]> git.uio.no Git - u/mrichter/AliRoot.git/blame - STEER/AliExternalTrackParam.cxx
git://git.uio.no / u / mrichter / AliRoot.git / blame
? search:
summary | shortlog | log | commit | commitdiff | tree
blob | blame (incremental) | history | HEAD
sin(phi)=1 is acceptable. However, for the error calculations, it is safer if sin...
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
CommitLineData
51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
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 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
4b189f98 28#include <TMatrixDSym.h>
d46683db 29#include <TPolyMarker3D.h>
30#include <TVector3.h>
cfdb62d4 31#include <TMatrixD.h>
d46683db 32
51ad6848 33#include "AliExternalTrackParam.h"
58e536c5 34#include "AliVVertex.h"
6c94f330 35#include "AliLog.h"
51ad6848 36
37ClassImp(AliExternalTrackParam)
38
ed5f2849 39Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
40
51ad6848 41//_____________________________________________________________________________
90e48c0c 42AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 43 AliVTrack(),
90e48c0c 44 fX(0),
c9ec41e8 45 fAlpha(0)
51ad6848 46{
90e48c0c 47 //
48 // default constructor
49 //
c9ec41e8 50 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
51 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 52}
53
6c94f330 54//_____________________________________________________________________________
55AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 56 AliVTrack(track),
6c94f330 57 fX(track.fX),
58 fAlpha(track.fAlpha)
59{
60 //
61 // copy constructor
62 //
63 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
64 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
65}
66
def9660e 67//_____________________________________________________________________________
68AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
69{
70 //
71 // assignment operator
72 //
73
74 if (this!=&trkPar) {
4f6e22bd 75 AliVTrack::operator=(trkPar);
def9660e 76 fX = trkPar.fX;
77 fAlpha = trkPar.fAlpha;
78
79 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
80 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
81 }
82
83 return *this;
84}
85
51ad6848 86//_____________________________________________________________________________
87AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
88 const Double_t param[5],
90e48c0c 89 const Double_t covar[15]) :
4f6e22bd 90 AliVTrack(),
90e48c0c 91 fX(x),
c9ec41e8 92 fAlpha(alpha)
51ad6848 93{
90e48c0c 94 //
95 // create external track parameters from given arguments
96 //
c9ec41e8 97 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
98 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 99}
100
4f6e22bd 101//_____________________________________________________________________________
102AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
103 AliVTrack(),
104 fX(0.),
105 fAlpha(0.)
106{
107 //
610e3088 108 // Constructor from virtual track,
109 // This is not a copy contructor !
4f6e22bd 110 //
610e3088 111
112 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
113 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
114 AliWarning("Calling the default constructor...");
115 AliExternalTrackParam();
116 return;
117 }
118
892be05f 119 Double_t xyz[3],pxpypz[3],cv[21];
120 vTrack->GetXYZ(xyz);
121 pxpypz[0]=vTrack->Px();
122 pxpypz[1]=vTrack->Py();
123 pxpypz[2]=vTrack->Pz();
4f6e22bd 124 vTrack->GetCovarianceXYZPxPyPz(cv);
125 Short_t sign = (Short_t)vTrack->Charge();
126
127 Set(xyz,pxpypz,cv,sign);
128}
129
90e48c0c 130//_____________________________________________________________________________
da4e3deb 131AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
132 Double_t cv[21],Short_t sign) :
4f6e22bd 133 AliVTrack(),
da4e3deb 134 fX(0.),
135 fAlpha(0.)
4f6e22bd 136{
137 //
138 // constructor from the global parameters
139 //
140
141 Set(xyz,pxpypz,cv,sign);
142}
143
144//_____________________________________________________________________________
145void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
146 Double_t cv[21],Short_t sign)
da4e3deb 147{
148 //
149 // create external track parameters from the global parameters
150 // x,y,z,px,py,pz and their 6x6 covariance matrix
151 // A.Dainese 10.10.08
152
aff56ff7 153 // Calculate alpha: the rotation angle of the corresponding local system.
154 //
155 // For global radial position inside the beam pipe, alpha is the
156 // azimuthal angle of the momentum projected on (x,y).
157 //
c99948ce 158 // For global radial position outside the ITS, alpha is the
aff56ff7 159 // azimuthal angle of the centre of the TPC sector in which the point
160 // xyz lies
161 //
162 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 163 Double_t radMax = 45.; // approximately ITS outer radius
164 if (radPos2 < radMax*radMax) { // inside the ITS
165
aff56ff7 166 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
c99948ce 167 } else { // outside the ITS
aff56ff7 168 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
169 fAlpha =
170 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
171 }
da4e3deb 172
173 // Get the vertex of origin and the momentum
174 TVector3 ver(xyz[0],xyz[1],xyz[2]);
175 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
176
177 // Rotate to the local coordinate system
178 ver.RotateZ(-fAlpha);
179 mom.RotateZ(-fAlpha);
180
181 // x of the reference plane
182 fX = ver.X();
183
184 Double_t charge = (Double_t)sign;
185
186 fP[0] = ver.Y();
187 fP[1] = ver.Z();
188 fP[2] = TMath::Sin(mom.Phi());
189 fP[3] = mom.Pz()/mom.Pt();
190 fP[4] = TMath::Sign(1/mom.Pt(),charge);
191
192 // Covariance matrix (formulas to be simplified)
193
194 Double_t pt=1./TMath::Abs(fP[4]);
195 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
196 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
197
198 Double_t m00=-sn;// m10=cs;
199 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
200 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
201 Double_t m35=pt, m45=-pt*pt*fP[3];
202
203 m43*=GetSign();
204 m44*=GetSign();
205 m45*=GetSign();
206
207 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
208 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
209 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
210 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
211 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
212 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
213 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
214
215 fC[0 ] = cv[0 ]+cv[2 ];
216 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
217 fC[2 ] = cv[5 ];
218 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
219 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
220 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
221 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
222 fC[11] = (cv[8]-fC[4]*m23)/m43;
223 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
224 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
225 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
226 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
227 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
228 Double_t b2=m23*m35;
229 Double_t b3=m43*m35;
230 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
231 Double_t b5=m24*m35;
232 Double_t b6=m44*m35;
233 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
234 fC[13] = b1/b3-b2*fC[8]/b3;
235 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 236
237 return;
da4e3deb 238}
239
51ad6848 240//_____________________________________________________________________________
c9ec41e8 241void AliExternalTrackParam::Reset() {
1530f89c 242 //
243 // Resets all the parameters to 0
244 //
c9ec41e8 245 fX=fAlpha=0.;
246 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
247 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 248}
249
3775b0ca 250//_____________________________________________________________________________
251void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
252 //
253 // Add "something" to the track covarince matrix.
254 // May be needed to account for unknown mis-calibration/mis-alignment
255 //
256 fC[0] +=c[0];
257 fC[1] +=c[1]; fC[2] +=c[2];
258 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
259 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
260 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
261}
262
263
c9ec41e8 264Double_t AliExternalTrackParam::GetP() const {
265 //---------------------------------------------------------------------
266 // This function returns the track momentum
267 // Results for (nearly) straight tracks are meaningless !
268 //---------------------------------------------------------------------
06fb4a2f 269 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 270 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 271}
272
1d99986f 273Double_t AliExternalTrackParam::Get1P() const {
274 //---------------------------------------------------------------------
275 // This function returns the 1/(track momentum)
276 //---------------------------------------------------------------------
277 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
278}
279
c9ec41e8 280//_______________________________________________________________________
c7bafca9 281Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 282 //------------------------------------------------------------------
283 // This function calculates the transverse impact parameter
284 // with respect to a point with global coordinates (x,y)
285 // in the magnetic field "b" (kG)
286 //------------------------------------------------------------------
5773defd 287 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 288 Double_t rp4=GetC(b);
c9ec41e8 289
290 Double_t xt=fX, yt=fP[0];
291
292 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
293 Double_t a = x*cs + y*sn;
294 y = -x*sn + y*cs; x=a;
295 xt-=x; yt-=y;
296
bfd20868 297 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2]));
298 a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
1530f89c 299 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
300}
301
302//_______________________________________________________________________
303void AliExternalTrackParam::
304GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
305 //------------------------------------------------------------------
306 // This function calculates the transverse and longitudinal impact parameters
307 // with respect to a point with global coordinates (x,y)
308 // in the magnetic field "b" (kG)
309 //------------------------------------------------------------------
bfd20868 310 Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1));
1530f89c 311 Double_t xt=fX, yt=fP[0];
312 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
313 Double_t a = x*cs + y*sn;
314 y = -x*sn + y*cs; x=a;
315 xt-=x; yt-=y;
316
317 Double_t rp4=GetC(b);
318 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
319 dz[0] = -(xt*f1 - yt*r1);
320 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
321 return;
322 }
323
324 sn=rp4*xt - f1; cs=rp4*yt + r1;
325 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
326 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
327 dz[0] = -a/(1 + rr);
bfd20868 328 Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2));
1530f89c 329 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 330}
331
49d13e89 332//_______________________________________________________________________
333Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
334 //------------------------------------------------------------------
335 // This function calculates the transverse impact parameter
336 // with respect to a point with global coordinates (xv,yv)
337 // neglecting the track curvature.
338 //------------------------------------------------------------------
339 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
340 Double_t x= xv*cs + yv*sn;
341 Double_t y=-xv*sn + yv*cs;
342
bfd20868 343 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
49d13e89 344
1530f89c 345 return -d;
49d13e89 346}
347
116b445b 348Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 349(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
350 Double_t (*Bethe)(Double_t)) {
116b445b 351 //------------------------------------------------------------------
352 // This function corrects the track parameters for the crossed material.
353 // "xOverX0" - X/X0, the thickness in units of the radiation length.
354 // "xTimesRho" - is the product length*density (g/cm^2).
355 // "mass" - the mass of this particle (GeV/c^2).
356 //------------------------------------------------------------------
357 Double_t &fP2=fP[2];
358 Double_t &fP3=fP[3];
359 Double_t &fP4=fP[4];
360
361 Double_t &fC22=fC[5];
362 Double_t &fC33=fC[9];
363 Double_t &fC43=fC[13];
364 Double_t &fC44=fC[14];
365
7dded1d5 366 //Apply angle correction, if requested
367 if(anglecorr) {
bfd20868 368 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
7dded1d5 369 xOverX0 *=angle;
370 xTimesRho *=angle;
371 }
372
116b445b 373 Double_t p=GetP();
374 Double_t p2=p*p;
375 Double_t beta2=p2/(p2 + mass*mass);
116b445b 376
9f2bec63 377 //Calculating the multiple scattering corrections******************
378 Double_t cC22 = 0.;
379 Double_t cC33 = 0.;
380 Double_t cC43 = 0.;
381 Double_t cC44 = 0.;
116b445b 382 if (xOverX0 != 0) {
383 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
384 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 385 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
bfd20868 386 cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3);
9f2bec63 387 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
388 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
389 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 390 }
391
9f2bec63 392 //Calculating the energy loss corrections************************
393 Double_t cP4=1.;
116b445b 394 if ((xTimesRho != 0.) && (beta2 < 1.)) {
d46683db 395 Double_t dE=Bethe(p/mass)*xTimesRho;
116b445b 396 Double_t e=TMath::Sqrt(p2 + mass*mass);
397 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
9f2bec63 398 cP4 = (1.- e/p2*dE);
399 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 400
116b445b 401
402 // Approximate energy loss fluctuation (M.Ivanov)
403 const Double_t knst=0.07; // To be tuned.
404 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 405 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 406
407 }
408
9f2bec63 409 //Applying the corrections*****************************
410 fC22 += cC22;
411 fC33 += cC33;
412 fC43 += cC43;
413 fC44 += cC44;
414 fP4 *= cP4;
415
116b445b 416 return kTRUE;
417}
418
419
ee5dba5e 420Bool_t AliExternalTrackParam::CorrectForMaterial
421(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 422 //------------------------------------------------------------------
116b445b 423 // Deprecated function !
424 // Better use CorrectForMeanMaterial instead of it.
425 //
c7bafca9 426 // This function corrects the track parameters for the crossed material
427 // "d" - the thickness (fraction of the radiation length)
428 // "x0" - the radiation length (g/cm^2)
429 // "mass" - the mass of this particle (GeV/c^2)
430 //------------------------------------------------------------------
431 Double_t &fP2=fP[2];
432 Double_t &fP3=fP[3];
433 Double_t &fP4=fP[4];
434
435 Double_t &fC22=fC[5];
436 Double_t &fC33=fC[9];
437 Double_t &fC43=fC[13];
438 Double_t &fC44=fC[14];
439
7b5ef2e6 440 Double_t p=GetP();
441 Double_t p2=p*p;
c7bafca9 442 Double_t beta2=p2/(p2 + mass*mass);
bfd20868 443 d*=TMath::Sqrt((1.+ fP3*fP3)/((1.-fP2)*(1.+fP2)));
c7bafca9 444
445 //Multiple scattering******************
9f2bec63 446 Double_t cC22 = 0.;
447 Double_t cC33 = 0.;
448 Double_t cC43 = 0.;
449 Double_t cC44 = 0.;
c7bafca9 450 if (d!=0) {
451 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
452 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 453 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
bfd20868 454 cC22 = theta2*(1.-fP2)*(1.+fP2)*(1. + fP3*fP3);
9f2bec63 455 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
456 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
457 cC44 = theta2*fP3*fP4*fP3*fP4;
c7bafca9 458 }
459
460 //Energy losses************************
9f2bec63 461 Double_t cP4=1.;
8fc1985d 462 if (x0!=0. && beta2<1) {
c7bafca9 463 d*=x0;
d46683db 464 Double_t dE=Bethe(p/mass)*d;
ee5dba5e 465 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 466 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
9f2bec63 467 cP4 = (1.- e/p2*dE);
ee5dba5e 468
469 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 470 const Double_t knst=0.07; // To be tuned.
471 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 472 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
ee5dba5e 473
c7bafca9 474 }
475
9f2bec63 476 fC22 += cC22;
477 fC33 += cC33;
478 fC43 += cC43;
479 fC44 += cC44;
480 fP4 *= cP4;
481
c7bafca9 482 return kTRUE;
483}
484
9c56b409 485Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
486 Double_t kp1,
487 Double_t kp2,
488 Double_t kp3,
489 Double_t kp4,
490 Double_t kp5) {
491 //
492 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
493 // It is normalized to 1 at the minimum.
494 //
495 // bg - beta*gamma
496 //
497 // The default values for the kp* parameters are for ALICE TPC.
498 // The returned value is in MIP units
499 //
500
501 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
502
503 Double_t aa = TMath::Power(beta,kp4);
504 Double_t bb = TMath::Power(1./bg,kp5);
505
506 bb=TMath::Log(kp3+bb);
507
508 return (kp2-aa-bb)*kp1/aa;
509}
510
511Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
512 Double_t kp0,
513 Double_t kp1,
514 Double_t kp2,
515 Double_t kp3,
516 Double_t kp4) {
517 //
518 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
519 //
520 // bg - beta*gamma
521 // kp0 - density [g/cm^3]
522 // kp1 - density effect first junction point
523 // kp2 - density effect second junction point
524 // kp3 - mean excitation energy [GeV]
525 // kp4 - mean Z/A
526 //
527 // The default values for the kp* parameters are for silicon.
528 // The returned value is in [GeV/(g/cm^2)].
529 //
530
531 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
532 const Double_t me = 0.511e-3; // [GeV/c^2]
533 const Double_t rho = kp0;
534 const Double_t x0 = kp1*2.303;
535 const Double_t x1 = kp2*2.303;
536 const Double_t mI = kp3;
537 const Double_t mZA = kp4;
538 const Double_t bg2 = bg*bg;
539 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
540
541 //*** Density effect
542 Double_t d2=0.;
543 const Double_t x=TMath::Log(bg);
544 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
545 if (x > x1) {
546 d2 = lhwI + x - 0.5;
547 } else if (x > x0) {
548 const Double_t r=(x1-x)/(x1-x0);
549 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
550 }
551
552 return mK*mZA*(1+bg2)/bg2*
553 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
554}
555
d46683db 556Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 557 //------------------------------------------------------------------
d46683db 558 // This is an approximation of the Bethe-Bloch formula,
559 // reasonable for solid materials.
560 // All the parameters are, in fact, for Si.
9b655cba 561 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 562 //------------------------------------------------------------------
a821848c 563
9c56b409 564 return BetheBlochGeant(bg);
d46683db 565}
ee5dba5e 566
d46683db 567Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
568 //------------------------------------------------------------------
569 // This is an approximation of the Bethe-Bloch formula,
570 // reasonable for gas materials.
571 // All the parameters are, in fact, for Ne.
9b655cba 572 // The returned value is in [GeV/(g/cm^2)]
d46683db 573 //------------------------------------------------------------------
574
575 const Double_t rho = 0.9e-3;
576 const Double_t x0 = 2.;
577 const Double_t x1 = 4.;
578 const Double_t mI = 140.e-9;
579 const Double_t mZA = 0.49555;
580
9c56b409 581 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 582}
583
49d13e89 584Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
585 //------------------------------------------------------------------
586 // Transform this track to the local coord. system rotated
587 // by angle "alpha" (rad) with respect to the global coord. system.
588 //------------------------------------------------------------------
dfcef74c 589 if (TMath::Abs(fP[2]) >= kAlmost1) {
590 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
591 return kFALSE;
592 }
593
49d13e89 594 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
595 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
596
597 Double_t &fP0=fP[0];
598 Double_t &fP2=fP[2];
599 Double_t &fC00=fC[0];
600 Double_t &fC10=fC[1];
601 Double_t &fC20=fC[3];
602 Double_t &fC21=fC[4];
603 Double_t &fC22=fC[5];
604 Double_t &fC30=fC[6];
605 Double_t &fC32=fC[8];
606 Double_t &fC40=fC[10];
607 Double_t &fC42=fC[12];
608
609 Double_t x=fX;
610 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
bfd20868 611 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
49d13e89 612
dfcef74c 613 Double_t tmp=sf*ca - cf*sa;
7248cf51 614 if (TMath::Abs(tmp) >= kAlmost1) {
615 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
616 AliWarning(Form("Rotation failed ! %.10e",tmp));
0b69bbb2 617 return kFALSE;
618 }
dfcef74c 619
49d13e89 620 fAlpha = alpha;
621 fX = x*ca + fP0*sa;
622 fP0= -x*sa + fP0*ca;
dfcef74c 623 fP2= tmp;
49d13e89 624
06fb4a2f 625 if (TMath::Abs(cf)<kAlmost0) {
626 AliError(Form("Too small cosine value %f",cf));
627 cf = kAlmost0;
628 }
629
49d13e89 630 Double_t rr=(ca+sf/cf*sa);
631
632 fC00 *= (ca*ca);
633 fC10 *= ca;
634 fC20 *= ca*rr;
635 fC21 *= rr;
636 fC22 *= rr*rr;
637 fC30 *= ca;
638 fC32 *= rr;
639 fC40 *= ca;
640 fC42 *= rr;
641
642 return kTRUE;
643}
644
645Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
646 //----------------------------------------------------------------
647 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
648 //----------------------------------------------------------------
49d13e89 649 Double_t dx=xk-fX;
e421f556 650 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 651
1530f89c 652 Double_t crv=GetC(b);
5773defd 653 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
654
49d13e89 655 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 656 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 657 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
658
659 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
660 Double_t
661 &fC00=fC[0],
662 &fC10=fC[1], &fC11=fC[2],
663 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
664 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
665 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
666
bfd20868 667 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
49d13e89 668
669 fX=xk;
670 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 671 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 672 fP2 += dx*crv;
673
674 //f = F - 1
675
676 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
677 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
678 Double_t f12= dx*fP3*f1/(r1*r1*r1);
679 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
680 Double_t f13= dx/r1;
681 Double_t f24= dx; f24*=cc;
682
683 //b = C*ft
684 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
685 Double_t b02=f24*fC40;
686 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
687 Double_t b12=f24*fC41;
688 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
689 Double_t b22=f24*fC42;
690 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
691 Double_t b42=f24*fC44;
692 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
693 Double_t b32=f24*fC43;
694
695 //a = f*b = f*C*ft
696 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
697 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
698 Double_t a22=f24*b42;
699
700 //F*C*Ft = C + (b + bt + a)
701 fC00 += b00 + b00 + a00;
702 fC10 += b10 + b01 + a01;
703 fC20 += b20 + b02 + a02;
704 fC30 += b30;
705 fC40 += b40;
706 fC11 += b11 + b11 + a11;
707 fC21 += b21 + b12 + a12;
708 fC31 += b31;
709 fC41 += b41;
710 fC22 += b22 + b22 + a22;
711 fC32 += b32;
712 fC42 += b42;
713
714 return kTRUE;
715}
716
9f2bec63 717Bool_t
718AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
719 //------------------------------------------------------------------
720 // Transform this track to the local coord. system rotated
721 // by angle "alpha" (rad) with respect to the global coord. system,
722 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
723 //------------------------------------------------------------------
724
725 //Save the parameters
726 Double_t as=fAlpha;
727 Double_t xs=fX;
728 Double_t ps[5], cs[15];
729 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
730 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
731
732 if (Rotate(alpha))
733 if (PropagateTo(x,b)) return kTRUE;
734
735 //Restore the parameters, if the operation failed
736 fAlpha=as;
737 fX=xs;
738 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
739 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
740 return kFALSE;
741}
742
266a0f9b 743Bool_t AliExternalTrackParam::PropagateBxByBz
744(Double_t alpha, Double_t x, Double_t b[3]) {
745 //------------------------------------------------------------------
746 // Transform this track to the local coord. system rotated
747 // by angle "alpha" (rad) with respect to the global coord. system,
748 // and propagate this track to the plane X=xk (cm),
749 // taking into account all three components of the B field, "b[3]" (kG)
750 //------------------------------------------------------------------
751
752 //Save the parameters
753 Double_t as=fAlpha;
754 Double_t xs=fX;
755 Double_t ps[5], cs[15];
756 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
757 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
758
759 if (Rotate(alpha))
760 if (PropagateToBxByBz(x,b)) return kTRUE;
761
762 //Restore the parameters, if the operation failed
763 fAlpha=as;
764 fX=xs;
765 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
766 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
767 return kFALSE;
768}
769
9f2bec63 770
052daaff 771void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
772Double_t p[3], Double_t bz) const {
773 //+++++++++++++++++++++++++++++++++++++++++
774 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
775 // Extrapolate track along simple helix in magnetic field
776 // Arguments: len -distance alogn helix, [cm]
777 // bz - mag field, [kGaus]
778 // Returns: x and p contain extrapolated positon and momentum
779 // The momentum returned for straight-line tracks is meaningless !
780 //+++++++++++++++++++++++++++++++++++++++++
781 GetXYZ(x);
782
2258e165 783 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 784 Double_t unit[3]; GetDirection(unit);
785 x[0]+=unit[0]*len;
786 x[1]+=unit[1]*len;
787 x[2]+=unit[2]*len;
788
789 p[0]=unit[0]/kAlmost0;
790 p[1]=unit[1]/kAlmost0;
791 p[2]=unit[2]/kAlmost0;
792 } else {
793 GetPxPyPz(p);
794 Double_t pp=GetP();
795 Double_t a = -kB2C*bz*GetSign();
796 Double_t rho = a/pp;
797 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
798 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
799 x[2] += p[2]*len/pp;
800
801 Double_t p0=p[0];
802 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
803 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
804 }
805}
806
807Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
808Double_t bz) const {
809 //+++++++++++++++++++++++++++++++++++++++++
810 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
811 // Finds point of intersection (if exists) of the helix with the plane.
812 // Stores result in fX and fP.
813 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
814 // and vector, normal to the plane
815 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
816 //+++++++++++++++++++++++++++++++++++++++++
817 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
818
819 //estimates initial helix length up to plane
820 Double_t s=
821 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
822 Double_t dist=99999,distPrev=dist;
823 Double_t x[3],p[3];
824 while(TMath::Abs(dist)>0.00001){
825 //calculates helix at the distance s from x0 ALONG the helix
826 Propagate(s,x,p,bz);
827
828 //distance between current helix position and plane
829 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
830
831 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
832 distPrev=dist;
833 s-=dist;
834 }
835 //on exit pnt is intersection point,norm is track vector at that point,
836 //all in MARS
837 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
838 return kTRUE;
839}
840
49d13e89 841Double_t
842AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
843 //----------------------------------------------------------------
844 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
845 //----------------------------------------------------------------
846 Double_t sdd = fC[0] + cov[0];
847 Double_t sdz = fC[1] + cov[1];
848 Double_t szz = fC[2] + cov[2];
849 Double_t det = sdd*szz - sdz*sdz;
850
851 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
852
853 Double_t d = fP[0] - p[0];
854 Double_t z = fP[1] - p[1];
855
856 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
857}
858
4b189f98 859Double_t AliExternalTrackParam::
860GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
861 //----------------------------------------------------------------
862 // Estimate the chi2 of the 3D space point "p" and
1e023a36 863 // the full covariance matrix "covyz" and "covxyz"
4b189f98 864 //
865 // Cov(x,x) ... : covxyz[0]
866 // Cov(y,x) ... : covxyz[1] covyz[0]
867 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
868 //----------------------------------------------------------------
869
870 Double_t res[3] = {
871 GetX() - p[0],
872 GetY() - p[1],
873 GetZ() - p[2]
874 };
875
876 Double_t f=GetSnp();
877 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
bfd20868 878 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
4b189f98 879 Double_t a=f/r, b=GetTgl()/r;
880
881 Double_t s2=333.*333.; //something reasonably big (cm^2)
882
883 TMatrixDSym v(3);
884 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
885 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
886 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
887
888 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
889 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
890 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
891
892 v.Invert();
893 if (!v.IsValid()) return kVeryBig;
894
895 Double_t chi2=0.;
896 for (Int_t i = 0; i < 3; i++)
897 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
898
899 return chi2;
acdfbc78 900}
901
902Double_t AliExternalTrackParam::
903GetPredictedChi2(const AliExternalTrackParam *t) const {
904 //----------------------------------------------------------------
905 // Estimate the chi2 (5 dof) of this track with respect to the track
906 // given by the argument.
907 // The two tracks must be in the same reference system
908 // and estimated at the same reference plane.
909 //----------------------------------------------------------------
910
911 if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) {
912 AliError("The reference systems of the tracks differ !");
913 return kVeryBig;
914 }
915 if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) {
916 AliError("The reference of the tracks planes differ !");
917 return kVeryBig;
918 }
919
920 TMatrixDSym c(5);
921 c(0,0)=GetSigmaY2();
922 c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
923 c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
924 c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
925 c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
926
927 c(0,0)+=t->GetSigmaY2();
928 c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
929 c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
930 c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
931 c(4,0)+=t->GetSigma1PtY();c(4,1)+=t->GetSigma1PtZ();c(4,2)+=t->GetSigma1PtSnp();c(4,3)+=t->GetSigma1PtTgl();c(4,4)+=t->GetSigma1Pt2();
932 c(0,1)=c(1,0);
933 c(0,2)=c(2,0); c(1,2)=c(2,1);
934 c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
935 c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
936
937 c.Invert();
938 if (!c.IsValid()) return kVeryBig;
939
940
941 Double_t res[5] = {
942 GetY() - t->GetY(),
943 GetZ() - t->GetZ(),
944 GetSnp() - t->GetSnp(),
945 GetTgl() - t->GetTgl(),
946 GetSigned1Pt() - t->GetSigned1Pt()
947 };
4b189f98 948
acdfbc78 949 Double_t chi2=0.;
950 for (Int_t i = 0; i < 5; i++)
951 for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
4b189f98 952
acdfbc78 953 return chi2;
4b189f98 954}
955
1e023a36 956Bool_t AliExternalTrackParam::
957PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
958 //----------------------------------------------------------------
959 // Propagate this track to the plane
960 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
961 // belongs to.
962 // The magnetic field is "bz" (kG)
963 //
964 // The track curvature and the change of the covariance matrix
965 // of the track parameters are negleted !
966 // (So the "step" should be small compared with 1/curvature)
967 //----------------------------------------------------------------
968
969 Double_t f=GetSnp();
970 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
bfd20868 971 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
1e023a36 972 Double_t a=f/r, b=GetTgl()/r;
973
974 Double_t s2=333.*333.; //something reasonably big (cm^2)
975
976 TMatrixDSym tV(3);
977 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
978 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
979 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
980
981 TMatrixDSym pV(3);
982 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
983 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
984 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
985
986 TMatrixDSym tpV(tV);
987 tpV+=pV;
988 tpV.Invert();
989 if (!tpV.IsValid()) return kFALSE;
990
991 TMatrixDSym pW(3),tW(3);
992 for (Int_t i=0; i<3; i++)
993 for (Int_t j=0; j<3; j++) {
994 pW(i,j)=tW(i,j)=0.;
995 for (Int_t k=0; k<3; k++) {
996 pW(i,j) += tV(i,k)*tpV(k,j);
997 tW(i,j) += pV(i,k)*tpV(k,j);
998 }
999 }
1000
1001 Double_t t[3] = {GetX(), GetY(), GetZ()};
1002
1003 Double_t x=0.;
1004 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
1005 Double_t crv=GetC(bz);
1006 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1007 f += crv*(x-fX);
1008 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
1009 fX=x;
1010
1011 fP[0]=0.;
1012 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
1013 fP[1]=0.;
1014 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
1015
1016 return kTRUE;
1017}
1018
e23a38cb 1019Double_t *AliExternalTrackParam::GetResiduals(
1020Double_t *p,Double_t *cov,Bool_t updated) const {
1021 //------------------------------------------------------------------
1022 // Returns the track residuals with the space point "p" having
1023 // the covariance matrix "cov".
1024 // If "updated" is kTRUE, the track parameters expected to be updated,
1025 // otherwise they must be predicted.
1026 //------------------------------------------------------------------
1027 static Double_t res[2];
1028
1029 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1030 if (updated) {
1031 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
1032 } else {
1033 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
1034 }
1035 Double_t det=r00*r11 - r01*r01;
1036
1037 if (TMath::Abs(det) < kAlmost0) return 0;
1038
1039 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 1040
1041 if (r00 < 0.) return 0;
1042 if (r11 < 0.) return 0;
1043
e23a38cb 1044 Double_t dy = fP[0] - p[0];
1045 Double_t dz = fP[1] - p[1];
1046
1047 res[0]=dy*TMath::Sqrt(r00);
1048 res[1]=dz*TMath::Sqrt(r11);
1049
1050 return res;
1051}
1052
49d13e89 1053Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
1054 //------------------------------------------------------------------
1055 // Update the track parameters with the space point "p" having
1056 // the covariance matrix "cov"
1057 //------------------------------------------------------------------
1058 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
1059 Double_t
1060 &fC00=fC[0],
1061 &fC10=fC[1], &fC11=fC[2],
1062 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1063 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1064 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1065
1066 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1067 r00+=fC00; r01+=fC10; r11+=fC11;
1068 Double_t det=r00*r11 - r01*r01;
1069
1070 if (TMath::Abs(det) < kAlmost0) return kFALSE;
1071
1072
1073 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
1074
1075 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
1076 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
1077 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
1078 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
1079 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
1080
1081 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1082 Double_t sf=fP2 + k20*dy + k21*dz;
1083 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1084
1085 fP0 += k00*dy + k01*dz;
1086 fP1 += k10*dy + k11*dz;
1087 fP2 = sf;
1088 fP3 += k30*dy + k31*dz;
1089 fP4 += k40*dy + k41*dz;
1090
1091 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1092 Double_t c12=fC21, c13=fC31, c14=fC41;
1093
1094 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1095 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1096 fC40-=k00*c04+k01*c14;
1097
1098 fC11-=k10*c01+k11*fC11;
1099 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1100 fC41-=k10*c04+k11*c14;
1101
1102 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1103 fC42-=k20*c04+k21*c14;
1104
1105 fC33-=k30*c03+k31*c13;
1106 fC43-=k30*c04+k31*c14;
1107
1108 fC44-=k40*c04+k41*c14;
1109
1110 return kTRUE;
1111}
1112
c7bafca9 1113void
1114AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1115 //--------------------------------------------------------------------
1116 // External track parameters -> helix parameters
1117 // "b" - magnetic field (kG)
1118 //--------------------------------------------------------------------
1119 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1120
1530f89c 1121 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1122
1123 hlx[5]=fX*cs - hlx[0]*sn; // x0
1124 hlx[0]=fX*sn + hlx[0]*cs; // y0
1125//hlx[1]= // z0
1126 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1127//hlx[3]= // tgl
1530f89c 1128 hlx[4]=GetC(b); // C
c7bafca9 1129}
1130
1131
1132static void Evaluate(const Double_t *h, Double_t t,
1133 Double_t r[3], //radius vector
1134 Double_t g[3], //first defivatives
1135 Double_t gg[3]) //second derivatives
1136{
1137 //--------------------------------------------------------------------
1138 // Calculate position of a point on a track and some derivatives
1139 //--------------------------------------------------------------------
1140 Double_t phase=h[4]*t+h[2];
1141 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1142
ba4550c4 1143 r[0] = h[5];
1144 r[1] = h[0];
1145 if (TMath::Abs(h[4])>kAlmost0) {
1146 r[0] += (sn - h[6])/h[4];
1147 r[1] -= (cs - h[7])/h[4];
1148 }
c7bafca9 1149 r[2] = h[1] + h[3]*t;
1150
1151 g[0] = cs; g[1]=sn; g[2]=h[3];
1152
1153 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1154}
1155
1156Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1157Double_t b, Double_t &xthis, Double_t &xp) const {
1158 //------------------------------------------------------------
1159 // Returns the (weighed !) distance of closest approach between
1160 // this track and the track "p".
1161 // Other returned values:
1162 // xthis, xt - coordinates of tracks' reference planes at the DCA
1163 //-----------------------------------------------------------
1164 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1165 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1166 Double_t dx2=dy2;
1167
c7bafca9 1168 Double_t p1[8]; GetHelixParameters(p1,b);
1169 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1170 Double_t p2[8]; p->GetHelixParameters(p2,b);
1171 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1172
1173
1174 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1175 Evaluate(p1,t1,r1,g1,gg1);
1176 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1177 Evaluate(p2,t2,r2,g2,gg2);
1178
1179 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1180 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1181
1182 Int_t max=27;
1183 while (max--) {
1184 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1185 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1186 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1187 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1188 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1189 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1190 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1191 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1192 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1193
1194 Double_t det=h11*h22-h12*h12;
1195
1196 Double_t dt1,dt2;
1197 if (TMath::Abs(det)<1.e-33) {
1198 //(quasi)singular Hessian
1199 dt1=-gt1; dt2=-gt2;
1200 } else {
1201 dt1=-(gt1*h22 - gt2*h12)/det;
1202 dt2=-(h11*gt2 - h12*gt1)/det;
1203 }
1204
1205 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1206
1207 //check delta(phase1) ?
1208 //check delta(phase2) ?
1209
1210 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1211 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1212 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1213 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1214 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1215 if (lmb < 0.)
358f16ae 1216 AliDebug(1," stopped at not a minimum !");
c7bafca9 1217 break;
1218 }
1219
1220 Double_t dd=dm;
1221 for (Int_t div=1 ; ; div*=2) {
1222 Evaluate(p1,t1+dt1,r1,g1,gg1);
1223 Evaluate(p2,t2+dt2,r2,g2,gg2);
1224 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1225 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1226 if (dd<dm) break;
1227 dt1*=0.5; dt2*=0.5;
1228 if (div>512) {
358f16ae 1229 AliDebug(1," overshoot !"); break;
c7bafca9 1230 }
1231 }
1232 dm=dd;
1233
1234 t1+=dt1;
1235 t2+=dt2;
1236
1237 }
1238
358f16ae 1239 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1240
1241 Double_t cs=TMath::Cos(GetAlpha());
1242 Double_t sn=TMath::Sin(GetAlpha());
1243 xthis=r1[0]*cs + r1[1]*sn;
1244
1245 cs=TMath::Cos(p->GetAlpha());
1246 sn=TMath::Sin(p->GetAlpha());
1247 xp=r2[0]*cs + r2[1]*sn;
1248
1249 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1250}
1251
1252Double_t AliExternalTrackParam::
1253PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1254 //--------------------------------------------------------------
1255 // Propagates this track and the argument track to the position of the
1256 // distance of closest approach.
1257 // Returns the (weighed !) distance of closest approach.
1258 //--------------------------------------------------------------
1259 Double_t xthis,xp;
1260 Double_t dca=GetDCA(p,b,xthis,xp);
1261
1262 if (!PropagateTo(xthis,b)) {
1263 //AliWarning(" propagation failed !");
1264 return 1e+33;
1265 }
1266
1267 if (!p->PropagateTo(xp,b)) {
1268 //AliWarning(" propagation failed !";
1269 return 1e+33;
1270 }
1271
1272 return dca;
1273}
1274
1275
58e536c5 1276Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1277Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1278 //
e99a34df 1279 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1280 // if the (rough) transverse impact parameter is not bigger then "maxd".
1281 // Magnetic field is "b" (kG).
1282 //
1283 // a) The track gets extapolated to the DCA to the vertex.
1284 // b) The impact parameters and their covariance matrix are calculated.
1285 //
1286 // In the case of success, the returned value is kTRUE
1287 // (otherwise, it's kFALSE)
1288 //
1289 Double_t alpha=GetAlpha();
1290 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1291 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1292 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1293 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1294 x-=xv; y-=yv;
1295
1296 //Estimate the impact parameter neglecting the track curvature
bfd20868 1297 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
f76701bf 1298 if (d > maxd) return kFALSE;
1299
1300 //Propagate to the DCA
2258e165 1301 Double_t crv=GetC(b);
e99a34df 1302 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1303
bfd20868 1304 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1305 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
e99a34df 1306 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1307 else cs=1.;
f76701bf 1308
1309 x = xv*cs + yv*sn;
1310 yv=-xv*sn + yv*cs; xv=x;
1311
1312 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
266a0f9b 1313
1314 if (dz==0) return kTRUE;
1315 dz[0] = GetParameter()[0] - yv;
1316 dz[1] = GetParameter()[1] - zv;
1317
1318 if (covar==0) return kTRUE;
1319 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
1320
1321 //***** Improvements by A.Dainese
1322 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1323 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1324 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1325 covar[1] = GetCovariance()[1]; // between (x,y) and z
1326 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1327 //*****
1328
1329 return kTRUE;
1330}
1331
1332Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
1333Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
1334 //
1335 // Propagate this track to the DCA to vertex "vtx",
1336 // if the (rough) transverse impact parameter is not bigger then "maxd".
1337 //
1338 // This function takes into account all three components of the magnetic
1339 // field given by the b[3] arument (kG)
1340 //
1341 // a) The track gets extapolated to the DCA to the vertex.
1342 // b) The impact parameters and their covariance matrix are calculated.
1343 //
1344 // In the case of success, the returned value is kTRUE
1345 // (otherwise, it's kFALSE)
1346 //
1347 Double_t alpha=GetAlpha();
1348 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1349 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
1350 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1351 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
1352 x-=xv; y-=yv;
1353
1354 //Estimate the impact parameter neglecting the track curvature
bfd20868 1355 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
266a0f9b 1356 if (d > maxd) return kFALSE;
1357
1358 //Propagate to the DCA
8567bf39 1359 Double_t crv=GetC(b[2]);
1360 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
266a0f9b 1361
bfd20868 1362 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1363 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
266a0f9b 1364 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1365 else cs=1.;
1366
1367 x = xv*cs + yv*sn;
1368 yv=-xv*sn + yv*cs; xv=x;
1369
1370 if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1371
1372 if (dz==0) return kTRUE;
1373 dz[0] = GetParameter()[0] - yv;
1374 dz[1] = GetParameter()[1] - zv;
1375
1376 if (covar==0) return kTRUE;
58e536c5 1377 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1378
1379 //***** Improvements by A.Dainese
1380 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1381 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1382 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1383 covar[1] = GetCovariance()[1]; // between (x,y) and z
1384 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1385 //*****
1386
29fbcc93 1387 return kTRUE;
f76701bf 1388}
1389
1390
b1149664 1391void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1392 //----------------------------------------------------------------
1393 // This function returns a unit vector along the track direction
1394 // in the global coordinate system.
1395 //----------------------------------------------------------------
1396 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1397 Double_t snp=fP[2];
bfd20868 1398 Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp));
b1149664 1399 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1400 d[0]=(csp*cs - snp*sn)/norm;
1401 d[1]=(snp*cs + csp*sn)/norm;
1402 d[2]=fP[3]/norm;
1403}
1404
c683ddc2 1405Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1406 //---------------------------------------------------------------------
1407 // This function returns the global track momentum components
1408 // Results for (nearly) straight tracks are meaningless !
1409 //---------------------------------------------------------------------
1410 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1411 return Local2GlobalMomentum(p,fAlpha);
1412}
a5e407e9 1413
def9660e 1414Double_t AliExternalTrackParam::Px() const {
957fb479 1415 //---------------------------------------------------------------------
1416 // Returns x-component of momentum
1417 // Result for (nearly) straight tracks is meaningless !
1418 //---------------------------------------------------------------------
def9660e 1419
957fb479 1420 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1421 GetPxPyPz(p);
1422
1423 return p[0];
1424}
1425
1426Double_t AliExternalTrackParam::Py() const {
957fb479 1427 //---------------------------------------------------------------------
1428 // Returns y-component of momentum
1429 // Result for (nearly) straight tracks is meaningless !
1430 //---------------------------------------------------------------------
def9660e 1431
957fb479 1432 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1433 GetPxPyPz(p);
1434
1435 return p[1];
1436}
1437
1438Double_t AliExternalTrackParam::Pz() const {
957fb479 1439 //---------------------------------------------------------------------
1440 // Returns z-component of momentum
1441 // Result for (nearly) straight tracks is meaningless !
1442 //---------------------------------------------------------------------
def9660e 1443
957fb479 1444 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1445 GetPxPyPz(p);
1446
1447 return p[2];
1448}
1449
c683ddc2 1450Double_t AliExternalTrackParam::Xv() const {
1451 //---------------------------------------------------------------------
1452 // Returns x-component of first track point
1453 //---------------------------------------------------------------------
1454
1455 Double_t r[3]={0.,0.,0.};
1456 GetXYZ(r);
1457
1458 return r[0];
1459}
1460
1461Double_t AliExternalTrackParam::Yv() const {
1462 //---------------------------------------------------------------------
1463 // Returns y-component of first track point
1464 //---------------------------------------------------------------------
1465
1466 Double_t r[3]={0.,0.,0.};
1467 GetXYZ(r);
1468
1469 return r[1];
1470}
1471
1472Double_t AliExternalTrackParam::Zv() const {
1473 //---------------------------------------------------------------------
1474 // Returns z-component of first track point
1475 //---------------------------------------------------------------------
1476
1477 Double_t r[3]={0.,0.,0.};
1478 GetXYZ(r);
1479
1480 return r[2];
1481}
1482
def9660e 1483Double_t AliExternalTrackParam::Theta() const {
1484 // return theta angle of momentum
1485
7cdd0c20 1486 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1487}
1488
1489Double_t AliExternalTrackParam::Phi() const {
957fb479 1490 //---------------------------------------------------------------------
1491 // Returns the azimuthal angle of momentum
1492 // 0 <= phi < 2*pi
1493 //---------------------------------------------------------------------
def9660e 1494
957fb479 1495 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1496 if (phi<0.) phi+=2.*TMath::Pi();
1497 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1498
1499 return phi;
def9660e 1500}
1501
1502Double_t AliExternalTrackParam::M() const {
1503 // return particle mass
1504
1505 // No mass information available so far.
1506 // Redifine in derived class!
1507
1508 return -999.;
1509}
1510
1511Double_t AliExternalTrackParam::E() const {
1512 // return particle energy
1513
1514 // No PID information available so far.
1515 // Redifine in derived class!
1516
1517 return -999.;
1518}
1519
1520Double_t AliExternalTrackParam::Eta() const {
1521 // return pseudorapidity
1522
1523 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1524}
1525
1526Double_t AliExternalTrackParam::Y() const {
1527 // return rapidity
1528
1529 // No PID information available so far.
1530 // Redifine in derived class!
1531
1532 return -999.;
1533}
1534
c9ec41e8 1535Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1536 //---------------------------------------------------------------------
1537 // This function returns the global track position
1538 //---------------------------------------------------------------------
1539 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1540 return Local2GlobalPosition(r,fAlpha);
51ad6848 1541}
1542
c9ec41e8 1543Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1544 //---------------------------------------------------------------------
1545 // This function returns the global covariance matrix of the track params
1546 //
1547 // Cov(x,x) ... : cv[0]
1548 // Cov(y,x) ... : cv[1] cv[2]
1549 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1550 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1551 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1552 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1553 //
c9ec41e8 1554 // Results for (nearly) straight tracks are meaningless !
1555 //---------------------------------------------------------------------
e421f556 1556 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1557 for (Int_t i=0; i<21; i++) cv[i]=0.;
1558 return kFALSE;
a5e407e9 1559 }
49d13e89 1560 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1561 for (Int_t i=0; i<21; i++) cv[i]=0.;
1562 return kFALSE;
1563 }
1564 Double_t pt=1./TMath::Abs(fP[4]);
1565 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1566 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1567
1568 Double_t m00=-sn, m10=cs;
1569 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1570 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1571 Double_t m35=pt, m45=-pt*pt*fP[3];
1572
854d5d49 1573 m43*=GetSign();
1574 m44*=GetSign();
1575 m45*=GetSign();
1576
c9ec41e8 1577 cv[0 ] = fC[0]*m00*m00;
1578 cv[1 ] = fC[0]*m00*m10;
1579 cv[2 ] = fC[0]*m10*m10;
1580 cv[3 ] = fC[1]*m00;
1581 cv[4 ] = fC[1]*m10;
1582 cv[5 ] = fC[2];
1583 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1584 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1585 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1586 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1587 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1588 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1589 cv[12] = fC[4]*m24 + fC[11]*m44;
1590 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1591 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1592 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1593 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1594 cv[17] = fC[7]*m35 + fC[11]*m45;
1595 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1596 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1597 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1598
c9ec41e8 1599 return kTRUE;
51ad6848 1600}
1601
51ad6848 1602
c9ec41e8 1603Bool_t
1604AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1605 //---------------------------------------------------------------------
1606 // This function returns the global track momentum extrapolated to
1607 // the radial position "x" (cm) in the magnetic field "b" (kG)
1608 //---------------------------------------------------------------------
c9ec41e8 1609 p[0]=fP[4];
1530f89c 1610 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1611 p[2]=fP[3];
1612 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1613}
1614
7cf7bb6c 1615Bool_t
1616AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1617 //---------------------------------------------------------------------
1618 // This function returns the local Y-coordinate of the intersection
1619 // point between this track and the reference plane "x" (cm).
1620 // Magnetic field "b" (kG)
1621 //---------------------------------------------------------------------
1622 Double_t dx=x-fX;
1623 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1624
1530f89c 1625 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1626
1627 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1628 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1629
60e55aee 1630 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 1631 y = fP[0] + dx*(f1+f2)/(r1+r2);
1632 return kTRUE;
1633}
1634
6c94f330 1635Bool_t
1636AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1637 //---------------------------------------------------------------------
1638 // This function returns the local Z-coordinate of the intersection
1639 // point between this track and the reference plane "x" (cm).
1640 // Magnetic field "b" (kG)
1641 //---------------------------------------------------------------------
1642 Double_t dx=x-fX;
1643 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1644
2258e165 1645 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1646
1647 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1648 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1649
60e55aee 1650 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
6c94f330 1651 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1652 return kTRUE;
1653}
1654
c9ec41e8 1655Bool_t
1656AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1657 //---------------------------------------------------------------------
1658 // This function returns the global track position extrapolated to
1659 // the radial position "x" (cm) in the magnetic field "b" (kG)
1660 //---------------------------------------------------------------------
c9ec41e8 1661 Double_t dx=x-fX;
e421f556 1662 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1663
1530f89c 1664 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1665
e421f556 1666 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1667 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1668
60e55aee 1669 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
c9ec41e8 1670 r[0] = x;
1671 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1672 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1673
c9ec41e8 1674 return Local2GlobalPosition(r,fAlpha);
51ad6848 1675}
1676
51ad6848 1677//_____________________________________________________________________________
1678void AliExternalTrackParam::Print(Option_t* /*option*/) const
1679{
1680// print the parameters and the covariance matrix
1681
1682 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1683 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1684 fP[0], fP[1], fP[2], fP[3], fP[4]);
1685 printf(" covariance: %12g\n", fC[0]);
1686 printf(" %12g %12g\n", fC[1], fC[2]);
1687 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1688 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1689 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1690 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1691 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1692}
5b77d93c 1693
c194ba83 1694Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1695 //
1696 // Get sinus at given x
1697 //
1530f89c 1698 Double_t crv=GetC(b);
c194ba83 1699 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1700 Double_t dx = x-fX;
1701 Double_t res = fP[2]+dx*crv;
1702 return res;
1703}
bf00ebb8 1704
1705Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1706 //------------------------------------------------------------------------
1707 // Get the distance between two tracks at the local position x
1708 // working in the local frame of this track.
1709 // Origin : Marian.Ivanov@cern.ch
1710 //-----------------------------------------------------------------------
1711 Double_t xyz[3];
1712 Double_t xyz2[3];
1713 xyz[0]=x;
1714 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1715 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1716 //
1717 //
1718 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1719 xyz2[0]=x;
1720 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1721 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1722 }else{
1723 //
1724 Double_t xyz1[3];
1725 Double_t dfi = param2->GetAlpha()-GetAlpha();
1726 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1727 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1728 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1729 //
1730 xyz1[0]=xyz2[0];
1731 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1732 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1733 //
1734 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1735 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1736 xyz2[2] = xyz1[2];
1737 }
1738 dist[0] = xyz[0]-xyz2[0];
1739 dist[1] = xyz[1]-xyz2[1];
1740 dist[2] = xyz[2]-xyz2[2];
1741
1742 return kTRUE;
1743}
0c19adf7 1744
1745
1746//
1747// Draw functionality.
1748// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1749//
1750
1751void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1752 //
1753 // Draw track line
1754 //
1755 if (minR>maxR) return ;
1756 if (stepR<=0) return ;
1757 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1758 if (npoints<1) return;
1759 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1760 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1761 polymarker->Draw();
1762}
1763
1764//
1765void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1766 //
1767 // Fill points in the polymarker
1768 //
1769 Int_t counter=0;
1770 for (Double_t r=minR; r<maxR; r+=stepR){
1771 Double_t point[3];
1772 GetXYZAt(r,magF,point);
1773 pol->SetPoint(counter,point[0],point[1], point[2]);
1774 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1775 counter++;
1776 }
1777}
0e8460af 1778
1779Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1780 //
1781 Int_t min = TMath::Min(i,j);
1782 Int_t max = TMath::Max(i,j);
1783
1784 return min+(max+1)*max/2;
1785}
8b6e3369 1786
1787
1788void AliExternalTrackParam::g3helx3(Double_t qfield,
1789 Double_t step,
1790 Double_t vect[7]) {
1791/******************************************************************
1792 * *
1793 * GEANT3 tracking routine in a constant field oriented *
1794 * along axis 3 *
1795 * Tracking is performed with a conventional *
1796 * helix step method *
1797 * *
1798 * Authors R.Brun, M.Hansroul ********* *
1799 * Rewritten V.Perevoztchikov *
1800 * *
1801 * Rewritten in C++ by I.Belikov *
1802 * *
1803 * qfield (kG) - particle charge times magnetic field *
1804 * step (cm) - step length along the helix *
1805 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
1806 * *
1807 ******************************************************************/
1808 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
bfd20868 1809 const Double_t kOvSqSix=TMath::Sqrt(1./6.);
8b6e3369 1810
1811 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
1812
1813 Double_t rho = qfield*kB2C/vect[ipp];
1814 Double_t tet = rho*step;
1815
1816 Double_t tsint, sintt, sint, cos1t;
1817 if (TMath::Abs(tet) > 0.15) {
1818 sint = TMath::Sin(tet);
1819 sintt = sint/tet;
1820 tsint = (tet - sint)/tet;
1821 Double_t t=TMath::Sin(0.5*tet);
1822 cos1t = 2*t*t/tet;
1823 } else {
1824 tsint = tet*tet/6.;
bfd20868 1825 sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint;
8b6e3369 1826 sint = tet*sintt;
1827 cos1t = 0.5*tet;
1828 }
1829
1830 Double_t f1 = step*sintt;
1831 Double_t f2 = step*cos1t;
1832 Double_t f3 = step*tsint*cosz;
1833 Double_t f4 = -tet*cos1t;
1834 Double_t f5 = sint;
1835
1836 vect[ix] += f1*cosx - f2*cosy;
1837 vect[iy] += f1*cosy + f2*cosx;
1838 vect[iz] += f1*cosz + f3;
1839
1840 vect[ipx] += f4*cosx - f5*cosy;
1841 vect[ipy] += f4*cosy + f5*cosx;
1842
1843}
1844
1845Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
1846 //----------------------------------------------------------------
1847 // Extrapolate this track to the plane X=xk in the field b[].
1848 //
1849 // X [cm] is in the "tracking coordinate system" of this track.
1850 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
1851 //----------------------------------------------------------------
1852
1853 Double_t dx=xk-fX;
1854 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
1855
1856 Double_t crv=GetC(b[2]);
1857 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
1858
1859 Double_t f1=fP[2], f2=f1 + crv*dx;
1860 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1861 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1862
1863
1864 // Estimate the covariance matrix
1865 Double_t &fP3=fP[3], &fP4=fP[4];
1866 Double_t
1867 &fC00=fC[0],
1868 &fC10=fC[1], &fC11=fC[2],
1869 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1870 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1871 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1872
bfd20868 1873 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
8b6e3369 1874
1875 //f = F - 1
1876 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
1877 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
1878 Double_t f12= dx*fP3*f1/(r1*r1*r1);
1879 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
1880 Double_t f13= dx/r1;
1881 Double_t f24= dx; f24*=cc;
1882
1883 //b = C*ft
1884 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
1885 Double_t b02=f24*fC40;
1886 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
1887 Double_t b12=f24*fC41;
1888 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
1889 Double_t b22=f24*fC42;
1890 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
1891 Double_t b42=f24*fC44;
1892 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
1893 Double_t b32=f24*fC43;
1894
1895 //a = f*b = f*C*ft
1896 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
1897 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
1898 Double_t a22=f24*b42;
1899
1900 //F*C*Ft = C + (b + bt + a)
1901 fC00 += b00 + b00 + a00;
1902 fC10 += b10 + b01 + a01;
1903 fC20 += b20 + b02 + a02;
1904 fC30 += b30;
1905 fC40 += b40;
1906 fC11 += b11 + b11 + a11;
1907 fC21 += b21 + b12 + a12;
1908 fC31 += b31;
1909 fC41 += b41;
1910 fC22 += b22 + b22 + a22;
1911 fC32 += b32;
1912 fC42 += b42;
1913
1914
1915 // Appoximate step length
1916 Double_t step=dx*TMath::Abs(r2 + f2*(f1+f2)/(r1+r2));
1917 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
1918
1919
1920 // Get the track's (x,y,z) and (px,py,pz) in the Global System
1921 Double_t r[3]; GetXYZ(r);
1922 Double_t p[3]; GetPxPyPz(p);
1923 Double_t pp=GetP();
1924 p[0] /= pp;
1925 p[1] /= pp;
1926 p[2] /= pp;
1927
1928
1929 // Rotate to the system where Bx=By=0.
1930 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
1931 Double_t cosphi=1., sinphi=0.;
1932 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
1933 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
1934 Double_t costet=1., sintet=0.;
1935 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
1936 Double_t vect[7];
1937
1938 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
1939 vect[1] = -sinphi*r[0] + cosphi*r[1];
1940 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
1941
1942 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
1943 vect[4] = -sinphi*p[0] + cosphi*p[1];
1944 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
1945
1946 vect[6] = pp;
1947
1948
1949 // Do the helix step
1950 g3helx3(GetSign()*bb,step,vect);
1951
1952
1953 // Rotate back to the Global System
1954 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
1955 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
1956 r[2] = -sintet*vect[0] + costet*vect[2];
1957
1958 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
1959 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
1960 p[2] = -sintet*vect[3] + costet*vect[5];
1961
1962
1963 // Rotate back to the Tracking System
1964 Double_t cosalp = TMath::Cos(fAlpha);
1965 Double_t sinalp =-TMath::Sin(fAlpha);
1966
1967 Double_t
1968 t = cosalp*r[0] - sinalp*r[1];
1969 r[1] = sinalp*r[0] + cosalp*r[1];
1970 r[0] = t;
1971
1972 t = cosalp*p[0] - sinalp*p[1];
1973 p[1] = sinalp*p[0] + cosalp*p[1];
1974 p[0] = t;
1975
1976
1977 // Do the final correcting step to the target plane (linear approximation)
1978 Double_t x=r[0], y=r[1], z=r[2];
1979 if (TMath::Abs(dx) > kAlmost0) {
1980 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
1981 dx = xk - r[0];
1982 x += dx;
1983 y += p[1]/p[0]*dx;
1984 z += p[2]/p[0]*dx;
1985 }
1986
1987
1988 // Calculate the track parameters
1989 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
1990 fX = x;
1991 fP[0] = y;
1992 fP[1] = z;
1993 fP[2] = p[1]/t;
1994 fP[3] = p[2]/t;
1995 fP[4] = GetSign()/(t*pp);
1996
1997 return kTRUE;
1998}
1999
cfdb62d4 2000Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
2001 //
2002 //Translation: in the event mixing, the tracks can be shifted
2003 //of the difference among primary vertices (vTrasl) and
2004 //the covariance matrix is changed accordingly
2005 //(covV = covariance of the primary vertex).
2006 //Origin: "Romita, Rossella" <R.Romita@gsi.de>
2007 //
2008 TVector3 translation;
2009 // vTrasl coordinates in the local system
2010 translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
2011 translation.RotateZ(-fAlpha);
2012 translation.GetXYZ(vTrasl);
2013
2014 //compute the new x,y,z of the track
5a87bb3d 2015 Double_t newX=fX-vTrasl[0];
2016 Double_t newY=fP[0]-vTrasl[1];
2017 Double_t newZ=fP[1]-vTrasl[2];
cfdb62d4 2018
2019 //define the new parameters
5a87bb3d 2020 Double_t newParam[5];
2021 newParam[0]=newY;
2022 newParam[1]=newZ;
2023 newParam[2]=fP[2];
2024 newParam[3]=fP[3];
2025 newParam[4]=fP[4];
cfdb62d4 2026
2027 // recompute the covariance matrix:
2028 // 1. covV in the local system
2029 Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
2030 TMatrixD qQi(3,3);
2031 qQi(0,0) = cosRot;
2032 qQi(0,1) = sinRot;
2033 qQi(0,2) = 0.;
2034 qQi(1,0) = -sinRot;
2035 qQi(1,1) = cosRot;
2036 qQi(1,2) = 0.;
2037 qQi(2,0) = 0.;
2038 qQi(2,1) = 0.;
2039 qQi(2,2) = 1.;
2040 TMatrixD uUi(3,3);
2041 uUi(0,0) = covV[0];
2042 uUi(0,0) = covV[0];
2043 uUi(1,0) = covV[1];
2044 uUi(0,1) = covV[1];
2045 uUi(2,0) = covV[3];
2046 uUi(0,2) = covV[3];
2047 uUi(1,1) = covV[2];
2048 uUi(2,2) = covV[5];
2049 uUi(1,2) = covV[4];
2050 if(uUi.Determinant() <= 0.) {return kFALSE;}
2051 TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
2052 TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
2053
2054 //2. compute the new covariance matrix of the track
2055 Double_t sigmaXX=m(0,0);
2056 Double_t sigmaXZ=m(2,0);
2057 Double_t sigmaXY=m(1,0);
2058 Double_t sigmaYY=GetSigmaY2()+m(1,1);
2059 Double_t sigmaYZ=fC[1]+m(1,2);
2060 Double_t sigmaZZ=fC[2]+m(2,2);
2061 Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
2062 Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
2063 Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
2064
2065 Double_t newCov[15];
2066 newCov[0]=covarianceYY;
2067 newCov[1]=covarianceYZ;
2068 newCov[2]=covarianceZZ;
2069 for(Int_t i=3;i<15;i++){
2070 newCov[i]=fC[i];
2071 }
2072
2073 // set the new parameters
2074
5a87bb3d 2075 Set(newX,fAlpha,newParam,newCov);
cfdb62d4 2076
2077 return kTRUE;
2078 }