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;
41 AliTPCTracklet::AliTPCTracklet()
42 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(-1),fOuter(0),
43 fInner(0),fPrimary(0) {
45 // The default constructor. It is intended to be used for I/O only.
49 AliTPCTracklet::AliTPCTracklet(const AliTPCseed *track,Int_t sector,
50 TrackType type,Bool_t storeClusters)
51 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(sector),fOuter(0),
52 fInner(0),fPrimary(0) {
54 // Contructor for a tracklet out of a track. Only clusters within a given
58 //TODO: only kalman works
60 for (Int_t i=0;i<160;++i) {
61 AliTPCclusterMI *c=track->GetClusterPointer(i);
62 if (c&&c->GetDetector()==sector)
67 fClusters=new AliTPCclusterMI[fNClusters];
68 for (Int_t i=0;i<160;++i) {
69 AliTPCclusterMI *c=track->GetClusterPointer(i);
70 if (c&&c->GetDetector()==sector)
71 fClusters[fNStoredClusters]=c;
78 FitKalman(track,sector);
82 FitLinear(track,sector,type);
85 FitRiemann(track,sector);
91 AliTPCTracklet::AliTPCTracklet(const TObjArray &/*clusters*/,Int_t sector,
92 TrackType /*type*/,Bool_t /*storeClusters*/)
93 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(sector),fOuter(0),
94 fInner(0),fPrimary(0) {
98 AliTPCTracklet::AliTPCTracklet(const AliTPCTracklet &t)
99 : TObject(t),fNClusters(t.fNClusters),fNStoredClusters(t.fNStoredClusters),fClusters(0),
100 fSector(t.fSector),fOuter(0),fInner(0),
103 // The copy constructor. You can copy tracklets!
107 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
108 for (int i=0;i<t.fNStoredClusters;++i)
109 fClusters[i]=t.fClusters[i];
112 fOuter=new AliExternalTrackParam(*t.fOuter);
114 fInner=new AliExternalTrackParam(*t.fInner);
116 fPrimary=new AliExternalTrackParam(*t.fPrimary);
119 AliTPCTracklet& AliTPCTracklet::operator=(const AliTPCTracklet &t) {
121 // The assignment constructor. You can assign tracklets!
124 fNClusters=t.fNClusters;
125 fNStoredClusters=fNStoredClusters;
128 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
129 for (int i=0;i<t.fNStoredClusters;++i)
130 fClusters[i]=t.fClusters[i];
139 fOuter=new AliExternalTrackParam(*t.fOuter);
150 fInner=new AliExternalTrackParam(*t.fInner);
159 *fPrimary=*t.fPrimary;
161 fPrimary=new AliExternalTrackParam(*t.fPrimary);
171 AliTPCTracklet::~AliTPCTracklet() {
173 // The destructor. Yes, you can even destruct tracklets.
181 void AliTPCTracklet::FitKalman(const AliTPCseed *track,Int_t sector) {
182 AliTPCseed *t=new AliTPCseed(*track);
183 if (!t->Rotate(TMath::DegToRad()*(sector%18*20.+10.)-t->GetAlpha())) {
187 // fit from inner to outer row
188 AliTPCseed *outerSeed=new AliTPCseed(*t);
190 for (Int_t i=0;i<160;++i) {
191 AliTPCclusterMI *c=t->GetClusterPointer(i);
192 if (c&&c->GetDetector()==sector) {
194 outerSeed->ResetCovariance(100.);
197 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
198 Double_t cov[3]={0.1,0.,0.1}; //TODO: correct error parametrisation
199 if (!outerSeed->PropagateTo(r[0]) ||
200 !static_cast<AliExternalTrackParam*>(outerSeed)->Update(&r[1],cov)) {
208 fOuter=new AliExternalTrackParam(*outerSeed);
210 // fit from outer to inner rows
211 AliTPCseed *innerSeed=new AliTPCseed(*t);
213 for (Int_t i=159;i>=0;--i) {
214 AliTPCclusterMI *c=t->GetClusterPointer(i);
215 if (c&&c->GetDetector()==sector) {
217 innerSeed->ResetCovariance(100.);
220 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
221 Double_t cov[3]={0.1,0.,0.1};
222 if (!innerSeed->PropagateTo(r[0]) ||
223 !static_cast<AliExternalTrackParam*>(innerSeed)->Update(&r[1],cov)) {
231 fInner=new AliExternalTrackParam(*innerSeed);
232 // propagate to the primary vertex
234 AliTPCseed *primarySeed=new AliTPCseed(*innerSeed);
235 Double_t pos[]={0.,0.,0.};
236 Double_t sigma[]={.1,.1,.1}; //TODO: is this correct?
237 AliESDVertex vertex(pos,sigma);
238 if (primarySeed->PropagateToVertex(&vertex))
239 fPrimary=new AliExternalTrackParam(*primarySeed);
241 // for better comparison one does not want to have alpha changed...
242 if (!fPrimary->Rotate(fInner->GetAlpha())) {
252 void AliTPCTracklet::FitLinear(const AliTPCseed *track,Int_t sector,
256 fy.StoreData(kFALSE);
257 fz.StoreData(kFALSE);
260 fy.SetFormula("1 ++ x");
261 fz.SetFormula("1 ++ x");
264 fy.SetFormula("1 ++ x ++ x*x");
265 fz.SetFormula("1 ++ x");
273 for (Int_t i=0;i<160;++i) {
274 AliTPCclusterMI *c=track->GetClusterPointer(i);
275 if (c&&c->GetDetector()==sector) {
276 Double_t x=c->GetX();
277 fy.AddPoint(&x,c->GetY());
278 fz.AddPoint(&x,c->GetZ());
279 xmax=TMath::Max(xmax,x);
280 xmin=TMath::Min(xmin,x);
285 Double_t a[3]={fy.GetParameter(0),
287 type==kQuadratic?fy.GetParameter(2):0.};
288 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
289 fy.GetCovarianceMatrixElement(1,0),
290 fy.GetCovarianceMatrixElement(1,1),
291 type==kQuadratic?fy.GetCovarianceMatrixElement(2,0):0.,
292 type==kQuadratic?fy.GetCovarianceMatrixElement(2,1):0.,
293 type==kQuadratic?fy.GetCovarianceMatrixElement(2,2):0.};
294 for (int i=0;i<6;++i) ca[i]*=fy.GetChisquare()/fNClusters;
295 Double_t b[2]={fz.GetParameter(0),
297 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
298 fz.GetCovarianceMatrixElement(1,0),
299 fz.GetCovarianceMatrixElement(1,1)};
300 for (int i=0;i<3;++i) cb[i]*=fz.GetChisquare()/fNClusters;
303 Double_t alpha=track->GetAlpha();
304 Quadratic2Helix(a,ca,b,cb,0.,p,c);
305 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
306 Quadratic2Helix(a,ca,b,cb,xmin,p,c);
307 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
308 Quadratic2Helix(a,ca,b,cb,xmax,p,c);
309 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
312 void AliTPCTracklet::Quadratic2Helix(Double_t *a,Double_t *ca,
313 Double_t *b,Double_t *cb,
315 Double_t *p,Double_t *c) {
316 // y(x)=a[0]+a[1]*x+a[2]*x^2
318 // parametrises the corosponding helix at x0
320 // get the polynoms at x0
321 Double_t a0=x0*x0*a[2] + x0*a[1] + a[0];
322 Double_t a1=2.*x0*a[2] + a[1];
324 Double_t ca00=ca[0]+x0*(2.*ca[1]+x0*(ca[2]+2.*ca[3]+x0*(2.*ca[4]+x0*ca[5])));
325 Double_t ca10=ca[1]+x0*(ca[2]+2.*ca[3]+x0*(3.*ca[4]+x0*2.*ca[5]));
326 Double_t ca11=ca[2]+x0*4.*(ca[4]+x0*ca[5]);
327 Double_t ca20=ca[3]+x0*(ca[4]+x0*ca[5]);
328 Double_t ca21=ca[3]+x0*2.*ca[5];
331 Double_t b0=x0*b[1] + b[0];
333 Double_t cb00=cb[0]+x0*(2.*cb[1]+x0*cb[2]);
334 Double_t cb10=cb[1]+x0*cb[2];
337 // transform to helix parameters
338 Double_t f =1.+a1*a1;
341 Double_t fi12=TMath::Sqrt(fi);
342 Double_t fi32=fi*fi12;
344 Double_t fi52=fi2*fi12;
345 Double_t fi3 =fi2*fi;
346 Double_t fi5 =fi2*fi3;
348 Double_t xyz[3]={0.}; // TODO...
349 Double_t fc=1./(GetBz(xyz)*kB2C);
355 p[4]=2.*a2*fi32*fc; // 1/pt
360 c[3] =ca10*fi32; // snp-y0
362 c[5] =ca11*fi3; // snp-snp
364 c[7] =cb10; // tgl-z0
366 c[9] =cb11; // tgl-tgl
367 c[10]=2.*(-3.*a1*a2*ca10+f*ca20)*fi3*fc; // 1/pt-y0
369 c[12]=2.*(-3.*a1*a2*ca11+f*ca21)*fi52*fc; // 1/pt-snp
370 c[13]=0.; // 1/pt-tgl
371 c[14]=(-12.*a1*a2*(-3.*a1*a2*ca11+2.*f*ca21)+4.*f2*ca22)*fi5
376 void AliTPCTracklet::FitRiemann(const AliTPCseed *track,Int_t sector) {
378 fy.StoreData(kFALSE);
379 fy.SetFormula("hyp2");
382 for (Int_t i=0;i<160;++i) {
383 AliTPCclusterMI *c=track->GetClusterPointer(i);
384 if (c&&c->GetDetector()==sector) {
385 Double_t x=c->GetX();
386 Double_t y=c->GetY();
387 Double_t xy[2]={x,y};
389 Double_t errx=1.,erry=1.;//TODO!
390 Double_t err=TMath::Sqrt(4.*x*x*errx+4.*y*y*erry);
392 fy.AddPoint(xy,r,err);
393 xmax=TMath::Max(xmax,x);
394 xmin=TMath::Min(xmin,x);
398 Double_t a[3]={fy.GetParameter(0),
401 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
402 fy.GetCovarianceMatrixElement(1,0),
403 fy.GetCovarianceMatrixElement(1,1),
404 fy.GetCovarianceMatrixElement(2,0),
405 fy.GetCovarianceMatrixElement(2,1),
406 fy.GetCovarianceMatrixElement(2,2)};
409 fz.StoreData(kFALSE);
410 fz.SetFormula("hyp1");
411 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
415 for (Int_t i=0;i<160;++i) {
416 AliTPCclusterMI *c=track->GetClusterPointer(i);
417 if (c&&c->GetDetector()==sector) {
418 Double_t x=c->GetX();
419 Double_t y=c->GetY();
422 phi+=2.*TMath::Abs(TMath::ATan2(.5*TMath::Sqrt(dx*dx+dy*dy),R));
424 fz.AddPoint(&phi,c->GetZ(),err);
430 Double_t b[2]={fz.GetParameter(0),
432 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
433 fz.GetCovarianceMatrixElement(1,0),
434 fz.GetCovarianceMatrixElement(1,1)};
438 Double_t alpha=track->GetAlpha();
439 if (Riemann2Helix(a,ca,b,cb,0.,p,c))
440 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
441 if (Riemann2Helix(a,ca,b,cb,xmin,p,c))
442 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
443 if (Riemann2Helix(a,ca,b,cb,xmax,p,c))
444 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
447 Bool_t AliTPCTracklet::Riemann2Helix(Double_t *a,Double_t */*ca*/,
448 Double_t *b,Double_t */*cb*/,
450 Double_t *p,Double_t *c) {
453 Double_t xr0=.5*a[1];
454 Double_t yr0=.5*a[2];
455 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
457 if (dx*dx>=R*R) return kFALSE;
458 Double_t dy=TMath::Sqrt(R*R-dx*dx); //sign!!
459 if (TMath::Abs(yr0+dy)>TMath::Abs(yr0-dy))
462 Double_t tgp=-dx/dy; //TODO: dy!=0
463 Double_t z0=b[0]+TMath::ATan(tgp)*b[1];
464 Double_t xyz[3]={x0,y0,z0};
465 Double_t fc=1./(GetBz(xyz)*kB2C);
469 p[2]=tgp/TMath::Sqrt(1.+tgp*tgp); // snp
471 p[4]=1./R*fc; // 1/pt
485 c[12]=0.; // 1/pt-snp
486 c[13]=0.; // 1/pt-tgl
487 c[14]=0.; // 1/pt-1/pt
492 TObjArray AliTPCTracklet::CreateTracklets(const AliTPCseed *track,
494 Bool_t storeClusters,
496 Int_t maxTracklets) {
497 // The tracklet factory: It creates several tracklets out of a track. They
498 // are created for sectors that fullfill the constraint of having enough
499 // clusters inside. Futhermore you can specify the maximum amount of
500 // tracklets that are to be created.
501 // The tracklets appear in a sorted fashion, beginning with those having the
504 Int_t sectors[72]={0};
505 for (Int_t i=0;i<160;++i) {
506 AliTPCclusterMI *c=track->GetClusterPointer(i);
508 ++sectors[c->GetDetector()];
511 TMath::Sort(72,sectors,indices);
513 if (maxTracklets>72) maxTracklets=72; // just to protect against "users".
514 for (Int_t i=0;i<maxTracklets&§ors[indices[i]]>=minClusters;++i) {
515 tracklets.Add(new AliTPCTracklet(track,indices[i],type,storeClusters));
520 TObjArray AliTPCTracklet::CreateTracklets(const TObjArray &/*clusters*/,
522 Bool_t /*storeClusters*/,
523 Int_t /*minClusters*/,
524 Int_t /*maxTracklets*/) {
531 Bool_t AliTPCTracklet::PropagateToMeanX(const AliTPCTracklet &t1,
532 const AliTPCTracklet &t2,
533 AliExternalTrackParam *&t1m,
534 AliExternalTrackParam *&t2m) {
535 // This function propagates two Tracklets to a common x-coordinate. This
536 // x is dermined as the one that is in the middle of the two tracklets (they
537 // are assumed to live on two distinct x-intervalls).
538 // The inner parametrisation of the outer Tracklet and the outer
539 // parametrisation of the inner Tracklet are used and propagated to this
540 // common x. This result is saved not inside the Tracklets but two new
541 // ExternalTrackParams are created (that means you might want to delete
543 // In the case that the alpha angles of the Tracklets differ both angles
544 // are tried out for this propagation.
545 // In case of any failure kFALSE is returned, no AliExternalTrackParam
546 // is created und the pointers are set to 0.
548 if (t1.GetInner() && t1.GetOuter() &&
549 t2.GetInner() && t2.GetOuter()) {
550 if (t1.GetOuter()->GetX()<t2.GetInner()->GetX()) {
551 t1m=new AliExternalTrackParam(*t1.GetOuter());
552 t2m=new AliExternalTrackParam(*t2.GetInner());
555 t1m=new AliExternalTrackParam(*t1.GetInner());
556 t2m=new AliExternalTrackParam(*t2.GetOuter());
558 Double_t mx=.5*(t1m->GetX()+t2m->GetX());
565 if (t1m->Rotate(t2m->GetAlpha())
566 && t1m->PropagateTo(mx,b1)
567 && t2m->PropagateTo(mx,b2));
569 if (t2m->Rotate(t1m->GetAlpha())
570 && t1m->PropagateTo(mx,b1)
571 && t2m->PropagateTo(mx,b2));
584 double AliTPCTracklet::GetBz(Double_t *xyz) {
585 if (AliTracker::UniformField())
586 return AliTracker::GetBz();
588 return AliTracker::GetBz(xyz);
591 void AliTPCTracklet::RandomND(Int_t ndim,const Double_t *p,const Double_t *c,
593 // This function generates a n-dimensional random variable x with mean
594 // p and covariance c.
595 // That is done using the cholesky decomposition of the covariance matrix,
596 // Begin_Latex C=U^{t} U End_Latex, with Begin_Latex U End_Latex being an
597 // upper triangular matrix. Given a vector v of iid gausian random variables
598 // with variance 1 one obtains the asked result as: Begin_Latex x=U^t v
600 // c is expected to be in a lower triangular format:
605 static TRandom3 random;
606 Double_t *c2= new Double_t[ndim*ndim];
608 for (Int_t i=0;i<ndim;++i)
609 for (Int_t j=0;j<=i;++j)
610 c2[i*ndim+j]=c2[j*ndim+i]=c[k++];
611 TMatrixDSym cm(ndim,c2);
613 TDecompChol chol(cm);
615 const TVectorD pv(ndim);
616 const_cast<TVectorD*>(&pv)->Use(ndim,const_cast<Double_t*>(p));
619 for (Int_t i=0;i<ndim;++i)
621 TMatrixD L=chol.GetU();
626 TEllipse AliTPCTracklet::ErrorEllipse(Double_t x,Double_t y,
627 Double_t sx,Double_t sy,Double_t sxy) {
629 r_{1,2}=1/2 (a+c#pm#sqrt{(a-c)^{2}+(2b)^{2}})
631 Double_t det1=1./(sx*sy-sxy*sxy);
633 Double_t b=-sxy*det1;
636 Double_t s=TMath::Sqrt(d*d+4.*b*b);
637 Double_t r1=TMath::Sqrt(.5*(a+c-s));
638 Double_t r2=TMath::Sqrt(.5*(a+c+s));
639 Double_t alpha=.5*TMath::ATan2(2.*b,d);
640 return TEllipse(x,y,r1,r2,0.,360.,alpha*TMath::RadToDeg());
643 void AliTPCTracklet::Test(const char* filename) {
646 AliTPCTracklet::Test("");
647 TFile f("AliTPCTrackletDebug.root");
648 TTree *t=f.Get("AliTPCTrackletDebug");
650 TEllipse e=AliTPCTracklet::ErrorEllipse(0.,0.,4.,1.,1.8);
653 TTreeSRedirector ds(filename);
660 for (Int_t i=0;i<10000;++i) {
663 ds<<"AliTPCTrackletDebug"
676 Double_t param[5]={0.};
677 Double_t covar[15]={1.,
682 AliExternalTrackParam track(x,alpha,param,covar);
686 for (Int_t i=0;i<points.GetNPoints();++i) {
689 Double_t param[5]={0.};
690 Double_t covar[15]={1.,
695 AliExternalTrackParam track(x,alpha,param,covar);
696 for (x=90.;x<250.;x+=1.) {
697 track.PropagateTo(x,b);