matrix components into data specified by an iterator begin and another to the end of the desired data (16 past start). More...
void	GetComponents (Scalar &xx, Scalar &xy, Scalar &xz, Scalar &xt, Scalar &yx, Scalar &yy, Scalar &yz, Scalar &yt, Scalar &zx, Scalar &zy, Scalar &zz, Scalar &zt, Scalar &tx, Scalar &ty, Scalar &tz, Scalar &tt) const
	Get the sixteen components into sixteen scalars. More...
template<class ForeignMatrix >
void	GetRotationMatrix (ForeignMatrix &m) const
	Get components into a linear algebra matrix of size at least 4x4, which must support operator()(i,j) for write access to elements (0,0) thru (3,3). More...
LorentzRotation	Inverse () const
	Return inverse of a rotation. More...
void	Invert ()
	Invert a Lorentz rotation in place. More...
bool	operator!= (const LorentzRotation &rhs) const
template<class Foreign4Vector >
Foreign4Vector	operator() (const Foreign4Vector &v) const
	Lorentz transformation operation on an arbitrary 4-vector v. More...
template<class CoordSystem >
LorentzVector< CoordSystem >	operator() (const LorentzVector< CoordSystem > &v) const
	Lorentz transformation operation on a LorentzVector in any coordinate system. More...
LorentzVector< ROOT::Math::PxPyPzE4D< double > >	operator() (const LorentzVector< ROOT::Math::PxPyPzE4D< double > > &v) const
	Lorentz transformation operation on a Minkowski ('Cartesian') LorentzVector. More...
template<class A4Vector >
A4Vector	operator* (const A4Vector &v) const
	Overload operator * for rotation on a vector. More...
LorentzRotation	operator* (const AxisAngle &a) const
LorentzRotation	operator* (const Boost &b) const
	Multiply (combine) this Lorentz rotation by a pure Lorentz boost. More...
LorentzRotation	operator* (const BoostX &b) const
LorentzRotation	operator* (const BoostY &b) const
LorentzRotation	operator* (const BoostZ &b) const
LorentzRotation	operator* (const EulerAngles &e) const
LorentzRotation	operator* (const LorentzRotation &r) const
	Multiply (combine) this Lorentz rotation by another LorentzRotation. More...
LorentzRotation	operator* (const Quaternion &q) const
LorentzRotation	operator* (const Rotation3D &r) const
	Multiply (combine) this Lorentz rotation by a 3-D Rotation. More...
LorentzRotation	operator* (const RotationX &rx) const
LorentzRotation	operator* (const RotationY &ry) const
LorentzRotation	operator* (const RotationZ &rz) const
template<class R >
LorentzRotation &	operator*= (const R &r)
	Post-Multiply (on right) by another LorentzRotation, Boost, or rotation : T = T*R. More...
LorentzRotation &	operator= (AxisAngle const &a)
LorentzRotation &	operator= (Boost const &b)
	Assign from a pure boost. More...
LorentzRotation &	operator= (BoostX const &b)
LorentzRotation &	operator= (BoostY const &b)
LorentzRotation &	operator= (BoostZ const &b)
template<class ForeignMatrix >
LorentzRotation &	operator= (const ForeignMatrix &m)
	Assign from a linear algebra matrix of size at least 4x4, which must support operator()(i,j) to obtain elements (0,3) thru (3,3). More...
LorentzRotation &	operator= (EulerAngles const &e)
LorentzRotation &	operator= (LorentzRotation const &rhs)
	Assign from another LorentzRotation. More...
LorentzRotation &	operator= (Quaternion const &q)
LorentzRotation &	operator= (Rotation3D const &r)
	Assign from a 3-D rotation. More...
LorentzRotation &	operator= (RotationX const &r)
LorentzRotation &	operator= (RotationY const &r)
LorentzRotation &	operator= (RotationZ const &r)
bool	operator== (const LorentzRotation &rhs) const
	Equality/inequality operators. More...
void	Rectify ()
	Re-adjust components to eliminate small deviations from a perfect orthosyplectic matrix. More...
template<class Foreign4Vector >
void	SetComponents (const Foreign4Vector &v1, const Foreign4Vector &v2, const Foreign4Vector &v3, const Foreign4Vector &v4)
	Set components from four orthosymplectic vectors (which must have methods x(), y(), z(), and t()) which will be used as the columns of the Lorentz rotation matrix. More...
template<class IT >
void	SetComponents (IT begin, IT end)
	Set the 16 matrix components given an iterator to the start of the desired data, and another to the end (16 past start). More...
void	SetComponents (Scalar xx, Scalar xy, Scalar xz, Scalar xt, Scalar yx, Scalar yy, Scalar yz, Scalar yt, Scalar zx, Scalar zy, Scalar zz, Scalar zt, Scalar tx, Scalar ty, Scalar tz, Scalar tt)
	Set the components from sixteen scalars – UNCHECKED for orthosymplectic. More...
template<class ForeignMatrix >
void	SetRotationMatrix (const ForeignMatrix &m)
	Set components from a linear algebra matrix of size at least 4x4, which must support operator()(i,j) to obtain elements (0,0) thru (3,3). More...

Private Attributes
Scalar	fM [16]

#include <Math/GenVector/LorentzRotation.h>

Member Typedef Documentation

Scalar

typedef double ROOT::Math::LorentzRotation::Scalar

Definition at line 58 of file LorentzRotation.h.

Member Enumeration Documentation

ELorentzRotationMatrixIndex

enum ROOT::Math::LorentzRotation::ELorentzRotationMatrixIndex

Enumerator
kXX
kXY
kXZ
kXT
kYX
kYY
kYZ
kYT
kZX
kZY
kZZ
kZT
kTX
kTY
kTZ
kTT

Definition at line 60 of file LorentzRotation.h.

Constructor & Destructor Documentation

LorentzRotation() [1/17]

ROOT::Math::LorentzRotation::LorentzRotation

(

)

Default constructor (identity transformation)

Definition at line 36 of file LorentzRotation.cxx.

LorentzRotation() [2/17]

template<class IT >

ROOT::Math::LorentzRotation::LorentzRotation ( IT  begin, IT  end  )

inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of sixteen Scalars.

Definition at line 79 of file LorentzRotation.h.

LorentzRotation() [3/17]

ROOT::Math::LorentzRotation::LorentzRotation ( LorentzRotation const &  r )

inline

Copy constructor.

Definition at line 87 of file LorentzRotation.h.

LorentzRotation() [4/17]

ROOT::Math::LorentzRotation::LorentzRotation ( Boost const &  b )

inlineexplicit

Construct from a pure boost.

Definition at line 94 of file LorentzRotation.h.

LorentzRotation() [5/17]

ROOT::Math::LorentzRotation::LorentzRotation ( BoostX const &  bx )

inlineexplicit

Definition at line 95 of file LorentzRotation.h.

LorentzRotation() [6/17]

ROOT::Math::LorentzRotation::LorentzRotation ( BoostY const &  by )

inlineexplicit

Definition at line 96 of file LorentzRotation.h.

LorentzRotation() [7/17]

ROOT::Math::LorentzRotation::LorentzRotation ( BoostZ const &  bz )

inlineexplicit

Definition at line 97 of file LorentzRotation.h.

LorentzRotation() [8/17]

ROOT::Math::LorentzRotation::LorentzRotation ( Rotation3D const &  r )

explicit

Construct from a 3-D rotation (no space-time mixing)

Definition at line 44 of file LorentzRotation.cxx.

LorentzRotation() [9/17]

ROOT::Math::LorentzRotation::LorentzRotation ( AxisAngle const &  a )

explicit

Definition at line 55 of file LorentzRotation.cxx.

LorentzRotation() [10/17]

ROOT::Math::LorentzRotation::LorentzRotation ( EulerAngles const &  e )

explicit

Definition at line 67 of file LorentzRotation.cxx.

LorentzRotation() [11/17]

ROOT::Math::LorentzRotation::LorentzRotation ( Quaternion const &  q )

explicit

Definition at line 79 of file LorentzRotation.cxx.

LorentzRotation() [12/17]

ROOT::Math::LorentzRotation::LorentzRotation ( RotationX const &  r )

explicit

Definition at line 91 of file LorentzRotation.cxx.

LorentzRotation() [13/17]

ROOT::Math::LorentzRotation::LorentzRotation ( RotationY const &  r )

explicit

Definition at line 101 of file LorentzRotation.cxx.

LorentzRotation() [14/17]

ROOT::Math::LorentzRotation::LorentzRotation ( RotationZ const &  r )

explicit

Definition at line 111 of file LorentzRotation.cxx.

LorentzRotation() [15/17]

template<class ForeignMatrix >

ROOT::Math::LorentzRotation::LorentzRotation ( const ForeignMatrix &  m )

inlineexplicit

Construct from a linear algebra matrix of size at least 4x4, which must support operator()(i,j) to obtain elements (0,3) thru (3,3).

Precondition: The matrix is assumed to be orthosymplectic. NO checking or re-adjusting is performed. Note: (0,0) refers to the XX component; (3,3) refers to the TT component.

Definition at line 118 of file LorentzRotation.h.

LorentzRotation() [16/17]

template<class Foreign4Vector >

ROOT::Math::LorentzRotation::LorentzRotation ( const Foreign4Vector &  v1, const Foreign4Vector &  v2, const Foreign4Vector &  v3, const Foreign4Vector &  v4  )

inline

Construct from four orthosymplectic vectors (which must have methods x(), y(), z() and t()) which will be used as the columns of the Lorentz rotation matrix.

The orthosymplectic conditions will be checked, and values adjusted so that the result will always be a good Lorentz rotation matrix.

Definition at line 128 of file LorentzRotation.h.

LorentzRotation() [17/17]

ROOT::Math::LorentzRotation::LorentzRotation ( Scalar  xx, Scalar  xy, Scalar  xz, Scalar  xt, Scalar  yx, Scalar  yy, Scalar  yz, Scalar  yt, Scalar  zx, Scalar  zy, Scalar  zz, Scalar  zt, Scalar  tx, Scalar  ty, Scalar  tz, Scalar  tt  )

inline

Raw constructor from sixteen Scalar components (without any checking)

Definition at line 137 of file LorentzRotation.h.

Member Function Documentation

GetComponents() [1/4]

template<class Foreign4Vector >

void ROOT::Math::LorentzRotation::GetComponents ( Foreign4Vector &  v1, Foreign4Vector &  v2, Foreign4Vector &  v3, Foreign4Vector &  v4  ) const

inline

Get components into four 4-vectors which will be the (orthosymplectic) columns of the rotation matrix.

(The 4-vector class must have a constructor from 4 Scalars used as x, y, z, t)

Definition at line 240 of file LorentzRotation.h.

GetComponents() [2/4]

template<class IT >

void ROOT::Math::LorentzRotation::GetComponents ( IT  begin ) const

inline

Get the 16 matrix components into data specified by an iterator begin.

Definition at line 282 of file LorentzRotation.h.

GetComponents() [3/4]

template<class IT >

void ROOT::Math::LorentzRotation::GetComponents ( IT  begin, IT  end  ) const

inline

Get the 16 matrix components into data specified by an iterator begin and another to the end of the desired data (16 past start).

Definition at line 269 of file LorentzRotation.h.

GetComponents() [4/4]

void ROOT::Math::LorentzRotation::GetComponents ( Scalar &  xx, Scalar &  xy, Scalar &  xz, Scalar &  xt, Scalar &  yx, Scalar &  yy, Scalar &  yz, Scalar &  yt, Scalar &  zx, Scalar &  zy, Scalar &  zz, Scalar &  zt, Scalar &  tx, Scalar &  ty, Scalar &  tz, Scalar &  tt  ) const

inline

Get the sixteen components into sixteen scalars.

Definition at line 333 of file LorentzRotation.h.

GetRotationMatrix()

template<class ForeignMatrix >

void ROOT::Math::LorentzRotation::GetRotationMatrix ( ForeignMatrix &  m ) const

inline

Get components into a linear algebra matrix of size at least 4x4, which must support operator()(i,j) for write access to elements (0,0) thru (3,3).

Definition at line 308 of file LorentzRotation.h.

Inverse()

LorentzRotation ROOT::Math::LorentzRotation::Inverse

(

)

const

Return inverse of a rotation.

Definition at line 186 of file LorentzRotation.cxx.

Invert()

void ROOT::Math::LorentzRotation::Invert

(

)

Invert a Lorentz rotation in place.

Definition at line 175 of file LorentzRotation.cxx.

operator!=()

bool ROOT::Math::LorentzRotation::operator!= ( const LorentzRotation &  rhs ) const

inline

Definition at line 453 of file LorentzRotation.h.

operator()() [1/3]

template<class Foreign4Vector >

Foreign4Vector ROOT::Math::LorentzRotation::operator() ( const Foreign4Vector &  v ) const

inline

Lorentz transformation operation on an arbitrary 4-vector v.

Preconditions: v must implement methods x(), y(), z(), and t() and the arbitrary vector type must have a constructor taking (x,y,z,t)

Definition at line 381 of file LorentzRotation.h.

operator()() [2/3]

template<class CoordSystem >

LorentzVector< CoordSystem > ROOT::Math::LorentzRotation::operator() ( const LorentzVector< CoordSystem > &  v ) const

inline

Lorentz transformation operation on a LorentzVector in any coordinate system.

Definition at line 368 of file LorentzRotation.h.

operator()() [3/3]

LorentzVector< ROOT::Math::PxPyPzE4D< double > > ROOT::Math::LorentzRotation::operator() ( const LorentzVector< ROOT::Math::PxPyPzE4D< double > > &  v ) const

inline

Lorentz transformation operation on a Minkowski ('Cartesian') LorentzVector.

Definition at line 350 of file LorentzRotation.h.

operator*() [1/13]

template<class A4Vector >

A4Vector ROOT::Math::LorentzRotation::operator* ( const A4Vector &  v ) const

inline

Overload operator * for rotation on a vector.

Definition at line 392 of file LorentzRotation.h.

operator*() [2/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const AxisAngle &  a ) const

inline

Definition at line 429 of file LorentzRotation.h.

operator*() [3/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const Boost &  b ) const

inline

Multiply (combine) this Lorentz rotation by a pure Lorentz boost.

Definition at line 420 of file LorentzRotation.h.

operator*() [4/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const BoostX &  b ) const

inline

Definition at line 421 of file LorentzRotation.h.

operator*() [5/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const BoostY &  b ) const

inline

Definition at line 422 of file LorentzRotation.h.

operator*() [6/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const BoostZ &  b ) const

inline

Definition at line 423 of file LorentzRotation.h.

operator*() [7/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const EulerAngles &  e ) const

inline

Definition at line 430 of file LorentzRotation.h.

operator*() [8/13]

LorentzRotation ROOT::Math::LorentzRotation::operator*

(

const LorentzRotation &

r

)

const

Multiply (combine) this Lorentz rotation by another LorentzRotation.

Definition at line 196 of file LorentzRotation.cxx.

operator*() [9/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const Quaternion &  q ) const

inline

Definition at line 431 of file LorentzRotation.h.

operator*() [10/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const Rotation3D &  r ) const

inline

Multiply (combine) this Lorentz rotation by a 3-D Rotation.

Definition at line 428 of file LorentzRotation.h.

operator*() [11/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const RotationX &  rx ) const

inline

Definition at line 432 of file LorentzRotation.h.

operator*() [12/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const RotationY &  ry ) const

inline

Definition at line 433 of file LorentzRotation.h.

operator*() [13/13]

LorentzRotation ROOT::Math::LorentzRotation::operator* ( const RotationZ &  rz ) const

inline

Definition at line 434 of file LorentzRotation.h.

operator*=()

template<class R >

LorentzRotation & ROOT::Math::LorentzRotation::operator*= ( const R &  r )

inline

Post-Multiply (on right) by another LorentzRotation, Boost, or rotation : T = T*R.

Definition at line 442 of file LorentzRotation.h.

operator=() [1/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( AxisAngle const &  a )

inline

Definition at line 178 of file LorentzRotation.h.

operator=() [2/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( Boost const &  b )

inline

Assign from a pure boost.

Definition at line 164 of file LorentzRotation.h.

operator=() [3/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( BoostX const &  b )

inline

Definition at line 166 of file LorentzRotation.h.

operator=() [4/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( BoostY const &  b )

inline

Definition at line 168 of file LorentzRotation.h.

operator=() [5/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( BoostZ const &  b )

inline

Definition at line 170 of file LorentzRotation.h.

operator=() [6/13]

template<class ForeignMatrix >

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( const ForeignMatrix &  m )

inline

Assign from a linear algebra matrix of size at least 4x4, which must support operator()(i,j) to obtain elements (0,3) thru (3,3).

Precondition: The matrix is assumed to be orthosymplectic. NO checking or re-adjusting is performed.

Definition at line 198 of file LorentzRotation.h.

operator=() [7/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( EulerAngles const &  e )

inline

Definition at line 180 of file LorentzRotation.h.

operator=() [8/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( LorentzRotation const &  rhs )

inline

Assign from another LorentzRotation.

Definition at line 152 of file LorentzRotation.h.

operator=() [9/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( Quaternion const &  q )

inline

Definition at line 182 of file LorentzRotation.h.

operator=() [10/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( Rotation3D const &  r )

inline

Assign from a 3-D rotation.

Definition at line 176 of file LorentzRotation.h.

operator=() [11/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( RotationX const &  r )

inline

Definition at line 188 of file LorentzRotation.h.

operator=() [12/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( RotationY const &  r )

inline

Definition at line 186 of file LorentzRotation.h.

operator=() [13/13]

LorentzRotation & ROOT::Math::LorentzRotation::operator= ( RotationZ const &  r )

inline

Definition at line 184 of file LorentzRotation.h.

operator==()

bool ROOT::Math::LorentzRotation::operator== ( const LorentzRotation &  rhs ) const

inline

Equality/inequality operators.

Definition at line 447 of file LorentzRotation.h.

Rectify()

void ROOT::Math::LorentzRotation::Rectify

(

)

Re-adjust components to eliminate small deviations from a perfect orthosyplectic matrix.

Definition at line 122 of file LorentzRotation.cxx.

SetComponents() [1/3]

template<class Foreign4Vector >

void ROOT::Math::LorentzRotation::SetComponents ( const Foreign4Vector &  v1, const Foreign4Vector &  v2, const Foreign4Vector &  v3, const Foreign4Vector &  v4  )

inline

Set components from four orthosymplectic vectors (which must have methods x(), y(), z(), and t()) which will be used as the columns of the Lorentz rotation matrix.

The values will be adjusted so that the result will always be a good Lorentz rotation matrix.

Definition at line 222 of file LorentzRotation.h.

SetComponents() [2/3]

template<class IT >

void ROOT::Math::LorentzRotation::SetComponents ( IT  begin, IT  end  )

inline

Set the 16 matrix components given an iterator to the start of the desired data, and another to the end (16 past start).

Definition at line 255 of file LorentzRotation.h.

SetComponents() [3/3]

void ROOT::Math::LorentzRotation::SetComponents ( Scalar  xx, Scalar  xy, Scalar  xz, Scalar  xt, Scalar  yx, Scalar  yy, Scalar  yz, Scalar  yt, Scalar  zx, Scalar  zy, Scalar  zz, Scalar  zt, Scalar  tx, Scalar  ty, Scalar  tz, Scalar  tt  )

inline

Set the components from sixteen scalars – UNCHECKED for orthosymplectic.

Definition at line 319 of file LorentzRotation.h.

SetRotationMatrix()

template<class ForeignMatrix >

void ROOT::Math::LorentzRotation::SetRotationMatrix ( const ForeignMatrix &  m )

inline

Set components from a linear algebra matrix of size at least 4x4, which must support operator()(i,j) to obtain elements (0,0) thru (3,3).

Precondition: The matrix is assumed to be orthosymplectic. NO checking or re-adjusting is performed.

Definition at line 294 of file LorentzRotation.h.

Member Data Documentation

fM

Scalar ROOT::Math::LorentzRotation::fM[16]

private

Definition at line 459 of file LorentzRotation.h.

Libraries for ROOT::Math::LorentzRotation:

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