1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
18 Revision 1.13 2002/10/22 15:53:08 alibrary
19 Introducing Riostream.h
21 Revision 1.12 2002/10/14 14:57:44 hristov
22 Merging the VirtualMC branch to the main development branch (HEAD)
24 Revision 1.8.10.2 2002/07/24 10:09:31 alibrary
27 RRevision 1.11 2002/06/13 12:09:58 hristov
30 Revision 1.10 2002/06/12 09:54:35 cblume
31 Update of tracking code provided by Sergei
33 Revision 1.8 2001/05/30 12:17:47 hristov
34 Loop variables declared once
36 Revision 1.7 2001/05/28 17:07:58 hristov
37 Last minute changes; ExB correction in AliTRDclusterizerV1; taking into account of material in G10 TEC frames and material between TEC planes (C.Blume,S.Sedykh)
39 Revision 1.4 2000/12/08 16:07:02 cblume
40 Update of the tracking by Sergei
42 Revision 1.3 2000/10/15 23:40:01 cblume
45 Revision 1.2 2000/10/06 16:49:46 cblume
48 Revision 1.1.2.1 2000/09/22 14:47:52 cblume
53 #include <Riostream.h>
56 #include "AliTRDgeometry.h"
57 #include "AliTRDcluster.h"
58 #include "AliTRDtrack.h"
59 #include "../TPC/AliTPCtrack.h"
64 //_____________________________________________________________________________
66 AliTRDtrack::AliTRDtrack(const AliTRDcluster *c, UInt_t index,
67 const Double_t xx[5], const Double_t cc[15],
68 Double_t xref, Double_t alpha) : AliKalmanTrack() {
69 //-----------------------------------------------------------------
70 // This is the main track constructor.
71 //-----------------------------------------------------------------
76 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
77 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
81 fY=xx[0]; fZ=xx[1]; fC=xx[2]; fE=xx[3]; fT=xx[4];
84 fCzy=cc[1]; fCzz=cc[2];
85 fCcy=cc[3]; fCcz=cc[4]; fCcc=cc[5];
86 fCey=cc[6]; fCez=cc[7]; fCec=cc[8]; fCee=cc[9];
87 fCty=cc[10]; fCtz=cc[11]; fCtc=cc[12]; fCte=cc[13]; fCtt=cc[14];
90 SetNumberOfClusters(1);
94 Double_t q = TMath::Abs(c->GetQ());
95 Double_t s = fX*fC - fE, t=fT;
96 if(s*s < 1) q *= TMath::Sqrt((1-s*s)/(1+t*t));
101 //_____________________________________________________________________________
102 AliTRDtrack::AliTRDtrack(const AliTRDtrack& t) : AliKalmanTrack(t) {
107 SetLabel(t.GetLabel());
108 fSeedLab=t.GetSeedLabel();
110 SetChi2(t.GetChi2());
116 fY=t.fY; fZ=t.fZ; fC=t.fC; fE=t.fE; fT=t.fT;
119 fCzy=t.fCzy; fCzz=t.fCzz;
120 fCcy=t.fCcy; fCcz=t.fCcz; fCcc=t.fCcc;
121 fCey=t.fCey; fCez=t.fCez; fCec=t.fCec; fCee=t.fCee;
122 fCty=t.fCty; fCtz=t.fCtz; fCtc=t.fCtc; fCte=t.fCte; fCtt=t.fCtt;
124 Int_t n=t.GetNumberOfClusters();
125 SetNumberOfClusters(n);
126 for (Int_t i=0; i<n; i++) {
127 fIndex[i]=t.fIndex[i];
132 //_____________________________________________________________________________
133 AliTRDtrack::AliTRDtrack(const AliKalmanTrack& t, Double_t alpha) {
135 // Constructor from AliTPCtrack or AliITStrack .
138 SetLabel(t.GetLabel());
140 SetNumberOfClusters(0);
145 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
146 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
148 Double_t x, p[5]; t.GetExternalParameters(x,p);
154 fY=p[0]; fZ=p[1]; fC=p[4]/x;
155 fE=fX*fC-p[2]; fT=p[3];
157 //Conversion of the covariance matrix
158 Double_t c[15]; t.GetExternalCovariance(c);
160 c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;
162 Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
163 Double_t c32=fX*c[13] - c[8];
164 Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];
167 fCzy=c[1 ]; fCzz=c[2 ];
168 fCcy=c[10]; fCcz=c[11]; fCcc=c[14];
169 fCey=c20; fCez=c21; fCec=c42; fCee=c22;
170 fCty=c[6 ]; fCtz=c[7 ]; fCtc=c[13]; fCte=c32; fCtt=c[9 ];
174 //____________________________________________________________________________
175 void AliTRDtrack::GetExternalParameters(Double_t& xr, Double_t x[5]) const {
177 // This function returns external TRD track representation
184 x[4]=fC*GetConvConst();
187 //_____________________________________________________________________________
188 void AliTRDtrack::GetExternalCovariance(Double_t cc[15]) const {
190 // This function returns external representation of the covriance matrix.
192 Double_t a=GetConvConst();
194 Double_t c22=fX*fX*fCcc-2*fX*fCec+fCee;
195 Double_t c32=fX*fCtc-fCte;
196 Double_t c20=fX*fCcy-fCey, c21=fX*fCcz-fCez, c42=fX*fCcc-fCec;
199 cc[1 ]=fCzy; cc[2 ]=fCzz;
200 cc[3 ]=c20; cc[4 ]=c21; cc[5 ]=c22;
201 cc[6 ]=fCty; cc[7 ]=fCtz; cc[8 ]=c32; cc[9 ]=fCtt;
202 cc[10]=fCcy*a; cc[11]=fCcz*a; cc[12]=c42*a; cc[13]=fCtc*a; cc[14]=fCcc*a*a;
206 //_____________________________________________________________________________
207 void AliTRDtrack::GetCovariance(Double_t cc[15]) const {
209 cc[1]=fCzy; cc[2]=fCzz;
210 cc[3]=fCcy; cc[4]=fCcz; cc[5]=fCcc;
211 cc[6]=fCey; cc[7]=fCez; cc[8]=fCec; cc[9]=fCee;
212 cc[10]=fCty; cc[11]=fCtz; cc[12]=fCtc; cc[13]=fCte; cc[14]=fCtt;
215 //_____________________________________________________________________________
216 Int_t AliTRDtrack::Compare(const TObject *o) const {
218 // Compares tracks according to their Y2 or curvature
220 AliTRDtrack *t=(AliTRDtrack*)o;
221 // Double_t co=t->GetSigmaY2();
222 // Double_t c =GetSigmaY2();
224 Double_t co=TMath::Abs(t->GetC());
225 Double_t c =TMath::Abs(GetC());
228 else if (c<co) return -1;
232 //_____________________________________________________________________________
233 void AliTRDtrack::CookdEdx(Double_t low, Double_t up) {
234 //-----------------------------------------------------------------
235 // Calculates dE/dX within the "low" and "up" cuts.
236 //-----------------------------------------------------------------
239 Int_t nc=GetNumberOfClusters();
241 Float_t sorted[kMAX_CLUSTERS_PER_TRACK];
242 for (i=0; i < nc; i++) {
250 for (i=0; i<nc-1; i++) {
251 if (sorted[i]<=sorted[i+1]) continue;
252 Float_t tmp=sorted[i];
253 sorted[i]=sorted[i+1]; sorted[i+1]=tmp;
258 Int_t nl=Int_t(low*nc), nu=Int_t(up*nc);
260 for (i=nl; i<=nu; i++) dedx += sorted[i];
269 //_____________________________________________________________________________
270 Int_t AliTRDtrack::PropagateTo(Double_t xk,Double_t x0,Double_t rho,Double_t pm)
272 // Propagates a track of particle with mass=pm to a reference plane
273 // defined by x=xk through media of density=rho and radiationLength=x0
276 if (TMath::Abs(fC*xk - fE) >= 0.99999) {
277 Int_t n=GetNumberOfClusters();
278 if (n>4) cerr<<n<<" AliTRDtrack warning: Propagation failed !\n";
282 Double_t x1=fX, x2=x1+(xk-x1), dx=x2-x1, y1=fY, z1=fZ;
283 Double_t c1=fC*x1 - fE;
284 if((c1*c1) > 1) return 0;
285 Double_t r1=sqrt(1.- c1*c1);
286 Double_t c2=fC*x2 - fE;
287 if((c2*c2) > 1) return 0;
288 Double_t r2=sqrt(1.- c2*c2);
290 fY += dx*(c1+c2)/(r1+r2);
291 fZ += dx*(c1+c2)/(c1*r2 + c2*r1)*fT;
294 Double_t rr=r1+r2, cc=c1+c2, xx=x1+x2;
295 Double_t f02= dx*(rr*xx + cc*(c1*x1/r1+c2*x2/r2))/(rr*rr);
296 Double_t f03=-dx*(2*rr + cc*(c1/r1 + c2/r2))/(rr*rr);
297 Double_t cr=c1*r2+c2*r1;
298 Double_t f12= dx*fT*(cr*xx-cc*(r1*x2-c2*c1*x1/r1+r2*x1-c1*c2*x2/r2))/(cr*cr);
299 Double_t f13=-dx*fT*(2*cr + cc*(c2*c1/r1-r1 + c1*c2/r2-r2))/(cr*cr);
300 Double_t f14= dx*cc/cr;
303 Double_t b00=f02*fCcy + f03*fCey, b01=f12*fCcy + f13*fCey + f14*fCty;
304 Double_t b10=f02*fCcz + f03*fCez, b11=f12*fCcz + f13*fCez + f14*fCtz;
305 Double_t b20=f02*fCcc + f03*fCec, b21=f12*fCcc + f13*fCec + f14*fCtc;
306 Double_t b30=f02*fCec + f03*fCee, b31=f12*fCec + f13*fCee + f14*fCte;
307 Double_t b40=f02*fCtc + f03*fCte, b41=f12*fCtc + f13*fCte + f14*fCtt;
310 Double_t a00=f02*b20+f03*b30,a01=f02*b21+f03*b31,a11=f12*b21+f13*b31+f14*b41;
312 //F*C*Ft = C + (a + b + bt)
314 fCzy += a01 + b01 + b10;
326 //Multiple scattering ******************
328 Double_t d=sqrt((x1-fX)*(x1-fX)+(y1-fY)*(y1-fY)+(z1-fZ)*(z1-fZ));
329 Double_t p2=GetPt()*GetPt()*(1.+fT*fT);
330 p2 = TMath::Min(p2,1e+08); // to avoid division by (1-1) for stiff tracks
331 Double_t beta2=p2/(p2 + pm*pm);
333 Double_t ey=fC*fX - fE, ez=fT;
334 Double_t xz=fC*ez, zz1=ez*ez+1, xy=fE+ey;
336 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
337 fCcc += xz*xz*theta2;
338 fCec += xz*ez*xy*theta2;
339 fCtc += xz*zz1*theta2;
340 fCee += (2*ey*ez*ez*fE+1-ey*ey+ez*ez+fE*fE*ez*ez)*theta2;
341 fCte += ez*zz1*xy*theta2;
342 fCtt += zz1*zz1*theta2;
345 //Energy losses************************
347 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d*rho;
348 //PH SetLength(GetLength()+d);
351 fC*=(1.- sqrt(p2+pm*pm)/p2*dE);
359 //_____________________________________________________________________________
360 Int_t AliTRDtrack::Update(const AliTRDcluster *c, Double_t chisq, UInt_t index, Double_t h01)
362 // Assignes found cluster to the track and updates track information
365 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2()*100.0;
367 r00+=(fCyy+2.0*h01*fCzy+h01*h01*fCzz);
368 r01+=(fCzy+h01*fCzz);
371 Double_t det=r00*r11 - r01*r01;
372 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
374 // Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
375 // Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
376 // Double_t k20=fCcy*r00+fCcz*r01, k21=fCcy*r01+fCcz*r11;
377 // Double_t k30=fCey*r00+fCez*r01, k31=fCey*r01+fCez*r11;
378 // Double_t k40=fCty*r00+fCtz*r01, k41=fCty*r01+fCtz*r11;
380 Double_t k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
381 Double_t k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
382 Double_t k20=fCcy*r00+fCcz*(r01+h01*r00),k21=fCcy*r01+fCcz*(r11+h01*r01);
383 Double_t k30=fCey*r00+fCez*(r01+h01*r00),k31=fCey*r01+fCez*(r11+h01*r01);
384 Double_t k40=fCty*r00+fCtz*(r01+h01*r00),k41=fCty*r01+fCtz*(r11+h01*r01);
386 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
390 Double_t cur=fC + k20*dy + k21*dz, eta=fE + k30*dy + k31*dz;
391 if (TMath::Abs(cur*fX-eta) >= 0.99999) {
392 // if (fN>4) cerr<<fN<<" AliTRDtrack warning: Filtering failed !\n";
396 fY += k00*dy + k01*dz;
397 fZ += k10*dy + k11*dz;
400 fT += k40*dy + k41*dz;
409 Double_t c01=fCzy, c02=fCcy, c03=fCey, c04=fCty;
410 Double_t c12=fCcz, c13=fCez, c14=fCtz;
412 fCyy-=k00*fCyy+k01*fCzy; fCzy-=k00*c01+k01*fCzz;
413 fCcy-=k00*c02+k01*c12; fCey-=k00*c03+k01*c13;
414 fCty-=k00*c04+k01*c14;
416 fCzz-=k10*c01+k11*fCzz;
417 fCcz-=k10*c02+k11*c12; fCez-=k10*c03+k11*c13;
418 fCtz-=k10*c04+k11*c14;
420 fCcc-=k20*c02+k21*c12; fCec-=k20*c03+k21*c13;
421 fCtc-=k20*c04+k21*c14;
423 fCee-=k30*c03+k31*c13;
424 fCte-=k30*c04+k31*c14;
426 fCtt-=k40*c04+k41*c14;
428 Int_t n=GetNumberOfClusters();
430 SetNumberOfClusters(n+1);
432 SetChi2(GetChi2()+chisq);
434 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
441 //_____________________________________________________________________________
442 Int_t AliTRDtrack::Rotate(Double_t alpha)
444 // Rotates track parameters in R*phi plane
448 Double_t x1=fX, y1=fY;
449 Double_t ca=cos(alpha), sa=sin(alpha);
450 Double_t r1=fC*fX - fE;
452 if (TMath::Abs(r1) >= 0.99999) {
453 Int_t n=GetNumberOfClusters();
454 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
460 fE=fE*ca + (fC*y1 + sqrt(1.- r1*r1))*sa;
462 Double_t r2=fC*fX - fE;
463 if (TMath::Abs(r2) >= 0.99999) {
464 Int_t n=GetNumberOfClusters();
465 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
469 Double_t y0=fY + sqrt(1.- r2*r2)/fC;
470 if ((fY-y0)*fC >= 0.) {
471 Int_t n=GetNumberOfClusters();
472 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !!!\n";
477 Double_t f00=ca-1, f32=(y1 - r1*x1/sqrt(1.- r1*r1))*sa,
478 f30=fC*sa, f33=(ca + sa*r1/sqrt(1.- r1*r1))-1;
481 Double_t b00=fCyy*f00, b03=fCyy*f30+fCcy*f32+fCey*f33;
482 Double_t b10=fCzy*f00, b13=fCzy*f30+fCcz*f32+fCez*f33;
483 Double_t b20=fCcy*f00, b23=fCcy*f30+fCcc*f32+fCec*f33;
484 Double_t b30=fCey*f00, b33=fCey*f30+fCec*f32+fCee*f33;
485 Double_t b40=fCty*f00, b43=fCty*f30+fCtc*f32+fCte*f33;
488 Double_t a00=f00*b00, a03=f00*b03, a33=f30*b03+f32*b23+f33*b33;
490 // *** Double_t dy2=fCyy;
492 //F*C*Ft = C + (a + b + bt)
503 // *** fCyy+=dy2*sa*sa*r1*r1/(1.- r1*r1);
504 // *** fCzz+=d2y*sa*sa*fT*fT/(1.- r1*r1);
510 //_____________________________________________________________________________
511 Double_t AliTRDtrack::GetPredictedChi2(const AliTRDcluster *c, Double_t h01) const
514 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
516 r00+=fCyy; r01+=fCzy; r11+=fCzz;
518 Double_t det=r00*r11 - r01*r01;
519 if (TMath::Abs(det) < 1.e-10) {
520 Int_t n=GetNumberOfClusters();
521 if (n>4) cerr<<n<<" AliTRDtrack warning: Singular matrix !\n";
524 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
526 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
530 return (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
535 //_________________________________________________________________________
536 void AliTRDtrack::GetPxPyPz(Double_t& px, Double_t& py, Double_t& pz) const
538 // Returns reconstructed track momentum in the global system.
540 Double_t pt=TMath::Abs(GetPt()); // GeV/c
544 if(r > 1) { py = pt; px = 0; }
545 else if(r < -1) { py = -pt; px = 0; }
547 y0=fY + sqrt(1.- r*r)/fC;
548 px=-pt*(fY-y0)*fC; //cos(phi);
549 py=-pt*(fE-fX*fC); //sin(phi);
552 Double_t tmp=px*TMath::Cos(fAlpha) - py*TMath::Sin(fAlpha);
553 py=px*TMath::Sin(fAlpha) + py*TMath::Cos(fAlpha);
558 //_________________________________________________________________________
559 void AliTRDtrack::GetGlobalXYZ(Double_t& x, Double_t& y, Double_t& z) const
561 // Returns reconstructed track coordinates in the global system.
563 x = fX; y = fY; z = fZ;
564 Double_t tmp=x*TMath::Cos(fAlpha) - y*TMath::Sin(fAlpha);
565 y=x*TMath::Sin(fAlpha) + y*TMath::Cos(fAlpha);
570 //_________________________________________________________________________
571 void AliTRDtrack::ResetCovariance() {
573 // Resets covariance matrix
578 fCcy=0.; fCcz=0.; fCcc*=10.;
579 fCey=0.; fCez=0.; fCec=0.; fCee*=10.;
580 fCty=0.; fCtz=0.; fCtc=0.; fCte=0.; fCtt*=10.;