library: libPhysics
#include "TLorentzRotation.h"

TLorentzRotation

class description - source file - inheritance tree (.pdf)

class TLorentzRotation : public TObject

Inheritance Chart:
TObject
<-
TLorentzRotation
 

    protected:

                       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)

    public:

                                            TLorentzRotation()
                                            TLorentzRotation(const TRotation&)
                                            TLorentzRotation(const TLorentzRotation&)
                                            TLorentzRotation(Double_t, Double_t, Double_t)
                                            TLorentzRotation(const TVector3&)
                           TLorentzRotation MatrixMultiplication(const TLorentzRotation&) const
                           TLorentzRotation operator*(const TLorentzRotation& m) const
                           TLorentzRotation Inverse() const
                                            ~TLorentzRotation()
                          TLorentzRotation& Boost(Double_t bx, Double_t by, Double_t bz)
                          TLorentzRotation& Boost(const TVector3& b)
                             static TClass* Class()
                          TLorentzRotation& Invert()
                            virtual TClass* IsA() const
                                     Bool_t IsIdentity() const
                                     Bool_t operator!=(const TLorentzRotation& r) const
                                   Double_t operator()(int, int) const
                             TLorentzVector operator*(const TLorentzVector& p) const
                          TLorentzRotation& operator*=(const TLorentzRotation& m)
                          TLorentzRotation& operator=(const TLorentzRotation& r)
                          TLorentzRotation& operator=(const TRotation& r)
                                     Bool_t operator==(const TLorentzRotation& r) const
      TLorentzRotation::TLorentzRotationRow operator[](int i) const
                          TLorentzRotation& Rotate(Double_t angle, const TVector3& axis)
                          TLorentzRotation& Rotate(Double_t angle, const TVector3* axis)
                          TLorentzRotation& RotateX(Double_t angle)
                          TLorentzRotation& RotateY(Double_t angle)
                          TLorentzRotation& RotateZ(Double_t angle)
                               virtual void ShowMembers(TMemberInspector& insp, char* parent)
                               virtual void Streamer(TBuffer& b)
                                       void StreamerNVirtual(TBuffer& b)
                          TLorentzRotation& Transform(const TLorentzRotation& m)
                          TLorentzRotation& Transform(const TRotation& m)
                                   Double_t TT() const
                                   Double_t TX() const
                                   Double_t TY() const
                                   Double_t TZ() const
                             TLorentzVector VectorMultiplication(const TLorentzVector& p) 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

Data Members


    protected:

      Double_t fxx  
      Double_t fxy  
      Double_t fxz  
      Double_t fxt  
      Double_t fyx  
      Double_t fyy  
      Double_t fyz  
      Double_t fyt  
      Double_t fzx  
      Double_t fzy  
      Double_t fzz  
      Double_t fzt  
      Double_t ftx  
      Double_t fty  
      Double_t ftz  
      Double_t ftt

Class Description

*-*-*-*-*-*-*-*-*-*-*-*The Physics Vector package *-*-*-*-*-*-*-*-*-*-*-*
*-*                    ==========================                       *
*-* The Physics Vector package consists of five classes:                *
*-*   - TVector2                                                        *
*-*   - TVector3                                                        *
*-*   - TRotation                                                       *
*-*   - TLorentzVector                                                  *
*-*   - TLorentzRotation                                                *
*-* It is a combination of CLHEPs Vector package written by             *
*-* Leif Lonnblad, Andreas Nilsson and Evgueni Tcherniaev               *
*-* and a ROOT package written by Pasha Murat.                          *
*-* for CLHEP see:  http://wwwinfo.cern.ch/asd/lhc++/clhep/             *
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

TLorentzRotation

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'*bx*bz  1+gamma'*by*by  gamma'*by*by  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 memberfunction 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
TLorentzRotation() : fxx(1.0), fxy(0.0), fxz(0.0), fxt(0.0), fyx(0.0), fyy(1.0), fyz(0.0), fyt(0.0), fzx(0.0), fzy(0.0), fzz(1.0), fzt(0.0), ftx(0.0), fty(0.0), ftz(0.0), ftt(1.0)
TLorentzRotation(const TRotation & r) : fxx(r.XX()), fxy(r.XY()), fxz(r.XZ()), fxt(0.0), fyx(r.YX()), fyy(r.YY()), fyz(r.YZ()), fyt(0.0), fzx(r.ZX()), fzy(r.ZY()), fzz(r.ZZ()), fzt(0.0), ftx(0.0), fty(0.0), ftz(0.0), ftt(1.0)
TLorentzRotation(const TLorentzRotation & r) : TObject(r), fxx(r.fxx), fxy(r.fxy), fxz(r.fxz), fxt(r.fxt), fyx(r.fyx), fyy(r.fyy), fyz(r.fyz), fyt(r.fyt), fzx(r.fzx), fzy(r.fzy), fzz(r.fzz), fzt(r.fzt), ftx(r.ftx), fty(r.fty), ftz(r.ftz), ftt(r.ftt)
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) : fxx(rxx), fxy(rxy), fxz(rxz), fxt(rxt), fyx(ryx), fyy(ryy), fyz(ryz), fyt(ryt), fzx(rzx), fzy(rzy), fzz(rzz), fzt(rzt), ftx(rtx), fty(rty), ftz(rtz), ftt(rtt)
TLorentzRotation(Double_t bx, Double_t by, Double_t bz)
TLorentzRotation(const TVector3 & p)
void SetBoost(Double_t bx, Double_t by, Double_t bz)
MatrixMultiplication(const TLorentzRotation & b) const



Inline Functions

                                         void ~TLorentzRotation()
                                     Double_t XX() const
                                     Double_t XY() const
                                     Double_t XZ() const
                                     Double_t XT() const
                                     Double_t YX() const
                                     Double_t YY() const
                                     Double_t YZ() const
                                     Double_t YT() const
                                     Double_t ZX() const
                                     Double_t ZY() const
                                     Double_t ZZ() const
                                     Double_t ZT() const
                                     Double_t TX() const
                                     Double_t TY() const
                                     Double_t TZ() const
                                     Double_t TT() const
        TLorentzRotation::TLorentzRotationRow operator[](int i) const
                                     Double_t operator()(int, int) const
                            TLorentzRotation& operator=(const TLorentzRotation& r)
                            TLorentzRotation& operator=(const TRotation& r)
                                       Bool_t operator==(const TLorentzRotation& r) const
                                       Bool_t operator!=(const TLorentzRotation& r) const
                                       Bool_t IsIdentity() const
                               TLorentzVector VectorMultiplication(const TLorentzVector& p) const
                               TLorentzVector operator*(const TLorentzVector& p) const
                             TLorentzRotation operator*(const TLorentzRotation& m) const
                            TLorentzRotation& operator*=(const TLorentzRotation& m)
                            TLorentzRotation& Transform(const TLorentzRotation& m)
                            TLorentzRotation& Transform(const TRotation& m)
                             TLorentzRotation Inverse() const
                            TLorentzRotation& Invert()
                            TLorentzRotation& Boost(Double_t bx, Double_t by, Double_t bz)
                            TLorentzRotation& Boost(const TVector3& b)
                            TLorentzRotation& RotateX(Double_t angle)
                            TLorentzRotation& RotateY(Double_t angle)
                            TLorentzRotation& RotateZ(Double_t angle)
                            TLorentzRotation& Rotate(Double_t angle, const TVector3& axis)
                            TLorentzRotation& Rotate(Double_t angle, const TVector3* axis)
                                      TClass* Class()
                                      TClass* IsA() const
                                         void ShowMembers(TMemberInspector& insp, char* parent)
                                         void Streamer(TBuffer& b)
                                         void StreamerNVirtual(TBuffer& b)

Author: Peter Malzacher 19/06/99
Last update: root/physics:$Name: $:$Id: TLorentzRotation.cxx,v 1.3 2003/09/03 06:08:34 brun Exp $

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