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87594435 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
acd84897 16/* $Id$ */
fb17acd4 17
87594435 18//-------------------------------------------------------------------------
19// Implementation of the AliKalmanTrack class
066782e8 20// that is the base for AliTPCtrack, AliITStrackV2 and AliTRDtrack
87594435 21// Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch
22//-------------------------------------------------------------------------
23
24#include "AliKalmanTrack.h"
74f9526e 25#include "AliPDG.h"
26#include "TPDGCode.h"
27#include "TDatabasePDG.h"
87594435 28
29ClassImp(AliKalmanTrack)
30
116cbefd 31Double_t AliKalmanTrack::fgConvConst;
9b280d80 32
e2afb3b6 33//_______________________________________________________________________
34AliKalmanTrack::AliKalmanTrack():
35 fLab(-3141593),
36 fChi2(0),
37 fMass(0.13957),
38 fN(0)
39{
116cbefd 40 //
41 // Default constructor
42 //
43 if (fgConvConst==0)
e2afb3b6 44 Fatal("AliKalmanTrack()","The magnetic field has not been set !\n");
74f9526e 45
46 fStartTimeIntegral = kFALSE;
47 fIntegratedLength = 0;
48 for(Int_t i=0; i<5; i++) fIntegratedTime[i] = 0;
e2afb3b6 49}
50
51//_______________________________________________________________________
52AliKalmanTrack::AliKalmanTrack(const AliKalmanTrack &t):
53 TObject(t),
54 fLab(t.fLab),
55 fChi2(t.fChi2),
56 fMass(t.fMass),
57 fN(t.fN)
58{
116cbefd 59 //
60 // Copy constructor
61 //
62 if (fgConvConst==0)
e2afb3b6 63 Fatal("AliKalmanTrack(const AliKalmanTrack&)",
64 "The magnetic field has not been set !\n");
74f9526e 65
66 fStartTimeIntegral = t.fStartTimeIntegral;
67 fIntegratedLength = t.fIntegratedLength;
68
69 for (Int_t i=0; i<5; i++)
70 fIntegratedTime[i] = t.fIntegratedTime[i];
71}
c5507f6d 72
73//_______________________________________________________________________
74Double_t AliKalmanTrack::GetX() const
75{
76 Warning("GetX()","Method must be overloaded !\n");
77 return 0.;
78}
79//_______________________________________________________________________
80Double_t AliKalmanTrack::GetdEdx() const
81{
82 Warning("GetdEdx()","Method must be overloaded !\n");
83 return 0.;
84}
85
86//_______________________________________________________________________
87Double_t AliKalmanTrack::GetY() const
88{
89 Double_t par[5];
90 Double_t localX = GetX();
91 GetExternalParameters(localX, par);
92 return par[0];
93}
94//_______________________________________________________________________
95Double_t AliKalmanTrack::GetZ() const
96{
97 Double_t par[5];
98 Double_t localX = GetX();
99 GetExternalParameters(localX, par);
100 return par[1];
101}
102//_______________________________________________________________________
103Double_t AliKalmanTrack::GetSnp() const
104{
105 Double_t par[5];
106 Double_t localX = GetX();
107 GetExternalParameters(localX, par);
108 return par[2];
109}
110//_______________________________________________________________________
111Double_t AliKalmanTrack::GetTgl() const
112{
113 Double_t par[5];
114 Double_t localX = GetX();
115 GetExternalParameters(localX, par);
116 return par[3];
117}
118//_______________________________________________________________________
119Double_t AliKalmanTrack::Get1Pt() const
120{
121 Double_t par[5];
122 Double_t localX = GetX();
123 GetExternalParameters(localX, par);
124 return par[4];
125}
126
127//_______________________________________________________________________
128Double_t AliKalmanTrack::Phi() const
129{
130// return global phi of track
131
132 Double_t par[5];
133 Double_t localX = GetX();
134 GetExternalParameters(localX, par);
135 Double_t phi = TMath::ASin(par[2]) + GetAlpha();
136 while (phi < 0) phi += TMath::TwoPi();
137 while (phi > TMath::TwoPi()) phi -= TMath::TwoPi();
138 return phi;
139}
140//_______________________________________________________________________
141Double_t AliKalmanTrack::SigmaPhi() const
142{
143// return error of global phi of track
144
145 Double_t par[5];
146 Double_t cov[15];
147 Double_t localX = GetX();
148 GetExternalParameters(localX, par);
149 GetExternalCovariance(cov);
150 return TMath::Sqrt(TMath::Abs(cov[5] / (1. - par[2]*par[2])));
151}
152//_______________________________________________________________________
153Double_t AliKalmanTrack::Theta() const
154{
155// return global theta of track
156
157 Double_t par[5];
158 Double_t localX = GetX();
159 GetExternalParameters(localX, par);
160 return TMath::Pi()/2. - TMath::ATan(par[3]);
161}
162//_______________________________________________________________________
163Double_t AliKalmanTrack::SigmaTheta() const
164{
165// return error of global theta of track
166
167 Double_t par[5];
168 Double_t cov[15];
169 Double_t localX = GetX();
170 GetExternalParameters(localX, par);
171 GetExternalCovariance(cov);
172 return TMath::Sqrt(TMath::Abs(cov[5])) / (1. + par[3]*par[3]);
173}
174//_______________________________________________________________________
175Double_t AliKalmanTrack::Px() const
176{
177// return x component of track momentum
178
179 Double_t par[5];
180 Double_t localX = GetX();
181 GetExternalParameters(localX, par);
182 Double_t phi = TMath::ASin(par[2]) + GetAlpha();
183 return TMath::Cos(phi) / TMath::Abs(par[4]);
184}
185//_______________________________________________________________________
186Double_t AliKalmanTrack::Py() const
187{
188// return y component of track momentum
189
190 Double_t par[5];
191 Double_t localX = GetX();
192 GetExternalParameters(localX, par);
193 Double_t phi = TMath::ASin(par[2]) + GetAlpha();
194 return TMath::Sin(phi) / TMath::Abs(par[4]);
195}
196//_______________________________________________________________________
197Double_t AliKalmanTrack::Pz() const
198{
199// return z component of track momentum
200
201 Double_t par[5];
202 Double_t localX = GetX();
203 GetExternalParameters(localX, par);
204 return par[3] / TMath::Abs(par[4]);
205}
206//_______________________________________________________________________
207Double_t AliKalmanTrack::Pt() const
208{
209// return transverse component of track momentum
210
211 Double_t par[5];
212 Double_t localX = GetX();
213 GetExternalParameters(localX, par);
214 return 1. / TMath::Abs(par[4]);
215}
216//_______________________________________________________________________
217Double_t AliKalmanTrack::SigmaPt() const
218{
219// return error of transverse component of track momentum
220
221 Double_t par[5];
222 Double_t cov[15];
223 Double_t localX = GetX();
224 GetExternalParameters(localX, par);
225 GetExternalCovariance(cov);
226 return TMath::Sqrt(cov[14]) / TMath::Abs(par[4]);
227}
228//_______________________________________________________________________
229Double_t AliKalmanTrack::P() const
230{
231// return total track momentum
232
233 Double_t par[5];
234 Double_t localX = GetX();
235 GetExternalParameters(localX, par);
236 return 1. / TMath::Abs(par[4] * TMath::Sin(TMath::ATan(par[3])));
237}
238//_______________________________________________________________________
239TVector3 AliKalmanTrack::Momentum() const
240{
241// return track momentum vector
242
243 Double_t par[5];
244 Double_t localX = GetX();
245 GetExternalParameters(localX, par);
246 Double_t phi = TMath::ASin(par[2]) + GetAlpha();
247 return TVector3(TMath::Cos(phi) / TMath::Abs(par[4]),
248 TMath::Sin(phi) / TMath::Abs(par[4]),
249 par[3] / TMath::Abs(par[4]));
250}
251
74f9526e 252//_______________________________________________________________________
253void AliKalmanTrack::StartTimeIntegral()
254{
49a7a79a 255 // Sylwester Radomski, GSI
256 // S.Radomski@gsi.de
74f9526e 257 //
258 // Start time integration
259 // To be called at Vertex by ITS tracker
260 //
261
262 //if (fStartTimeIntegral)
263 // Warning("StartTimeIntegral", "Reseting Recorded Time.");
264
265 fStartTimeIntegral = kTRUE;
5d8718b8 266 for(Int_t i=0; i<fgkTypes; i++) fIntegratedTime[i] = 0;
74f9526e 267 fIntegratedLength = 0;
268}
269//_______________________________________________________________________
270void AliKalmanTrack:: AddTimeStep(Double_t length)
271{
272 //
273 // Add step to integrated time
274 // this method should be called by a sublasses at the end
275 // of the PropagateTo function or by a tracker
276 // each time step is made.
277 //
278 // If integration not started function does nothing
279 //
280 // Formula
281 // dt = dl * sqrt(p^2 + m^2) / p
282 // p = pT * (1 + tg^2 (lambda) )
283 //
284 // pt = 1/external parameter [4]
285 // tg lambda = external parameter [3]
286 //
287 //
288 // Sylwester Radomski, GSI
289 // S.Radomski@gsi.de
290 //
291
5d8718b8 292 static const Double_t kcc = 2.99792458e-2;
74f9526e 293
294 if (!fStartTimeIntegral) return;
295
296 fIntegratedLength += length;
297
5d8718b8 298 static Int_t pdgCode[fgkTypes] = {kElectron, kMuonMinus, kPiPlus, kKPlus, kProton};
74f9526e 299 TDatabasePDG *db = TDatabasePDG::Instance();
300
301 Double_t xr, param[5];
302 Double_t pt, tgl;
303
304 GetExternalParameters(xr, param);
305 pt = 1/param[4] ;
306 tgl = param[3];
307
308 Double_t p = TMath::Abs(pt * TMath::Sqrt(1+tgl*tgl));
309
310 if (length > 100) return;
311
5d8718b8 312 for (Int_t i=0; i<fgkTypes; i++) {
74f9526e 313
314 Double_t mass = db->GetParticle(pdgCode[i])->Mass();
315 Double_t correction = TMath::Sqrt( pt*pt * (1 + tgl*tgl) + mass * mass ) / p;
5d8718b8 316 Double_t time = length * correction / kcc;
74f9526e 317
318 //cout << mass << "\t" << pt << "\t" << p << "\t"
319 // << correction << endl;
320
321 fIntegratedTime[i] += time;
322 }
e2afb3b6 323}
324
74f9526e 325//_______________________________________________________________________
326
327Double_t AliKalmanTrack::GetIntegratedTime(Int_t pdg) const
328{
49a7a79a 329 // Sylwester Radomski, GSI
330 // S.Radomski@gsi.de
74f9526e 331 //
332 // Return integrated time hypothesis for a given particle
333 // type assumption.
334 //
335 // Input parameter:
336 // pdg - Pdg code of a particle type
337 //
338
339
340 if (!fStartTimeIntegral) {
341 Warning("GetIntegratedTime","Time integration not started");
342 return 0.;
343 }
344
5d8718b8 345 static Int_t pdgCode[fgkTypes] = {kElectron, kMuonMinus, kPiPlus, kKPlus, kProton};
74f9526e 346
5d8718b8 347 for (Int_t i=0; i<fgkTypes; i++)
74f9526e 348 if (pdgCode[i] == TMath::Abs(pdg)) return fIntegratedTime[i];
349
350 Warning(":GetIntegratedTime","Particle type [%d] not found", pdg);
351 return 0;
352}
353//_______________________________________________________________________
354
355void AliKalmanTrack::PrintTime() const
356{
49a7a79a 357 // Sylwester Radomski, GSI
358 // S.Radomski@gsi.de
359 //
74f9526e 360 // For testing
361 // Prints time for all hypothesis
362 //
363
5d8718b8 364 static Int_t pdgCode[fgkTypes] = {kElectron, kMuonMinus, kPiPlus, kKPlus, kProton};
74f9526e 365
5d8718b8 366 for (Int_t i=0; i<fgkTypes; i++)
74f9526e 367 printf("%d: %.2f ", pdgCode[i], fIntegratedTime[i]);
368 printf("\n");
369}
370
49a7a79a 371static void External2Helix(const AliKalmanTrack *t, Double_t helix[6]) {
372 //--------------------------------------------------------------------
373 // External track parameters -> helix parameters
374 //--------------------------------------------------------------------
375 Double_t alpha,x,cs,sn;
376 t->GetExternalParameters(x,helix); alpha=t->GetAlpha();
377
378 cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
379 helix[5]=x*cs - helix[0]*sn; // x0
380 helix[0]=x*sn + helix[0]*cs; // y0
381//helix[1]= // z0
382 helix[2]=TMath::ASin(helix[2]) + alpha; // phi0
383//helix[3]= // tgl
384 helix[4]=helix[4]/t->GetConvConst(); // C
385}
386
387static void Evaluate(const Double_t *h, Double_t t,
388 Double_t r[3], //radius vector
389 Double_t g[3], //first defivatives
390 Double_t gg[3]) //second derivatives
391{
392 //--------------------------------------------------------------------
393 // Calculate position of a point on a track and some derivatives
394 //--------------------------------------------------------------------
395 Double_t phase=h[4]*t+h[2];
396 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
397
398 r[0] = h[5] + (sn - h[6])/h[4];
399 r[1] = h[0] - (cs - h[7])/h[4];
400 r[2] = h[1] + h[3]*t;
401
402 g[0] = cs; g[1]=sn; g[2]=h[3];
403
404 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
405}
406
407Double_t AliKalmanTrack::
408GetDCA(const AliKalmanTrack *p, Double_t &xthis, Double_t &xp) const {
409 //------------------------------------------------------------
410 // Returns the (weighed !) distance of closest approach between
411 // this track and the track passed as the argument.
412 // Other returned values:
413 // xthis, xt - coordinates of tracks' reference planes at the DCA
414 //-----------------------------------------------------------
415 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
416 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
417 Double_t dx2=dy2;
418
419 //dx2=dy2=dz2=1.;
420
421 Double_t p1[8]; External2Helix(this,p1);
422 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
423 Double_t p2[8]; External2Helix(p,p2);
424 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
425
426
427 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
428 Evaluate(p1,t1,r1,g1,gg1);
429 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
430 Evaluate(p2,t2,r2,g2,gg2);
74f9526e 431
49a7a79a 432 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
433 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
434
435 Int_t max=27;
436 while (max--) {
437 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
438 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
439 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
440 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
441 (g1[2]*g1[2] - dz*gg1[2])/dz2;
442 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
443 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
444 (g2[2]*g2[2] + dz*gg2[2])/dz2;
445 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
446
447 Double_t det=h11*h22-h12*h12;
448
449 Double_t dt1,dt2;
450 if (TMath::Abs(det)<1.e-33) {
451 //(quasi)singular Hessian
452 dt1=-gt1; dt2=-gt2;
453 } else {
454 dt1=-(gt1*h22 - gt2*h12)/det;
455 dt2=-(h11*gt2 - h12*gt1)/det;
456 }
457
458 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
459
460 //check delta(phase1) ?
461 //check delta(phase2) ?
462
463 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
464 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
465 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
466 Warning("GetDCA"," stopped at not a stationary point !\n");
467 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
468 if (lmb < 0.)
469 Warning("GetDCA"," stopped at not a minimum !\n");
470 break;
471 }
472
473 Double_t dd=dm;
474 for (Int_t div=1 ; ; div*=2) {
475 Evaluate(p1,t1+dt1,r1,g1,gg1);
476 Evaluate(p2,t2+dt2,r2,g2,gg2);
477 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
478 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
479 if (dd<dm) break;
480 dt1*=0.5; dt2*=0.5;
481 if (div>512) {
482 Warning("GetDCA"," overshoot !\n"); break;
483 }
484 }
485 dm=dd;
486
487 t1+=dt1;
488 t2+=dt2;
489
490 }
491
492 if (max<=0) Warning("GetDCA"," too many iterations !\n");
493
494 Double_t cs=TMath::Cos(GetAlpha());
495 Double_t sn=TMath::Sin(GetAlpha());
496 xthis=r1[0]*cs + r1[1]*sn;
497
498 cs=TMath::Cos(p->GetAlpha());
499 sn=TMath::Sin(p->GetAlpha());
500 xp=r2[0]*cs + r2[1]*sn;
501
502 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
503}
504
505Double_t AliKalmanTrack::
506PropagateToDCA(AliKalmanTrack *p, Double_t d, Double_t x0) {
507 //--------------------------------------------------------------
508 // Propagates this track and the argument track to the position of the
509 // distance of closest approach.
510 // Returns the (weighed !) distance of closest approach.
511 //--------------------------------------------------------------
512 Double_t xthis,xp;
513 Double_t dca=GetDCA(p,xthis,xp);
514
515 if (!PropagateTo(xthis,d,x0)) {
516 //Warning("PropagateToDCA"," propagation failed !\n");
517 return 1e+33;
518 }
519
520 if (!p->PropagateTo(xp,d,x0)) {
521 //Warning("PropagateToDCA"," propagation failed !\n";
522 return 1e+33;
523 }
524
525 return dca;
526}