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 #include <Riostream.h>
21 #include "AliTRDgeometry.h"
22 #include "AliTRDcluster.h"
23 #include "AliTRDtrack.h"
24 #include "AliTRDclusterCorrection.h"
25 #include "AliTrackReference.h"
27 ClassImp(AliTRDtracklet)
31 AliTRDtracklet::AliTRDtracklet():fY(0),fZ(0),fX(0),fAlpha(0),fSigma2(0),fP0(0),fP1(0),fNFound(0),fNCross(0),fPlane(0),fExpectedSigma2(0),fChi2(0),fTilt(0),fMaxPos(0),fMaxPos4(0),fMaxPos5(0){
34 //_____________________________________________________________________________
36 AliTRDtrack::AliTRDtrack(const AliTRDcluster *c, UInt_t index,
37 const Double_t xx[5], const Double_t cc[15],
38 Double_t xref, Double_t alpha) : AliKalmanTrack() {
39 //-----------------------------------------------------------------
40 // This is the main track constructor.
41 //-----------------------------------------------------------------
46 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
47 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
51 fY=xx[0]; fZ=xx[1]; fE=xx[2]; fT=xx[3]; fC=xx[4];
56 fCzy=cc[1]; fCzz=cc[2];
57 fCey=cc[3]; fCez=cc[4]; fCee=cc[5];
58 fCty=cc[6]; fCtz=cc[7]; fCte=cc[8]; fCtt=cc[9];
59 fCcy=cc[10]; fCcz=cc[11]; fCce=cc[12]; fCct=cc[13]; fCcc=cc[14];
62 SetNumberOfClusters(1);
67 for (Int_t i=0;i<kNPlane;i++){
82 Double_t q = TMath::Abs(c->GetQ());
83 Double_t s = fX*fC - fE, t=fT;
84 if(s*s < 1) q *= TMath::Sqrt((1-s*s)/(1+t*t));
88 // initialisation [SR, GSI 18.02.2003] (i startd for 1)
89 for(UInt_t i=1; i<kMAX_CLUSTERS_PER_TRACK; i++) {
92 fIndexBackup[i] = 0; //bacup indexes MI
94 for (Int_t i=0;i<3;i++) { fBudget[i]=0;};
98 //_____________________________________________________________________________
99 AliTRDtrack::AliTRDtrack(const AliTRDtrack& t) : AliKalmanTrack(t) {
104 SetLabel(t.GetLabel());
105 fSeedLab=t.GetSeedLabel();
107 SetChi2(t.GetChi2());
111 for (Int_t i=0;i<kNPlane;i++){
112 fdEdxPlane[i] = t.fdEdxPlane[i];
113 fTimBinPlane[i] = t.fTimBinPlane[i];
114 fTracklets[i] = t.fTracklets[i];
119 fNRotate = t.fNRotate;
120 fStopped = t.fStopped;
122 fNExpected = t.fNExpected;
123 fNExpectedLast = t.fNExpectedLast;
126 fChi2Last = t.fChi2Last;
132 fY=t.fY; fZ=t.fZ; fE=t.fE; fT=t.fT; fC=t.fC;
135 fCzy=t.fCzy; fCzz=t.fCzz;
136 fCey=t.fCey; fCez=t.fCez; fCee=t.fCee;
137 fCty=t.fCty; fCtz=t.fCtz; fCte=t.fCte; fCtt=t.fCtt;
138 fCcy=t.fCcy; fCcz=t.fCcz; fCce=t.fCce; fCct=t.fCct; fCcc=t.fCcc;
140 Int_t n=t.GetNumberOfClusters();
141 SetNumberOfClusters(n);
142 for (Int_t i=0; i<n; i++) {
143 fIndex[i]=t.fIndex[i];
144 fIndexBackup[i]=t.fIndex[i]; // MI - backup indexes
148 // initialisation (i starts from n) [SR, GSI, 18.02.2003]
149 for(UInt_t i=n; i<kMAX_CLUSTERS_PER_TRACK; i++) {
152 fIndexBackup[i] = 0; //MI backup indexes
154 for (Int_t i=0;i<6;i++){
155 fTracklets[i] = t.fTracklets[i];
157 for (Int_t i=0;i<3;i++) { fBudget[i]=t.fBudget[i];};
160 //_____________________________________________________________________________
161 AliTRDtrack::AliTRDtrack(const AliKalmanTrack& t, Double_t alpha)
164 // Constructor from AliTPCtrack or AliITStrack .
167 SetLabel(t.GetLabel());
169 SetMass(t.GetMass());
170 SetNumberOfClusters(0);
172 fdEdx=t.GetPIDsignal();
173 for (Int_t i=0;i<kNPlane;i++){
175 fTimBinPlane[i] = -1;
191 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
192 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
194 Double_t x, p[5]; t.GetExternalParameters(x,p);
200 fT=p[3]; x=GetLocalConvConst();
204 //Conversion of the covariance matrix
205 Double_t c[15]; t.GetExternalCovariance(c);
207 c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;
209 Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
210 Double_t c32=fX*c[13] - c[8];
211 Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];
214 fCzy=c[1 ]; fCzz=c[2 ];
215 fCey=c20; fCez=c21; fCee=c22;
216 fCty=c[6 ]; fCtz=c[7 ]; fCte=c32; fCtt=c[9 ];
217 fCcy=c[10]; fCcz=c[11]; fCce=c42; fCct=c[13]; fCcc=c[14];
219 // Initialization [SR, GSI, 18.02.2003]
220 for(UInt_t i=0; i<kMAX_CLUSTERS_PER_TRACK; i++) {
223 fIndexBackup[i] = 0; // MI backup indexes
226 for (Int_t i=0;i<3;i++) { fBudget[i]=0;};
228 //_____________________________________________________________________________
229 AliTRDtrack::AliTRDtrack(const AliESDtrack& t)
232 // Constructor from AliESDtrack
235 SetLabel(t.GetLabel());
237 SetMass(t.GetMass());
238 SetNumberOfClusters(t.GetTRDclusters(fIndex));
239 Int_t ncl = t.GetTRDclusters(fIndexBackup);
240 for (UInt_t i=ncl;i<kMAX_CLUSTERS_PER_TRACK;i++) {
242 fIndex[i] = 0; //MI store indexes
244 fdEdx=t.GetTRDsignal();
245 for (Int_t i=0;i<kNPlane;i++){
246 fdEdxPlane[i] = t.GetTRDsignals(i);
247 fTimBinPlane[i] = t.GetTRDTimBin(i);
262 fAlpha = t.GetAlpha();
263 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
264 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
266 Double_t x, p[5]; t.GetExternalParameters(x,p);
267 //Conversion of the covariance matrix
268 Double_t c[15]; t.GetExternalCovariance(c);
269 if (t.GetStatus()&AliESDtrack::kTRDbackup){
270 fAlpha=t.GetOuterAlpha();
271 t.GetOuterExternalParameters(x,p);
272 t.GetOuterExternalCovariance(c);
273 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
274 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
280 fZ=p[1]; SaveLocalConvConst();
281 fT=p[3]; x=GetLocalConvConst();
286 c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;
288 Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
289 Double_t c32=fX*c[13] - c[8];
290 Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];
293 fCzy=c[1 ]; fCzz=c[2 ];
294 fCey=c20; fCez=c21; fCee=c22;
295 fCty=c[6 ]; fCtz=c[7 ]; fCte=c32; fCtt=c[9 ];
296 fCcy=c[10]; fCcz=c[11]; fCce=c42; fCct=c[13]; fCcc=c[14];
298 // Initialization [SR, GSI, 18.02.2003]
299 for(UInt_t i=0; i<kMAX_CLUSTERS_PER_TRACK; i++) {
301 // fIndex[i] = 0; //MI store indexes
304 for (Int_t i=0;i<3;i++) { fBudget[i]=0;};
305 if ((t.GetStatus()&AliESDtrack::kTIME) == 0) return;
307 Double_t times[10]; t.GetIntegratedTimes(times); SetIntegratedTimes(times);
308 SetIntegratedLength(t.GetIntegratedLength());
313 AliTRDtrack * AliTRDtrack::MakeTrack(const AliTrackReference *ref, Double_t mass)
316 // Make dummy track from the track reference
317 // negative mass means opposite charge
321 for (Int_t i=0;i<15;i++) cc[i]=0;
322 Double_t x = ref->X(), y = ref->Y(), z = ref->Z();
323 Double_t alpha = TMath::ATan2(y,x);
324 Double_t xr = TMath::Sqrt(x*x+y*y);
327 xx[3] = ref->Pz()/ref->Pt();
329 Float_t xyz[3]={x,y,z};
330 Float_t convConst = 0;
331 (AliKalmanTrack::GetFieldMap())->Field(xyz,b);
332 convConst=1000/0.299792458/(1e-13 - b[2]);
333 xx[4] = 1./(convConst*ref->Pt());
334 if (mass<0) xx[4]*=-1.; // negative mass - negative direction
335 Double_t lcos = (x*ref->Px()+y*ref->Py())/(xr*ref->Pt());
336 Double_t lsin = TMath::Sin(TMath::ACos(lcos));
337 if (mass<0) lsin*=-1.;
338 xx[2] = xr*xx[4]-lsin;
340 AliTRDtrack * track = new AliTRDtrack(&cl,100,xx,cc,xr,alpha);
341 track->SetMass(TMath::Abs(mass));
342 track->StartTimeIntegral();
347 AliTRDtrack::~AliTRDtrack()
352 if (fBackupTrack) delete fBackupTrack;
358 Float_t AliTRDtrack::StatusForTOF()
361 Float_t res = (0.2 + 0.8*(fN/(fNExpected+5.)))*(0.4+0.6*fTracklets[5].GetN()/20.);
362 res *= (0.25+0.8*40./(40.+fBudget[2]));
366 if (GetNumberOfClusters()<20) return 0; //
367 if (fN>110&&fChi2/(Float_t(fN))<3) return 3; //gold
368 if (fNLast>30&&fChi2Last/(Float_t(fNLast))<3) return 3; //gold
369 if (fNLast>20&&fChi2Last/(Float_t(fNLast))<2) return 3; //gold
370 if (fNLast/(fNExpectedLast+3.)>0.8 && fChi2Last/Float_t(fNLast)<5&&fNLast>20) return 2; //silber
371 if (fNLast>5 &&((fNLast+1.)/(fNExpectedLast+1.))>0.8&&fChi2Last/(fNLast-5.)<6) return 1;
378 //____________________________________________________________________________
379 void AliTRDtrack::GetExternalParameters(Double_t& xr, Double_t x[5]) const {
381 // This function returns external TRD track representation
391 //_____________________________________________________________________________
392 void AliTRDtrack::GetExternalCovariance(Double_t cc[15]) const {
394 // This function returns external representation of the covriance matrix.
396 Double_t a=GetLocalConvConst();
398 Double_t c22=fX*fX*fCcc-2*fX*fCce+fCee;
399 Double_t c32=fX*fCct-fCte;
400 Double_t c20=fX*fCcy-fCey, c21=fX*fCcz-fCez, c42=fX*fCcc-fCce;
403 cc[1 ]=fCzy; cc[2 ]=fCzz;
404 cc[3 ]=c20; cc[4 ]=c21; cc[5 ]=c22;
405 cc[6 ]=fCty; cc[7 ]=fCtz; cc[8 ]=c32; cc[9 ]=fCtt;
406 cc[10]=fCcy*a; cc[11]=fCcz*a; cc[12]=c42*a; cc[13]=fCct*a; cc[14]=fCcc*a*a;
411 //_____________________________________________________________________________
412 void AliTRDtrack::GetCovariance(Double_t cc[15]) const {
415 cc[1]=fCzy; cc[2]=fCzz;
416 cc[3]=fCey; cc[4]=fCez; cc[5]=fCee;
417 cc[6]=fCcy; cc[7]=fCcz; cc[8]=fCce; cc[9]=fCcc;
418 cc[10]=fCty; cc[11]=fCtz; cc[12]=fCte; cc[13]=fCct; cc[14]=fCtt;
422 //_____________________________________________________________________________
423 Int_t AliTRDtrack::Compare(const TObject *o) const {
425 // Compares tracks according to their Y2 or curvature
427 AliTRDtrack *t=(AliTRDtrack*)o;
428 // Double_t co=t->GetSigmaY2();
429 // Double_t c =GetSigmaY2();
431 Double_t co=TMath::Abs(t->GetC());
432 Double_t c =TMath::Abs(GetC());
435 else if (c<co) return -1;
439 //_____________________________________________________________________________
440 void AliTRDtrack::CookdEdx(Double_t low, Double_t up) {
441 //-----------------------------------------------------------------
442 // Calculates dE/dX within the "low" and "up" cuts.
443 //-----------------------------------------------------------------
446 //Int_t nc=GetNumberOfClusters();
453 Float_t sorted[kMAX_CLUSTERS_PER_TRACK];
454 for (i=0; i < nc; i++) {
457 Int_t nl=Int_t(low*nc), nu=Int_t(up*nc);
459 //for (i=nl; i<=nu; i++) dedx += sorted[i];
461 for (i=0; i<nc; i++) dedx += sorted[i]; // ADDED by PS
462 if((nu-nl)) dedx /= (nu-nl); // ADDED by PS
466 // now real truncated mean
467 for (i=0; i < nc; i++) {
468 sorted[i]=TMath::Abs(fdQdl[i]);
470 Int_t * index = new Int_t[nc];
471 TMath::Sort(nc, sorted, index,kFALSE);
473 for (i=nl; i<=nu; i++) dedx += sorted[index[i]];
482 //_____________________________________________________________________________
483 Int_t AliTRDtrack::PropagateTo(Double_t xk,Double_t x0,Double_t rho)
485 // Propagates a track of particle with mass=pm to a reference plane
486 // defined by x=xk through media of density=rho and radiationLength=x0
488 if (xk == fX) return 1;
490 if (TMath::Abs(fC*xk - fE) >= 0.90000) {
491 // Int_t n=GetNumberOfClusters();
492 //if (n>4) cerr << n << " AliTRDtrack: Propagation failed, \tPt = "
493 // << GetPt() << "\t" << GetLabel() << "\t" << GetMass() << endl;
496 Double_t lcc=GetLocalConvConst();
498 // track Length measurement [SR, GSI, 17.02.2003]
499 Double_t oldX = fX, oldY = fY, oldZ = fZ;
501 Double_t x1=fX, x2=x1+(xk-x1), dx=x2-x1, y1=fY, z1=fZ;
502 Double_t c1=fC*x1 - fE;
503 if((c1*c1) > 1) return 0;
504 Double_t r1=sqrt(1.- c1*c1);
505 Double_t c2=fC*x2 - fE;
506 if((c2*c2) > 1) return 0;
507 Double_t r2=sqrt(1.- c2*c2);
509 fY += dx*(c1+c2)/(r1+r2);
510 fZ += dx*(c1+c2)/(c1*r2 + c2*r1)*fT;
513 Double_t rr=r1+r2, cc=c1+c2, xx=x1+x2;
514 Double_t f02=-dx*(2*rr + cc*(c1/r1 + c2/r2))/(rr*rr);
515 Double_t f04= dx*(rr*xx + cc*(c1*x1/r1+c2*x2/r2))/(rr*rr);
516 Double_t cr=c1*r2+c2*r1;
517 Double_t f12=-dx*fT*(2*cr + cc*(c2*c1/r1-r1 + c1*c2/r2-r2))/(cr*cr);
518 Double_t f13= dx*cc/cr;
519 Double_t f14=dx*fT*(cr*xx-cc*(r1*x2-c2*c1*x1/r1+r2*x1-c1*c2*x2/r2))/(cr*cr);
522 Double_t b00=f02*fCey + f04*fCcy, b01=f12*fCey + f14*fCcy + f13*fCty;
523 Double_t b10=f02*fCez + f04*fCcz, b11=f12*fCez + f14*fCcz + f13*fCtz;
524 Double_t b20=f02*fCee + f04*fCce, b21=f12*fCee + f14*fCce + f13*fCte;
525 Double_t b30=f02*fCte + f04*fCct, b31=f12*fCte + f14*fCct + f13*fCtt;
526 Double_t b40=f02*fCce + f04*fCcc, b41=f12*fCce + f14*fCcc + f13*fCct;
529 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a11=f12*b21+f14*b41+f13*b31;
531 //F*C*Ft = C + (a + b + bt)
533 fCzy += a01 + b01 + b10;
544 //Change of the magnetic field *************
545 SaveLocalConvConst();
547 fC*=lcc/GetLocalConvConst();
550 //Multiple scattering ******************
551 Double_t d=sqrt((x1-fX)*(x1-fX)+(y1-fY)*(y1-fY)+(z1-fZ)*(z1-fZ));
552 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
553 Double_t beta2=p2/(p2 + GetMass()*GetMass());
554 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
556 Double_t ey=fC*fX - fE, ez=fT;
557 Double_t xz=fC*ez, zz1=ez*ez+1, xy=fE+ey;
559 fCee += (2*ey*ez*ez*fE+1-ey*ey+ez*ez+fE*fE*ez*ez)*theta2;
560 fCte += ez*zz1*xy*theta2;
561 fCtt += zz1*zz1*theta2;
562 fCce += xz*ez*xy*theta2;
563 fCct += xz*zz1*theta2;
564 fCcc += xz*xz*theta2;
566 Double_t dc22 = (1-ey*ey+xz*xz*fX*fX)*theta2;
567 Double_t dc32 = (xz*fX*zz1)*theta2;
568 Double_t dc33 = (zz1*zz1)*theta2;
569 Double_t dc42 = (xz*fX*xz)*theta2;
570 Double_t dc43 = (zz1*xz)*theta2;
571 Double_t dc44 = (xz*xz)*theta2;
579 //Energy losses************************
580 if((5940*beta2/(1-beta2+1e-10) - beta2) < 0) return 0;
582 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho;
584 // suspicious part - think about it ?
585 Double_t kinE = TMath::Sqrt(p2);
586 if (dE>0.8*kinE) dE = 0.8*kinE; //
587 if (dE<0) dE = 0.0; // not valid region for Bethe bloch
593 fC*=(1.- sqrt(p2+GetMass()*GetMass())/p2*dE);
595 // Double_t sigmade = 0.1*dE*TMath::Sqrt(TMath::Sqrt(1+fT*fT)*90./(d+0.0001)); // 20 percent fluctuation - normalized to some length
596 Double_t sigmade = 0.07*TMath::Sqrt(TMath::Abs(dE)); // energy loss fluctuation
597 Double_t sigmac2 = sigmade*sigmade*fC*fC*(p2+GetMass()*GetMass())/(p2*p2);
599 fCee += fX*fX*sigmac2;
601 // track time measurement [SR, GSI 17.02.2002]
603 if (IsStartedTimeIntegral()) {
604 Double_t l2 = TMath::Sqrt((fX-oldX)*(fX-oldX) + (fY-oldY)*(fY-oldY) + (fZ-oldZ)*(fZ-oldZ));
605 if (TMath::Abs(l2*fC)>0.0001){
606 // make correction for curvature if neccesary
607 l2 = 0.5*TMath::Sqrt((fX-oldX)*(fX-oldX) + (fY-oldY)*(fY-oldY));
608 l2 = 2*TMath::ASin(l2*fC)/fC;
609 l2 = TMath::Sqrt(l2*l2+(fZ-oldZ)*(fZ-oldZ));
618 //_____________________________________________________________________________
619 Int_t AliTRDtrack::Update(const AliTRDcluster *c, Double_t chisq, UInt_t index, Double_t h01)
621 // Assignes found cluster to the track and updates track information
623 Bool_t fNoTilt = kTRUE;
624 if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
625 // add angular effect to the error contribution - MI
626 Float_t tangent2 = (fC*fX-fE)*(fC*fX-fE);
627 if (tangent2 < 0.90000){
628 tangent2 = tangent2/(1.-tangent2);
630 Float_t errang = tangent2*0.04; //
631 Float_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12.);
633 Double_t r00=c->GetSigmaY2() +errang, r01=0., r11=c->GetSigmaZ2()*100.;
634 r00+=fCyy; r01+=fCzy; r11+=fCzz;
635 Double_t det=r00*r11 - r01*r01;
636 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
638 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
639 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
640 Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
641 Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
642 Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;
644 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
645 Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;
649 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
650 // Int_t n=GetNumberOfClusters();
651 //if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
654 fY += k00*dy + k01*dz;
655 fZ += k10*dy + k11*dz;
657 //fT += k30*dy + k31*dz;
661 Double_t xu_factor = 100.; // empirical factor set by C.Xu
662 // in the first tilt version
663 dy=c->GetY() - fY; dz=c->GetZ() - fZ;
666 if (TMath::Abs(dz)>padlength/2.){
667 Float_t dy2 = c->GetY() - fY;
668 Float_t sign = (dz>0) ? -1.: 1.;
669 dy2+=h01*sign*padlength/2.;
676 r00=c->GetSigmaY2()+errang+add, r01=0., r11=c->GetSigmaZ2()*xu_factor;
677 r00+=(fCyy+2.0*h01*fCzy+h01*h01*fCzz);
678 r01+=(fCzy+h01*fCzz);
681 det=r00*r11 - r01*r01;
682 tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
684 k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
685 k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
686 k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
687 k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
688 k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);
691 cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
692 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
693 // Int_t n=GetNumberOfClusters();
694 //if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
697 fY += k00*dy + k01*dz;
698 fZ += k10*dy + k11*dz;
700 fT += k30*dy + k31*dz;
710 Double_t c01=fCzy, c02=fCey, c03=fCty, c04=fCcy;
711 Double_t c12=fCez, c13=fCtz, c14=fCcz;
714 fCyy-=k00*fCyy+k01*fCzy; fCzy-=k00*c01+k01*fCzz;
715 fCey-=k00*c02+k01*c12; fCty-=k00*c03+k01*c13;
716 fCcy-=k00*c04+k01*c14;
718 fCzz-=k10*c01+k11*fCzz;
719 fCez-=k10*c02+k11*c12; fCtz-=k10*c03+k11*c13;
720 fCcz-=k10*c04+k11*c14;
722 fCee-=k20*c02+k21*c12; fCte-=k20*c03+k21*c13;
723 fCce-=k20*c04+k21*c14;
725 fCtt-=k30*c03+k31*c13;
726 fCct-=k40*c03+k41*c13;
727 //fCct-=k30*c04+k31*c14; // symmetric formula MI
729 fCcc-=k40*c04+k41*c14;
731 Int_t n=GetNumberOfClusters();
733 SetNumberOfClusters(n+1);
735 SetChi2(GetChi2()+chisq);
736 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
740 //_____________________________________________________________________________
741 Int_t AliTRDtrack::UpdateMI(const AliTRDcluster *c, Double_t chisq, UInt_t index, Double_t h01,
744 // Assignes found cluster to the track and updates track information
746 Bool_t fNoTilt = kTRUE;
747 if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
748 // add angular effect to the error contribution and make correction - MI
749 //AliTRDclusterCorrection *corrector = AliTRDclusterCorrection::GetCorrection();
751 Double_t tangent2 = (fC*fX-fE)*(fC*fX-fE);
752 if (tangent2 < 0.90000){
753 tangent2 = tangent2/(1.-tangent2);
755 Double_t tangent = TMath::Sqrt(tangent2);
756 if ((fC*fX-fE)<0) tangent*=-1;
757 // Double_t correction = 0*plane;
758 Double_t errang = tangent2*0.04; //
759 Double_t errsys =0.025*0.025*20; //systematic error part
761 if (c->GetNPads()==4) extend=2;
762 //if (c->GetNPads()==5) extend=3;
763 //if (c->GetNPads()==6) extend=3;
764 //if (c->GetQ()<15) return 1;
769 correction = corrector->GetCorrection(plane,c->GetLocalTimeBin(),tangent);
770 if (TMath::Abs(correction)>0){
772 errang = corrector->GetSigma(plane,c->GetLocalTimeBin(),tangent);
774 errang += tangent2*0.04;
779 // Double_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12.);
781 Double_t r00=(c->GetSigmaY2() +errang+errsys)*extend, r01=0., r11=c->GetSigmaZ2()*10000.;
782 r00+=fCyy; r01+=fCzy; r11+=fCzz;
783 Double_t det=r00*r11 - r01*r01;
784 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
786 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
787 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
788 Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
789 Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
790 Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;
792 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
793 Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;
797 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
798 // Int_t n=GetNumberOfClusters();
799 //if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
802 fY += k00*dy + k01*dz;
803 fZ += k10*dy + k11*dz;
805 //fT += k30*dy + k31*dz;
809 Double_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12);
811 Double_t xu_factor = 1000.; // empirical factor set by C.Xu
812 // in the first tilt version
813 dy=c->GetY() - fY; dz=c->GetZ() - fZ;
814 //dy=dy+h01*dz+correction;
816 Double_t tiltdz = dz;
817 if (TMath::Abs(tiltdz)>padlength/2.) {
818 tiltdz = TMath::Sign(padlength/2,dz);
824 if (TMath::Abs(dz)>padlength/2.){
825 //Double_t dy2 = c->GetY() - fY;
826 //Double_t sign = (dz>0) ? -1.: 1.;
827 //dy2-=h01*sign*padlength/2.;
831 Double_t s00 = (c->GetSigmaY2()+errang)*extend+errsys+add; // error pad
832 Double_t s11 = c->GetSigmaZ2()*xu_factor; // error pad-row
834 r00 = fCyy + 2*fCzy*h01 + fCzz*h01*h01+s00;
835 r01 = fCzy + fCzz*h01;
837 det = r00*r11 - r01*r01;
839 tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
842 k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
843 k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
844 k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
845 k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
846 k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);
849 cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
850 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
851 //Int_t n=GetNumberOfClusters();
852 // if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
855 fY += k00*dy + k01*dz;
856 fZ += k10*dy + k11*dz;
858 fT += k30*dy + k31*dz;
871 Double_t oldyy = fCyy, oldzz = fCzz; //, oldee=fCee, oldcc =fCcc;
872 Double_t oldzy = fCzy, oldey = fCey, oldty=fCty, oldcy =fCcy;
873 Double_t oldez = fCez, oldtz = fCtz, oldcz=fCcz;
874 //Double_t oldte = fCte, oldce = fCce;
875 //Double_t oldct = fCct;
877 fCyy-=k00*oldyy+k01*oldzy;
878 fCzy-=k10*oldyy+k11*oldzy;
879 fCey-=k20*oldyy+k21*oldzy;
880 fCty-=k30*oldyy+k31*oldzy;
881 fCcy-=k40*oldyy+k41*oldzy;
883 fCzz-=k10*oldzy+k11*oldzz;
884 fCez-=k20*oldzy+k21*oldzz;
885 fCtz-=k30*oldzy+k31*oldzz;
886 fCcz-=k40*oldzy+k41*oldzz;
888 fCee-=k20*oldey+k21*oldez;
889 fCte-=k30*oldey+k31*oldez;
890 fCce-=k40*oldey+k41*oldez;
892 fCtt-=k30*oldty+k31*oldtz;
893 fCct-=k40*oldty+k41*oldtz;
895 fCcc-=k40*oldcy+k41*oldcz;
898 Int_t n=GetNumberOfClusters();
900 SetNumberOfClusters(n+1);
902 SetChi2(GetChi2()+chisq);
903 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
910 //_____________________________________________________________________________
911 Int_t AliTRDtrack::UpdateMI(const AliTRDtracklet &tracklet)
914 // Assignes found tracklet to the track and updates track information
917 Double_t r00=(tracklet.GetTrackletSigma2()), r01=0., r11= 10000.;
918 r00+=fCyy; r01+=fCzy; r11+=fCzz;
920 Double_t det=r00*r11 - r01*r01;
921 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
924 Double_t dy=tracklet.GetY() - fY, dz=tracklet.GetZ() - fZ;
927 Double_t s00 = tracklet.GetTrackletSigma2(); // error pad
928 Double_t s11 = 100000; // error pad-row
929 Float_t h01 = tracklet.GetTilt();
931 // r00 = fCyy + 2*fCzy*h01 + fCzz*h01*h01+s00;
932 r00 = fCyy + fCzz*h01*h01+s00;
933 // r01 = fCzy + fCzz*h01;
936 det = r00*r11 - r01*r01;
938 tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
940 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
941 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
942 Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
943 Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
944 Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;
947 // k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
948 // k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
949 // k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
950 // k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
951 // k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);
954 Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;
955 // cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
956 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
957 //Int_t n=GetNumberOfClusters();
958 // if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
968 fY += k00*dy + k01*dz;
969 fZ += k10*dy + k11*dz;
971 fT += k30*dy + k31*dz;
978 Double_t oldyy = fCyy, oldzz = fCzz; //, oldee=fCee, oldcc =fCcc;
979 Double_t oldzy = fCzy, oldey = fCey, oldty=fCty, oldcy =fCcy;
980 Double_t oldez = fCez, oldtz = fCtz, oldcz=fCcz;
981 //Double_t oldte = fCte, oldce = fCce;
982 //Double_t oldct = fCct;
984 fCyy-=k00*oldyy+k01*oldzy;
985 fCzy-=k10*oldyy+k11*oldzy;
986 fCey-=k20*oldyy+k21*oldzy;
987 fCty-=k30*oldyy+k31*oldzy;
988 fCcy-=k40*oldyy+k41*oldzy;
990 fCzz-=k10*oldzy+k11*oldzz;
991 fCez-=k20*oldzy+k21*oldzz;
992 fCtz-=k30*oldzy+k31*oldzz;
993 fCcz-=k40*oldzy+k41*oldzz;
995 fCee-=k20*oldey+k21*oldez;
996 fCte-=k30*oldey+k31*oldez;
997 fCce-=k40*oldey+k41*oldez;
999 fCtt-=k30*oldty+k31*oldtz;
1000 fCct-=k40*oldty+k41*oldtz;
1002 fCcc-=k40*oldcy+k41*oldcz;
1005 Int_t n=GetNumberOfClusters();
1007 SetNumberOfClusters(n+1);
1009 SetChi2(GetChi2()+chisq);
1010 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
1017 //_____________________________________________________________________________
1018 Int_t AliTRDtrack::Rotate(Double_t alpha, Bool_t absolute)
1020 // Rotates track parameters in R*phi plane
1021 // if absolute rotation alpha is in global system
1022 // otherwise alpha rotation is relative to the current rotation angle
1032 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
1033 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
1035 Double_t x1=fX, y1=fY;
1036 Double_t ca=cos(alpha), sa=sin(alpha);
1037 Double_t r1=fC*fX - fE;
1041 if((r1*r1) > 1) return 0;
1042 fE=fE*ca + (fC*y1 + sqrt(1.- r1*r1))*sa;
1044 Double_t r2=fC*fX - fE;
1045 if (TMath::Abs(r2) >= 0.90000) {
1046 Int_t n=GetNumberOfClusters();
1047 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
1051 if((r2*r2) > 1) return 0;
1052 Double_t y0=fY + sqrt(1.- r2*r2)/fC;
1053 if ((fY-y0)*fC >= 0.) {
1054 Int_t n=GetNumberOfClusters();
1055 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !!!\n";
1060 Double_t f00=ca-1, f24=(y1 - r1*x1/sqrt(1.- r1*r1))*sa,
1061 f20=fC*sa, f22=(ca + sa*r1/sqrt(1.- r1*r1))-1;
1064 Double_t b00=fCyy*f00, b02=fCyy*f20+fCcy*f24+fCey*f22;
1065 Double_t b10=fCzy*f00, b12=fCzy*f20+fCcz*f24+fCez*f22;
1066 Double_t b20=fCey*f00, b22=fCey*f20+fCce*f24+fCee*f22;
1067 Double_t b30=fCty*f00, b32=fCty*f20+fCct*f24+fCte*f22;
1068 Double_t b40=fCcy*f00, b42=fCcy*f20+fCcc*f24+fCce*f22;
1071 Double_t a00=f00*b00, a02=f00*b02, a22=f20*b02+f24*b42+f22*b22;
1073 //F*C*Ft = C + (a + b + bt)
1074 fCyy += a00 + 2*b00;
1076 fCey += a02+b20+b02;
1081 fCee += a22 + 2*b22;
1088 //_____________________________________________________________________________
1089 Double_t AliTRDtrack::GetPredictedChi2(const AliTRDcluster *c, Double_t h01) const
1092 Bool_t fNoTilt = kTRUE;
1093 if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
1094 Double_t chi2, dy, r00, r01, r11;
1098 r00=c->GetSigmaY2();
1102 Double_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12);
1104 r00=c->GetSigmaY2(); r01=0.; r11=c->GetSigmaZ2();
1105 r00+=fCyy; r01+=fCzy; r11+=fCzz;
1107 Double_t det=r00*r11 - r01*r01;
1108 if (TMath::Abs(det) < 1.e-10) {
1109 Int_t n=GetNumberOfClusters();
1110 if (n>4) cerr<<n<<" AliTRDtrack warning: Singular matrix !\n";
1113 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
1114 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
1115 Double_t tiltdz = dz;
1116 if (TMath::Abs(tiltdz)>padlength/2.) {
1117 tiltdz = TMath::Sign(padlength/2,dz);
1122 chi2 = (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
1128 //_________________________________________________________________________
1129 void AliTRDtrack::GetPxPyPz(Double_t& px, Double_t& py, Double_t& pz) const
1131 // Returns reconstructed track momentum in the global system.
1133 Double_t pt=TMath::Abs(GetPt()); // GeV/c
1134 Double_t r=fC*fX-fE;
1137 if(r > 1) { py = pt; px = 0; }
1138 else if(r < -1) { py = -pt; px = 0; }
1140 y0=fY + sqrt(1.- r*r)/fC;
1141 px=-pt*(fY-y0)*fC; //cos(phi);
1142 py=-pt*(fE-fX*fC); //sin(phi);
1145 Double_t tmp=px*TMath::Cos(fAlpha) - py*TMath::Sin(fAlpha);
1146 py=px*TMath::Sin(fAlpha) + py*TMath::Cos(fAlpha);
1151 //_________________________________________________________________________
1152 void AliTRDtrack::GetGlobalXYZ(Double_t& x, Double_t& y, Double_t& z) const
1154 // Returns reconstructed track coordinates in the global system.
1156 x = fX; y = fY; z = fZ;
1157 Double_t tmp=x*TMath::Cos(fAlpha) - y*TMath::Sin(fAlpha);
1158 y=x*TMath::Sin(fAlpha) + y*TMath::Cos(fAlpha);
1163 //_________________________________________________________________________
1164 void AliTRDtrack::ResetCovariance() {
1166 // Resets covariance matrix
1171 fCey=0.; fCez=0.; fCee*=10.;
1172 fCty=0.; fCtz=0.; fCte=0.; fCtt*=10.;
1173 fCcy=0.; fCcz=0.; fCce=0.; fCct=0.; fCcc*=10.;
1176 void AliTRDtrack::ResetCovariance(Float_t mult) {
1178 // Resets covariance matrix
1183 fCey*=0.; fCez*=0.; fCee*=mult;
1184 fCty*=0.; fCtz*=0.; fCte*=0.; fCtt*=1.;
1185 fCcy*=0.; fCcz*=0.; fCce*=0.; fCct*=0.; fCcc*=mult;
1192 void AliTRDtrack::MakeBackupTrack()
1196 if (fBackupTrack) delete fBackupTrack;
1197 fBackupTrack = new AliTRDtrack(*this);
1201 Int_t AliTRDtrack::GetProlongation(Double_t xk, Double_t &y, Double_t &z){
1203 // Find prolongation at given x
1204 // return 0 if not exist
1206 Double_t c1=fC*fX - fE;
1207 if (TMath::Abs(c1)>1.) return 0;
1208 Double_t r1=TMath::Sqrt(1.- c1*c1);
1209 Double_t c2=fC*xk - fE;
1210 if (TMath::Abs(c2)>1.) return 0;
1211 Double_t r2=TMath::Sqrt(1.- c2*c2);
1212 y =fY + (xk-fX)*(c1+c2)/(r1+r2);
1213 z =fZ + (xk-fX)*(c1+c2)/(c1*r2 + c2*r1)*fT;
1220 Int_t AliTRDtrack::PropagateToX(Double_t xr, Double_t step)
1223 // Propagate track to given x position
1224 // works inside of the 20 degree segmentation (local cooordinate frame for TRD , TPC, TOF)
1226 // material budget from geo manager
1228 Double_t xyz0[3], xyz1[3],y,z;
1229 const Double_t alphac = TMath::Pi()/9.;
1230 const Double_t talphac = TMath::Tan(alphac*0.5);
1231 // critical alpha - cross sector indication
1233 Double_t dir = (fX>xr) ? -1.:1.;
1235 for (Double_t x=fX+dir*step;dir*x<dir*xr;x+=dir*step){
1237 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1238 GetProlongation(x,y,z);
1239 xyz1[0] = x*TMath::Cos(fAlpha)+y*TMath::Sin(fAlpha);
1240 xyz1[1] = x*TMath::Sin(fAlpha)-y*TMath::Cos(fAlpha);
1243 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
1245 if (param[0]>0&¶m[1]>0) PropagateTo(x,param[1],param[0]);
1249 if (fY<-fX*talphac){
1259 Int_t AliTRDtrack::PropagateToR(Double_t r,Double_t step)
1262 // propagate track to the radial position
1263 // rotation always connected to the last track position
1265 Double_t xyz0[3], xyz1[3],y,z;
1266 Double_t radius = TMath::Sqrt(fX*fX+fY*fY);
1267 Double_t dir = (radius>r) ? -1.:1.; // direction +-
1269 for (Double_t x=radius+dir*step;dir*x<dir*r;x+=dir*step){
1270 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1271 Double_t alpha = TMath::ATan2(xyz0[1],xyz0[0]);
1272 Rotate(alpha,kTRUE);
1273 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1274 GetProlongation(x,y,z);
1275 xyz1[0] = x*TMath::Cos(alpha)+y*TMath::Sin(alpha);
1276 xyz1[1] = x*TMath::Sin(alpha)-y*TMath::Cos(alpha);
1279 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
1280 if (param[1]<=0) param[1] =100000000;
1281 PropagateTo(x,param[1],param[0]);
1283 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1284 Double_t alpha = TMath::ATan2(xyz0[1],xyz0[0]);
1285 Rotate(alpha,kTRUE);
1286 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1287 GetProlongation(r,y,z);
1288 xyz1[0] = r*TMath::Cos(alpha)+y*TMath::Sin(alpha);
1289 xyz1[1] = r*TMath::Sin(alpha)-y*TMath::Cos(alpha);
1292 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
1294 if (param[1]<=0) param[1] =100000000;
1295 PropagateTo(r,param[1],param[0]);