1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
18 ///////////////////////////////////////////////////////////////////////////
20 // Perform various Lorentz transformations.
25 // Float_t a[3]={0.1,0.2,0.3};
26 // Float_t ea[3]={0.01,0.02,0.03};
28 // beta.SetVector(a,"car");
29 // beta.SetErrors(ea,"car");
35 // Float_t b[4]={14,1,2,3};
36 // Float_t eb[4]={1.4,0.1,0.2,0.3};
38 // p.SetVector(b,"car");
39 // p.SetErrors(eb,"car");
40 // Ali4Vector pprim=b1.Boost(p);
44 // p=b1.Inverse(pprim);
48 // Float_t c[4]={5,0,0,4};
49 // Float_t ec[4]={0.5,0,0,0.4};
51 // q.SetVector(c,"car");
52 // q.SetErrors(ec,"car");
55 // b2.Set4Momentum(q);
58 //--- Author: Nick van Eijndhoven 14-may-1996 UU-SAP Utrecht
59 //- Modified: NvE $Date$ UU-SAP Utrecht
60 ///////////////////////////////////////////////////////////////////////////
64 ClassImp(AliBoost) // Class implementation to enable ROOT I/O
68 // Creation of a Lorentz boost object and initialisation of parameters.
69 // Beta is set to (0,0,0) and consequently Gamma=1.
70 // All errors are initialised to 0.
71 Double_t a[3]={0,0,0};
72 fBeta.SetVector(a,"sph");
77 ///////////////////////////////////////////////////////////////////////////
80 // Default destructor.
82 ///////////////////////////////////////////////////////////////////////////
83 void AliBoost::SetBeta(Ali3Vector b)
85 // Setting of boost parameters on basis of beta 3-vector.
86 // The errors on the beta 3-vector are taken from the input 3-vector.
87 // The gamma value and its error are calculated accordingly.
89 Double_t beta2=fBeta.Dot(fBeta);
90 Double_t dbeta2=fBeta.GetResultError();
94 cout << " *AliBoost::SetBeta* beta > 1." << endl;
98 Double_t temp=1.-beta2;
101 fGamma=sqrt(1./temp);
102 fDgamma=fabs(dbeta2/(2.*pow(temp,1.5)));
105 ///////////////////////////////////////////////////////////////////////////
106 void AliBoost::Set4Momentum(Ali4Vector& p)
108 // Setting of boost parameters on basis of momentum 4-vector data.
109 // The errors of the input 4-vector are used to calculate the
110 // errors on the beta 3-vector and the gamma factor.
111 Double_t E=p.GetScalar();
112 Double_t dE=p.GetResultError();
115 cout << " *AliBoost::Set4Momentum* Unphysical situation." << endl;
120 Ali3Vector b=p.Get3Vector();
121 Double_t vb[3],eb[3];
122 b.GetVector(vb,"car");
123 b.GetErrors(eb,"car");
125 for (Int_t i=0; i<3; i++)
127 eb[i]=sqrt(pow(eb[i]/E,2)+pow(vb[i]*dE/(E*E),2));
129 b.SetErrors(eb,"car");
133 ///////////////////////////////////////////////////////////////////////////
134 Ali3Vector AliBoost::GetBetaVector()
136 // Provide the beta 3-vector.
139 ///////////////////////////////////////////////////////////////////////////
140 Double_t AliBoost::GetBeta()
142 // Provide the norm of the beta 3-vector.
143 // The error on the value can be obtained via GetResultError().
144 Double_t norm=fBeta.GetNorm();
145 fDresult=fBeta.GetResultError();
148 ///////////////////////////////////////////////////////////////////////////
149 Double_t AliBoost::GetGamma()
151 // Provide the gamma factor.
152 // The error on the value can be obtained via GetResultError().
156 ///////////////////////////////////////////////////////////////////////////
157 Double_t AliBoost::GetResultError()
159 // Provide the error on the result of an operation yielding a scalar.
160 // E.g. GetBeta() or GetGamma()
163 ///////////////////////////////////////////////////////////////////////////
164 void AliBoost::Info(TString f)
166 // Printing of the boost parameter info in coordinate frame f.
167 Double_t beta=fBeta.GetNorm();
168 Double_t dbeta=fBeta.GetResultError();
169 cout << " *AliBoost::Info* beta : " << beta << " error : " << dbeta
170 << " gamma : " << fGamma << " error : " << fDgamma << endl;
174 ///////////////////////////////////////////////////////////////////////////
175 Ali4Vector AliBoost::Boost(Ali4Vector& v)
177 // Perform the Lorentz boost on the 4-vector v.
178 // Error propagation is performed automatically.
179 // Note : As an approximation Beta and p.Dot(Beta) are considered as
180 // independent quantities.
182 Double_t beta=fBeta.GetNorm();
183 Double_t dbeta=fBeta.GetResultError();
185 Double_t beta2=pow(beta,2);
189 Double_t E=v.GetScalar();
190 Double_t dE=v.GetResultError();
192 Ali3Vector p=v.Get3Vector();
194 Double_t pdotbeta=p.Dot(fBeta);
195 Double_t dpdotbeta=p.GetResultError();
197 // Determine the new vector components
198 Double_t Eprim=fGamma*(E-pdotbeta);
200 Double_t z=((fGamma-1.)*pdotbeta/beta2)-fGamma*E;
201 Ali3Vector add=fBeta*z;
203 // Determine errors on the new vector components
204 Double_t dEprim=sqrt(pow((E-pdotbeta)*fDgamma,2)+pow(fGamma*dE,2)
205 +pow(fGamma*dpdotbeta,2));
206 Double_t dz=sqrt( pow(((fGamma-1.)/beta2)*dpdotbeta,2) + pow(fGamma*dE,2)
208 ((2./beta)-(4.*pow(beta,3)-6.*pow(beta,5))/(2.*pow((pow(beta,4)-pow(beta,6)),1.5)))*pdotbeta
209 +beta*E/pow(fGamma,3))*dbeta,2) );
211 Double_t vb[3],eb[3];
212 fBeta.GetVector(vb,"car");
213 fBeta.GetErrors(eb,"car");
214 for (Int_t i=0; i<3; i++)
216 eb[i]=sqrt(pow(z*eb[i],2)+pow(vb[i]*dz,2));
218 add.SetErrors(eb,"car");
220 // Calculate the new 3-vector
221 Ali3Vector pprim=p+add;
223 // Set the components and errors of the new 4-vector
225 w.SetVector(Eprim,pprim);
226 w.SetScalarError(dEprim);
235 ///////////////////////////////////////////////////////////////////////////
236 Ali4Vector AliBoost::Inverse(Ali4Vector& vprim)
238 // Perform the inverse Lorentz boost on the 4-vector vprim.
239 // Error propagation is performed automatically.
240 // Note : As an approximation Beta and pprim.Dot(Beta) are considered as
241 // independent quantities.
243 Double_t beta=fBeta.GetNorm();
244 Double_t dbeta=fBeta.GetResultError();
246 Double_t beta2=pow(beta,2);
250 Double_t Eprim=vprim.GetScalar();
251 Double_t dEprim=vprim.GetResultError();
253 Ali3Vector pprim=vprim.Get3Vector();
255 Double_t pprimdotbeta=pprim.Dot(fBeta);
256 Double_t dpprimdotbeta=pprim.GetResultError();
258 // Determine the new vector components
259 Double_t E=fGamma*(Eprim+pprimdotbeta);
261 Double_t z=((fGamma-1.)*pprimdotbeta/beta2)+fGamma*Eprim;
262 Ali3Vector add=fBeta*z;
264 // Determine errors on the prime-vector components
265 Double_t dE=sqrt(pow((Eprim+pprimdotbeta)*fDgamma,2)+pow(fGamma*dEprim,2)
266 +pow(fGamma*dpprimdotbeta,2));
267 Double_t dz=sqrt( pow(((fGamma-1.)/beta2)*dpprimdotbeta,2) + pow(fGamma*dEprim,2)
269 ((2./beta)-(4.*pow(beta,3)-6.*pow(beta,5))/(2.*pow((pow(beta,4)-pow(beta,6)),1.5)))*pprimdotbeta
270 -beta*Eprim/pow(fGamma,3))*dbeta,2) );
272 Double_t vb[3],eb[3];
273 fBeta.GetVector(vb,"car");
274 fBeta.GetErrors(eb,"car");
275 for (Int_t i=0; i<3; i++)
277 eb[i]=sqrt(pow(z*eb[i],2)+pow(vb[i]*dz,2));
279 add.SetErrors(eb,"car");
281 // Calculate the new 3-vector
282 Ali3Vector p=pprim+add;
284 // Set the components and errors of the new 4-vector
287 w.SetScalarError(dE);
296 ///////////////////////////////////////////////////////////////////////////