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;
129 fNStoredClusters=fNStoredClusters;
132 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
133 for (int i=0;i<t.fNStoredClusters;++i)
134 fClusters[i]=t.fClusters[i];
143 fOuter=new AliExternalTrackParam(*t.fOuter);
154 fInner=new AliExternalTrackParam(*t.fInner);
163 *fPrimary=*t.fPrimary;
165 fPrimary=new AliExternalTrackParam(*t.fPrimary);
175 AliTPCTracklet::~AliTPCTracklet() {
177 // The destructor. Yes, you can even destruct tracklets.
185 void AliTPCTracklet::FitKalman(const AliTPCseed *track,Int_t sector) {
187 // Fit using Kalman filter
189 AliTPCseed *t=new AliTPCseed(*track);
190 if (!t->Rotate(TMath::DegToRad()*(sector%18*20.+10.)-t->GetAlpha())) {
194 // fit from inner to outer row
195 AliTPCseed *outerSeed=new AliTPCseed(*t);
197 for (Int_t i=0;i<160;++i) {
198 AliTPCclusterMI *c=t->GetClusterPointer(i);
199 if (c && RejectCluster(c,outerSeed)) continue;
200 if (c&&c->GetDetector()==sector) {
202 outerSeed->ResetCovariance(100.);
205 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
206 Double_t cov[3]={0.1,0.,0.1}; //TODO: correct error parametrisation
207 if (!outerSeed->PropagateTo(r[0]) ||
208 !static_cast<AliExternalTrackParam*>(outerSeed)->Update(&r[1],cov)) {
216 fOuter=new AliExternalTrackParam(*outerSeed);
218 // fit from outer to inner rows
219 AliTPCseed *innerSeed=new AliTPCseed(*t);
221 for (Int_t i=159;i>=0;--i) {
222 AliTPCclusterMI *c=t->GetClusterPointer(i);
223 if (c && RejectCluster(c, innerSeed)) continue;
224 if (c&&c->GetDetector()==sector) {
226 innerSeed->ResetCovariance(100.);
229 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
230 Double_t cov[3]={0.1,0.,0.1};
231 if (!innerSeed->PropagateTo(r[0]) ||
232 !static_cast<AliExternalTrackParam*>(innerSeed)->Update(&r[1],cov)) {
240 fInner=new AliExternalTrackParam(*innerSeed);
241 // propagate to the primary vertex
243 AliTPCseed *primarySeed=new AliTPCseed(*innerSeed);
244 Double_t pos[]={0.,0.,0.};
245 Double_t sigma[]={.1,.1,.1}; //TODO: is this correct?
246 AliESDVertex vertex(pos,sigma);
247 if (primarySeed->PropagateToVertex(&vertex))
248 fPrimary=new AliExternalTrackParam(*primarySeed);
250 // for better comparison one does not want to have alpha changed...
251 if (fPrimary) if (!fPrimary->Rotate(fInner->GetAlpha())) {
261 void AliTPCTracklet::FitLinear(const AliTPCseed *track,Int_t sector,
265 fy.StoreData(kFALSE);
266 fz.StoreData(kFALSE);
269 fy.SetFormula("1 ++ x");
270 fz.SetFormula("1 ++ x");
273 fy.SetFormula("1 ++ x ++ x*x");
274 fz.SetFormula("1 ++ x");
282 for (Int_t i=0;i<160;++i) {
283 AliTPCclusterMI *c=track->GetClusterPointer(i);
284 if (c && RejectCluster(c)) continue;
285 if (c&&c->GetDetector()==sector) {
286 Double_t x=c->GetX();
287 fy.AddPoint(&x,c->GetY());
288 fz.AddPoint(&x,c->GetZ());
289 xmax=TMath::Max(xmax,x);
290 xmin=TMath::Min(xmin,x);
295 Double_t a[3]={fy.GetParameter(0),
297 type==kQuadratic?fy.GetParameter(2):0.};
298 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
299 fy.GetCovarianceMatrixElement(1,0),
300 fy.GetCovarianceMatrixElement(1,1),
301 type==kQuadratic?fy.GetCovarianceMatrixElement(2,0):0.,
302 type==kQuadratic?fy.GetCovarianceMatrixElement(2,1):0.,
303 type==kQuadratic?fy.GetCovarianceMatrixElement(2,2):0.};
304 for (int i=0;i<6;++i) ca[i]*=fy.GetChisquare()/fNClusters;
305 Double_t b[2]={fz.GetParameter(0),
307 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
308 fz.GetCovarianceMatrixElement(1,0),
309 fz.GetCovarianceMatrixElement(1,1)};
310 for (int i=0;i<3;++i) cb[i]*=fz.GetChisquare()/fNClusters;
313 Double_t alpha=track->GetAlpha();
314 Quadratic2Helix(a,ca,b,cb,0.,p,c);
315 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
316 Quadratic2Helix(a,ca,b,cb,xmin,p,c);
317 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
318 Quadratic2Helix(a,ca,b,cb,xmax,p,c);
319 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
322 void AliTPCTracklet::Quadratic2Helix(Double_t *a,Double_t *ca,
323 Double_t *b,Double_t *cb,
325 Double_t *p,Double_t *c) {
326 // y(x)=a[0]+a[1]*x+a[2]*x^2
328 // parametrises the corosponding helix at x0
330 // get the polynoms at x0
331 Double_t a0=x0*x0*a[2] + x0*a[1] + a[0];
332 Double_t a1=2.*x0*a[2] + a[1];
334 Double_t ca00=ca[0]+x0*(2.*ca[1]+x0*(ca[2]+2.*ca[3]+x0*(2.*ca[4]+x0*ca[5])));
335 Double_t ca10=ca[1]+x0*(ca[2]+2.*ca[3]+x0*(3.*ca[4]+x0*2.*ca[5]));
336 Double_t ca11=ca[2]+x0*4.*(ca[4]+x0*ca[5]);
337 Double_t ca20=ca[3]+x0*(ca[4]+x0*ca[5]);
338 Double_t ca21=ca[3]+x0*2.*ca[5];
341 Double_t b0=x0*b[1] + b[0];
343 Double_t cb00=cb[0]+x0*(2.*cb[1]+x0*cb[2]);
344 Double_t cb10=cb[1]+x0*cb[2];
347 // transform to helix parameters
348 Double_t f =1.+a1*a1;
351 Double_t fi12=TMath::Sqrt(fi);
352 Double_t fi32=fi*fi12;
354 Double_t fi52=fi2*fi12;
355 Double_t fi3 =fi2*fi;
356 Double_t fi5 =fi2*fi3;
358 Double_t xyz[3]={0.}; // TODO...
359 Double_t fc=1./(GetBz(xyz)*kB2C);
365 p[4]=2.*a2*fi32*fc; // 1/pt
370 c[3] =ca10*fi32; // snp-y0
372 c[5] =ca11*fi3; // snp-snp
374 c[7] =cb10; // tgl-z0
376 c[9] =cb11; // tgl-tgl
377 c[10]=2.*(-3.*a1*a2*ca10+f*ca20)*fi3*fc; // 1/pt-y0
379 c[12]=2.*(-3.*a1*a2*ca11+f*ca21)*fi52*fc; // 1/pt-snp
380 c[13]=0.; // 1/pt-tgl
381 c[14]=(-12.*a1*a2*(-3.*a1*a2*ca11+2.*f*ca21)+4.*f2*ca22)*fi5
386 void AliTPCTracklet::FitRiemann(const AliTPCseed *track,Int_t sector) {
388 fy.StoreData(kFALSE);
389 fy.SetFormula("hyp2");
392 for (Int_t i=0;i<160;++i) {
393 AliTPCclusterMI *c=track->GetClusterPointer(i);
394 if (c && RejectCluster(c)) continue;
395 if (c&&c->GetDetector()==sector) {
396 Double_t x=c->GetX();
397 Double_t y=c->GetY();
398 Double_t xy[2]={x,y};
400 Double_t errx=1.,erry=1.;//TODO!
401 Double_t err=TMath::Sqrt(4.*x*x*errx+4.*y*y*erry);
403 fy.AddPoint(xy,r,err);
404 xmax=TMath::Max(xmax,x);
405 xmin=TMath::Min(xmin,x);
409 Double_t a[3]={fy.GetParameter(0),
412 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
413 fy.GetCovarianceMatrixElement(1,0),
414 fy.GetCovarianceMatrixElement(1,1),
415 fy.GetCovarianceMatrixElement(2,0),
416 fy.GetCovarianceMatrixElement(2,1),
417 fy.GetCovarianceMatrixElement(2,2)};
420 fz.StoreData(kFALSE);
421 fz.SetFormula("hyp1");
422 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
426 for (Int_t i=0;i<160;++i) {
427 AliTPCclusterMI *c=track->GetClusterPointer(i);
428 if (c && RejectCluster(c)) continue;
429 if (c&&c->GetDetector()==sector) {
430 Double_t x=c->GetX();
431 Double_t y=c->GetY();
434 phi+=2.*TMath::Abs(TMath::ATan2(.5*TMath::Sqrt(dx*dx+dy*dy),R));
436 fz.AddPoint(&phi,c->GetZ(),err);
442 Double_t b[2]={fz.GetParameter(0),
444 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
445 fz.GetCovarianceMatrixElement(1,0),
446 fz.GetCovarianceMatrixElement(1,1)};
450 Double_t alpha=track->GetAlpha();
451 if (Riemann2Helix(a,ca,b,cb,0.,p,c))
452 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
453 if (Riemann2Helix(a,ca,b,cb,xmin,p,c))
454 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
455 if (Riemann2Helix(a,ca,b,cb,xmax,p,c))
456 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
459 Bool_t AliTPCTracklet::Riemann2Helix(Double_t *a,Double_t */*ca*/,
460 Double_t *b,Double_t */*cb*/,
462 Double_t *p,Double_t *c) {
465 Double_t xr0=.5*a[1];
466 Double_t yr0=.5*a[2];
467 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
469 if (dx*dx>=R*R) return kFALSE;
470 Double_t dy=TMath::Sqrt(R*R-dx*dx); //sign!!
471 if (TMath::Abs(yr0+dy)>TMath::Abs(yr0-dy))
474 Double_t tgp=-dx/dy; //TODO: dy!=0
475 Double_t z0=b[0]+TMath::ATan(tgp)*b[1];
476 Double_t xyz[3]={x0,y0,z0};
477 Double_t fc=1./(GetBz(xyz)*kB2C);
481 p[2]=tgp/TMath::Sqrt(1.+tgp*tgp); // snp
483 p[4]=1./R*fc; // 1/pt
497 c[12]=0.; // 1/pt-snp
498 c[13]=0.; // 1/pt-tgl
499 c[14]=0.; // 1/pt-1/pt
504 TObjArray AliTPCTracklet::CreateTracklets(const AliTPCseed *track,
506 Bool_t storeClusters,
508 Int_t maxTracklets) {
509 // The tracklet factory: It creates several tracklets out of a track. They
510 // are created for sectors that fullfill the constraint of having enough
511 // clusters inside. Futhermore you can specify the maximum amount of
512 // tracklets that are to be created.
513 // The tracklets appear in a sorted fashion, beginning with those having the
516 Int_t sectors[72]={0};
517 for (Int_t i=0;i<160;++i) {
518 AliTPCclusterMI *c=track->GetClusterPointer(i);
519 if (c && RejectCluster(c)) continue;
521 ++sectors[c->GetDetector()];
524 TMath::Sort(72,sectors,indices);
526 if (maxTracklets>72) maxTracklets=72; // just to protect against "users".
527 for (Int_t i=0;i<maxTracklets&§ors[indices[i]]>=minClusters;++i) {
528 tracklets.Add(new AliTPCTracklet(track,indices[i],type,storeClusters));
533 TObjArray AliTPCTracklet::CreateTracklets(const TObjArray &/*clusters*/,
535 Bool_t /*storeClusters*/,
536 Int_t /*minClusters*/,
537 Int_t /*maxTracklets*/) {
544 Bool_t AliTPCTracklet::PropagateToMeanX(const AliTPCTracklet &t1,
545 const AliTPCTracklet &t2,
546 AliExternalTrackParam *&t1m,
547 AliExternalTrackParam *&t2m) {
548 // This function propagates two Tracklets to a common x-coordinate. This
549 // x is dermined as the one that is in the middle of the two tracklets (they
550 // are assumed to live on two distinct x-intervalls).
551 // The inner parametrisation of the outer Tracklet and the outer
552 // parametrisation of the inner Tracklet are used and propagated to this
553 // common x. This result is saved not inside the Tracklets but two new
554 // ExternalTrackParams are created (that means you might want to delete
556 // In the case that the alpha angles of the Tracklets differ both angles
557 // are tried out for this propagation.
558 // In case of any failure kFALSE is returned, no AliExternalTrackParam
559 // is created und the pointers are set to 0.
561 if (t1.GetInner() && t1.GetOuter() &&
562 t2.GetInner() && t2.GetOuter()) {
563 if (t1.GetOuter()->GetX()<t2.GetInner()->GetX()) {
564 t1m=new AliExternalTrackParam(*t1.GetOuter());
565 t2m=new AliExternalTrackParam(*t2.GetInner());
568 t1m=new AliExternalTrackParam(*t1.GetInner());
569 t2m=new AliExternalTrackParam(*t2.GetOuter());
571 Double_t mx=.5*(t1m->GetX()+t2m->GetX());
578 if (t1m->Rotate(t2m->GetAlpha())
579 && t1m->PropagateTo(mx,b1)
580 && t2m->PropagateTo(mx,b2));
582 if (t2m->Rotate(t1m->GetAlpha())
583 && t1m->PropagateTo(mx,b1)
584 && t2m->PropagateTo(mx,b2));
597 double AliTPCTracklet::GetBz(Double_t *xyz) {
598 if (AliTracker::UniformField())
599 return AliTracker::GetBz();
601 return AliTracker::GetBz(xyz);
604 void AliTPCTracklet::RandomND(Int_t ndim,const Double_t *p,const Double_t *c,
606 // This function generates a n-dimensional random variable x with mean
607 // p and covariance c.
608 // That is done using the cholesky decomposition of the covariance matrix,
609 // Begin_Latex C=U^{t} U End_Latex, with Begin_Latex U End_Latex being an
610 // upper triangular matrix. Given a vector v of iid gausian random variables
611 // with variance 1 one obtains the asked result as: Begin_Latex x=U^t v
613 // c is expected to be in a lower triangular format:
618 static TRandom3 random;
619 Double_t *c2= new Double_t[ndim*ndim];
621 for (Int_t i=0;i<ndim;++i)
622 for (Int_t j=0;j<=i;++j)
623 c2[i*ndim+j]=c2[j*ndim+i]=c[k++];
624 TMatrixDSym cm(ndim,c2);
626 TDecompChol chol(cm);
628 const TVectorD pv(ndim);
629 const_cast<TVectorD*>(&pv)->Use(ndim,const_cast<Double_t*>(p));
632 for (Int_t i=0;i<ndim;++i)
634 TMatrixD L=chol.GetU();
639 TEllipse AliTPCTracklet::ErrorEllipse(Double_t x,Double_t y,
640 Double_t sx,Double_t sy,Double_t sxy) {
642 r_{1,2}=1/2 (a+c#pm#sqrt{(a-c)^{2}+(2b)^{2}})
644 Double_t det1=1./(sx*sy-sxy*sxy);
646 Double_t b=-sxy*det1;
649 Double_t s=TMath::Sqrt(d*d+4.*b*b);
650 Double_t r1=TMath::Sqrt(.5*(a+c-s));
651 Double_t r2=TMath::Sqrt(.5*(a+c+s));
652 Double_t alpha=.5*TMath::ATan2(2.*b,d);
653 return TEllipse(x,y,r1,r2,0.,360.,alpha*TMath::RadToDeg());
656 void AliTPCTracklet::Test(const char* filename) {
659 AliTPCTracklet::Test("");
660 TFile f("AliTPCTrackletDebug.root");
661 TTree *t=f.Get("AliTPCTrackletDebug");
663 TEllipse e=AliTPCTracklet::ErrorEllipse(0.,0.,4.,1.,1.8);
666 TTreeSRedirector ds(filename);
673 for (Int_t i=0;i<10000;++i) {
676 ds<<"AliTPCTrackletDebug"
689 Double_t param[5]={0.};
690 Double_t covar[15]={1.,
695 AliExternalTrackParam track(x,alpha,param,covar);
699 for (Int_t i=0;i<points.GetNPoints();++i) {
702 Double_t param[5]={0.};
703 Double_t covar[15]={1.,
708 AliExternalTrackParam track(x,alpha,param,covar);
709 for (x=90.;x<250.;x+=1.) {
710 track.PropagateTo(x,b);
718 Bool_t AliTPCTracklet::RejectCluster(AliTPCclusterMI* cl, AliExternalTrackParam * param){
720 // check the acceptance of cluster
721 // Cut on edge effects
723 Bool_t isReject = kFALSE;
724 Float_t edgeY = cl->GetX()*TMath::Tan(TMath::Pi()/18);
725 Float_t dist = edgeY - TMath::Abs(cl->GetY());
726 if (param) dist = edgeY - TMath::Abs(param->GetY());
727 if (dist<fgEdgeCutY) isReject=kTRUE;
728 if (cl->GetType()<0) isReject=kTRUE;