* provided "as is" without express or implied warranty. *
**************************************************************************/
-/*
-$Log$
-*/
+// $Id$
+
+///////////////////////////////////////////////////////////////////////////
+// Class AliBoost
+// Perform various Lorentz transformations.
+//
+// Example :
+// =========
+//
+// Float_t a[3]={0.1,0.2,0.3};
+// Float_t ea[3]={0.01,0.02,0.03};
+// Ali3Vector beta;
+// beta.SetVector(a,"car");
+// beta.SetErrors(ea,"car");
+//
+// AliBoost b1;
+// b1.SetBeta(beta);
+// b1.Data();
+//
+// Float_t b[4]={14,1,2,3};
+// Float_t eb[4]={1.4,0.1,0.2,0.3};
+// Ali4Vector p;
+// p.SetVector(b,"car");
+// p.SetErrors(eb,"car");
+// Ali4Vector pprim=b1.Boost(p);
+// p.Data();
+// pprim.Data();
+//
+// p=b1.Inverse(pprim);
+// pprim.Data();
+// p.Data();
+//
+// Float_t c[4]={5,0,0,4};
+// Float_t ec[4]={0.5,0,0,0.4};
+// Ali4Vector q;
+// q.SetVector(c,"car");
+// q.SetErrors(ec,"car");
+//
+// AliBoost b2;
+// b2.Set4Momentum(q);
+// b2.Data("sph");
+//
+//--- Author: Nick van Eijndhoven 14-may-1996 UU-SAP Utrecht
+//- Modified: NvE $Date$ UU-SAP Utrecht
+///////////////////////////////////////////////////////////////////////////
#include "AliBoost.h"
+#include "Riostream.h"
ClassImp(AliBoost) // Class implementation to enable ROOT I/O
-AliBoost::AliBoost()
+AliBoost::AliBoost() : TObject()
{
-// Creation of a Lorentz boost object and initialisation of parameters
- fGamma=1;
- fBeta2=0;
+// Creation of a Lorentz boost object and initialisation of parameters.
+// Beta is set to (0,0,0) and consequently Gamma=1.
+// All errors are initialised to 0.
Double_t a[3]={0,0,0};
fBeta.SetVector(a,"sph");
+ fGamma=1;
+ fDgamma=0;
+ fDresult=0;
}
///////////////////////////////////////////////////////////////////////////
AliBoost::~AliBoost()
{
-// Default destructor
+// Default destructor.
}
///////////////////////////////////////////////////////////////////////////
-void AliBoost::SetBeta(Ali3Vector b)
+AliBoost::AliBoost(const AliBoost& b) : TObject(b)
{
-// Setting of boost parameters on basis of beta 3-vector
- fBeta2=b.Dot(b);
+// Copy constructor
+ fBeta=b.fBeta;
+ fGamma=b.fGamma;
+ fDgamma=b.fDgamma;
+ fDresult=b.fDresult;
+}
+///////////////////////////////////////////////////////////////////////////
+void AliBoost::SetBeta(Ali3Vector& b)
+{
+// Setting of boost parameters on basis of beta 3-vector.
+// The errors on the beta 3-vector are taken from the input 3-vector.
+// The gamma value and its error are calculated accordingly.
fBeta=b;
+ Double_t beta2=fBeta.Dot(fBeta);
+ Double_t dbeta2=fBeta.GetResultError();
- if (fBeta2 > 1.)
+ if (beta2 > 1.)
{
cout << " *AliBoost::SetBeta* beta > 1." << endl;
}
- Double_t test=1.-fBeta2;
fGamma=0;
- if (test > 0.) fGamma=sqrt(1./test);
-}
-///////////////////////////////////////////////////////////////////////////
-void AliBoost::SetGamma(Double_t g,Ali3Vector v)
-{
-// Setting of boost parameters on basis of gamma and direction 3-vector
- if (g >= 1.)
- {
- fGamma=g;
- fBeta2=1.-(1./(fGamma*fGamma));
- fBeta=v*sqrt(fBeta2);
- }
- else
+ fDgamma=0;
+ Double_t temp=1.-beta2;
+ if (temp > 0.)
{
- cout << " *AliBoost::SetGamma* Invalid input gamma = " << g << endl;
+ fGamma=sqrt(1./temp);
+ fDgamma=fabs(dbeta2/(2.*pow(temp,1.5)));
}
}
///////////////////////////////////////////////////////////////////////////
void AliBoost::Set4Momentum(Ali4Vector& p)
{
-// Setting of boost parameters on basis of momentum 4-vector data
+// Setting of boost parameters on basis of momentum 4-vector data.
+// The errors of the input 4-vector are used to calculate the
+// errors on the beta 3-vector and the gamma factor.
Double_t E=p.GetScalar();
+ Double_t dE=p.GetResultError();
if (E <= 0.)
{
cout << " *AliBoost::Set4Momentum* Unphysical situation." << endl;
- p.Info();
+ p.Data();
}
else
{
Ali3Vector b=p.Get3Vector();
+ Double_t vb[3],eb[3];
+ b.GetVector(vb,"car");
+ b.GetErrors(eb,"car");
b=b/E;
+ for (Int_t i=0; i<3; i++)
+ {
+ eb[i]=sqrt(pow(eb[i]/E,2)+pow(vb[i]*dE/(E*E),2));
+ }
+ b.SetErrors(eb,"car");
SetBeta(b);
}
}
///////////////////////////////////////////////////////////////////////////
-Ali3Vector AliBoost::GetBetaVector()
+Ali3Vector AliBoost::GetBetaVector() const
{
-// Provide the the beta 3-vector
+// Provide the beta 3-vector.
return fBeta;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliBoost::GetBeta()
{
-// Provide the norm of the beta 3-vector
- return sqrt(fBeta2);
+// Provide the norm of the beta 3-vector.
+// The error on the value can be obtained via GetResultError().
+ Double_t norm=fBeta.GetNorm();
+ fDresult=fBeta.GetResultError();
+ return norm;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliBoost::GetGamma()
{
-// Provide the gamma factor
+// Provide the gamma factor.
+// The error on the value can be obtained via GetResultError().
+ fDresult=fDgamma;
return fGamma;
}
///////////////////////////////////////////////////////////////////////////
-void AliBoost::Info(TString f)
+Double_t AliBoost::GetResultError() const
{
-// Printing of the boost parameter info in coordinate frame f
-
- cout << " *AliBoost::Info* beta = " << sqrt(fBeta2) << " gamma = " << fGamma << endl
- << " Beta";
- fBeta.Info(f);
+// Provide the error on the result of an operation yielding a scalar.
+// E.g. GetBeta() or GetGamma()
+ return fDresult;
+}
+///////////////////////////////////////////////////////////////////////////
+void AliBoost::Data(TString f)
+{
+// Printing of the boost parameter info in coordinate frame f.
+ Double_t beta=fBeta.GetNorm();
+ Double_t dbeta=fBeta.GetResultError();
+ cout << " *AliBoost::Data* beta : " << beta << " error : " << dbeta
+ << " gamma : " << fGamma << " error : " << fDgamma << endl;
+ cout << " Beta";
+ fBeta.Data(f);
}
///////////////////////////////////////////////////////////////////////////
Ali4Vector AliBoost::Boost(Ali4Vector& v)
{
-// Perform the Lorentz boost on the 4-vector v
- if (fBeta2 > 1.e-20)
+// Perform the Lorentz boost on the 4-vector v.
+// Error propagation is performed automatically.
+// Note : As an approximation Beta and p.Dot(Beta) are considered as
+// independent quantities.
+
+ Double_t beta=fBeta.GetNorm();
+ Double_t dbeta=fBeta.GetResultError();
+
+ Double_t beta2=pow(beta,2);
+
+ if (beta > 1.e-10)
{
Double_t E=v.GetScalar();
+ Double_t dE=v.GetResultError();
+
Ali3Vector p=v.Get3Vector();
+
Double_t pdotbeta=p.Dot(fBeta);
+ Double_t dpdotbeta=p.GetResultError();
+
+ // Determine the new vector components
+ Double_t Eprim=fGamma*(E-pdotbeta);
+
+ Double_t z=((fGamma-1.)*pdotbeta/beta2)-fGamma*E;
+ Ali3Vector add=fBeta*z;
+
+ // Determine errors on the new vector components
+ Double_t dEprim=sqrt(pow((E-pdotbeta)*fDgamma,2)+pow(fGamma*dE,2)
+ +pow(fGamma*dpdotbeta,2));
+ Double_t dz=sqrt( pow(((fGamma-1.)/beta2)*dpdotbeta,2) + pow(fGamma*dE,2)
+ +pow((
+ ((2./beta)-(4.*pow(beta,3)-6.*pow(beta,5))/(2.*pow((pow(beta,4)-pow(beta,6)),1.5)))*pdotbeta
+ +beta*E/pow(fGamma,3))*dbeta,2) );
- Double_t Eprim;
- Eprim=fGamma*(E-pdotbeta);
+ Double_t vb[3],eb[3];
+ fBeta.GetVector(vb,"car");
+ fBeta.GetErrors(eb,"car");
+ for (Int_t i=0; i<3; i++)
+ {
+ eb[i]=sqrt(pow(z*eb[i],2)+pow(vb[i]*dz,2));
+ }
+ add.SetErrors(eb,"car");
- Ali3Vector term1,term2,pprim;
- term1=fBeta*((fGamma-1.)*pdotbeta/fBeta2);
- term2=fBeta*(fGamma*E);
- pprim=p+term1-term2;
+ // Calculate the new 3-vector
+ Ali3Vector pprim=p+add;
+ // Set the components and errors of the new 4-vector
Ali4Vector w;
w.SetVector(Eprim,pprim);
+ w.SetScalarError(dEprim);
return w;
}
///////////////////////////////////////////////////////////////////////////
Ali4Vector AliBoost::Inverse(Ali4Vector& vprim)
{
-// Perform the inverse Lorentz boost on the 4-vector vprim
- if (fBeta2 > 1.e-20)
+// Perform the inverse Lorentz boost on the 4-vector vprim.
+// Error propagation is performed automatically.
+// Note : As an approximation Beta and pprim.Dot(Beta) are considered as
+// independent quantities.
+
+ Double_t beta=fBeta.GetNorm();
+ Double_t dbeta=fBeta.GetResultError();
+
+ Double_t beta2=pow(beta,2);
+
+ if (beta > 1.e-10)
{
Double_t Eprim=vprim.GetScalar();
+ Double_t dEprim=vprim.GetResultError();
+
Ali3Vector pprim=vprim.Get3Vector();
+
Double_t pprimdotbeta=pprim.Dot(fBeta);
+ Double_t dpprimdotbeta=pprim.GetResultError();
+
+ // Determine the new vector components
+ Double_t E=fGamma*(Eprim+pprimdotbeta);
+
+ Double_t z=((fGamma-1.)*pprimdotbeta/beta2)+fGamma*Eprim;
+ Ali3Vector add=fBeta*z;
+
+ // Determine errors on the prime-vector components
+ Double_t dE=sqrt(pow((Eprim+pprimdotbeta)*fDgamma,2)+pow(fGamma*dEprim,2)
+ +pow(fGamma*dpprimdotbeta,2));
+ Double_t dz=sqrt( pow(((fGamma-1.)/beta2)*dpprimdotbeta,2) + pow(fGamma*dEprim,2)
+ +pow((
+ ((2./beta)-(4.*pow(beta,3)-6.*pow(beta,5))/(2.*pow((pow(beta,4)-pow(beta,6)),1.5)))*pprimdotbeta
+ -beta*Eprim/pow(fGamma,3))*dbeta,2) );
- Double_t E;
- E=fGamma*(Eprim+pprimdotbeta);
+ Double_t vb[3],eb[3];
+ fBeta.GetVector(vb,"car");
+ fBeta.GetErrors(eb,"car");
+ for (Int_t i=0; i<3; i++)
+ {
+ eb[i]=sqrt(pow(z*eb[i],2)+pow(vb[i]*dz,2));
+ }
+ add.SetErrors(eb,"car");
- Ali3Vector term1,term2,p;
- term1=fBeta*((fGamma-1.)*pprimdotbeta/fBeta2);
- term2=fBeta*(fGamma*Eprim);
- p=pprim+term1+term2;
+ // Calculate the new 3-vector
+ Ali3Vector p=pprim+add;
+ // Set the components and errors of the new 4-vector
Ali4Vector w;
w.SetVector(E,p);
+ w.SetScalarError(dE);
return w;
}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff