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46d29e70 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/*
17$Log$
0a29d0f1 18Revision 1.8 2001/05/30 12:17:47 hristov
19Loop variables declared once
20
3ab6f951 21Revision 1.7 2001/05/28 17:07:58 hristov
22Last minute changes; ExB correction in AliTRDclusterizerV1; taking into account of material in G10 TEC frames and material between TEC planes (C.Blume,S.Sedykh)
23
2a941f4e 24Revision 1.4 2000/12/08 16:07:02 cblume
25Update of the tracking by Sergei
26
bbf92647 27Revision 1.3 2000/10/15 23:40:01 cblume
28Remove AliTRDconst
29
0e9c2ad5 30Revision 1.2 2000/10/06 16:49:46 cblume
31Made Getters const
32
46d29e70 33Revision 1.1.2.1 2000/09/22 14:47:52 cblume
34Add the tracking code
35
36*/
37
38#include <iostream.h>
5443e65e 39#include <TObject.h>
46d29e70 40
46d29e70 41#include "AliTRDgeometry.h"
42#include "AliTRDcluster.h"
43#include "AliTRDtrack.h"
5443e65e 44#include "../TPC/AliTPCtrack.h"
46d29e70 45
46ClassImp(AliTRDtrack)
47
48
49//_____________________________________________________________________________
50
a819a5f7 51AliTRDtrack::AliTRDtrack(const AliTRDcluster *c, UInt_t index,
5443e65e 52 const Double_t xx[5], const Double_t cc[15],
53 Double_t xref, Double_t alpha) : AliKalmanTrack() {
46d29e70 54 //-----------------------------------------------------------------
55 // This is the main track constructor.
56 //-----------------------------------------------------------------
5443e65e 57
58 fSeedLab = -1;
46d29e70 59
60 fAlpha=alpha;
5443e65e 61 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
62 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
63
46d29e70 64 fX=xref;
65
66 fY=xx[0]; fZ=xx[1]; fC=xx[2]; fE=xx[3]; fT=xx[4];
67
68 fCyy=cc[0];
69 fCzy=cc[1]; fCzz=cc[2];
70 fCcy=cc[3]; fCcz=cc[4]; fCcc=cc[5];
71 fCey=cc[6]; fCez=cc[7]; fCec=cc[8]; fCee=cc[9];
72 fCty=cc[10]; fCtz=cc[11]; fCtc=cc[12]; fCte=cc[13]; fCtt=cc[14];
73
5443e65e 74 fIndex[0]=index;
75 SetNumberOfClusters(1);
76
77 fdEdx=0.;
a2b90f83 78
5443e65e 79 Double_t q = TMath::Abs(c->GetQ());
a819a5f7 80 Double_t s = fX*fC - fE, t=fT;
5443e65e 81 if(s*s < 1) q *= TMath::Sqrt((1-s*s)/(1+t*t));
82
83 fdQdl[0] = q;
46d29e70 84}
85
86//_____________________________________________________________________________
5443e65e 87AliTRDtrack::AliTRDtrack(const AliTRDtrack& t) : AliKalmanTrack(t) {
46d29e70 88 //
89 // Copy constructor.
90 //
91
5443e65e 92 SetLabel(t.GetLabel());
93 fSeedLab=t.GetSeedLabel();
46d29e70 94
5443e65e 95 SetChi2(t.GetChi2());
46d29e70 96 fdEdx=t.fdEdx;
97
98 fAlpha=t.fAlpha;
99 fX=t.fX;
100
101 fY=t.fY; fZ=t.fZ; fC=t.fC; fE=t.fE; fT=t.fT;
102
103 fCyy=t.fCyy;
104 fCzy=t.fCzy; fCzz=t.fCzz;
105 fCcy=t.fCcy; fCcz=t.fCcz; fCcc=t.fCcc;
106 fCey=t.fCey; fCez=t.fCez; fCec=t.fCec; fCee=t.fCee;
107 fCty=t.fCty; fCtz=t.fCtz; fCtc=t.fCtc; fCte=t.fCte; fCtt=t.fCtt;
108
5443e65e 109 Int_t n=t.GetNumberOfClusters();
110 SetNumberOfClusters(n);
111 for (Int_t i=0; i<n; i++) {
a819a5f7 112 fIndex[i]=t.fIndex[i];
113 fdQdl[i]=t.fdQdl[i];
114 }
5443e65e 115}
116
117//_____________________________________________________________________________
118AliTRDtrack::AliTRDtrack(const AliKalmanTrack& t, Double_t alpha) {
119 //
120 // Constructor from AliTPCtrack or AliITStrack .
121 //
122
123 SetLabel(t.GetLabel());
124 SetChi2(0.);
125 SetNumberOfClusters(0);
126
127 fdEdx=0;
128
129 fAlpha = alpha;
130 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
131 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
132
133 Double_t x, p[5]; t.GetExternalParameters(x,p);
134
135 fX=x;
136
137 x = GetConvConst();
138
139 fY=p[0]; fZ=p[1]; fC=p[4]/x;
140 fE=fX*fC-p[2]; fT=p[3];
141
142 //Conversion of the covariance matrix
143 Double_t c[15]; t.GetExternalCovariance(c);
144
145 c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;
146
147 Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
148 Double_t c32=fX*c[13] - c[8];
149 Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];
150
151 fCyy=c[0 ];
152 fCzy=c[1 ]; fCzz=c[2 ];
153 fCcy=c[10]; fCcz=c[11]; fCcc=c[14];
154 fCey=c20; fCez=c21; fCec=c42; fCee=c22;
155 fCty=c[6 ]; fCtz=c[7 ]; fCtc=c[13]; fCte=c32; fCtt=c[9 ];
156
157}
158
159//____________________________________________________________________________
160void AliTRDtrack::GetExternalParameters(Double_t& xr, Double_t x[5]) const {
161 //
162 // This function returns external TRD track representation
163 //
164 xr=fX;
165 x[0]=GetY();
166 x[1]=GetZ();
167 x[2]=GetSnp();
168 x[3]=GetTgl();
169 x[4]=fC*GetConvConst();
170}
171
172//_____________________________________________________________________________
173void AliTRDtrack::GetExternalCovariance(Double_t cc[15]) const {
174 //
175 // This function returns external representation of the covriance matrix.
176 //
177 Double_t a=GetConvConst();
178
179 Double_t c22=fX*fX*fCcc-2*fX*fCec+fCee;
180 Double_t c32=fX*fCtc-fCte;
181 Double_t c20=fX*fCcy-fCey, c21=fX*fCcz-fCez, c42=fX*fCcc-fCec;
182
183 cc[0 ]=fCyy;
184 cc[1 ]=fCzy; cc[2 ]=fCzz;
185 cc[3 ]=c20; cc[4 ]=c21; cc[5 ]=c22;
186 cc[6 ]=fCty; cc[7 ]=fCtz; cc[8 ]=c32; cc[9 ]=fCtt;
187 cc[10]=fCcy*a; cc[11]=fCcz*a; cc[12]=c42*a; cc[13]=fCtc*a; cc[14]=fCcc*a*a;
188}
189
46d29e70 190
191//_____________________________________________________________________________
192void AliTRDtrack::GetCovariance(Double_t cc[15]) const {
193 cc[0]=fCyy;
194 cc[1]=fCzy; cc[2]=fCzz;
195 cc[3]=fCcy; cc[4]=fCcz; cc[5]=fCcc;
196 cc[6]=fCey; cc[7]=fCez; cc[8]=fCec; cc[9]=fCee;
197 cc[10]=fCty; cc[11]=fCtz; cc[12]=fCtc; cc[13]=fCte; cc[14]=fCtt;
198}
199
200//_____________________________________________________________________________
2a941f4e 201Int_t AliTRDtrack::Compare(const TObject *o) const {
46d29e70 202
5443e65e 203// Compares tracks according to their Y2 or curvature
46d29e70 204
205 AliTRDtrack *t=(AliTRDtrack*)o;
206 // Double_t co=t->GetSigmaY2();
207 // Double_t c =GetSigmaY2();
208
209 Double_t co=TMath::Abs(t->GetC());
210 Double_t c =TMath::Abs(GetC());
211
212 if (c>co) return 1;
213 else if (c<co) return -1;
214 return 0;
215}
216
a819a5f7 217//_____________________________________________________________________________
218void AliTRDtrack::CookdEdx(Double_t low, Double_t up) {
219 //-----------------------------------------------------------------
220 // Calculates dE/dX within the "low" and "up" cuts.
221 //-----------------------------------------------------------------
5443e65e 222
a819a5f7 223 Int_t i;
5443e65e 224 Int_t nc=GetNumberOfClusters();
a819a5f7 225
5443e65e 226 Float_t sorted[kMAX_CLUSTERS_PER_TRACK];
227 for (i=0; i < nc; i++) {
228 sorted[i]=fdQdl[i];
229 }
a819a5f7 230
231 Int_t swap;
5443e65e 232
a819a5f7 233 do {
234 swap=0;
235 for (i=0; i<nc-1; i++) {
236 if (sorted[i]<=sorted[i+1]) continue;
237 Float_t tmp=sorted[i];
238 sorted[i]=sorted[i+1]; sorted[i+1]=tmp;
239 swap++;
240 }
241 } while (swap);
242
243 Int_t nl=Int_t(low*nc), nu=Int_t(up*nc);
244 Float_t dedx=0;
245 for (i=nl; i<=nu; i++) dedx += sorted[i];
246 dedx /= (nu-nl+1);
5443e65e 247
a819a5f7 248 SetdEdx(dedx);
249}
250
251
252
46d29e70 253//_____________________________________________________________________________
254Int_t AliTRDtrack::PropagateTo(Double_t xk,Double_t x0,Double_t rho,Double_t pm)
255{
256 // Propagates a track of particle with mass=pm to a reference plane
257 // defined by x=xk through media of density=rho and radiationLength=x0
258
5443e65e 259
46d29e70 260 if (TMath::Abs(fC*xk - fE) >= 0.99999) {
5443e65e 261 Int_t n=GetNumberOfClusters();
262 if (n>4) cerr<<n<<" AliTRDtrack warning: Propagation failed !\n";
46d29e70 263 return 0;
264 }
265
266 Double_t x1=fX, x2=x1+(xk-x1), dx=x2-x1, y1=fY, z1=fZ;
5443e65e 267 Double_t c1=fC*x1 - fE;
268 if((c1*c1) > 1) return 0;
269 Double_t r1=sqrt(1.- c1*c1);
270 Double_t c2=fC*x2 - fE;
271 if((c2*c2) > 1) return 0;
272 Double_t r2=sqrt(1.- c2*c2);
46d29e70 273
274 fY += dx*(c1+c2)/(r1+r2);
275 fZ += dx*(c1+c2)/(c1*r2 + c2*r1)*fT;
276
277 //f = F - 1
278 Double_t rr=r1+r2, cc=c1+c2, xx=x1+x2;
279 Double_t f02= dx*(rr*xx + cc*(c1*x1/r1+c2*x2/r2))/(rr*rr);
280 Double_t f03=-dx*(2*rr + cc*(c1/r1 + c2/r2))/(rr*rr);
281 Double_t cr=c1*r2+c2*r1;
282 Double_t f12= dx*fT*(cr*xx-cc*(r1*x2-c2*c1*x1/r1+r2*x1-c1*c2*x2/r2))/(cr*cr);
283 Double_t f13=-dx*fT*(2*cr + cc*(c2*c1/r1-r1 + c1*c2/r2-r2))/(cr*cr);
284 Double_t f14= dx*cc/cr;
285
286 //b = C*ft
287 Double_t b00=f02*fCcy + f03*fCey, b01=f12*fCcy + f13*fCey + f14*fCty;
288 Double_t b10=f02*fCcz + f03*fCez, b11=f12*fCcz + f13*fCez + f14*fCtz;
289 Double_t b20=f02*fCcc + f03*fCec, b21=f12*fCcc + f13*fCec + f14*fCtc;
290 Double_t b30=f02*fCec + f03*fCee, b31=f12*fCec + f13*fCee + f14*fCte;
291 Double_t b40=f02*fCtc + f03*fCte, b41=f12*fCtc + f13*fCte + f14*fCtt;
292
293 //a = f*b = f*C*ft
294 Double_t a00=f02*b20+f03*b30,a01=f02*b21+f03*b31,a11=f12*b21+f13*b31+f14*b41;
295
296 //F*C*Ft = C + (a + b + bt)
297 fCyy += a00 + 2*b00;
298 fCzy += a01 + b01 + b10;
299 fCcy += b20;
300 fCey += b30;
301 fCty += b40;
302 fCzz += a11 + 2*b11;
303 fCcz += b21;
304 fCez += b31;
305 fCtz += b41;
306
307 fX=x2;
308
309
310 //Multiple scattering ******************
311
312 Double_t d=sqrt((x1-fX)*(x1-fX)+(y1-fY)*(y1-fY)+(z1-fZ)*(z1-fZ));
313 Double_t p2=GetPt()*GetPt()*(1.+fT*fT);
5443e65e 314 p2 = TMath::Min(p2,1e+08); // to avoid division by (1-1) for stiff tracks
46d29e70 315 Double_t beta2=p2/(p2 + pm*pm);
316
317 Double_t ey=fC*fX - fE, ez=fT;
318 Double_t xz=fC*ez, zz1=ez*ez+1, xy=fE+ey;
319
320 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
321 fCcc += xz*xz*theta2;
322 fCec += xz*ez*xy*theta2;
323 fCtc += xz*zz1*theta2;
324 fCee += (2*ey*ez*ez*fE+1-ey*ey+ez*ez+fE*fE*ez*ez)*theta2;
325 fCte += ez*zz1*xy*theta2;
326 fCtt += zz1*zz1*theta2;
327
328
329 //Energy losses************************
5443e65e 330 if (x1 < x2) d=-d;
46d29e70 331 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d*rho;
5443e65e 332 SetLength(GetLength()+d);
333
334 cc = fC;
46d29e70 335 fC*=(1.- sqrt(p2+pm*pm)/p2*dE);
5443e65e 336 fE+=fX*(fC-cc);
46d29e70 337
338 return 1;
339
340}
341
46d29e70 342//_____________________________________________________________________________
5443e65e 343Int_t AliTRDtrack::Update(const AliTRDcluster *c, Double_t chisq, UInt_t index)
46d29e70 344{
345 // Assignes found cluster to the track and updates track information
346
a819a5f7 347 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
46d29e70 348 r00+=fCyy; r01+=fCzy; r11+=fCzz;
349 Double_t det=r00*r11 - r01*r01;
350 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
351
352 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
353 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
354 Double_t k20=fCcy*r00+fCcz*r01, k21=fCcy*r01+fCcz*r11;
355 Double_t k30=fCey*r00+fCez*r01, k31=fCey*r01+fCez*r11;
356 Double_t k40=fCty*r00+fCtz*r01, k41=fCty*r01+fCtz*r11;
357
358 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
359 Double_t cur=fC + k20*dy + k21*dz, eta=fE + k30*dy + k31*dz;
360 if (TMath::Abs(cur*fX-eta) >= 0.99999) {
5443e65e 361 Int_t n=GetNumberOfClusters();
362 if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
363 return 0;
46d29e70 364 }
365
366 fY += k00*dy + k01*dz;
367 fZ += k10*dy + k11*dz;
368 fC = cur;
369 fE = eta;
370 fT += k40*dy + k41*dz;
371
372 Double_t c01=fCzy, c02=fCcy, c03=fCey, c04=fCty;
373 Double_t c12=fCcz, c13=fCez, c14=fCtz;
374
375 fCyy-=k00*fCyy+k01*fCzy; fCzy-=k00*c01+k01*fCzz;
376 fCcy-=k00*c02+k01*c12; fCey-=k00*c03+k01*c13;
377 fCty-=k00*c04+k01*c14;
378
379 fCzz-=k10*c01+k11*fCzz;
380 fCcz-=k10*c02+k11*c12; fCez-=k10*c03+k11*c13;
381 fCtz-=k10*c04+k11*c14;
382
383 fCcc-=k20*c02+k21*c12; fCec-=k20*c03+k21*c13;
384 fCtc-=k20*c04+k21*c14;
385
386 fCee-=k30*c03+k31*c13;
387 fCte-=k30*c04+k31*c14;
388
389 fCtt-=k40*c04+k41*c14;
390
5443e65e 391 Int_t n=GetNumberOfClusters();
392 fIndex[n]=index;
393 SetNumberOfClusters(n+1);
46d29e70 394
5443e65e 395 SetChi2(GetChi2()+chisq);
46d29e70 396 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
5443e65e 397
398 return 1;
46d29e70 399}
400
401//_____________________________________________________________________________
402Int_t AliTRDtrack::Rotate(Double_t alpha)
403{
404 // Rotates track parameters in R*phi plane
405
406 fAlpha += alpha;
407
408 Double_t x1=fX, y1=fY;
409 Double_t ca=cos(alpha), sa=sin(alpha);
410 Double_t r1=fC*fX - fE;
411
5443e65e 412 if (TMath::Abs(r1) >= 0.99999) {
413 Int_t n=GetNumberOfClusters();
414 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
415 return 0;
416 }
417
46d29e70 418 fX = x1*ca + y1*sa;
419 fY=-x1*sa + y1*ca;
420 fE=fE*ca + (fC*y1 + sqrt(1.- r1*r1))*sa;
421
422 Double_t r2=fC*fX - fE;
423 if (TMath::Abs(r2) >= 0.99999) {
5443e65e 424 Int_t n=GetNumberOfClusters();
425 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
46d29e70 426 return 0;
427 }
428
429 Double_t y0=fY + sqrt(1.- r2*r2)/fC;
430 if ((fY-y0)*fC >= 0.) {
5443e65e 431 Int_t n=GetNumberOfClusters();
432 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !!!\n";
46d29e70 433 return 0;
434 }
435
436 //f = F - 1
437 Double_t f00=ca-1, f32=(y1 - r1*x1/sqrt(1.- r1*r1))*sa,
438 f30=fC*sa, f33=(ca + sa*r1/sqrt(1.- r1*r1))-1;
439
440 //b = C*ft
441 Double_t b00=fCyy*f00, b03=fCyy*f30+fCcy*f32+fCey*f33;
442 Double_t b10=fCzy*f00, b13=fCzy*f30+fCcz*f32+fCez*f33;
443 Double_t b20=fCcy*f00, b23=fCcy*f30+fCcc*f32+fCec*f33;
444 Double_t b30=fCey*f00, b33=fCey*f30+fCec*f32+fCee*f33;
445 Double_t b40=fCty*f00, b43=fCty*f30+fCtc*f32+fCte*f33;
446
447 //a = f*b = f*C*ft
448 Double_t a00=f00*b00, a03=f00*b03, a33=f30*b03+f32*b23+f33*b33;
449
450 // *** Double_t dy2=fCyy;
451
452 //F*C*Ft = C + (a + b + bt)
453 fCyy += a00 + 2*b00;
454 fCzy += b10;
455 fCcy += b20;
456 fCey += a03+b30+b03;
457 fCty += b40;
458 fCez += b13;
459 fCec += b23;
460 fCee += a33 + 2*b33;
461 fCte += b43;
462
463 // *** fCyy+=dy2*sa*sa*r1*r1/(1.- r1*r1);
464 // *** fCzz+=d2y*sa*sa*fT*fT/(1.- r1*r1);
465
466 return 1;
467}
468
469
46d29e70 470//_____________________________________________________________________________
471Double_t AliTRDtrack::GetPredictedChi2(const AliTRDcluster *c) const
472{
a819a5f7 473 /*
474 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
46d29e70 475 r00+=fCyy; r01+=fCzy; r11+=fCzz;
476
477 Double_t det=r00*r11 - r01*r01;
478 if (TMath::Abs(det) < 1.e-10) {
479 if (fN>4) cerr<<fN<<" AliTRDtrack warning: Singular matrix !\n";
480 return 1e10;
481 }
482 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
483
484 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
485
486 return (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
a819a5f7 487 */
488
489 Double_t dy=c->GetY() - fY;
490 Double_t r00=c->GetSigmaY2();
491
492 return (dy*dy)/r00;
493
46d29e70 494}
495
496
497//_________________________________________________________________________
498void AliTRDtrack::GetPxPyPz(Double_t& px, Double_t& py, Double_t& pz) const
499{
500 // Returns reconstructed track momentum in the global system.
501
502 Double_t pt=TMath::Abs(GetPt()); // GeV/c
503 Double_t r=fC*fX-fE;
5443e65e 504
505 Double_t y0;
506 if(r > 1) { py = pt; px = 0; }
507 else if(r < -1) { py = -pt; px = 0; }
508 else {
509 y0=fY + sqrt(1.- r*r)/fC;
510 px=-pt*(fY-y0)*fC; //cos(phi);
511 py=-pt*(fE-fX*fC); //sin(phi);
512 }
46d29e70 513 pz=pt*fT;
514 Double_t tmp=px*TMath::Cos(fAlpha) - py*TMath::Sin(fAlpha);
515 py=px*TMath::Sin(fAlpha) + py*TMath::Cos(fAlpha);
516 px=tmp;
517
518}
519
5443e65e 520//_________________________________________________________________________
521void AliTRDtrack::GetGlobalXYZ(Double_t& x, Double_t& y, Double_t& z) const
46d29e70 522{
5443e65e 523 // Returns reconstructed track coordinates in the global system.
524
525 x = fX; y = fY; z = fZ;
526 Double_t tmp=x*TMath::Cos(fAlpha) - y*TMath::Sin(fAlpha);
527 y=x*TMath::Sin(fAlpha) + y*TMath::Cos(fAlpha);
528 x=tmp;
529
530}
3ab6f951 531
5443e65e 532//_________________________________________________________________________
533void AliTRDtrack::ResetCovariance() {
534 //
535 // Resets covariance matrix
536 //
46d29e70 537
5443e65e 538 fCyy*=10.;
539 fCzy=0.; fCzz*=10.;
540 fCcy=0.; fCcz=0.; fCcc*=10.;
541 fCey=0.; fCez=0.; fCec=0.; fCee*=10.;
542 fCty=0.; fCtz=0.; fCtc=0.; fCte=0.; fCtt*=10.;
46d29e70 543
5443e65e 544}