ROOT   Reference Guide
TLorentzRotation Class Reference

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 |
XPoint xy[kMAXMK]
Definition: TGX11.cxx:122
auto * tt
Definition: textangle.C:16

### 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 |
double gamma(double x)

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

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
double Double_t
Definition: RtypesCore.h:57
The TLorentzRotation class describes Lorentz transformations including Lorentz boosts and rotations (...
auto * m
Definition: textangle.C:8
auto * l
Definition: textangle.C:4

### Transformations of a LorentzRotation

#### Compound transformations

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

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
#define b(i)
Definition: RSha256.hxx:100
#define c(i)
Definition: RSha256.hxx:101
auto * a
Definition: textangle.C:12

#### Lorentz boosts

Double_t bx, by, bz;
TVector3 v(bx,by,bz);
l.Boost(v);
l.Boost(bx,by,bz);
TVector3 is a general three vector class, which can be used for the description of different vectors ...
Definition: TVector3.h:22

#### Rotations

TVector3 axis;
l.RotateX(TMath::Pi()); // rotation around x-axis
l.Rotate(.5,axis);// rotation around specified vector
constexpr Double_t Pi()
Definition: TMath.h:38

#### 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.:

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

Definition at line 20 of file TLorentzRotation.h.

## Classes

class  TLorentzRotationRow

## Public Member Functions

TLorentzRotation ()

TLorentzRotation (const TLorentzRotation &)

TLorentzRotation (const TRotation &)

TLorentzRotation (const TVector3 &)

TLorentzRotation (Double_t, Double_t, Double_t)

TLorentzRotationBoost (const TVector3 &)

TLorentzRotationBoost (Double_t, Double_t, Double_t)

TLorentzRotation Inverse () const

TLorentzRotationInvert ()

Bool_t IsIdentity () const

TLorentzRotation MatrixMultiplication (const TLorentzRotation &) const

Bool_t operator!= (const TLorentzRotation &) const

Double_t operator() (int, int) const

TLorentzRotation operator* (const TLorentzRotation &) const

TLorentzVector operator* (const TLorentzVector &) const

TLorentzRotationoperator*= (const TLorentzRotation &)

TLorentzRotationoperator= (const TLorentzRotation &)

TLorentzRotationoperator= (const TRotation &)

Bool_t operator== (const TLorentzRotation &) const

TLorentzRotationRow operator[] (int) const

TLorentzRotationRotate (Double_t, const TVector3 &)

TLorentzRotationRotate (Double_t, const TVector3 *)

TLorentzRotationRotateX (Double_t)

TLorentzRotationRotateY (Double_t)

TLorentzRotationRotateZ (Double_t)

TLorentzRotationTransform (const TLorentzRotation &)

TLorentzRotationTransform (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...

Append graphics object to current pad. More...

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

ULong_t CheckedHash ()
Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...

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

virtual void Clear (Option_t *="")

virtual TObjectClone (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 TObjectDrawClone (Option_t *option="") const

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 TObjectFindObject (const char *name) const
Must be redefined in derived classes. More...

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

virtual Option_tGetDrawOption () 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_tGetOption () 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...

Bool_t HasInconsistentHash () const
Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. 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...

R__ALWAYS_INLINE Bool_t IsOnHeap () const

virtual Bool_t IsSortable () const

R__ALWAYS_INLINE 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...

voidoperator new (size_t sz)

voidoperator new (size_t sz, void *vp)

voidoperator new[] (size_t sz)

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

TObjectoperator= (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)

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

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...

R__ALWAYS_INLINE 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

Public Types inherited from TObject
enum  {
kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,
}

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

enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum  EStatusBits {
kCanDelete = BIT(0) , kMustCleanup = 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...

Protected Types inherited from TObject
enum  { kOnlyPrepStep = BIT(3) }

#include <TLorentzRotation.h>

Inheritance diagram for TLorentzRotation:
[legend]

## ◆ TLorentzRotation() [1/6]

 TLorentzRotation::TLorentzRotation ( )

Definition at line 136 of file TLorentzRotation.cxx.

## ◆ TLorentzRotation() [2/6]

 TLorentzRotation::TLorentzRotation ( const TRotation & r )

Definition at line 142 of file TLorentzRotation.cxx.

## ◆ TLorentzRotation() [3/6]

 TLorentzRotation::TLorentzRotation ( const TLorentzRotation & r )

Definition at line 148 of file TLorentzRotation.cxx.

## ◆ TLorentzRotation() [4/6]

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

Definition at line 164 of file TLorentzRotation.cxx.

## ◆ TLorentzRotation() [5/6]

 TLorentzRotation::TLorentzRotation ( const TVector3 & p )

Definition at line 172 of file TLorentzRotation.cxx.

## ◆ TLorentzRotation() [6/6]

 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 154 of file TLorentzRotation.cxx.

## ◆ Boost() [1/2]

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

Definition at line 282 of file TLorentzRotation.h.

## ◆ Boost() [2/2]

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

Definition at line 278 of file TLorentzRotation.h.

## ◆ Inverse()

 TLorentzRotation TLorentzRotation::Inverse ( ) const
inline

Definition at line 267 of file TLorentzRotation.h.

## ◆ Invert()

 TLorentzRotation & TLorentzRotation::Invert ( )
inline

Definition at line 274 of file TLorentzRotation.h.

## ◆ IsIdentity()

 Bool_t TLorentzRotation::IsIdentity ( ) const
inline

Definition at line 231 of file TLorentzRotation.h.

## ◆ MatrixMultiplication()

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

Definition at line 221 of file TLorentzRotation.cxx.

## ◆ operator!=()

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

Definition at line 223 of file TLorentzRotation.h.

## ◆ operator()()

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

Definition at line 177 of file TLorentzRotation.cxx.

## ◆ operator*() [1/2]

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

Definition at line 251 of file TLorentzRotation.h.

## ◆ operator*() [2/2]

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

Definition at line 247 of file TLorentzRotation.h.

## ◆ operator*=()

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

Definition at line 255 of file TLorentzRotation.h.

## ◆ operator=() [1/2]

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

Definition at line 171 of file TLorentzRotation.h.

## ◆ operator=() [2/2]

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

Definition at line 188 of file TLorentzRotation.h.

## ◆ operator==()

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

Definition at line 206 of file TLorentzRotation.h.

## ◆ operator[]()

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

Definition at line 167 of file TLorentzRotation.h.

## ◆ Rotate() [1/2]

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

Definition at line 298 of file TLorentzRotation.h.

## ◆ Rotate() [2/2]

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

Definition at line 302 of file TLorentzRotation.h.

## ◆ RotateX()

 TLorentzRotation & TLorentzRotation::RotateX ( Double_t angle )
inline

Definition at line 286 of file TLorentzRotation.h.

## ◆ RotateY()

 TLorentzRotation & TLorentzRotation::RotateY ( Double_t angle )
inline

Definition at line 290 of file TLorentzRotation.h.

## ◆ RotateZ()

 TLorentzRotation & TLorentzRotation::RotateZ ( Double_t angle )
inline

Definition at line 294 of file TLorentzRotation.h.

## ◆ SetBoost()

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

Definition at line 204 of file TLorentzRotation.cxx.

## ◆ Transform() [1/2]

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

Definition at line 259 of file TLorentzRotation.h.

## ◆ Transform() [2/2]

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

Definition at line 263 of file TLorentzRotation.h.

## ◆ TT()

 Double_t TLorentzRotation::TT ( ) const
inline

Definition at line 158 of file TLorentzRotation.h.

## ◆ TX()

 Double_t TLorentzRotation::TX ( ) const
inline

Definition at line 155 of file TLorentzRotation.h.

## ◆ TY()

 Double_t TLorentzRotation::TY ( ) const
inline

Definition at line 156 of file TLorentzRotation.h.

## ◆ TZ()

 Double_t TLorentzRotation::TZ ( ) const
inline

Definition at line 157 of file TLorentzRotation.h.

## ◆ VectorMultiplication()

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

Definition at line 240 of file TLorentzRotation.h.

## ◆ XT()

 Double_t TLorentzRotation::XT ( ) const
inline

Definition at line 146 of file TLorentzRotation.h.

## ◆ XX()

 Double_t TLorentzRotation::XX ( ) const
inline

Definition at line 143 of file TLorentzRotation.h.

## ◆ XY()

 Double_t TLorentzRotation::XY ( ) const
inline

Definition at line 144 of file TLorentzRotation.h.

## ◆ XZ()

 Double_t TLorentzRotation::XZ ( ) const
inline

Definition at line 145 of file TLorentzRotation.h.

## ◆ YT()

 Double_t TLorentzRotation::YT ( ) const
inline

Definition at line 150 of file TLorentzRotation.h.

## ◆ YX()

 Double_t TLorentzRotation::YX ( ) const
inline

Definition at line 147 of file TLorentzRotation.h.

## ◆ YY()

 Double_t TLorentzRotation::YY ( ) const
inline

Definition at line 148 of file TLorentzRotation.h.

## ◆ YZ()

 Double_t TLorentzRotation::YZ ( ) const
inline

Definition at line 149 of file TLorentzRotation.h.

## ◆ ZT()

 Double_t TLorentzRotation::ZT ( ) const
inline

Definition at line 154 of file TLorentzRotation.h.

## ◆ ZX()

 Double_t TLorentzRotation::ZX ( ) const
inline

Definition at line 151 of file TLorentzRotation.h.

## ◆ ZY()

 Double_t TLorentzRotation::ZY ( ) const
inline

Definition at line 152 of file TLorentzRotation.h.

## ◆ ZZ()

 Double_t TLorentzRotation::ZZ ( ) const
inline

Definition at line 153 of file TLorentzRotation.h.

## ◆ ftt

 Double_t TLorentzRotation::ftt
protected

Definition at line 125 of file TLorentzRotation.h.

## ◆ ftx

 Double_t TLorentzRotation::ftx
protected

Definition at line 125 of file TLorentzRotation.h.

## ◆ fty

 Double_t TLorentzRotation::fty
protected

Definition at line 125 of file TLorentzRotation.h.

## ◆ ftz

 Double_t TLorentzRotation::ftz
protected

Definition at line 125 of file TLorentzRotation.h.

## ◆ fxt

 Double_t TLorentzRotation::fxt
protected

Definition at line 122 of file TLorentzRotation.h.

## ◆ fxx

 Double_t TLorentzRotation::fxx
protected

Definition at line 122 of file TLorentzRotation.h.

## ◆ fxy

 Double_t TLorentzRotation::fxy
protected

Definition at line 122 of file TLorentzRotation.h.

## ◆ fxz

 Double_t TLorentzRotation::fxz
protected

Definition at line 122 of file TLorentzRotation.h.

## ◆ fyt

 Double_t TLorentzRotation::fyt
protected

Definition at line 123 of file TLorentzRotation.h.

## ◆ fyx

 Double_t TLorentzRotation::fyx
protected

Definition at line 123 of file TLorentzRotation.h.

## ◆ fyy

 Double_t TLorentzRotation::fyy
protected

Definition at line 123 of file TLorentzRotation.h.

## ◆ fyz

 Double_t TLorentzRotation::fyz
protected

Definition at line 123 of file TLorentzRotation.h.

## ◆ fzt

 Double_t TLorentzRotation::fzt
protected

Definition at line 124 of file TLorentzRotation.h.

## ◆ fzx

 Double_t TLorentzRotation::fzx
protected

Definition at line 124 of file TLorentzRotation.h.

## ◆ fzy

 Double_t TLorentzRotation::fzy
protected

Definition at line 124 of file TLorentzRotation.h.

## ◆ fzz

 Double_t TLorentzRotation::fzz
protected

Definition at line 124 of file TLorentzRotation.h.

Libraries for TLorentzRotation:
[legend]

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