The TLorentzRotation class describes Lorentz transformations including Lorentz boosts and rotations (see TRotation)

         | xx  xy  xz  xt |
         |                |
         | yx  yy  yz  yt |
lambda = |                |
         | zx  zy  zz  zt |
         |                |
         | tx  ty  tz  tt |

Declaration

By default it is initialized to the identity matrix, but it may also be intialized by an other TLorentzRotation, by a pure TRotation or by a boost:

TLorentzRotation l; // l is initialized as identity TLorentzRotation m(l); // m = l TRotation r; TLorentzRotation lr(r); TLorentzRotation lb1(bx,by,bz); TVector3 b; TLorentzRotation lb2(b);

The Matrix for a Lorentz boosts is:

| 1+gamma'*bx*bx  gamma'*bx*by   gamma'*bx*bz  gamma*bx |
|  gamma'*by*bx  1+gamma'*by*by  gamma'*by*bz  gamma*by |
|  gamma'*bz*bx   gamma'*bz*by  1+gamma'*bz*bz gamma*bz |
|    gamma*bx       gamma*by       gamma*bz     gamma   |

with the boost vector b=(bx,by,bz) and gamma=1/Sqrt(1-beta*beta) and gamma'=(gamma-1)/beta*beta.

Access to the matrix components/Comparisons

Access to the matrix components is possible through the member functions XX(), XY() .. TT(), through the operator (int,int):

Double_t xx;
TLorentzRotation l;
xx = l.XX(); // gets the xx component
xx = l(0,0); // gets the xx component
if (l==m) {...} // test for equality
if (l !=m) {...} // test for inequality
if (l.IsIdentity()) {...} // test for identity

Transformations of a LorentzRotation

Compound transformations

There are four possibilities to find the product of two TLorentzRotation transformations:

TLorentzRotation a,b,c;
c = b*a;// product
c = a.MatrixMultiplication(b); // a is unchanged
a *= b;// Attention: a=a*b
c = a.Transform(b)// a=b*a then c=a

Lorentz boosts

Double_t bx, by, bz;
TVector3 v(bx,by,bz);
TLorentzRotation l;
l.Boost(v);
l.Boost(bx,by,bz);

Rotations

TVector3 axis;
l.RotateX(TMath::Pi()); // rotation around x-axis
l.Rotate(.5,axis);// rotation around specified vector

Inverse transformation

The matrix for the inverse transformation of a TLorentzRotation is as follows:

| xx  yx  zx -tx |
|                |
| xy  yy  zy -ty |
|                |
| xz  yz  zz -tz |
|                |
|-xt -yt -zt  tt |

To return the inverse transformation keeping the current unchanged use the member function Inverse(). Invert() inverts the current TLorentzRotation:

l1 = l2.Inverse(); // l1 is inverse of l2, l2 unchanged

l1 = l2.Invert(); // invert l2, then l1=l2

Transformation of a TLorentzVector

To apply TLorentzRotation to TLorentzVector you can use either the VectorMultiplication() member function or the * operator. You can also use the Transform() function and the *= operator of the TLorentzVector class.:

TLorentzVector v;
...
v=l.VectorMultiplication(v);
v = l * v;
v.Transform(l);
v *= l; // Attention v = l*v

Definition at line 24 of file TLorentzRotation.h.

Classes
class	TLorentzRotationRow

Public Member Functions
	TLorentzRotation ()

	TLorentzRotation (const TRotation &)

	TLorentzRotation (const TLorentzRotation &)

	TLorentzRotation (Double_t, Double_t, Double_t)

	TLorentzRotation (const TVector3 &)

TLorentzRotation &	Boost (Double_t, Double_t, Double_t)

TLorentzRotation &	Boost (const TVector3 &)

TLorentzRotation	Inverse () const

TLorentzRotation &	Invert ()

Bool_t	IsIdentity () const

TLorentzRotation	MatrixMultiplication (const TLorentzRotation &) const

Bool_t	operator!= (const TLorentzRotation &) const

Double_t	operator() (int, int) const

TLorentzVector	operator* (const TLorentzVector &) const

TLorentzRotation	operator* (const TLorentzRotation &) const

TLorentzRotation &	operator*= (const TLorentzRotation &)

TLorentzRotation &	operator= (const TLorentzRotation &)

TLorentzRotation &	operator= (const TRotation &)

Bool_t	operator== (const TLorentzRotation &) const

TLorentzRotationRow	operator[] (int) const

TLorentzRotation &	Rotate (Double_t, const TVector3 &)

TLorentzRotation &	Rotate (Double_t, const TVector3 *)

TLorentzRotation &	RotateX (Double_t)

TLorentzRotation &	RotateY (Double_t)

TLorentzRotation &	RotateZ (Double_t)

TLorentzRotation &	Transform (const TLorentzRotation &)

TLorentzRotation &	Transform (const TRotation &)

Double_t	TT () const

Double_t	TX () const

Double_t	TY () const

Double_t	TZ () const

TLorentzVector	VectorMultiplication (const TLorentzVector &) const

Double_t	XT () const

Double_t	XX () const

Double_t	XY () const

Double_t	XZ () const

Double_t	YT () const

Double_t	YX () const

Double_t	YY () const

Double_t	YZ () const

Double_t	ZT () const

Double_t	ZX () const

Double_t	ZY () const

Double_t	ZZ () const

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current pad. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

void	SetBit (UInt_t f)

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Protected Member Functions
	TLorentzRotation (Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t)

void	SetBoost (Double_t, Double_t, Double_t)

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

Protected Attributes
Double_t	ftt

Double_t	ftx

Double_t	fty

Double_t	ftz

Double_t	fxt

Double_t	fxx

Double_t	fxy

Double_t	fxz

Double_t	fyt

Double_t	fyx

Double_t	fyy

Double_t	fyz

Double_t	fzt

Double_t	fzx

Double_t	fzy

Double_t	fzz

Additional Inherited Members
Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

#include <TLorentzRotation.h>

Inheritance diagram for TLorentzRotation:

[legend]

Constructor & Destructor Documentation

TLorentzRotation::TLorentzRotation ( )

Definition at line 137 of file TLorentzRotation.cxx.

TLorentzRotation::TLorentzRotation ( const TRotation & r )

Definition at line 143 of file TLorentzRotation.cxx.

TLorentzRotation::TLorentzRotation ( const TLorentzRotation & r )

Definition at line 149 of file TLorentzRotation.cxx.

TLorentzRotation::TLorentzRotation	(	Double_t	bx,
		Double_t	by,
		Double_t	bz
	)

Definition at line 165 of file TLorentzRotation.cxx.

TLorentzRotation::TLorentzRotation ( const TVector3 & p )

Definition at line 173 of file TLorentzRotation.cxx.

TLorentzRotation::TLorentzRotation	(	Double_t	rxx,
		Double_t	rxy,
		Double_t	rxz,
		Double_t	rxt,
		Double_t	ryx,
		Double_t	ryy,
		Double_t	ryz,
		Double_t	ryt,
		Double_t	rzx,
		Double_t	rzy,
		Double_t	rzz,
		Double_t	rzt,
		Double_t	rtx,
		Double_t	rty,
		Double_t	rtz,
		Double_t	rtt
	)

protected

Definition at line 155 of file TLorentzRotation.cxx.

Member Function Documentation

TLorentzRotation & TLorentzRotation::Boost	(	Double_t	bx,
		Double_t	by,
		Double_t	bz
	)

inline

Definition at line 282 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::Boost ( const TVector3 & b )

inline

Definition at line 286 of file TLorentzRotation.h.

TLorentzRotation TLorentzRotation::Inverse ( ) const

inline

Definition at line 271 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::Invert ( )

inline

Definition at line 278 of file TLorentzRotation.h.

Bool_t TLorentzRotation::IsIdentity ( ) const

inline

Definition at line 235 of file TLorentzRotation.h.

TLorentzRotation TLorentzRotation::MatrixMultiplication ( const TLorentzRotation & b ) const

Definition at line 222 of file TLorentzRotation.cxx.

Bool_t TLorentzRotation::operator!= ( const TLorentzRotation & r ) const

inline

Definition at line 227 of file TLorentzRotation.h.

Double_t TLorentzRotation::operator()	(	int	i,
		int	j
	)		const

Definition at line 178 of file TLorentzRotation.cxx.

TLorentzVector TLorentzRotation::operator* ( const TLorentzVector & p ) const

inline

Definition at line 251 of file TLorentzRotation.h.

TLorentzRotation TLorentzRotation::operator* ( const TLorentzRotation & m ) const

inline

Definition at line 255 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::operator*= ( const TLorentzRotation & m )

inline

Definition at line 259 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::operator= ( const TLorentzRotation & r )

inline

Definition at line 175 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::operator= ( const TRotation & r )

inline

Definition at line 192 of file TLorentzRotation.h.

Bool_t TLorentzRotation::operator== ( const TLorentzRotation & r ) const

inline

Definition at line 210 of file TLorentzRotation.h.

TLorentzRotation::TLorentzRotationRow TLorentzRotation::operator[] ( int i ) const

inline

Definition at line 171 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::Rotate	(	Double_t	angle,
		const TVector3 &	axis
	)

inline

Definition at line 302 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::Rotate	(	Double_t	angle,
		const TVector3 *	axis
	)

inline

Definition at line 306 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::RotateX ( Double_t angle )

inline

Definition at line 290 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::RotateY ( Double_t angle )

inline

Definition at line 294 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::RotateZ ( Double_t angle )

inline

Definition at line 298 of file TLorentzRotation.h.

void TLorentzRotation::SetBoost	(	Double_t	bx,
		Double_t	by,
		Double_t	bz
	)

protected

Definition at line 205 of file TLorentzRotation.cxx.

TLorentzRotation & TLorentzRotation::Transform ( const TLorentzRotation & m )

inline

Definition at line 263 of file TLorentzRotation.h.

TLorentzRotation & TLorentzRotation::Transform ( const TRotation & m )

inline

Definition at line 267 of file TLorentzRotation.h.

Double_t TLorentzRotation::TT ( ) const

inline

Definition at line 162 of file TLorentzRotation.h.

Double_t TLorentzRotation::TX ( ) const

inline

Definition at line 159 of file TLorentzRotation.h.

Double_t TLorentzRotation::TY ( ) const

inline

Definition at line 160 of file TLorentzRotation.h.

Double_t TLorentzRotation::TZ ( ) const

inline

Definition at line 161 of file TLorentzRotation.h.

TLorentzVector TLorentzRotation::VectorMultiplication ( const TLorentzVector & p ) const

inline

Definition at line 244 of file TLorentzRotation.h.

Double_t TLorentzRotation::XT ( ) const

inline

Definition at line 150 of file TLorentzRotation.h.

Double_t TLorentzRotation::XX ( ) const

inline

Definition at line 147 of file TLorentzRotation.h.

Double_t TLorentzRotation::XY ( ) const

inline

Definition at line 148 of file TLorentzRotation.h.

Double_t TLorentzRotation::XZ ( ) const

inline

Definition at line 149 of file TLorentzRotation.h.

Double_t TLorentzRotation::YT ( ) const

inline

Definition at line 154 of file TLorentzRotation.h.

Double_t TLorentzRotation::YX ( ) const

inline

Definition at line 151 of file TLorentzRotation.h.

Double_t TLorentzRotation::YY ( ) const

inline

Definition at line 152 of file TLorentzRotation.h.

Double_t TLorentzRotation::YZ ( ) const

inline

Definition at line 153 of file TLorentzRotation.h.

Double_t TLorentzRotation::ZT ( ) const

inline

Definition at line 158 of file TLorentzRotation.h.

Double_t TLorentzRotation::ZX ( ) const

inline

Definition at line 155 of file TLorentzRotation.h.

Double_t TLorentzRotation::ZY ( ) const

inline

Definition at line 156 of file TLorentzRotation.h.

Double_t TLorentzRotation::ZZ ( ) const

inline

Definition at line 157 of file TLorentzRotation.h.

Member Data Documentation

Double_t TLorentzRotation::ftt

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::ftx

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fty

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::ftz

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fxt

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fxx

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fxy

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fxz

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fyt

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fyx

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fyy

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fyz

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fzt

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fzx

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fzy

protected

Definition at line 126 of file TLorentzRotation.h.

Double_t TLorentzRotation::fzz

protected

Definition at line 126 of file TLorentzRotation.h.

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

math/physics/inc/TLorentzRotation.h
math/physics/src/TLorentzRotation.cxx

Declaration

Access to the matrix components/Comparisons

Transformations of a LorentzRotation

Compound transformations

Lorentz boosts

Rotations

Inverse transformation

Transformation of a TLorentzVector

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation