Adding new classes for TPC alingment - Magnus Mager
[u/mrichter/AliRoot.git] / TPC / AliTPCTracklet.cxx
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69209e2c 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
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 **************************************************************************/
15
16////
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.
20////
21////
22////
23
69209e2c 24#include "AliTPCTracklet.h"
25#include "TObjArray.h"
9318a5b4 26#include "TLinearFitter.h"
69209e2c 27#include "AliTPCseed.h"
28#include "AliESDVertex.h"
9318a5b4 29#include "AliTracker.h"
30#include "TTreeStream.h"
31#include "TRandom3.h"
32#include "TDecompChol.h"
33
34#include <iostream>
35using namespace std;
69209e2c 36
37ClassImp(AliTPCTracklet)
38
9318a5b4 39const Double_t AliTPCTracklet::kB2C=0.299792458e-3;
40
69209e2c 41AliTPCTracklet::AliTPCTracklet()
9318a5b4 42 : fNClusters(0),fNStoredClusters(0),fClusters(0),fSector(-1),fOuter(0),
43 fInner(0),fPrimary(0) {
69209e2c 44 ////
45 // The default constructor. It is intended to be used for I/O only.
46 ////
47}
48
9318a5b4 49AliTPCTracklet::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) {
69209e2c 53 ////
54 // Contructor for a tracklet out of a track. Only clusters within a given
55 // sector are used.
56 ///
69209e2c 57
9318a5b4 58 //TODO: only kalman works
59
69209e2c 60 for (Int_t i=0;i<160;++i) {
9318a5b4 61 AliTPCclusterMI *c=track->GetClusterPointer(i);
62 if (c&&c->GetDetector()==sector)
63 ++fNClusters;
69209e2c 64 }
9318a5b4 65
66 if (storeClusters) {
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;
72 ++fNStoredClusters;
69209e2c 73 }
74 }
9318a5b4 75
76 switch (type) {
77 case kKalman:
78 FitKalman(track,sector);
79 break;
80 case kLinear:
81 case kQuadratic:
82 FitLinear(track,sector,type);
83 break;
84 case kRiemann:
85 FitRiemann(track,sector);
86 break;
69209e2c 87 }
69209e2c 88
9318a5b4 89}
69209e2c 90
9318a5b4 91AliTPCTracklet::AliTPCTracklet(const TObjArray &clusters,Int_t sector,
92 TrackType type,Bool_t storeClusters) {
93 //TODO: write it!
69209e2c 94}
95
96AliTPCTracklet::AliTPCTracklet(const AliTPCTracklet &t)
9318a5b4 97 : fNClusters(t.fNClusters),fNStoredClusters(t.fNStoredClusters),fClusters(0),
98 fSector(t.fSector),fOuter(0),fInner(0),
69209e2c 99 fPrimary(0) {
100 ////
101 // The copy constructor. You can copy tracklets!
102 ////
103
9318a5b4 104 if (t.fClusters) {
105 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
106 for (int i=0;i<t.fNStoredClusters;++i)
107 fClusters[i]=t.fClusters[i];
108 }
69209e2c 109 if (t.fOuter)
110 fOuter=new AliExternalTrackParam(*t.fOuter);
111 if (t.fInner)
112 fInner=new AliExternalTrackParam(*t.fInner);
113 if (t.fPrimary)
114 fPrimary=new AliExternalTrackParam(*t.fPrimary);
115}
116
117AliTPCTracklet& AliTPCTracklet::operator=(const AliTPCTracklet &t) {
118 ////
119 // The assignment constructor. You can assign tracklets!
120 ////
69209e2c 121 if (this!=&t) {
9318a5b4 122 fNClusters=t.fNClusters;
123 fNStoredClusters=fNStoredClusters;
124 delete fClusters;
125 if (t.fClusters) {
126 fClusters=new AliTPCclusterMI[t.fNStoredClusters];
127 for (int i=0;i<t.fNStoredClusters;++i)
128 fClusters[i]=t.fClusters[i];
129 }
130 else
131 fClusters=0;
132 fSector=t.fSector;
69209e2c 133 if (t.fOuter) {
134 if (fOuter)
135 *fOuter=*t.fOuter;
136 else
137 fOuter=new AliExternalTrackParam(*t.fOuter);
138 }
139 else {
140 delete fOuter;
141 fOuter=0;
142 }
143
144 if (t.fInner) {
145 if (fInner)
146 *fInner=*t.fInner;
147 else
148 fInner=new AliExternalTrackParam(*t.fInner);
149 }
150 else {
151 delete fInner;
152 fInner=0;
153 }
154
155 if (t.fPrimary) {
156 if (fPrimary)
157 *fPrimary=*t.fPrimary;
158 else
159 fPrimary=new AliExternalTrackParam(*t.fPrimary);
160 }
161 else {
162 delete fPrimary;
163 fPrimary=0;
164 }
165 }
166 return *this;
167}
168
169AliTPCTracklet::~AliTPCTracklet() {
170 //
171 // The destructor. Yes, you can even destruct tracklets.
172 //
9318a5b4 173 delete fClusters;
69209e2c 174 delete fOuter;
175 delete fInner;
176 delete fPrimary;
177}
178
9318a5b4 179void AliTPCTracklet::FitKalman(const AliTPCseed *track,Int_t sector) {
180 AliTPCseed *t=new AliTPCseed(*track);
181 if (!t->Rotate(TMath::DegToRad()*(sector%18*20.+10.)-t->GetAlpha())) {
182 delete t;
183 return;
184 }
185 // fit from inner to outer row
186 AliTPCseed *outerSeed=new AliTPCseed(*t);
187 Int_t n=0;
188 for (Int_t i=0;i<160;++i) {
189 AliTPCclusterMI *c=t->GetClusterPointer(i);
190 if (c&&c->GetDetector()==sector) {
191 if (n==1) {
192 outerSeed->ResetCovariance(100.);
193 }
194 ++n;
195 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
196 Double_t cov[3]={0.1,0.,0.1}; //TODO: correct error parametrisation
197 if (!outerSeed->PropagateTo(r[0]) ||
198 !static_cast<AliExternalTrackParam*>(outerSeed)->Update(&r[1],cov)) {
199 delete outerSeed;
200 outerSeed=0;
201 break;
202 }
203 }
204 }
205 if (outerSeed)
206 fOuter=new AliExternalTrackParam(*outerSeed);
207 delete outerSeed;
208 // fit from outer to inner rows
209 AliTPCseed *innerSeed=new AliTPCseed(*t);
210 n=0;
211 for (Int_t i=159;i>=0;--i) {
212 AliTPCclusterMI *c=t->GetClusterPointer(i);
213 if (c&&c->GetDetector()==sector) {
214 if (n==1) {
215 innerSeed->ResetCovariance(100.);
216 }
217 ++n;
218 Double_t r[3]={c->GetX(),c->GetY(),c->GetZ()};
219 Double_t cov[3]={0.1,0.,0.1};
220 if (!innerSeed->PropagateTo(r[0]) ||
221 !static_cast<AliExternalTrackParam*>(innerSeed)->Update(&r[1],cov)) {
222 delete innerSeed;
223 innerSeed=0;
224 break;
225 }
226 }
227 }
228 if (innerSeed)
229 fInner=new AliExternalTrackParam(*innerSeed);
230 // propagate to the primary vertex
231 if (innerSeed) {
232 AliTPCseed *primarySeed=new AliTPCseed(*innerSeed);
233 Double_t pos[]={0.,0.,0.};
234 Double_t sigma[]={.1,.1,.1}; //TODO: is this correct?
235 AliESDVertex vertex(pos,sigma);
236 if (primarySeed->PropagateToVertex(&vertex))
237 fPrimary=new AliExternalTrackParam(*primarySeed);
238 delete primarySeed;
239 // for better comparison one does not want to have alpha changed...
240 if (!fPrimary->Rotate(fInner->GetAlpha())) {
241 delete fPrimary;
242 fPrimary=0;
243 }
244 }
245 delete innerSeed;
246
247 delete t;
248}
249
250void AliTPCTracklet::FitLinear(const AliTPCseed *track,Int_t sector,
251 TrackType type) {
252 TLinearFitter fy(1);
253 TLinearFitter fz(1);
254 fy.StoreData(kFALSE);
255 fz.StoreData(kFALSE);
256 switch (type) {
257 case kLinear:
258 fy.SetFormula("1 ++ x");
259 fz.SetFormula("1 ++ x");
260 break;
261 case kQuadratic:
262 fy.SetFormula("1 ++ x ++ x*x");
263 fz.SetFormula("1 ++ x");
264 break;
265 }
266 Double_t xmax=-1.;
267 Double_t xmin=1000.;
268 for (Int_t i=0;i<160;++i) {
269 AliTPCclusterMI *c=track->GetClusterPointer(i);
270 if (c&&c->GetDetector()==sector) {
271 Double_t x=c->GetX();
272 fy.AddPoint(&x,c->GetY());
273 fz.AddPoint(&x,c->GetZ());
274 xmax=TMath::Max(xmax,x);
275 xmin=TMath::Min(xmin,x);
276 }
277 }
278 fy.Eval();
279 fz.Eval();
280 Double_t a[3]={fy.GetParameter(0),
281 fy.GetParameter(1),
282 type==kQuadratic?fy.GetParameter(2):0.};
283 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
284 fy.GetCovarianceMatrixElement(1,0),
285 fy.GetCovarianceMatrixElement(1,1),
286 type==kQuadratic?fy.GetCovarianceMatrixElement(2,0):0.,
287 type==kQuadratic?fy.GetCovarianceMatrixElement(2,1):0.,
288 type==kQuadratic?fy.GetCovarianceMatrixElement(2,2):0.};
289 for (int i=0;i<6;++i) ca[i]*=fy.GetChisquare()/fNClusters;
290 Double_t b[2]={fz.GetParameter(0),
291 fz.GetParameter(1)};
292 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
293 fz.GetCovarianceMatrixElement(1,0),
294 fz.GetCovarianceMatrixElement(1,1)};
295 for (int i=0;i<3;++i) cb[i]*=fz.GetChisquare()/fNClusters;
296 Double_t p[5];
297 Double_t c[15];
298 Double_t alpha=track->GetAlpha();
299 Quadratic2Helix(a,ca,b,cb,0.,p,c);
300 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
301 Quadratic2Helix(a,ca,b,cb,xmin,p,c);
302 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
303 Quadratic2Helix(a,ca,b,cb,xmax,p,c);
304 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
305}
306
307void AliTPCTracklet::Quadratic2Helix(Double_t *a,Double_t *ca,
308 Double_t *b,Double_t *cb,
309 Double_t x0,
310 Double_t *p,Double_t *c) {
311 // y(x)=a[0]+a[1]*x+a[2]*x^2
312 // z(x)=b[0]+b[1]*x
313 // parametrises the corosponding helix at x0
314
315 // get the polynoms at x0
316 Double_t a0=x0*x0*a[2] + x0*a[1] + a[0];
317 Double_t a1=2.*x0*a[2] + a[1];
318 Double_t a2= a[2];
319 Double_t ca00=ca[0]+x0*(2.*ca[1]+x0*(ca[2]+2.*ca[3]+x0*(2.*ca[4]+x0*ca[5])));
320 Double_t ca10=ca[1]+x0*(ca[2]+2.*ca[3]+x0*(3.*ca[4]+x0*2.*ca[5]));
321 Double_t ca11=ca[2]+x0*4.*(ca[4]+x0*ca[5]);
322 Double_t ca20=ca[3]+x0*(ca[4]+x0*ca[5]);
323 Double_t ca21=ca[3]+x0*2.*ca[5];
324 Double_t ca22=ca[5];
325
326 Double_t b0=x0*b[1] + b[0];
327 Double_t b1= b[1];
328 Double_t cb00=cb[0]+x0*(2.*cb[1]+x0*cb[2]);
329 Double_t cb10=cb[1]+x0*cb[2];
330 Double_t cb11=cb[2];
331
332 // transform to helix parameters
333 Double_t f =1.+a1*a1;
334 Double_t f2 =f*f;
335 Double_t fi =1./f;
336 Double_t fi12=TMath::Sqrt(fi);
337 Double_t fi32=fi*fi12;
338 Double_t fi2 =fi*fi;
339 Double_t fi52=fi2*fi12;
340 Double_t fi3 =fi2*fi;
341 Double_t fi5 =fi2*fi3;
342
343 Double_t xyz[3]={0.}; // TODO...
344 Double_t fc=1./(GetBz(xyz)*kB2C);
345
346 p[0]=a0; // y0
347 p[1]=b0; // z0
348 p[2]=a1*fi12; // snp
349 p[3]=b1; // tgl
350 p[4]=2.*a2*fi32*fc; // 1/pt
351
352 c[0] =ca00; // y0-y0
353 c[1] =0.; // z0-y0
354 c[2] =cb00; // z0-z0
355 c[3] =ca10*fi32; // snp-y0
356 c[4] =0.; // snp-z0
357 c[5] =ca11*fi3; // snp-snp
358 c[6] =0.; // tgl-y0
359 c[7] =cb10; // tgl-z0
360 c[8] =0.; // tgl-snp
361 c[9] =cb11; // tgl-tgl
362 c[10]=2.*(-3.*a1*a2*ca10+f*ca20)*fi3*fc; // 1/pt-y0
363 c[11]=0.; // 1/pt-z0
364 c[12]=2.*(-3.*a1*a2*ca11+f*ca21)*fi52*fc; // 1/pt-snp
365 c[13]=0.; // 1/pt-tgl
366 c[14]=(-12.*a1*a2*(-3.*a1*a2*ca11+2.*f*ca21)+4.*f2*ca22)*fi5
367 *fc*fc; // 1/pt-1/pt
368}
369
370
371void AliTPCTracklet::FitRiemann(const AliTPCseed *track,Int_t sector) {
372 TLinearFitter fy(2);
373 fy.StoreData(kFALSE);
374 fy.SetFormula("hyp2");
375 Double_t xmax=-1.;
376 Double_t xmin=1000.;
377 for (Int_t i=0;i<160;++i) {
378 AliTPCclusterMI *c=track->GetClusterPointer(i);
379 if (c&&c->GetDetector()==sector) {
380 Double_t x=c->GetX();
381 Double_t y=c->GetY();
382 Double_t xy[2]={x,y};
383 Double_t r=x*x+y*y;
384 Double_t errx=1.,erry=1.;//TODO!
385 Double_t err=TMath::Sqrt(4.*x*x*errx+4.*y*y*erry);
386 err=1.;
387 fy.AddPoint(xy,r,err);
388 xmax=TMath::Max(xmax,x);
389 xmin=TMath::Min(xmin,x);
390 }
391 }
392 fy.Eval();
393 Double_t a[3]={fy.GetParameter(0),
394 fy.GetParameter(1),
395 fy.GetParameter(2)};
396 Double_t ca[6]={fy.GetCovarianceMatrixElement(0,0),
397 fy.GetCovarianceMatrixElement(1,0),
398 fy.GetCovarianceMatrixElement(1,1),
399 fy.GetCovarianceMatrixElement(2,0),
400 fy.GetCovarianceMatrixElement(2,1),
401 fy.GetCovarianceMatrixElement(2,2)};
402
403 TLinearFitter fz(1);
404 fz.StoreData(kFALSE);
405 fz.SetFormula("hyp1");
406 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
407 Double_t oldx=0.;
408 Double_t oldy=R;
409 Double_t phi=0.;
410 for (Int_t i=0;i<160;++i) {
411 AliTPCclusterMI *c=track->GetClusterPointer(i);
412 if (c&&c->GetDetector()==sector) {
413 Double_t x=c->GetX();
414 Double_t y=c->GetY();
415 Double_t dx=x-oldx;
416 Double_t dy=y-oldy;
417 phi+=2.*TMath::Abs(TMath::ATan2(.5*TMath::Sqrt(dx*dx+dy*dy),R));
418 Double_t err=1.;
419 fz.AddPoint(&phi,c->GetZ(),err);
420 oldx=x;
421 oldy=y;
422 }
423 }
424 fz.Eval();
425 Double_t b[2]={fz.GetParameter(0),
426 fz.GetParameter(1)};
427 Double_t cb[3]={fz.GetCovarianceMatrixElement(0,0),
428 fz.GetCovarianceMatrixElement(1,0),
429 fz.GetCovarianceMatrixElement(1,1)};
430
431 Double_t p[5];
432 Double_t c[15];
433 Double_t alpha=track->GetAlpha();
434 if (Riemann2Helix(a,ca,b,cb,0.,p,c))
435 fPrimary=new AliExternalTrackParam(0.,alpha,p,c);
436 if (Riemann2Helix(a,ca,b,cb,xmin,p,c))
437 fInner=new AliExternalTrackParam(xmin,alpha,p,c);
438 if (Riemann2Helix(a,ca,b,cb,xmax,p,c))
439 fOuter=new AliExternalTrackParam(xmax,alpha,p,c);
440}
441
442Bool_t AliTPCTracklet::Riemann2Helix(Double_t *a,Double_t *ca,
443 Double_t *b,Double_t *cb,
444 Double_t x0,
445 Double_t *p,Double_t *c) {
446 //TODO: signs!
447
448 Double_t xr0=.5*a[1];
449 Double_t yr0=.5*a[2];
450 Double_t R=.5*TMath::Sqrt(4.*a[0]+a[1]*a[1]+a[2]*a[2]);
451 Double_t dx=x0-xr0;
452 if (dx*dx>=R*R) return kFALSE;
453 Double_t dy=TMath::Sqrt(R*R-dx*dx); //sign!!
454 if (TMath::Abs(yr0+dy)>TMath::Abs(yr0-dy))
455 dy=-dy;
456 Double_t y0=yr0+dy;
457 Double_t tgp=-dx/dy; //TODO: dy!=0
458 Double_t z0=b[0]+TMath::ATan(tgp)*b[1];
459 Double_t xyz[3]={x0,y0,z0};
460 Double_t fc=1./(GetBz(xyz)*kB2C);
461 fc=1;
462 p[0]=y0; // y0
463 p[1]=z0; // z0
464 p[2]=tgp/TMath::Sqrt(1.+tgp*tgp); // snp
465 p[3]=b[1]; // tgl
466 p[4]=1./R*fc; // 1/pt
467
468 c[0] =0.; // y0-y0
469 c[1] =0.; // z0-y0
470 c[2] =0.; // z0-z0
471 c[3] =0.; // snp-y0
472 c[4] =0.; // snp-z0
473 c[5] =0.; // snp-snp
474 c[6] =0.; // tgl-y0
475 c[7] =0.; // tgl-z0
476 c[8] =0.; // tgl-snp
477 c[9] =0.; // tgl-tgl
478 c[10]=0.; // 1/pt-y0
479 c[11]=0.; // 1/pt-z0
480 c[12]=0.; // 1/pt-snp
481 c[13]=0.; // 1/pt-tgl
482 c[14]=0.; // 1/pt-1/pt
483
484 return kTRUE;
485}
486
487TObjArray AliTPCTracklet::CreateTracklets(const AliTPCseed *track,
488 TrackType type,
489 Bool_t storeClusters,
69209e2c 490 Int_t minClusters,
491 Int_t maxTracklets) {
492// The tracklet factory: It creates several tracklets out of a track. They
493// are created for sectors that fullfill the constraint of having enough
494// clusters inside. Futhermore you can specify the maximum amount of
495// tracklets that are to be created.
496// The tracklets appear in a sorted fashion, beginning with those having the
497// most clusters.
498
499 Int_t sectors[72]={0};
500 for (Int_t i=0;i<160;++i) {
9318a5b4 501 AliTPCclusterMI *c=track->GetClusterPointer(i);
69209e2c 502 if (c)
503 ++sectors[c->GetDetector()];
504 }
505 Int_t indices[72];
506 TMath::Sort(72,sectors,indices);
507 TObjArray tracklets;
508 if (maxTracklets>72) maxTracklets=72; // just to protect against "users".
509 for (Int_t i=0;i<maxTracklets&&sectors[indices[i]]>=minClusters;++i) {
9318a5b4 510 tracklets.Add(new AliTPCTracklet(track,indices[i],type,storeClusters));
69209e2c 511 }
512 return tracklets;
513}
9318a5b4 514
515TObjArray AliTPCTracklet::CreateTracklets(const TObjArray &clusters,
516 TrackType type,
517 Bool_t storeClusters,
518 Int_t minClusters,
519 Int_t maxTracklets) {
520
521}
522
523Bool_t AliTPCTracklet::PropagateToMeanX(const AliTPCTracklet &t1,
524 const AliTPCTracklet &t2,
525 AliExternalTrackParam *&t1m,
526 AliExternalTrackParam *&t2m) {
527 // This function propagates two Tracklets to a common x-coordinate. This
528 // x is dermined as the one that is in the middle of the two tracklets (they
529 // are assumed to live on two distinct x-intervalls).
530 // The inner parametrisation of the outer Tracklet and the outer
531 // parametrisation of the inner Tracklet are used and propagated to this
532 // common x. This result is saved not inside the Tracklets but two new
533 // ExternalTrackParams are created (that means you might want to delete
534 // them).
535 // In the case that the alpha angles of the Tracklets differ both angles
536 // are tried out for this propagation.
537 // In case of any failure kFALSE is returned, no AliExternalTrackParam
538 // is created und the pointers are set to 0.
539
540 if (t1.GetInner() && t1.GetOuter() &&
541 t2.GetInner() && t2.GetOuter()) {
542 if (t1.GetOuter()->GetX()<t2.GetInner()->GetX()) {
543 t1m=new AliExternalTrackParam(*t1.GetOuter());
544 t2m=new AliExternalTrackParam(*t2.GetInner());
545 }
546 else {
547 t1m=new AliExternalTrackParam(*t1.GetInner());
548 t2m=new AliExternalTrackParam(*t2.GetOuter());
549 }
550 Double_t mx=.5*(t1m->GetX()+t2m->GetX());
551 Double_t b1,b2;
552 Double_t xyz[3];
553 t1m->GetXYZ(xyz);
554 b1=GetBz(xyz);
555 t2m->GetXYZ(xyz);
556 b2=GetBz(xyz);
557 if (t1m->Rotate(t2m->GetAlpha())
558 && t1m->PropagateTo(mx,b1)
559 && t2m->PropagateTo(mx,b2));
560 else
561 if (t2m->Rotate(t1m->GetAlpha())
562 && t1m->PropagateTo(mx,b1)
563 && t2m->PropagateTo(mx,b2));
564 else {
565 delete t1m;
566 delete t2m;
567 t1m=t2m=0;
568 }
569 }
570 else {
571 t1m=t2m=0;
572 }
573 return t1m&&t2m;
574}
575
576double AliTPCTracklet::GetBz(Double_t *xyz) {
577 if (AliTracker::UniformField())
578 return AliTracker::GetBz();
579 else
580 return AliTracker::GetBz(xyz);
581}
582
583void AliTPCTracklet::RandomND(Int_t ndim,const Double_t *p,const Double_t *c,
584 Double_t *x) {
585 // This function generates a n-dimensional random variable x with mean
586 // p and covariance c.
587 // That is done using the cholesky decomposition of the covariance matrix,
588 // Begin_Latex C=U^{t} U End_Latex, with Begin_Latex U End_Latex being an
589 // upper triangular matrix. Given a vector v of iid gausian random variables
590 // with variance 1 one obtains the asked result as: Begin_Latex x=U^t v
591 // End_Latex.
592 // c is expected to be in a lower triangular format:
593 // c[0]
594 // c[1] c[2]
595 // c[3] c[4] c[5]
596 // etc.
597 static TRandom3 random;
598 Double_t *c2= new Double_t[ndim*ndim];
599 Int_t k=0;
600 for (Int_t i=0;i<ndim;++i)
601 for (Int_t j=0;j<=i;++j)
602 c2[i*ndim+j]=c2[j*ndim+i]=c[k++];
603 TMatrixDSym cm(ndim,c2);
604 delete[] c2;
605 TDecompChol chol(cm);
606 chol.Decompose();
607 const TVectorD pv(ndim);
608 const_cast<TVectorD*>(&pv)->Use(ndim,const_cast<Double_t*>(p));
609 TVectorD xv(ndim);
610 xv.Use(ndim,x);
611 for (Int_t i=0;i<ndim;++i)
612 xv[i]=random.Gaus();
613 TMatrixD L=chol.GetU();
614 L.T();
615 xv=L*xv+pv;
616}
617
618TEllipse AliTPCTracklet::ErrorEllipse(Double_t x,Double_t y,
619 Double_t sx,Double_t sy,Double_t sxy) {
620 /* Begin_Latex
621 r_{1,2}=1/2 (a+c#pm#sqrt{(a-c)^{2}+(2b)^{2}})
622 End_Latex */
623 Double_t det1=1./(sx*sy-sxy*sxy);
624 Double_t a=sy*det1;
625 Double_t b=-sxy*det1;
626 Double_t c=sx*det1;
627 Double_t d=c-a;
628 Double_t s=TMath::Sqrt(d*d+4.*b*b);
629 Double_t r1=TMath::Sqrt(.5*(a+c-s));
630 Double_t r2=TMath::Sqrt(.5*(a+c+s));
631 Double_t alpha=.5*TMath::ATan2(2.*b,d);
632 return TEllipse(x,y,r1,r2,0.,360.,alpha*TMath::RadToDeg());
633}
634
635void AliTPCTracklet::Test(const char* filename) {
636 /*
637 aliroot
638 AliTPCTracklet::Test("");
639 TFile f("AliTPCTrackletDebug.root");
640 TTree *t=f.Get("AliTPCTrackletDebug");
641 t->Draw("p0:p4");
642 TEllipse e=AliTPCTracklet::ErrorEllipse(0.,0.,4.,1.,1.8);
643 e.Draw();
644 */
645 TTreeSRedirector ds("AliTPCTrackletDebug.root");
646 Double_t p[5]={0.};
647 Double_t c[15]={4.,
648 0.,4.,
649 0.,0.,9.,
650 0.,0.,0.,16.,
651 1.8,0.,0.,0.,1.};
652 for (Int_t i=0;i<10000;++i) {
653 Double_t x[5];
654 RandomND(5,p,c,x);
655 ds<<"AliTPCTrackletDebug"
656 <<"p0="<<x[0]
657 <<"p1="<<x[1]
658 <<"p2="<<x[2]
659 <<"p3="<<x[3]
660 <<"p4="<<x[4]
661 <<"\n";
662 }
663
664 /*
665 Double_t b;
666 Double_t x=0.;
667 Double_t alpha=0.;
668 Double_t param[5]={0.};
669 Double_t covar[15]={1.,
670 0.,1.,
671 0.,0.,1.,
672 0.,0.,0.,1.,
673 0.,0.,0.,0.,1.};
674 AliExternalTrackParam track(x,alpha,param,covar);
675
676
677
678 for (Int_t i=0;i<points.GetNPoints();++i) {
679 Double_t x=0.;
680 Double_t alpha=0.;
681 Double_t param[5]={0.};
682 Double_t covar[15]={1.,
683 0.,1.,
684 0.,0.,1.,
685 0.,0.,0.,1.,
686 0.,0.,0.,0.,1.};
687 AliExternalTrackParam track(x,alpha,param,covar);
688 for (x=90.;x<250.;x+=1.) {
689 track.PropagateTo(x,b);
690 AliTPCclusterMI c();
691 }
692 }
693 */
694}