The TLorentzRotation class describes Lorentz transformations including Lorentz boosts and rotations (see TRotation)
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| yx yy yz yt |
lambda = | |
| zx zy zz zt |
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Option_t Option_t TPoint xy
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):
if (
l.IsIdentity()) {...}
The TLorentzRotation class describes Lorentz transformations including Lorentz boosts and rotations (...
Transformations of a LorentzRotation
Compound transformations
There are four possibilities to find the product of two TLorentzRotation transformations:
TLorentzRotation MatrixMultiplication(const TLorentzRotation &) const
TLorentzRotation & Transform(const TLorentzRotation &)
Lorentz boosts
Rotations
Inverse transformation
The matrix for the inverse transformation of a TLorentzRotation is as follows:
| xx yx zx -tx |
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| xz yz zz -tz |
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To return the inverse transformation keeping the current unchanged use the member function Inverse(). Invert() inverts the current TLorentzRotation:
l1 = l2.Inverse();
l1 = l2.Invert();
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);
Definition at line 20 of file TLorentzRotation.h.
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| | TLorentzRotation () |
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| | TLorentzRotation (const TLorentzRotation &) |
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| | TLorentzRotation (const TRotation &) |
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| | TLorentzRotation (const TVector3 &) |
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| | TLorentzRotation (Double_t, Double_t, Double_t) |
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| TLorentzRotation & | Boost (const TVector3 &) |
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| TLorentzRotation & | Boost (Double_t, Double_t, Double_t) |
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| TLorentzRotation | Inverse () const |
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| TLorentzRotation & | Invert () |
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| TClass * | IsA () const override |
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| Bool_t | IsIdentity () const |
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| TLorentzRotation | MatrixMultiplication (const TLorentzRotation &) const |
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| Bool_t | operator!= (const TLorentzRotation &) const |
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| Double_t | operator() (int, int) const |
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| TLorentzRotation | operator* (const TLorentzRotation &) const |
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| TLorentzVector | operator* (const TLorentzVector &) const |
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| TLorentzRotation & | operator*= (const TLorentzRotation &) |
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| TLorentzRotation & | operator= (const TLorentzRotation &) |
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| TLorentzRotation & | operator= (const TRotation &) |
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| Bool_t | operator== (const TLorentzRotation &) const |
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| TLorentzRotationRow | operator[] (int) const |
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| TLorentzRotation & | Rotate (Double_t, const TVector3 &) |
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| TLorentzRotation & | Rotate (Double_t, const TVector3 *) |
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| TLorentzRotation & | RotateX (Double_t) |
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| TLorentzRotation & | RotateY (Double_t) |
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| TLorentzRotation & | RotateZ (Double_t) |
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| void | Streamer (TBuffer &) override |
| | Stream an object of class TObject.
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| void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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| TLorentzRotation & | Transform (const TLorentzRotation &) |
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| TLorentzRotation & | Transform (const TRotation &) |
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| Double_t | TT () const |
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| Double_t | TX () const |
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| Double_t | TY () const |
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| Double_t | TZ () const |
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| TLorentzVector | VectorMultiplication (const TLorentzVector &) const |
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| Double_t | XT () const |
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| Double_t | XX () const |
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| Double_t | XY () const |
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| Double_t | XZ () const |
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| Double_t | YT () const |
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| Double_t | YX () const |
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| Double_t | YY () const |
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| Double_t | YZ () const |
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| Double_t | ZT () const |
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| Double_t | ZX () const |
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| Double_t | ZY () const |
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| Double_t | ZZ () const |
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| | TObject () |
| | TObject constructor.
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| | TObject (const TObject &object) |
| | TObject copy ctor.
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| virtual | ~TObject () |
| | TObject destructor.
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| void | AbstractMethod (const char *method) const |
| | Use this method to implement an "abstract" method that you don't want to leave purely abstract.
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| virtual void | AppendPad (Option_t *option="") |
| | Append graphics object to current pad.
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| virtual void | Browse (TBrowser *b) |
| | Browse object. May be overridden for another default action.
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| 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.
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| virtual const char * | ClassName () const |
| | Returns name of class to which the object belongs.
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| virtual void | Clear (Option_t *="") |
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| virtual TObject * | Clone (const char *newname="") const |
| | Make a clone of an object using the Streamer facility.
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| virtual Int_t | Compare (const TObject *obj) const |
| | Compare abstract method.
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| virtual void | Copy (TObject &object) const |
| | Copy this to obj.
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| virtual void | Delete (Option_t *option="") |
| | Delete this object.
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| virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
| | Computes distance from point (px,py) to the object.
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| virtual void | Draw (Option_t *option="") |
| | Default Draw method for all objects.
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| virtual void | DrawClass () const |
| | Draw class inheritance tree of the class to which this object belongs.
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| virtual TObject * | DrawClone (Option_t *option="") const |
| | Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1).
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| virtual void | Dump () const |
| | Dump contents of object on stdout.
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| virtual void | Error (const char *method, const char *msgfmt,...) const |
| | Issue error message.
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| virtual void | Execute (const char *method, const char *params, Int_t *error=nullptr) |
| | Execute method on this object with the given parameter string, e.g.
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| virtual void | Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr) |
| | Execute method on this object with parameters stored in the TObjArray.
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| virtual void | ExecuteEvent (Int_t event, Int_t px, Int_t py) |
| | Execute action corresponding to an event at (px,py).
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| virtual void | Fatal (const char *method, const char *msgfmt,...) const |
| | Issue fatal error message.
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| virtual TObject * | FindObject (const char *name) const |
| | Must be redefined in derived classes.
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| virtual TObject * | FindObject (const TObject *obj) const |
| | Must be redefined in derived classes.
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| virtual Option_t * | GetDrawOption () const |
| | Get option used by the graphics system to draw this object.
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| virtual const char * | GetIconName () const |
| | Returns mime type name of object.
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| virtual const char * | GetName () const |
| | Returns name of object.
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| virtual char * | GetObjectInfo (Int_t px, Int_t py) const |
| | Returns string containing info about the object at position (px,py).
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| virtual Option_t * | GetOption () const |
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| virtual const char * | GetTitle () const |
| | Returns title of object.
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| virtual UInt_t | GetUniqueID () const |
| | Return the unique object id.
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| virtual Bool_t | HandleTimer (TTimer *timer) |
| | Execute action in response of a timer timing out.
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| virtual ULong_t | Hash () const |
| | Return hash value for this object.
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| 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.
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| virtual void | Info (const char *method, const char *msgfmt,...) const |
| | Issue info message.
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| virtual Bool_t | InheritsFrom (const char *classname) const |
| | Returns kTRUE if object inherits from class "classname".
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| virtual Bool_t | InheritsFrom (const TClass *cl) const |
| | Returns kTRUE if object inherits from TClass cl.
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| virtual void | Inspect () const |
| | Dump contents of this object in a graphics canvas.
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| void | InvertBit (UInt_t f) |
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| Bool_t | IsDestructed () const |
| | IsDestructed.
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| virtual Bool_t | IsEqual (const TObject *obj) const |
| | Default equal comparison (objects are equal if they have the same address in memory).
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| virtual Bool_t | IsFolder () const |
| | Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).
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| R__ALWAYS_INLINE Bool_t | IsOnHeap () const |
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| virtual Bool_t | IsSortable () const |
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| R__ALWAYS_INLINE Bool_t | IsZombie () const |
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| virtual void | ls (Option_t *option="") const |
| | The ls function lists the contents of a class on stdout.
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| 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).
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| virtual Bool_t | Notify () |
| | This method must be overridden to handle object notification.
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| void | Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const |
| | Use this method to declare a method obsolete.
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| void | operator delete (void *ptr) |
| | Operator delete.
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| void | operator delete[] (void *ptr) |
| | Operator delete [].
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| void * | operator new (size_t sz) |
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| void * | operator new (size_t sz, void *vp) |
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| void * | operator new[] (size_t sz) |
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| void * | operator new[] (size_t sz, void *vp) |
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| TObject & | operator= (const TObject &rhs) |
| | TObject assignment operator.
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| virtual void | Paint (Option_t *option="") |
| | This method must be overridden if a class wants to paint itself.
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| virtual void | Pop () |
| | Pop on object drawn in a pad to the top of the display list.
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| virtual void | Print (Option_t *option="") const |
| | This method must be overridden when a class wants to print itself.
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| virtual Int_t | Read (const char *name) |
| | Read contents of object with specified name from the current directory.
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| virtual void | RecursiveRemove (TObject *obj) |
| | Recursively remove this object from a list.
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| void | ResetBit (UInt_t f) |
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| virtual void | SaveAs (const char *filename="", Option_t *option="") const |
| | Save this object in the file specified by filename.
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| virtual void | SavePrimitive (std::ostream &out, Option_t *option="") |
| | Save a primitive as a C++ statement(s) on output stream "out".
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| void | SetBit (UInt_t f) |
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| void | SetBit (UInt_t f, Bool_t set) |
| | Set or unset the user status bits as specified in f.
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| virtual void | SetDrawOption (Option_t *option="") |
| | Set drawing option for object.
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| virtual void | SetUniqueID (UInt_t uid) |
| | Set the unique object id.
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| void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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| virtual void | SysError (const char *method, const char *msgfmt,...) const |
| | Issue system error message.
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| R__ALWAYS_INLINE Bool_t | TestBit (UInt_t f) const |
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| Int_t | TestBits (UInt_t f) const |
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| virtual void | UseCurrentStyle () |
| | Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.
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| virtual void | Warning (const char *method, const char *msgfmt,...) const |
| | Issue warning message.
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| virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) |
| | Write this object to the current directory.
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| virtual Int_t | Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const |
| | Write this object to the current directory.
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Public Member Functions inherited from TObject
