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 t.GetTRDExternalParameters(x,fAlpha,p,c);
271 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
272 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
278 fZ=p[1]; SaveLocalConvConst();
279 fT=p[3]; x=GetLocalConvConst();
284 c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;
286 Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
287 Double_t c32=fX*c[13] - c[8];
288 Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];
291 fCzy=c[1 ]; fCzz=c[2 ];
292 fCey=c20; fCez=c21; fCee=c22;
293 fCty=c[6 ]; fCtz=c[7 ]; fCte=c32; fCtt=c[9 ];
294 fCcy=c[10]; fCcz=c[11]; fCce=c42; fCct=c[13]; fCcc=c[14];
296 // Initialization [SR, GSI, 18.02.2003]
297 for(UInt_t i=0; i<kMAX_CLUSTERS_PER_TRACK; i++) {
299 // fIndex[i] = 0; //MI store indexes
302 for (Int_t i=0;i<3;i++) { fBudget[i]=0;};
303 if ((t.GetStatus()&AliESDtrack::kTIME) == 0) return;
305 Double_t times[10]; t.GetIntegratedTimes(times); SetIntegratedTimes(times);
306 SetIntegratedLength(t.GetIntegratedLength());
311 AliTRDtrack * AliTRDtrack::MakeTrack(const AliTrackReference *ref, Double_t mass)
314 // Make dummy track from the track reference
315 // negative mass means opposite charge
319 for (Int_t i=0;i<15;i++) cc[i]=0;
320 Double_t x = ref->X(), y = ref->Y(), z = ref->Z();
321 Double_t alpha = TMath::ATan2(y,x);
322 Double_t xr = TMath::Sqrt(x*x+y*y);
325 xx[3] = ref->Pz()/ref->Pt();
327 Float_t xyz[3]={x,y,z};
328 Float_t convConst = 0;
329 (AliKalmanTrack::GetFieldMap())->Field(xyz,b);
330 convConst=1000/0.299792458/(1e-13 - b[2]);
331 xx[4] = 1./(convConst*ref->Pt());
332 if (mass<0) xx[4]*=-1.; // negative mass - negative direction
333 Double_t lcos = (x*ref->Px()+y*ref->Py())/(xr*ref->Pt());
334 Double_t lsin = TMath::Sin(TMath::ACos(lcos));
335 if (mass<0) lsin*=-1.;
336 xx[2] = xr*xx[4]-lsin;
338 AliTRDtrack * track = new AliTRDtrack(&cl,100,xx,cc,xr,alpha);
339 track->SetMass(TMath::Abs(mass));
340 track->StartTimeIntegral();
345 AliTRDtrack::~AliTRDtrack()
350 if (fBackupTrack) delete fBackupTrack;
356 Float_t AliTRDtrack::StatusForTOF()
359 Float_t res = (0.2 + 0.8*(fN/(fNExpected+5.)))*(0.4+0.6*fTracklets[5].GetN()/20.);
360 res *= (0.25+0.8*40./(40.+fBudget[2]));
364 if (GetNumberOfClusters()<20) return 0; //
365 if (fN>110&&fChi2/(Float_t(fN))<3) return 3; //gold
366 if (fNLast>30&&fChi2Last/(Float_t(fNLast))<3) return 3; //gold
367 if (fNLast>20&&fChi2Last/(Float_t(fNLast))<2) return 3; //gold
368 if (fNLast/(fNExpectedLast+3.)>0.8 && fChi2Last/Float_t(fNLast)<5&&fNLast>20) return 2; //silber
369 if (fNLast>5 &&((fNLast+1.)/(fNExpectedLast+1.))>0.8&&fChi2Last/(fNLast-5.)<6) return 1;
376 //____________________________________________________________________________
377 void AliTRDtrack::GetExternalParameters(Double_t& xr, Double_t x[5]) const {
379 // This function returns external TRD track representation
389 //_____________________________________________________________________________
390 void AliTRDtrack::GetExternalCovariance(Double_t cc[15]) const {
392 // This function returns external representation of the covriance matrix.
394 Double_t a=GetLocalConvConst();
396 Double_t c22=fX*fX*fCcc-2*fX*fCce+fCee;
397 Double_t c32=fX*fCct-fCte;
398 Double_t c20=fX*fCcy-fCey, c21=fX*fCcz-fCez, c42=fX*fCcc-fCce;
401 cc[1 ]=fCzy; cc[2 ]=fCzz;
402 cc[3 ]=c20; cc[4 ]=c21; cc[5 ]=c22;
403 cc[6 ]=fCty; cc[7 ]=fCtz; cc[8 ]=c32; cc[9 ]=fCtt;
404 cc[10]=fCcy*a; cc[11]=fCcz*a; cc[12]=c42*a; cc[13]=fCct*a; cc[14]=fCcc*a*a;
409 //_____________________________________________________________________________
410 void AliTRDtrack::GetCovariance(Double_t cc[15]) const {
413 cc[1]=fCzy; cc[2]=fCzz;
414 cc[3]=fCey; cc[4]=fCez; cc[5]=fCee;
415 cc[6]=fCcy; cc[7]=fCcz; cc[8]=fCce; cc[9]=fCcc;
416 cc[10]=fCty; cc[11]=fCtz; cc[12]=fCte; cc[13]=fCct; cc[14]=fCtt;
420 //_____________________________________________________________________________
421 Int_t AliTRDtrack::Compare(const TObject *o) const {
423 // Compares tracks according to their Y2 or curvature
425 AliTRDtrack *t=(AliTRDtrack*)o;
426 // Double_t co=t->GetSigmaY2();
427 // Double_t c =GetSigmaY2();
429 Double_t co=TMath::Abs(t->GetC());
430 Double_t c =TMath::Abs(GetC());
433 else if (c<co) return -1;
437 //_____________________________________________________________________________
438 void AliTRDtrack::CookdEdx(Double_t low, Double_t up) {
439 //-----------------------------------------------------------------
440 // Calculates dE/dX within the "low" and "up" cuts.
441 //-----------------------------------------------------------------
444 //Int_t nc=GetNumberOfClusters();
451 Float_t sorted[kMAX_CLUSTERS_PER_TRACK];
452 for (i=0; i < nc; i++) {
455 Int_t nl=Int_t(low*nc), nu=Int_t(up*nc);
457 //for (i=nl; i<=nu; i++) dedx += sorted[i];
459 for (i=0; i<nc; i++) dedx += sorted[i]; // ADDED by PS
460 if((nu-nl)) dedx /= (nu-nl); // ADDED by PS
464 // now real truncated mean
465 for (i=0; i < nc; i++) {
466 sorted[i]=TMath::Abs(fdQdl[i]);
468 Int_t * index = new Int_t[nc];
469 TMath::Sort(nc, sorted, index,kFALSE);
471 for (i=nl; i<=nu; i++) dedx += sorted[index[i]];
478 //_____________________________________________________________________________
479 Int_t AliTRDtrack::PropagateTo(Double_t xk,Double_t x0,Double_t rho)
481 // Propagates a track of particle with mass=pm to a reference plane
482 // defined by x=xk through media of density=rho and radiationLength=x0
484 if (xk == fX) return 1;
486 if (TMath::Abs(fC*xk - fE) >= 0.90000) {
487 // Int_t n=GetNumberOfClusters();
488 //if (n>4) cerr << n << " AliTRDtrack: Propagation failed, \tPt = "
489 // << GetPt() << "\t" << GetLabel() << "\t" << GetMass() << endl;
492 Double_t lcc=GetLocalConvConst();
494 // track Length measurement [SR, GSI, 17.02.2003]
495 Double_t oldX = fX, oldY = fY, oldZ = fZ;
497 Double_t x1=fX, x2=x1+(xk-x1), dx=x2-x1, y1=fY, z1=fZ;
498 Double_t c1=fC*x1 - fE;
499 if((c1*c1) > 1) return 0;
500 Double_t r1=sqrt(1.- c1*c1);
501 Double_t c2=fC*x2 - fE;
502 if((c2*c2) > 1) return 0;
503 Double_t r2=sqrt(1.- c2*c2);
505 fY += dx*(c1+c2)/(r1+r2);
506 fZ += dx*(c1+c2)/(c1*r2 + c2*r1)*fT;
509 Double_t rr=r1+r2, cc=c1+c2, xx=x1+x2;
510 Double_t f02=-dx*(2*rr + cc*(c1/r1 + c2/r2))/(rr*rr);
511 Double_t f04= dx*(rr*xx + cc*(c1*x1/r1+c2*x2/r2))/(rr*rr);
512 Double_t cr=c1*r2+c2*r1;
513 Double_t f12=-dx*fT*(2*cr + cc*(c2*c1/r1-r1 + c1*c2/r2-r2))/(cr*cr);
514 Double_t f13= dx*cc/cr;
515 Double_t f14=dx*fT*(cr*xx-cc*(r1*x2-c2*c1*x1/r1+r2*x1-c1*c2*x2/r2))/(cr*cr);
518 Double_t b00=f02*fCey + f04*fCcy, b01=f12*fCey + f14*fCcy + f13*fCty;
519 Double_t b10=f02*fCez + f04*fCcz, b11=f12*fCez + f14*fCcz + f13*fCtz;
520 Double_t b20=f02*fCee + f04*fCce, b21=f12*fCee + f14*fCce + f13*fCte;
521 Double_t b30=f02*fCte + f04*fCct, b31=f12*fCte + f14*fCct + f13*fCtt;
522 Double_t b40=f02*fCce + f04*fCcc, b41=f12*fCce + f14*fCcc + f13*fCct;
525 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a11=f12*b21+f14*b41+f13*b31;
527 //F*C*Ft = C + (a + b + bt)
529 fCzy += a01 + b01 + b10;
540 //Change of the magnetic field *************
541 SaveLocalConvConst();
543 fC*=lcc/GetLocalConvConst();
546 //Multiple scattering ******************
547 Double_t d=sqrt((x1-fX)*(x1-fX)+(y1-fY)*(y1-fY)+(z1-fZ)*(z1-fZ));
548 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
549 Double_t beta2=p2/(p2 + GetMass()*GetMass());
550 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
552 Double_t ey=fC*fX - fE, ez=fT;
553 Double_t xz=fC*ez, zz1=ez*ez+1, xy=fE+ey;
555 fCee += (2*ey*ez*ez*fE+1-ey*ey+ez*ez+fE*fE*ez*ez)*theta2;
556 fCte += ez*zz1*xy*theta2;
557 fCtt += zz1*zz1*theta2;
558 fCce += xz*ez*xy*theta2;
559 fCct += xz*zz1*theta2;
560 fCcc += xz*xz*theta2;
562 Double_t dc22 = (1-ey*ey+xz*xz*fX*fX)*theta2;
563 Double_t dc32 = (xz*fX*zz1)*theta2;
564 Double_t dc33 = (zz1*zz1)*theta2;
565 Double_t dc42 = (xz*fX*xz)*theta2;
566 Double_t dc43 = (zz1*xz)*theta2;
567 Double_t dc44 = (xz*xz)*theta2;
575 //Energy losses************************
576 if((5940*beta2/(1-beta2+1e-10) - beta2) < 0) return 0;
578 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho;
580 // suspicious part - think about it ?
581 Double_t kinE = TMath::Sqrt(p2);
582 if (dE>0.8*kinE) dE = 0.8*kinE; //
583 if (dE<0) dE = 0.0; // not valid region for Bethe bloch
589 fC*=(1.- sqrt(p2+GetMass()*GetMass())/p2*dE);
591 // Double_t sigmade = 0.1*dE*TMath::Sqrt(TMath::Sqrt(1+fT*fT)*90./(d+0.0001)); // 20 percent fluctuation - normalized to some length
592 Double_t sigmade = 0.07*TMath::Sqrt(TMath::Abs(dE)); // energy loss fluctuation
593 Double_t sigmac2 = sigmade*sigmade*fC*fC*(p2+GetMass()*GetMass())/(p2*p2);
595 fCee += fX*fX*sigmac2;
597 // track time measurement [SR, GSI 17.02.2002]
599 if (IsStartedTimeIntegral()) {
600 Double_t l2 = TMath::Sqrt((fX-oldX)*(fX-oldX) + (fY-oldY)*(fY-oldY) + (fZ-oldZ)*(fZ-oldZ));
601 if (TMath::Abs(l2*fC)>0.0001){
602 // make correction for curvature if neccesary
603 l2 = 0.5*TMath::Sqrt((fX-oldX)*(fX-oldX) + (fY-oldY)*(fY-oldY));
604 l2 = 2*TMath::ASin(l2*fC)/fC;
605 l2 = TMath::Sqrt(l2*l2+(fZ-oldZ)*(fZ-oldZ));
614 //_____________________________________________________________________________
615 Int_t AliTRDtrack::Update(const AliTRDcluster *c, Double_t chisq, UInt_t index, Double_t h01)
617 // Assignes found cluster to the track and updates track information
619 Bool_t fNoTilt = kTRUE;
620 if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
621 // add angular effect to the error contribution - MI
622 Float_t tangent2 = (fC*fX-fE)*(fC*fX-fE);
623 if (tangent2 < 0.90000){
624 tangent2 = tangent2/(1.-tangent2);
626 Float_t errang = tangent2*0.04; //
627 Float_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12.);
629 Double_t r00=c->GetSigmaY2() +errang, r01=0., r11=c->GetSigmaZ2()*100.;
630 r00+=fCyy; r01+=fCzy; r11+=fCzz;
631 Double_t det=r00*r11 - r01*r01;
632 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
634 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
635 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
636 Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
637 Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
638 Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;
640 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
641 Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;
645 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
646 // Int_t n=GetNumberOfClusters();
647 //if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
650 fY += k00*dy + k01*dz;
651 fZ += k10*dy + k11*dz;
653 //fT += k30*dy + k31*dz;
657 Double_t xu_factor = 100.; // empirical factor set by C.Xu
658 // in the first tilt version
659 dy=c->GetY() - fY; dz=c->GetZ() - fZ;
662 if (TMath::Abs(dz)>padlength/2.){
663 Float_t dy2 = c->GetY() - fY;
664 Float_t sign = (dz>0) ? -1.: 1.;
665 dy2+=h01*sign*padlength/2.;
672 r00=c->GetSigmaY2()+errang+add, r01=0., r11=c->GetSigmaZ2()*xu_factor;
673 r00+=(fCyy+2.0*h01*fCzy+h01*h01*fCzz);
674 r01+=(fCzy+h01*fCzz);
677 det=r00*r11 - r01*r01;
678 tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
680 k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
681 k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
682 k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
683 k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
684 k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);
687 cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
688 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
689 // Int_t n=GetNumberOfClusters();
690 //if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
693 fY += k00*dy + k01*dz;
694 fZ += k10*dy + k11*dz;
696 fT += k30*dy + k31*dz;
706 Double_t c01=fCzy, c02=fCey, c03=fCty, c04=fCcy;
707 Double_t c12=fCez, c13=fCtz, c14=fCcz;
710 fCyy-=k00*fCyy+k01*fCzy; fCzy-=k00*c01+k01*fCzz;
711 fCey-=k00*c02+k01*c12; fCty-=k00*c03+k01*c13;
712 fCcy-=k00*c04+k01*c14;
714 fCzz-=k10*c01+k11*fCzz;
715 fCez-=k10*c02+k11*c12; fCtz-=k10*c03+k11*c13;
716 fCcz-=k10*c04+k11*c14;
718 fCee-=k20*c02+k21*c12; fCte-=k20*c03+k21*c13;
719 fCce-=k20*c04+k21*c14;
721 fCtt-=k30*c03+k31*c13;
722 fCct-=k40*c03+k41*c13;
723 //fCct-=k30*c04+k31*c14; // symmetric formula MI
725 fCcc-=k40*c04+k41*c14;
727 Int_t n=GetNumberOfClusters();
729 SetNumberOfClusters(n+1);
731 SetChi2(GetChi2()+chisq);
732 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
736 //_____________________________________________________________________________
737 Int_t AliTRDtrack::UpdateMI(const AliTRDcluster *c, Double_t chisq, UInt_t index, Double_t h01,
740 // Assignes found cluster to the track and updates track information
742 Bool_t fNoTilt = kTRUE;
743 if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
744 // add angular effect to the error contribution and make correction - MI
745 //AliTRDclusterCorrection *corrector = AliTRDclusterCorrection::GetCorrection();
747 Double_t tangent2 = (fC*fX-fE)*(fC*fX-fE);
748 if (tangent2 < 0.90000){
749 tangent2 = tangent2/(1.-tangent2);
751 Double_t tangent = TMath::Sqrt(tangent2);
752 if ((fC*fX-fE)<0) tangent*=-1;
753 // Double_t correction = 0*plane;
754 Double_t errang = tangent2*0.04; //
755 Double_t errsys =0.025*0.025*20; //systematic error part
757 if (c->GetNPads()==4) extend=2;
758 //if (c->GetNPads()==5) extend=3;
759 //if (c->GetNPads()==6) extend=3;
760 //if (c->GetQ()<15) return 1;
765 correction = corrector->GetCorrection(plane,c->GetLocalTimeBin(),tangent);
766 if (TMath::Abs(correction)>0){
768 errang = corrector->GetSigma(plane,c->GetLocalTimeBin(),tangent);
770 errang += tangent2*0.04;
775 // Double_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12.);
777 Double_t r00=(c->GetSigmaY2() +errang+errsys)*extend, r01=0., r11=c->GetSigmaZ2()*10000.;
778 r00+=fCyy; r01+=fCzy; r11+=fCzz;
779 Double_t det=r00*r11 - r01*r01;
780 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
782 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
783 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
784 Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
785 Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
786 Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;
788 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
789 Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;
793 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
794 // Int_t n=GetNumberOfClusters();
795 //if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
798 fY += k00*dy + k01*dz;
799 fZ += k10*dy + k11*dz;
801 //fT += k30*dy + k31*dz;
805 Double_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12);
807 Double_t xu_factor = 1000.; // empirical factor set by C.Xu
808 // in the first tilt version
809 dy=c->GetY() - fY; dz=c->GetZ() - fZ;
810 //dy=dy+h01*dz+correction;
812 Double_t tiltdz = dz;
813 if (TMath::Abs(tiltdz)>padlength/2.) {
814 tiltdz = TMath::Sign(padlength/2,dz);
820 if (TMath::Abs(dz)>padlength/2.){
821 //Double_t dy2 = c->GetY() - fY;
822 //Double_t sign = (dz>0) ? -1.: 1.;
823 //dy2-=h01*sign*padlength/2.;
827 Double_t s00 = (c->GetSigmaY2()+errang)*extend+errsys+add; // error pad
828 Double_t s11 = c->GetSigmaZ2()*xu_factor; // error pad-row
830 r00 = fCyy + 2*fCzy*h01 + fCzz*h01*h01+s00;
831 r01 = fCzy + fCzz*h01;
833 det = r00*r11 - r01*r01;
835 tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
838 k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
839 k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
840 k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
841 k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
842 k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);
845 cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
846 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
847 //Int_t n=GetNumberOfClusters();
848 // if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
851 fY += k00*dy + k01*dz;
852 fZ += k10*dy + k11*dz;
854 fT += k30*dy + k31*dz;
867 Double_t oldyy = fCyy, oldzz = fCzz; //, oldee=fCee, oldcc =fCcc;
868 Double_t oldzy = fCzy, oldey = fCey, oldty=fCty, oldcy =fCcy;
869 Double_t oldez = fCez, oldtz = fCtz, oldcz=fCcz;
870 //Double_t oldte = fCte, oldce = fCce;
871 //Double_t oldct = fCct;
873 fCyy-=k00*oldyy+k01*oldzy;
874 fCzy-=k10*oldyy+k11*oldzy;
875 fCey-=k20*oldyy+k21*oldzy;
876 fCty-=k30*oldyy+k31*oldzy;
877 fCcy-=k40*oldyy+k41*oldzy;
879 fCzz-=k10*oldzy+k11*oldzz;
880 fCez-=k20*oldzy+k21*oldzz;
881 fCtz-=k30*oldzy+k31*oldzz;
882 fCcz-=k40*oldzy+k41*oldzz;
884 fCee-=k20*oldey+k21*oldez;
885 fCte-=k30*oldey+k31*oldez;
886 fCce-=k40*oldey+k41*oldez;
888 fCtt-=k30*oldty+k31*oldtz;
889 fCct-=k40*oldty+k41*oldtz;
891 fCcc-=k40*oldcy+k41*oldcz;
894 Int_t n=GetNumberOfClusters();
896 SetNumberOfClusters(n+1);
898 SetChi2(GetChi2()+chisq);
899 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
906 //_____________________________________________________________________________
907 Int_t AliTRDtrack::UpdateMI(const AliTRDtracklet &tracklet)
910 // Assignes found tracklet to the track and updates track information
913 Double_t r00=(tracklet.GetTrackletSigma2()), r01=0., r11= 10000.;
914 r00+=fCyy; r01+=fCzy; r11+=fCzz;
916 Double_t det=r00*r11 - r01*r01;
917 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
920 Double_t dy=tracklet.GetY() - fY, dz=tracklet.GetZ() - fZ;
923 Double_t s00 = tracklet.GetTrackletSigma2(); // error pad
924 Double_t s11 = 100000; // error pad-row
925 Float_t h01 = tracklet.GetTilt();
927 // r00 = fCyy + 2*fCzy*h01 + fCzz*h01*h01+s00;
928 r00 = fCyy + fCzz*h01*h01+s00;
929 // r01 = fCzy + fCzz*h01;
932 det = r00*r11 - r01*r01;
934 tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
936 Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
937 Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
938 Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
939 Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
940 Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;
943 // k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
944 // k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
945 // k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
946 // k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
947 // k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);
950 Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;
951 // cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
952 if (TMath::Abs(cur*fX-eta) >= 0.90000) {
953 //Int_t n=GetNumberOfClusters();
954 // if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
964 fY += k00*dy + k01*dz;
965 fZ += k10*dy + k11*dz;
967 fT += k30*dy + k31*dz;
974 Double_t oldyy = fCyy, oldzz = fCzz; //, oldee=fCee, oldcc =fCcc;
975 Double_t oldzy = fCzy, oldey = fCey, oldty=fCty, oldcy =fCcy;
976 Double_t oldez = fCez, oldtz = fCtz, oldcz=fCcz;
977 //Double_t oldte = fCte, oldce = fCce;
978 //Double_t oldct = fCct;
980 fCyy-=k00*oldyy+k01*oldzy;
981 fCzy-=k10*oldyy+k11*oldzy;
982 fCey-=k20*oldyy+k21*oldzy;
983 fCty-=k30*oldyy+k31*oldzy;
984 fCcy-=k40*oldyy+k41*oldzy;
986 fCzz-=k10*oldzy+k11*oldzz;
987 fCez-=k20*oldzy+k21*oldzz;
988 fCtz-=k30*oldzy+k31*oldzz;
989 fCcz-=k40*oldzy+k41*oldzz;
991 fCee-=k20*oldey+k21*oldez;
992 fCte-=k30*oldey+k31*oldez;
993 fCce-=k40*oldey+k41*oldez;
995 fCtt-=k30*oldty+k31*oldtz;
996 fCct-=k40*oldty+k41*oldtz;
998 fCcc-=k40*oldcy+k41*oldcz;
1001 Int_t n=GetNumberOfClusters();
1003 SetNumberOfClusters(n+1);
1005 SetChi2(GetChi2()+chisq);
1006 // cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;
1013 //_____________________________________________________________________________
1014 Int_t AliTRDtrack::Rotate(Double_t alpha, Bool_t absolute)
1016 // Rotates track parameters in R*phi plane
1017 // if absolute rotation alpha is in global system
1018 // otherwise alpha rotation is relative to the current rotation angle
1028 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
1029 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
1031 Double_t x1=fX, y1=fY;
1032 Double_t ca=cos(alpha), sa=sin(alpha);
1033 Double_t r1=fC*fX - fE;
1037 if((r1*r1) > 1) return 0;
1038 fE=fE*ca + (fC*y1 + sqrt(1.- r1*r1))*sa;
1040 Double_t r2=fC*fX - fE;
1041 if (TMath::Abs(r2) >= 0.90000) {
1042 Int_t n=GetNumberOfClusters();
1043 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
1047 if((r2*r2) > 1) return 0;
1048 Double_t y0=fY + sqrt(1.- r2*r2)/fC;
1049 if ((fY-y0)*fC >= 0.) {
1050 Int_t n=GetNumberOfClusters();
1051 if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !!!\n";
1056 Double_t f00=ca-1, f24=(y1 - r1*x1/sqrt(1.- r1*r1))*sa,
1057 f20=fC*sa, f22=(ca + sa*r1/sqrt(1.- r1*r1))-1;
1060 Double_t b00=fCyy*f00, b02=fCyy*f20+fCcy*f24+fCey*f22;
1061 Double_t b10=fCzy*f00, b12=fCzy*f20+fCcz*f24+fCez*f22;
1062 Double_t b20=fCey*f00, b22=fCey*f20+fCce*f24+fCee*f22;
1063 Double_t b30=fCty*f00, b32=fCty*f20+fCct*f24+fCte*f22;
1064 Double_t b40=fCcy*f00, b42=fCcy*f20+fCcc*f24+fCce*f22;
1067 Double_t a00=f00*b00, a02=f00*b02, a22=f20*b02+f24*b42+f22*b22;
1069 //F*C*Ft = C + (a + b + bt)
1070 fCyy += a00 + 2*b00;
1072 fCey += a02+b20+b02;
1077 fCee += a22 + 2*b22;
1084 //_____________________________________________________________________________
1085 Double_t AliTRDtrack::GetPredictedChi2(const AliTRDcluster *c, Double_t h01) const
1088 Bool_t fNoTilt = kTRUE;
1089 if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
1090 Double_t chi2, dy, r00, r01, r11;
1094 r00=c->GetSigmaY2();
1098 Double_t padlength = TMath::Sqrt(c->GetSigmaZ2()*12);
1100 r00=c->GetSigmaY2(); r01=0.; r11=c->GetSigmaZ2();
1101 r00+=fCyy; r01+=fCzy; r11+=fCzz;
1103 Double_t det=r00*r11 - r01*r01;
1104 if (TMath::Abs(det) < 1.e-10) {
1105 Int_t n=GetNumberOfClusters();
1106 if (n>4) cerr<<n<<" AliTRDtrack warning: Singular matrix !\n";
1109 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
1110 Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
1111 Double_t tiltdz = dz;
1112 if (TMath::Abs(tiltdz)>padlength/2.) {
1113 tiltdz = TMath::Sign(padlength/2,dz);
1118 chi2 = (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
1124 //_________________________________________________________________________
1125 void AliTRDtrack::GetPxPyPz(Double_t& px, Double_t& py, Double_t& pz) const
1127 // Returns reconstructed track momentum in the global system.
1129 Double_t pt=TMath::Abs(GetPt()); // GeV/c
1130 Double_t r=fC*fX-fE;
1133 if(r > 1) { py = pt; px = 0; }
1134 else if(r < -1) { py = -pt; px = 0; }
1136 y0=fY + sqrt(1.- r*r)/fC;
1137 px=-pt*(fY-y0)*fC; //cos(phi);
1138 py=-pt*(fE-fX*fC); //sin(phi);
1141 Double_t tmp=px*TMath::Cos(fAlpha) - py*TMath::Sin(fAlpha);
1142 py=px*TMath::Sin(fAlpha) + py*TMath::Cos(fAlpha);
1147 //_________________________________________________________________________
1148 void AliTRDtrack::GetGlobalXYZ(Double_t& x, Double_t& y, Double_t& z) const
1150 // Returns reconstructed track coordinates in the global system.
1152 x = fX; y = fY; z = fZ;
1153 Double_t tmp=x*TMath::Cos(fAlpha) - y*TMath::Sin(fAlpha);
1154 y=x*TMath::Sin(fAlpha) + y*TMath::Cos(fAlpha);
1159 //_________________________________________________________________________
1160 void AliTRDtrack::ResetCovariance() {
1162 // Resets covariance matrix
1167 fCey=0.; fCez=0.; fCee*=10.;
1168 fCty=0.; fCtz=0.; fCte=0.; fCtt*=10.;
1169 fCcy=0.; fCcz=0.; fCce=0.; fCct=0.; fCcc*=10.;
1172 void AliTRDtrack::ResetCovariance(Float_t mult) {
1174 // Resets covariance matrix
1179 fCey*=0.; fCez*=0.; fCee*=mult;
1180 fCty*=0.; fCtz*=0.; fCte*=0.; fCtt*=1.;
1181 fCcy*=0.; fCcz*=0.; fCce*=0.; fCct*=0.; fCcc*=mult;
1188 void AliTRDtrack::MakeBackupTrack()
1192 if (fBackupTrack) delete fBackupTrack;
1193 fBackupTrack = new AliTRDtrack(*this);
1197 Int_t AliTRDtrack::GetProlongation(Double_t xk, Double_t &y, Double_t &z){
1199 // Find prolongation at given x
1200 // return 0 if not exist
1202 Double_t c1=fC*fX - fE;
1203 if (TMath::Abs(c1)>1.) return 0;
1204 Double_t r1=TMath::Sqrt(1.- c1*c1);
1205 Double_t c2=fC*xk - fE;
1206 if (TMath::Abs(c2)>1.) return 0;
1207 Double_t r2=TMath::Sqrt(1.- c2*c2);
1208 y =fY + (xk-fX)*(c1+c2)/(r1+r2);
1209 z =fZ + (xk-fX)*(c1+c2)/(c1*r2 + c2*r1)*fT;
1216 Int_t AliTRDtrack::PropagateToX(Double_t xr, Double_t step)
1219 // Propagate track to given x position
1220 // works inside of the 20 degree segmentation (local cooordinate frame for TRD , TPC, TOF)
1222 // material budget from geo manager
1224 Double_t xyz0[3], xyz1[3],y,z;
1225 const Double_t alphac = TMath::Pi()/9.;
1226 const Double_t talphac = TMath::Tan(alphac*0.5);
1227 // critical alpha - cross sector indication
1229 Double_t dir = (fX>xr) ? -1.:1.;
1231 for (Double_t x=fX+dir*step;dir*x<dir*xr;x+=dir*step){
1233 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1234 GetProlongation(x,y,z);
1235 xyz1[0] = x*TMath::Cos(fAlpha)+y*TMath::Sin(fAlpha);
1236 xyz1[1] = x*TMath::Sin(fAlpha)-y*TMath::Cos(fAlpha);
1239 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
1241 if (param[0]>0&¶m[1]>0) PropagateTo(x,param[1],param[0]);
1245 if (fY<-fX*talphac){
1255 Int_t AliTRDtrack::PropagateToR(Double_t r,Double_t step)
1258 // propagate track to the radial position
1259 // rotation always connected to the last track position
1261 Double_t xyz0[3], xyz1[3],y,z;
1262 Double_t radius = TMath::Sqrt(fX*fX+fY*fY);
1263 Double_t dir = (radius>r) ? -1.:1.; // direction +-
1265 for (Double_t x=radius+dir*step;dir*x<dir*r;x+=dir*step){
1266 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1267 Double_t alpha = TMath::ATan2(xyz0[1],xyz0[0]);
1268 Rotate(alpha,kTRUE);
1269 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1270 GetProlongation(x,y,z);
1271 xyz1[0] = x*TMath::Cos(alpha)+y*TMath::Sin(alpha);
1272 xyz1[1] = x*TMath::Sin(alpha)-y*TMath::Cos(alpha);
1275 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
1276 if (param[1]<=0) param[1] =100000000;
1277 PropagateTo(x,param[1],param[0]);
1279 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1280 Double_t alpha = TMath::ATan2(xyz0[1],xyz0[0]);
1281 Rotate(alpha,kTRUE);
1282 GetGlobalXYZ(xyz0[0],xyz0[1],xyz0[2]);
1283 GetProlongation(r,y,z);
1284 xyz1[0] = r*TMath::Cos(alpha)+y*TMath::Sin(alpha);
1285 xyz1[1] = r*TMath::Sin(alpha)-y*TMath::Cos(alpha);
1288 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
1290 if (param[1]<=0) param[1] =100000000;
1291 PropagateTo(r,param[1],param[0]);