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 **************************************************************************/
17 // This class stores a tracklet (a track that lives only in a single TPC
18 // sector). Its objects can be constructed out of TPCseeds, that are
19 // holding the necessary cluster information.
24 #include "AliTPCTracklet.h"
25 #include "TObjArray.h"
26 #include "TLinearFitter.h"
27 #include "AliTPCseed.h"
28 #include "AliESDVertex.h"
29 #include "AliTracker.h"
30 #include "TTreeStream.h"
32 #include "TDecompChol.h"
37 ClassImp(AliTPCTracklet)
39 const Double_t AliTPCTracklet::kB2C=0.299792458e-3;
40 Float_t AliTPCTracklet::fgEdgeCutY=3;
41 Float_t AliTPCTracklet::fgEdgeCutX=0;
43 AliTPCTracklet::AliTPCTracklet()
44 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(-1),fOuter(0),
45 fInner(0),fPrimary(0) {
47 // The default constructor. It is intended to be used for I/O only.
51 AliTPCTracklet::AliTPCTracklet(const AliTPCseed *track,Int_t sector,
52 TrackType type,Bool_t storeClusters)
53 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(sector),fOuter(0),
54 fInner(0),fPrimary(0) {
56 // Contructor for a tracklet out of a track. Only clusters within a given
60 //TODO: only kalman works
62 for (Int_t i=0;i<160;++i) {
63 AliTPCclusterMI *c=track->GetClusterPointer(i);
64 if (c && RejectCluster(c)) continue;
65 if (c&&c->GetDetector()==sector)
70 fClusters=new AliTPCclusterMI[fNClusters];
71 for (Int_t i=0;i<160;++i) {
72 AliTPCclusterMI *c=track->GetClusterPointer(i);
73 if (c && RejectCluster(c)) continue;
74 if (c&&c->GetDetector()==sector)
75 fClusters[fNStoredClusters]=*c;
82 FitKalman(track,sector);
86 FitLinear(track,sector,type);
89 FitRiemann(track,sector);
95 AliTPCTracklet::AliTPCTracklet(const TObjArray &/*clusters*/,Int_t sector,
96 TrackType /*type*/,Bool_t /*storeClusters*/)
97 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(sector),fOuter(0),
98 fInner(0),fPrimary(0) {
102 AliTPCTracklet::AliTPCTracklet(const AliTPCTracklet &t)
103 : TObject(t),fNClusters(t.fNClusters),fNStoredClusters(t.fNStoredClusters),fClusters(0),
104 fSector(t.fSector),fOuter(0),fInner(0),
107 // The copy constructor. You can copy tracklets!
111 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
112 for (int i=0;i<t.fNStoredClusters;++i)
113 fClusters[i]=t.fClusters[i];
116 fOuter=new AliExternalTrackParam(*t.fOuter);
118 fInner=new AliExternalTrackParam(*t.fInner);
120 fPrimary=new AliExternalTrackParam(*t.fPrimary);
123 AliTPCTracklet& AliTPCTracklet::operator=(const AliTPCTracklet &t) {
125 // The assignment constructor. You can assign tracklets!
128 fNClusters=t.fNClusters;
131 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
132 for (int i=0;i<t.fNStoredClusters;++i)
133 fClusters[i]=t.fClusters[i];
142 fOuter=new AliExternalTrackParam(*t.fOuter);
153 fInner=new AliExternalTrackParam(*t.fInner);
162 *fPrimary=*t.fPrimary;
164 fPrimary=new AliExternalTrackParam(*t.fPrimary);
174 AliTPCTracklet::~AliTPCTracklet() {
176 // The destructor. Yes, you can even destruct tracklets.
188 void AliTPCTracklet::FitKalman(const AliTPCseed *seed,Int_t sector) {
190 // Fit using Kalman filter
192 AliTPCseed *track=new AliTPCseed(*seed);
193 if (!track->Rotate(TMath::DegToRad()*(sector%18*20.+10.)-track->GetAlpha())) {
197 // fit from inner to outer row
199 for (Int_t i=0;i<15;i++) covar[i]=0;
202 covar[5]=1.*1./(64.*64.);
203 covar[9]=1.*1./(64.*64.);
204 covar[14]=0; // keep pt
205 Float_t xmin=1000, xmax=-10000;
206 Int_t imin=158, imax=0;
207 for (Int_t i=0;i<160;i++) {
208 AliTPCclusterMI *c=track->GetClusterPointer(i);
210 if (c->GetDetector()!=sector) continue;
211 if (c->GetX()<xmin) xmin=c->GetX();
212 if (c->GetX()>xmax) xmax=c->GetX();
221 for (Float_t x=track->GetX(); x<xmin; x++) track->PropagateTo(x);
222 track->AddCovariance(covar);
224 AliExternalTrackParam paramIn;
225 AliExternalTrackParam paramOut;
230 for (Int_t i=imin; i<=imax; i++){
231 AliTPCclusterMI *c=track->GetClusterPointer(i);
233 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
234 Double_t cov[3]={0.01,0.,0.01}; //TODO: correct error parametrisation
235 AliTPCseed::GetError(c, track,cov[0],cov[2]);
238 if (!track->PropagateTo(r[0])) {
242 if (RejectCluster(c,track)) continue;
243 if ( !((static_cast<AliExternalTrackParam*>(track)->Update(&r[1],cov)))) isOK=kFALSE;
245 if (!isOK) { delete track; return;}
246 track->AddCovariance(covar);
250 for (Int_t i=imax; i>=imin; i--){
251 AliTPCclusterMI *c=track->GetClusterPointer(i);
253 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
254 Double_t cov[3]={0.01,0.,0.01};
255 AliTPCseed::GetError(c, track,cov[0],cov[2]);
258 if (!track->PropagateTo(r[0])) {
262 if (RejectCluster(c,track)) continue;
263 if ( !((static_cast<AliExternalTrackParam*>(track)->Update(&r[1],cov)))) isOK=kFALSE;
265 if (!isOK) { delete track; return;}
267 track->AddCovariance(covar);
270 for (Int_t i=imin; i<=imax; i++){
271 AliTPCclusterMI *c=track->GetClusterPointer(i);
273 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
274 Double_t cov[3]={0.01,0.,0.01};
275 AliTPCseed::GetError(c, track,cov[0],cov[2]);
278 if (!track->PropagateTo(r[0])) {
282 if (RejectCluster(c,track)) continue;
283 if ( !((static_cast<AliExternalTrackParam*>(track)->Update(&r[1],cov)))) isOK=kFALSE;
285 if (!isOK) { delete track; return;}
290 fOuter=new AliExternalTrackParam(paramOut);
291 fInner=new AliExternalTrackParam(paramIn);
299 void AliTPCTracklet::FitLinear(const AliTPCseed *track,Int_t sector,
303 fy.StoreData(kFALSE);
304 fz.StoreData(kFALSE);
307 fy.SetFormula("1 ++ x");
308 fz.SetFormula("1 ++ x");
311 fy.SetFormula("1 ++ x ++ x*x");
312 fz.SetFormula("1 ++ x");
320 for (Int_t i=0;i<160;++i) {
321 AliTPCclusterMI *c=track->GetClusterPointer(i);
322 if (c && RejectCluster(c)) continue;
323 if (c&&c->GetDetector()==sector) {
324 Double_t x=c->GetX();
325 fy.AddPoint(&x,c->GetY());
326 fz.AddPoint(&x,c->GetZ());
327 xmax=TMath::Max(xmax,x);
328 xmin=TMath::Min(xmin,x);
333 Double_t a[3]={fy.GetParameter(0),
335 type==kQuadratic?fy.GetParameter(2):0.};
336 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
337 fy.GetCovarianceMatrixElement(1,0),
338 fy.GetCovarianceMatrixElement(1,1),
339 type==kQuadratic?fy.GetCovarianceMatrixElement(2,0):0.,
340 type==kQuadratic?fy.GetCovarianceMatrixElement(2,1):0.,
341 type==kQuadratic?fy.GetCovarianceMatrixElement(2,2):0.};
342 for (int i=0;i<6;++i) ca[i]*=fy.GetChisquare()/fNClusters;
343 Double_t b[2]={fz.GetParameter(0),
345 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
346 fz.GetCovarianceMatrixElement(1,0),
347 fz.GetCovarianceMatrixElement(1,1)};
348 for (int i=0;i<3;++i) cb[i]*=fz.GetChisquare()/fNClusters;
351 Double_t alpha=track->GetAlpha();
352 Quadratic2Helix(a,ca,b,cb,0.,p,c);
353 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
354 Quadratic2Helix(a,ca,b,cb,xmin,p,c);
355 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
356 Quadratic2Helix(a,ca,b,cb,xmax,p,c);
357 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
360 void AliTPCTracklet::Quadratic2Helix(Double_t *a,Double_t *ca,
361 Double_t *b,Double_t *cb,
363 Double_t *p,Double_t *c) {
364 // y(x)=a[0]+a[1]*x+a[2]*x^2
366 // parametrises the corosponding helix at x0
368 // get the polynoms at x0
369 Double_t a0=x0*x0*a[2] + x0*a[1] + a[0];
370 Double_t a1=2.*x0*a[2] + a[1];
372 Double_t ca00=ca[0]+x0*(2.*ca[1]+x0*(ca[2]+2.*ca[3]+x0*(2.*ca[4]+x0*ca[5])));
373 Double_t ca10=ca[1]+x0*(ca[2]+2.*ca[3]+x0*(3.*ca[4]+x0*2.*ca[5]));
374 Double_t ca11=ca[2]+x0*4.*(ca[4]+x0*ca[5]);
375 Double_t ca20=ca[3]+x0*(ca[4]+x0*ca[5]);
376 Double_t ca21=ca[3]+x0*2.*ca[5];
379 Double_t b0=x0*b[1] + b[0];
381 Double_t cb00=cb[0]+x0*(2.*cb[1]+x0*cb[2]);
382 Double_t cb10=cb[1]+x0*cb[2];
385 // transform to helix parameters
386 Double_t f =1.+a1*a1;
389 Double_t fi12=TMath::Sqrt(fi);
390 Double_t fi32=fi*fi12;
392 Double_t fi52=fi2*fi12;
393 Double_t fi3 =fi2*fi;
394 Double_t fi5 =fi2*fi3;
396 Double_t xyz[3]={0.}; // TODO...
397 Double_t fc=1./(GetBz(xyz)*kB2C);
403 p[4]=2.*a2*fi32*fc; // 1/pt
408 c[3] =ca10*fi32; // snp-y0
410 c[5] =ca11*fi3; // snp-snp
412 c[7] =cb10; // tgl-z0
414 c[9] =cb11; // tgl-tgl
415 c[10]=2.*(-3.*a1*a2*ca10+f*ca20)*fi3*fc; // 1/pt-y0
417 c[12]=2.*(-3.*a1*a2*ca11+f*ca21)*fi52*fc; // 1/pt-snp
418 c[13]=0.; // 1/pt-tgl
419 c[14]=(-12.*a1*a2*(-3.*a1*a2*ca11+2.*f*ca21)+4.*f2*ca22)*fi5
424 void AliTPCTracklet::FitRiemann(const AliTPCseed *track,Int_t sector) {
426 fy.StoreData(kFALSE);
427 fy.SetFormula("hyp2");
430 for (Int_t i=0;i<160;++i) {
431 AliTPCclusterMI *c=track->GetClusterPointer(i);
432 if (c && RejectCluster(c)) continue;
433 if (c&&c->GetDetector()==sector) {
434 Double_t x=c->GetX();
435 Double_t y=c->GetY();
436 Double_t xy[2]={x,y};
438 Double_t errx=1.,erry=1.;//TODO!
439 Double_t err=TMath::Sqrt(4.*x*x*errx+4.*y*y*erry);
441 fy.AddPoint(xy,r,err);
442 xmax=TMath::Max(xmax,x);
443 xmin=TMath::Min(xmin,x);
447 Double_t a[3]={fy.GetParameter(0),
450 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
451 fy.GetCovarianceMatrixElement(1,0),
452 fy.GetCovarianceMatrixElement(1,1),
453 fy.GetCovarianceMatrixElement(2,0),
454 fy.GetCovarianceMatrixElement(2,1),
455 fy.GetCovarianceMatrixElement(2,2)};
458 fz.StoreData(kFALSE);
459 fz.SetFormula("hyp1");
460 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
464 for (Int_t i=0;i<160;++i) {
465 AliTPCclusterMI *c=track->GetClusterPointer(i);
466 if (c && RejectCluster(c)) continue;
467 if (c&&c->GetDetector()==sector) {
468 Double_t x=c->GetX();
469 Double_t y=c->GetY();
472 phi+=2.*TMath::Abs(TMath::ATan2(.5*TMath::Sqrt(dx*dx+dy*dy),R));
474 fz.AddPoint(&phi,c->GetZ(),err);
480 Double_t b[2]={fz.GetParameter(0),
482 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
483 fz.GetCovarianceMatrixElement(1,0),
484 fz.GetCovarianceMatrixElement(1,1)};
488 Double_t alpha=track->GetAlpha();
489 if (Riemann2Helix(a,ca,b,cb,0.,p,c))
490 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
491 if (Riemann2Helix(a,ca,b,cb,xmin,p,c))
492 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
493 if (Riemann2Helix(a,ca,b,cb,xmax,p,c))
494 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
497 Bool_t AliTPCTracklet::Riemann2Helix(Double_t *a,Double_t */*ca*/,
498 Double_t *b,Double_t */*cb*/,
500 Double_t *p,Double_t *c) {
503 Double_t xr0=.5*a[1];
504 Double_t yr0=.5*a[2];
505 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
507 if (dx*dx>=R*R) return kFALSE;
508 Double_t dy=TMath::Sqrt((R-dx)*(R+dx)); //sign!!
509 if (TMath::Abs(yr0+dy)>TMath::Abs(yr0-dy))
512 Double_t tgp=-dx/dy; //TODO: dy!=0
513 Double_t z0=b[0]+TMath::ATan(tgp)*b[1];
514 Double_t xyz[3]={x0,y0,z0};
515 Double_t fc=1./(GetBz(xyz)*kB2C);
519 p[2]=tgp/TMath::Sqrt(1.+tgp*tgp); // snp
521 p[4]=1./R*fc; // 1/pt
535 c[12]=0.; // 1/pt-snp
536 c[13]=0.; // 1/pt-tgl
537 c[14]=0.; // 1/pt-1/pt
542 TObjArray AliTPCTracklet::CreateTracklets(const AliTPCseed *track,
544 Bool_t storeClusters,
546 Int_t maxTracklets) {
547 // The tracklet factory: It creates several tracklets out of a track. They
548 // are created for sectors that fullfill the constraint of having enough
549 // clusters inside. Futhermore you can specify the maximum amount of
550 // tracklets that are to be created.
551 // The tracklets appear in a sorted fashion, beginning with those having the
554 Int_t sectors[72]={0};
555 for (Int_t i=0;i<160;++i) {
556 AliTPCclusterMI *c=track->GetClusterPointer(i);
557 if (c && RejectCluster(c)) continue;
559 ++sectors[c->GetDetector()];
562 TMath::Sort(72,sectors,indices);
564 if (maxTracklets>72) maxTracklets=72; // just to protect against "users".
565 for (Int_t i=0;i<maxTracklets&§ors[indices[i]]>=minClusters;++i) {
566 tracklets.Add(new AliTPCTracklet(track,indices[i],type,storeClusters));
571 TObjArray AliTPCTracklet::CreateTracklets(const TObjArray &/*clusters*/,
573 Bool_t /*storeClusters*/,
574 Int_t /*minClusters*/,
575 Int_t /*maxTracklets*/) {
582 Bool_t AliTPCTracklet::PropagateToMeanX(const AliTPCTracklet &t1,
583 const AliTPCTracklet &t2,
584 AliExternalTrackParam *&t1m,
585 AliExternalTrackParam *&t2m) {
586 // This function propagates two Tracklets to a common x-coordinate. This
587 // x is dermined as the one that is in the middle of the two tracklets (they
588 // are assumed to live on two distinct x-intervalls).
589 // The inner parametrisation of the outer Tracklet and the outer
590 // parametrisation of the inner Tracklet are used and propagated to this
591 // common x. This result is saved not inside the Tracklets but two new
592 // ExternalTrackParams are created (that means you might want to delete
594 // In the case that the alpha angles of the Tracklets differ both angles
595 // are tried out for this propagation.
596 // In case of any failure kFALSE is returned, no AliExternalTrackParam
597 // is created und the pointers are set to 0.
599 if (t1.GetInner() && t1.GetOuter() &&
600 t2.GetInner() && t2.GetOuter()) {
601 if (t1.GetOuter()->GetX()<t2.GetInner()->GetX()) {
602 t1m=new AliExternalTrackParam(*t1.GetOuter());
603 t2m=new AliExternalTrackParam(*t2.GetInner());
606 t1m=new AliExternalTrackParam(*t1.GetInner());
607 t2m=new AliExternalTrackParam(*t2.GetOuter());
609 Double_t mx=.5*(t1m->GetX()+t2m->GetX());
614 Double_t b1[3]; AliTracker::GetBxByBz(xyz,b1);
617 Double_t b2[3]; AliTracker::GetBxByBz(xyz,b2);
618 if (t1m->Rotate(t2m->GetAlpha())
619 //&& t1m->PropagateTo(mx,b1)
620 //&& t2m->PropagateTo(mx,b2));
621 && t1m->PropagateToBxByBz(mx,b1)
622 && t2m->PropagateToBxByBz(mx,b2));
624 if (t2m->Rotate(t1m->GetAlpha())
625 //&& t1m->PropagateTo(mx,b1)
626 //&& t2m->PropagateTo(mx,b2));
627 && t1m->PropagateToBxByBz(mx,b1)
628 && t2m->PropagateToBxByBz(mx,b2));
641 double AliTPCTracklet::GetBz(Double_t *xyz)
643 return AliTracker::GetBz(xyz);
646 void AliTPCTracklet::RandomND(Int_t ndim,const Double_t *p,const Double_t *c,
648 // This function generates a n-dimensional random variable x with mean
649 // p and covariance c.
650 // That is done using the cholesky decomposition of the covariance matrix,
651 // Begin_Latex C=U^{t} U End_Latex, with Begin_Latex U End_Latex being an
652 // upper triangular matrix. Given a vector v of iid gausian random variables
653 // with variance 1 one obtains the asked result as: Begin_Latex x=U^t v
655 // c is expected to be in a lower triangular format:
660 static TRandom3 random;
661 Double_t *c2= new Double_t[ndim*ndim];
663 for (Int_t i=0;i<ndim;++i)
664 for (Int_t j=0;j<=i;++j)
665 c2[i*ndim+j]=c2[j*ndim+i]=c[k++];
666 TMatrixDSym cm(ndim,c2);
668 TDecompChol chol(cm);
670 const TVectorD pv(ndim);
671 const_cast<TVectorD*>(&pv)->Use(ndim,const_cast<Double_t*>(p));
674 for (Int_t i=0;i<ndim;++i)
676 TMatrixD L=chol.GetU();
681 TEllipse AliTPCTracklet::ErrorEllipse(Double_t x,Double_t y,
682 Double_t sx,Double_t sy,Double_t sxy) {
684 r_{1,2}=1/2 (a+c#pm#sqrt{(a-c)^{2}+(2b)^{2}})
686 Double_t det1=1./(sx*sy-sxy*sxy);
688 Double_t b=-sxy*det1;
691 Double_t s=TMath::Sqrt(d*d+4.*b*b);
692 Double_t r1=TMath::Sqrt(.5*(a+c-s));
693 Double_t r2=TMath::Sqrt(.5*(a+c+s));
694 Double_t alpha=.5*TMath::ATan2(2.*b,d);
695 return TEllipse(x,y,r1,r2,0.,360.,alpha*TMath::RadToDeg());
698 void AliTPCTracklet::Test(const char* filename) {
701 AliTPCTracklet::Test("");
702 TFile f("AliTPCTrackletDebug.root");
703 TTree *t=f.Get("AliTPCTrackletDebug");
705 TEllipse e=AliTPCTracklet::ErrorEllipse(0.,0.,4.,1.,1.8);
708 TTreeSRedirector ds(filename);
715 for (Int_t i=0;i<10000;++i) {
718 ds<<"AliTPCTrackletDebug"
731 Double_t param[5]={0.};
732 Double_t covar[15]={1.,
737 AliExternalTrackParam track(x,alpha,param,covar);
741 for (Int_t i=0;i<points.GetNPoints();++i) {
744 Double_t param[5]={0.};
745 Double_t covar[15]={1.,
750 AliExternalTrackParam track(x,alpha,param,covar);
751 for (x=90.;x<250.;x+=1.) {
752 track.PropagateTo(x,b);
760 Bool_t AliTPCTracklet::RejectCluster(AliTPCclusterMI* cl, AliExternalTrackParam * param){
762 // check the acceptance of cluster
763 // Cut on edge effects
765 Bool_t isReject = kFALSE;
766 Float_t edgeY = cl->GetX()*TMath::Tan(TMath::Pi()/18);
767 Float_t dist = edgeY - TMath::Abs(cl->GetY());
768 if (param) dist = edgeY - TMath::Abs(param->GetY());
769 if (dist<fgEdgeCutY) isReject=kTRUE;
770 if (cl->GetType()<0) isReject=kTRUE;