// LorentzVector doxygen page

/**

  \page LorentzVectorPage  LorentzVector Classes


To avoid exposing templated parameter to the users, typedefs are defined for all types of  vectors based an double's and float's. To use them, one must include the header file <em>Math/Vector4D.h</em>.
The following typedef's, defined in the header file <em>Math/Vector4Dfwd.h</em>, are available for the different instantiations of the template class ROOT::Math::LorentzVector:    

<ul>
<li>ROOT::Math::XYZTVector  vector based on x,y,z,t coordinates (cartesian) in double precision
<li>ROOT::Math::XYZTVectorF  vector based on x,y,z,t coordinates (cartesian) in float precision
<li>ROOT::Math::PtEtaPhiEVector vector based on pt (rho),eta,phi and E (t) coordinates  in double precision
<li>ROOT::Math::PtEtaPhiMVector vector based on pt (rho),eta,phi and M (t) coordinates  in double precision
<li>ROOT::Math::PxPyPzMVector vector based on px,py,pz and M (mass) coordinates  in double precision
</ul>
The metric used for all the LorentzVector's is (-,-,-,+)

<p> 
<h4>Constructors and Assignment</h4>
The following declarations are available: 
<pre>
XYZTVector               v1;               // create an empty vector (x = 0, y = 0, z = 0, t = 0) 
XYZTVector               v2(1,2,3,4);      // create a vector with x=1, y = 2, z = 3, t = 4 
PtEtaPhiEVector          v3(1,2,PI,5);     // create a vector with pt = 1, eta = 2, phi = PI, E = 5
</pre>
Note that each type of vector is constructed by passing its coordinates representations, so a XYZTVector(1,2,3,4) is different from a PtEtaPhiEVector(1,2,3,4). 
<p>
In addition the Vector classes can be constructed by any vector, which implements the accessors x(), y() and z() and t(). 
This cann be another ROOT::Math::LorentzVector based on a different coordinate system or even any vector of a different package, like the CLHEP HepLorentzVector that implements the required signature.  
<pre>
XYZTVector               v1(1,2,3,4); 
PtEtaPhiEVector          v2(v1);
 
CLHEP::HepLorentzVector  q(1,2,3,4); 
XYZTVector               v3(q)  
</pre>

<h4>Coordinate Accessors</h4>
All the same coordinate accessors are available through the interface of the class ROOT::Math::LorentzVector.
For example: 
<pre>
v1.X(); v1.X(); v1.Z(); v1.T()             // returns cartesian components for the cartesian vector v1
v2.Px(); v2.Py(); v2.Pz(); v2.E()          // returns cartesian components for the cylindrical vector v2
v1.Pt(); v1.Eta(); v1.Phi(); v1.M()        // returns other components for the cartesian vector v1
</pre>
In addition, all the 4 coordinates of the vector can be retrieved with the GetCoordinates method: 
<pre>
double d[4];
v1.GetCoordinates(d);                      // fill d array with (x,y,z,t) components of v1
v2.GetCoordinates(d);                      // fill d array with (pt,eta,phi,e) components of v2
std::vector<double> w(4);                 
v1.GetCoordinates(w.begin(),w.end());      // fill std::vector with (x,y,z,t) components of v1
</pre>
To get information on all the coordinate accessors see the reference documentation of ROOT::Math::LorentzVector 


<h4>Setter Methods</h4>
One can set only all the three coordinates via: 
<pre>
v1.SetCoordinates(c1,c2,c3,c4);            // sets the (x,y,z,t) for a XYZTVector  
v2.SetCoordinates(c1,c2,c3,c4);            // sets pt,eta,phi,e for a PtEtaPhiEVector
v2.SetXYZ(x,y,z,t);                        // sets the 4 cartesian components for the PtEtaPhiEVector 
</pre> 
Single coordinate setter methods are available for the basic vector coordinates, like SetX() for a XYZTVector or SetPt() for a PtEtaPhiEVector. Attempting to do a SetX() on a non cartesian vector will not compile.  
<pre>
XYZTVector v1;      v1.SetX(1)             // OK setting x for a cartesian vector
PtEtaPhiEVector v2; v2.SetX(1)             // ERROR: cannot set X for a non-cartesian vector. Method will not compile
v2.SetR(1)                                 // OK setting Pt for a  PtEtaPhiEVector vector
</pre>

In addition there are setter methods from C arrays or iterators.
<pre>
double d[4] = {1.,2.,3.,4.};
XYZTVector v;
v.SetCoordinates(d);                      // set (x,y,z,t) components of v using values from d
</pre>
or for example from an std::vector using the iterators
<pre>
std::vector<double> w(4);   
v.SetCoordinates(w.begin(),w.end());      // set (x,y,z,t) components of v using values from w
</pre>


<h4>Arithmetic Operations</h4>
The following operations are possible between LorentzVectors classes, even of different coordinate system types: 
( v and w are two  LorentzVector of the same type, q is a generic LorentzVector  implementing x(), y(), z() and t() and a  is a generic scalar type: double, flot, int, etc.... )  
<pre>
v += q; 
v -= q;
v  = -q; 
v *= a;
v /= a; 
w = v + q;
w = v - q; 
w = v * a;
w = a * v;
w = v / a;
</pre>
<h4>Comparison</h4>
<pre>
v == w;                                   
v != w; 
</pre>
<h4>Other Methods</h4>
<pre>
a =  v.Dot(q);                           // dot product in metric (+,+,+,-) of two LorentzVector's
XYZVector s = v.Vect()                   // return the spatial components (x,y,z) 
v.Beta();                                // return beta and gamma value 
v.Gamma()                                // (vector must be time-like otherwise result is meaningless)
XYZVector b = v.BoostToCM()              // return boost vector which will bring the Vector in its mas frame (P=0)
</pre>


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