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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// Implementation of the ITS track class
18//
19// Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch
20// dEdx analysis by: Boris Batyunya, JINR, Boris.Batiounia@cern.ch
21///////////////////////////////////////////////////////////////////////////
22#include <TMath.h>
23
24#include "AliCluster.h"
25#include "AliESDtrack.h"
26#include "AliITStrackV2.h"
27#include "AliStrLine.h"
28
29ClassImp(AliITStrackV2)
30
31const Int_t kWARN=5;
32
33//____________________________________________________________________________
34AliITStrackV2::AliITStrackV2():AliKalmanTrack(),
35 fX(0),
36 fAlpha(0),
37 fdEdx(0),
38 fP0(0),
39 fP1(0),
40 fP2(0),
41 fP3(0),
42 fP4(0),
43 fC00(0),
44 fC10(0),
45 fC11(0),
46 fC20(0),
47 fC21(0),
48 fC22(0),
49 fC30(0),
50 fC31(0),
51 fC32(0),
52 fC33(0),
53 fC40(0),
54 fC41(0),
55 fC42(0),
56 fC43(0),
57 fC44(0),
58 fESDtrack(0)
59{
60 for(Int_t i=0; i<kMaxLayer; i++) fIndex[i]=0;
61 for(Int_t i=0; i<4; i++) fdEdxSample[i]=0;
62}
63
64
65//____________________________________________________________________________
66AliITStrackV2::AliITStrackV2(AliESDtrack& t,Bool_t c) throw (const Char_t *) :
67AliKalmanTrack() {
68 //------------------------------------------------------------------
69 // Conversion ESD track -> ITS track.
70 // If c==kTRUE, create the ITS track out of the constrained params.
71 //------------------------------------------------------------------
72 SetNumberOfClusters(t.GetITSclusters(fIndex));
73 SetLabel(t.GetLabel());
74 SetMass(t.GetMass());
75 //
76 //
77
78 fdEdx=t.GetITSsignal();
79 fAlpha = t.GetAlpha();
80 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
81 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
82
83 //Conversion of the track parameters
84 Double_t x,p[5];
85 if (c) t.GetConstrainedExternalParameters(fAlpha,x,p);
86 else t.GetExternalParameters(x,p);
87 fX=x;
88 fP0=p[0];
89 fP1=p[1]; SaveLocalConvConst();
90 fP2=p[2];
91 fP3=p[3]; x=GetLocalConvConst();
92 fP4=p[4]/x;
93
94 //Conversion of the covariance matrix
95 Double_t cv[15];
96 if (c) t.GetConstrainedExternalCovariance(cv);
97 else t.GetExternalCovariance(cv);
98 fC00=cv[0 ];
99 fC10=cv[1 ]; fC11=cv[2 ];
100 fC20=cv[3 ]; fC21=cv[4 ]; fC22=cv[5 ];
101 fC30=cv[6 ]; fC31=cv[7 ]; fC32=cv[8 ]; fC33=cv[9 ];
102 fC40=cv[10]/x; fC41=cv[11]/x; fC42=cv[12]/x; fC43=cv[13]/x; fC44=cv[14]/x/x;
103
104 if (t.GetStatus()&AliESDtrack::kTIME) {
105 StartTimeIntegral();
106 Double_t times[10]; t.GetIntegratedTimes(times); SetIntegratedTimes(times);
107 SetIntegratedLength(t.GetIntegratedLength());
108 }
109 fESDtrack=&t;
110
111 // if (!Invariant()) throw "AliITStrackV2: conversion failed !\n";
112 for(Int_t i=0; i<4; i++) fdEdxSample[i]=0;
113}
114
115void AliITStrackV2::UpdateESDtrack(ULong_t flags) const {
116 fESDtrack->UpdateTrackParams(this,flags);
117}
118
119//____________________________________________________________________________
120AliITStrackV2::AliITStrackV2(const AliITStrackV2& t) : AliKalmanTrack(t) {
121 //------------------------------------------------------------------
122 //Copy constructor
123 //------------------------------------------------------------------
124 fX=t.fX;
125 fAlpha=t.fAlpha;
126 fdEdx=t.fdEdx;
127
128 fP0=t.fP0; fP1=t.fP1; fP2=t.fP2; fP3=t.fP3; fP4=t.fP4;
129
130 fC00=t.fC00;
131 fC10=t.fC10; fC11=t.fC11;
132 fC20=t.fC20; fC21=t.fC21; fC22=t.fC22;
133 fC30=t.fC30; fC31=t.fC31; fC32=t.fC32; fC33=t.fC33;
134 fC40=t.fC40; fC41=t.fC41; fC42=t.fC42; fC43=t.fC43; fC44=t.fC44;
135
136 Int_t n=GetNumberOfClusters();
137 for (Int_t i=0; i<n; i++) {
138 fIndex[i]=t.fIndex[i];
139 if (i<4) fdEdxSample[i]=t.fdEdxSample[i];
140 }
141 fESDtrack=t.fESDtrack;
142}
143
144//_____________________________________________________________________________
145Int_t AliITStrackV2::Compare(const TObject *o) const {
146 //-----------------------------------------------------------------
147 // This function compares tracks according to the their curvature
148 //-----------------------------------------------------------------
149 AliITStrackV2 *t=(AliITStrackV2*)o;
150 //Double_t co=TMath::Abs(t->Get1Pt());
151 //Double_t c =TMath::Abs(Get1Pt());
152 Double_t co=t->GetSigmaY2()*t->GetSigmaZ2();
153 Double_t c =GetSigmaY2()*GetSigmaZ2();
154 if (c>co) return 1;
155 else if (c<co) return -1;
156 return 0;
157}
158
159//_____________________________________________________________________________
160void AliITStrackV2::GetExternalCovariance(Double_t cc[15]) const {
161 //-------------------------------------------------------------------------
162 // This function returns an external representation of the covriance matrix.
163 // (See comments in AliTPCtrack.h about external track representation)
164 //-------------------------------------------------------------------------
165 Double_t a=GetLocalConvConst();
166
167 cc[0 ]=fC00;
168 cc[1 ]=fC10; cc[2 ]=fC11;
169 cc[3 ]=fC20; cc[4 ]=fC21; cc[5 ]=fC22;
170 cc[6 ]=fC30; cc[7 ]=fC31; cc[8 ]=fC32; cc[9 ]=fC33;
171 cc[10]=fC40*a; cc[11]=fC41*a; cc[12]=fC42*a; cc[13]=fC43*a; cc[14]=fC44*a*a;
172}
173
174//____________________________________________________________________________
175Int_t AliITStrackV2::PropagateToVertex(Double_t d,Double_t x0) {
176 //------------------------------------------------------------------
177 //This function propagates a track to the minimal distance from the origin
178 //------------------------------------------------------------------
179 //Double_t xv=fP2*(fX*fP2 - fP0*TMath::Sqrt(1.- fP2*fP2)); //linear approxim.
180 Double_t tgf=-(fP4*fX - fP2)/(fP4*fP0 + TMath::Sqrt(1 - fP2*fP2));
181 Double_t snf=tgf/TMath::Sqrt(1.+ tgf*tgf);
182 Double_t xv=(snf - fP2)/fP4 + fX;
183 return PropagateTo(xv,d,x0);
184}
185
186//____________________________________________________________________________
187Int_t AliITStrackV2::
188GetGlobalXYZat(Double_t xk, Double_t &x, Double_t &y, Double_t &z) const {
189 //------------------------------------------------------------------
190 //This function returns a track position in the global system
191 //------------------------------------------------------------------
192 Double_t dx=xk-fX;
193 Double_t f1=fP2, f2=f1 + fP4*dx;
194 if (TMath::Abs(f2) >= 0.9999) {
195 Int_t n=GetNumberOfClusters();
196 if (n>kWARN)
197 Warning("GetGlobalXYZat","Propagation failed (%d) !\n",n);
198 return 0;
199 }
200
201 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
202
203 Double_t yk = fP0 + dx*(f1+f2)/(r1+r2);
204 Double_t zk = fP1 + dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
205
206 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
207 x = xk*cs - yk*sn;
208 y = xk*sn + yk*cs;
209 z = zk;
210
211 return 1;
212}
213
214//_____________________________________________________________________________
215void AliITStrackV2::ApproximateHelixWithLine(Double_t xk, AliStrLine *line)
216{
217 //------------------------------------------------------------
218 // Approximate the track (helix) with a straight line tangent to the
219 // helix in the point defined by r (F. Prino, prino@to.infn.it)
220 //------------------------------------------------------------
221 Double_t mom[3];
222 Double_t azim = TMath::ASin(fP2)+fAlpha;
223 Double_t theta = TMath::Pi()/2. - TMath::ATan(fP3);
224 mom[0] = TMath::Sin(theta)*TMath::Cos(azim);
225 mom[1] = TMath::Sin(theta)*TMath::Sin(azim);
226 mom[2] = TMath::Cos(theta);
227 Double_t pos[3];
228 GetGlobalXYZat(xk,pos[0],pos[1],pos[2]);
229 line->SetP0(pos);
230 line->SetCd(mom);
231}
232//_____________________________________________________________________________
233Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c) const
234{
235 //-----------------------------------------------------------------
236 // This function calculates a predicted chi2 increment.
237 //-----------------------------------------------------------------
238 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
239 r00+=fC00; r01+=fC10; r11+=fC11;
240 //
241 Double_t det=r00*r11 - r01*r01;
242 if (TMath::Abs(det) < 1.e-30) {
243 Int_t n=GetNumberOfClusters();
244 if (n>kWARN)
245 Warning("GetPredictedChi2","Singular matrix (%d) !\n",n);
246 return 1e10;
247 }
248 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
249
250 Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1;
251
252 return (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
253}
254
255//____________________________________________________________________________
256Int_t AliITStrackV2::CorrectForMaterial(Double_t d, Double_t x0) {
257 //------------------------------------------------------------------
258 //This function corrects the track parameters for crossed material
259 //------------------------------------------------------------------
260 Double_t p2=(1.+ fP3*fP3)/(Get1Pt()*Get1Pt());
261 Double_t beta2=p2/(p2 + GetMass()*GetMass());
262 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
263
264 //Multiple scattering******************
265 if (d!=0) {
266 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
267 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
268 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
269 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
270 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
271 fC44 += theta2*fP3*fP4*fP3*fP4;
272 }
273
274 //Energy losses************************
275 if (x0!=0.) {
276 d*=x0;
277 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
278 if (beta2/(1-beta2)>3.5*3.5)
279 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
280
281 fP4*=(1.- TMath::Sqrt(p2+GetMass()*GetMass())/p2*dE);
282 }
283
284 if (!Invariant()) return 0;
285
286 return 1;
287}
288
289//____________________________________________________________________________
290Int_t AliITStrackV2::PropagateTo(Double_t xk, Double_t d, Double_t x0) {
291 //------------------------------------------------------------------
292 //This function propagates a track
293 //------------------------------------------------------------------
294 Double_t x1=fX, x2=xk, dx=x2-x1;
295 Double_t f1=fP2, f2=f1 + fP4*dx;
296 if (TMath::Abs(f2) >= 0.98) {
297 // MI change - don't propagate highly inclined tracks
298 // covariance matrix distorted
299 //Int_t n=GetNumberOfClusters();
300 //if (n>kWARN)
301 // Warning("PropagateTo","Propagation failed !\n",n);
302 return 0;
303 }
304 Double_t lcc=GetLocalConvConst();
305
306 // old position [SR, GSI, 17.02.2003]
307 Double_t oldX = fX, oldY = fP0, oldZ = fP1;
308
309 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
310
311 fP0 += dx*(f1+f2)/(r1+r2);
312 fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
313 fP2 += dx*fP4;
314
315 //f = F - 1
316
317 Double_t f02= dx/(r1*r1*r1);
318 Double_t f04=0.5*dx*dx/(r1*r1*r1);
319 Double_t f12= dx*fP3*f1/(r1*r1*r1);
320 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1);
321 Double_t f13= dx/r1;
322 Double_t f24= dx;
323
324 //b = C*ft
325 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
326 Double_t b02=f24*fC40;
327 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
328 Double_t b12=f24*fC41;
329 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
330 Double_t b22=f24*fC42;
331 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
332 Double_t b42=f24*fC44;
333 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
334 Double_t b32=f24*fC43;
335
336 //a = f*b = f*C*ft
337 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
338 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
339 Double_t a22=f24*b42;
340
341 //F*C*Ft = C + (b + bt + a)
342 fC00 += b00 + b00 + a00;
343 fC10 += b10 + b01 + a01;
344 fC20 += b20 + b02 + a02;
345 fC30 += b30;
346 fC40 += b40;
347 fC11 += b11 + b11 + a11;
348 fC21 += b21 + b12 + a12;
349 fC31 += b31;
350 fC41 += b41;
351 fC22 += b22 + b22 + a22;
352 fC32 += b32;
353 fC42 += b42;
354
355 fX=x2;
356
357 //Change of the magnetic field *************
358 SaveLocalConvConst();
359 fP4*=lcc/GetLocalConvConst();
360
361 if (!CorrectForMaterial(d,x0)) return 0;
362
363 // Integrated Time [SR, GSI, 17.02.2003]
364 if (IsStartedTimeIntegral() && fX>oldX) {
365 Double_t l2 = (fX-oldX)*(fX-oldX)+(fP0-oldY)*(fP0-oldY)+
366 (fP1-oldZ)*(fP1-oldZ);
367 AddTimeStep(TMath::Sqrt(l2));
368 }
369 //
370
371 return 1;
372}
373
374//____________________________________________________________________________
375Int_t AliITStrackV2::Update(const AliCluster* c, Double_t chi2, UInt_t index) {
376 //------------------------------------------------------------------
377 //This function updates track parameters
378 //------------------------------------------------------------------
379 Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4;
380 Double_t c00=fC00;
381 Double_t c10=fC10, c11=fC11;
382 Double_t c20=fC20, c21=fC21, c22=fC22;
383 Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33;
384 Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44;
385
386
387 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
388 r00+=fC00; r01+=fC10; r11+=fC11;
389 Double_t det=r00*r11 - r01*r01;
390 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
391
392
393 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
394 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
395 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
396 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
397 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
398
399 Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1;
400 Double_t sf=fP2 + k20*dy + k21*dz;
401
402 fP0 += k00*dy + k01*dz;
403 fP1 += k10*dy + k11*dz;
404 fP2 = sf;
405 fP3 += k30*dy + k31*dz;
406 fP4 += k40*dy + k41*dz;
407
408 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
409 Double_t c12=fC21, c13=fC31, c14=fC41;
410
411 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
412 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
413 fC40-=k00*c04+k01*c14;
414
415 fC11-=k10*c01+k11*fC11;
416 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
417 fC41-=k10*c04+k11*c14;
418
419 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
420 fC42-=k20*c04+k21*c14;
421
422 fC33-=k30*c03+k31*c13;
423 fC43-=k30*c04+k31*c14;
424
425 fC44-=k40*c04+k41*c14;
426
427 if (!Invariant()) {
428 fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4;
429 fC00=c00;
430 fC10=c10; fC11=c11;
431 fC20=c20; fC21=c21; fC22=c22;
432 fC30=c30; fC31=c31; fC32=c32; fC33=c33;
433 fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44;
434 return 0;
435 }
436
437 if (chi2<0) return 1;
438
439 Int_t n=GetNumberOfClusters();
440 fIndex[n]=index;
441 SetNumberOfClusters(n+1);
442 SetChi2(GetChi2()+chi2);
443
444 return 1;
445}
446
447Int_t AliITStrackV2::Invariant() const {
448 //------------------------------------------------------------------
449 // This function is for debugging purpose only
450 //------------------------------------------------------------------
451 Int_t n=GetNumberOfClusters();
452
453 if (TMath::Abs(fP2)>=0.9999){
454 if (n>kWARN) Warning("Invariant","fP2=%f\n",fP2);
455 return 0;
456 }
457 if (fC00<=0 || fC00>9.) {
458 if (n>kWARN) Warning("Invariant","fC00=%f\n",fC00);
459 return 0;
460 }
461 if (fC11<=0 || fC11>9.) {
462 if (n>kWARN) Warning("Invariant","fC11=%f\n",fC11);
463 return 0;
464 }
465 if (fC22<=0 || fC22>1.) {
466 if (n>kWARN) Warning("Invariant","fC22=%f\n",fC22);
467 return 0;
468 }
469 if (fC33<=0 || fC33>1.) {
470 if (n>kWARN) Warning("Invariant","fC33=%f\n",fC33);
471 return 0;
472 }
473 if (fC44<=0 || fC44>6e-5) {
474 if (n>kWARN) Warning("Invariant","fC44=%f\n",fC44);
475 return 0;
476 }
477 return 1;
478}
479
480//____________________________________________________________________________
481Int_t AliITStrackV2::Propagate(Double_t alp,Double_t xk) {
482 //------------------------------------------------------------------
483 //This function propagates a track
484 //------------------------------------------------------------------
485 Double_t alpha=fAlpha, x=fX;
486 Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4;
487 Double_t c00=fC00;
488 Double_t c10=fC10, c11=fC11;
489 Double_t c20=fC20, c21=fC21, c22=fC22;
490 Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33;
491 Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44;
492
493 if (alp < -TMath::Pi()) alp += 2*TMath::Pi();
494 else if (alp >= TMath::Pi()) alp -= 2*TMath::Pi();
495 Double_t ca=TMath::Cos(alp-fAlpha), sa=TMath::Sin(alp-fAlpha);
496 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
497
498 // **** rotation **********************
499 {
500 fAlpha = alp;
501 fX = x*ca + p0*sa;
502 fP0= -x*sa + p0*ca;
503 fP2= sf*ca - cf*sa;
504
505 Double_t rr=(ca+sf/cf*sa);
506
507 fC00 *= (ca*ca);
508 fC10 *= ca;
509 fC20 *= ca*rr;
510 fC30 *= ca;
511 fC40 *= ca;
512 //fC11 = fC11;
513 fC21 *= rr;
514 //fC31 = fC31;
515 //fC41 = fC41;
516 fC22 *= rr*rr;
517 fC32 *= rr;
518 fC42 *= rr;
519 //fC33=fC33;
520 //fC43=fC43;
521 //fC44=fC44;
522
523 }
524
525 // **** translation ******************
526 {
527 Double_t dx=xk-fX;
528 Double_t f1=fP2, f2=f1 + fP4*dx;
529 if (TMath::Abs(f2) >= 0.98) {
530 // don't propagate highly inclined tracks MI
531 return 0;
532 }
533 // Int_t n=GetNumberOfClusters();
534 // if (n>kWARN)
535 // Warning("Propagate","Propagation failed (%d) !\n",n);
536 // return 0;
537 //}
538 Double_t lcc=GetLocalConvConst();
539
540 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
541
542 fX=xk;
543 fP0 += dx*(f1+f2)/(r1+r2);
544 fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
545 fP2 += dx*fP4;
546
547 //Change of the magnetic field *************
548 SaveLocalConvConst();
549 fP4*=lcc/GetLocalConvConst();
550
551 //f = F - 1
552
553 Double_t f02= dx/(r1*r1*r1);
554 Double_t f04=0.5*dx*dx/(r1*r1*r1);
555 Double_t f12= dx*fP3*f1/(r1*r1*r1);
556 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1);
557 Double_t f13= dx/r1;
558 Double_t f24= dx;
559
560 //b = C*ft
561 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
562 Double_t b02=f24*fC40;
563 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
564 Double_t b12=f24*fC41;
565 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
566 Double_t b22=f24*fC42;
567 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
568 Double_t b42=f24*fC44;
569 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
570 Double_t b32=f24*fC43;
571
572 //a = f*b = f*C*ft
573 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
574 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
575 Double_t a22=f24*b42;
576
577 //F*C*Ft = C + (b + bt + a)
578 fC00 += b00 + b00 + a00;
579 fC10 += b10 + b01 + a01;
580 fC20 += b20 + b02 + a02;
581 fC30 += b30;
582 fC40 += b40;
583 fC11 += b11 + b11 + a11;
584 fC21 += b21 + b12 + a12;
585 fC31 += b31;
586 fC41 += b41;
587 fC22 += b22 + b22 + a22;
588 fC32 += b32;
589 fC42 += b42;
590
591 if (!Invariant()) {
592 fAlpha=alpha;
593 fX=x;
594 fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4;
595 fC00=c00;
596 fC10=c10; fC11=c11;
597 fC20=c20; fC21=c21; fC22=c22;
598 fC30=c30; fC31=c31; fC32=c32; fC33=c33;
599 fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44;
600 return 0;
601 }
602 }
603
604 return 1;
605}
606
607
608Double_t AliITStrackV2::GetD(Double_t x, Double_t y) const {
609 //------------------------------------------------------------------
610 // This function calculates the transverse impact parameter
611 // with respect to a point with global coordinates (x,y)
612 //------------------------------------------------------------------
613 Double_t xt=fX, yt=fP0;
614
615 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
616 Double_t a = x*cs + y*sn;
617 y = -x*sn + y*cs; x=a;
618 xt-=x; yt-=y;
619
620 sn=fP4*xt - fP2; cs=fP4*yt + TMath::Sqrt(1.- fP2*fP2);
621 a=2*(xt*fP2 - yt*TMath::Sqrt(1.- fP2*fP2))-fP4*(xt*xt + yt*yt);
622 if (fP4<0) a=-a;
623 return a/(1 + TMath::Sqrt(sn*sn + cs*cs));
624}
625
626Double_t AliITStrackV2::GetZat(Double_t x) const {
627 //------------------------------------------------------------------
628 // This function calculates the z at given x point - in current coordinate system
629 //------------------------------------------------------------------
630 Double_t x1=fX, x2=x, dx=x2-x1;
631 //
632 Double_t f1=fP2, f2=f1 + fP4*dx;
633 if (TMath::Abs(f2) >= 0.9999) {
634 return 10000000;
635 }
636 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
637 Double_t z = fP1 + dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
638 return z;
639}
640
641
642
643
644Int_t AliITStrackV2::Improve(Double_t x0,Double_t xyz[3],Double_t ers[3]) {
645 //------------------------------------------------------------------
646 //This function improves angular track parameters
647 //------------------------------------------------------------------
648 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
649 //Double_t xv = xyz[0]*cs + xyz[1]*sn; // vertex
650 Double_t yv =-xyz[0]*sn + xyz[1]*cs; // in the
651 Double_t zv = xyz[2]; // local frame
652 Double_t dy=fP0-yv, dz=fP1-zv;
653 Double_t r2=fX*fX+dy*dy;
654 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
655 Double_t beta2=p2/(p2 + GetMass()*GetMass());
656 x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp()));
657 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0;
658 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*x0*9.36*2.33;
659 {
660 Double_t dummy=4/r2-fP4*fP4;
661 if (dummy < 0) return 0;
662 Double_t parp=0.5*(fP4*fX + dy*TMath::Sqrt(dummy));
663 Double_t sigma2p = theta2*(1.- GetSnp()*GetSnp())*(1. + GetTgl()*GetTgl());
664 sigma2p += fC00/r2*(1.- dy*dy/r2)*(1.- dy*dy/r2);
665 sigma2p += ers[1]*ers[1]/r2;
666 sigma2p += 0.25*fC44*fX*fX;
667 Double_t eps2p=sigma2p/(fC22+sigma2p);
668 fP0 += fC20/(fC22+sigma2p)*(parp-fP2);
669 fP2 = eps2p*fP2 + (1-eps2p)*parp;
670 fC22 *= eps2p;
671 fC20 *= eps2p;
672 }
673 {
674 Double_t parl=0.5*fP4*dz/TMath::ASin(0.5*fP4*TMath::Sqrt(r2));
675 Double_t sigma2l=theta2;
676 sigma2l += fC11/r2+fC00*dy*dy*dz*dz/(r2*r2*r2);
677 sigma2l += ers[2]*ers[2]/r2;
678 Double_t eps2l=sigma2l/(fC33+sigma2l);
679 fP1 += fC31/(fC33+sigma2l)*(parl-fP3);
680 fP4 += fC43/(fC33+sigma2l)*(parl-fP3);
681 fP3 = eps2l*fP3 + (1-eps2l)*parl;
682 fC33 *= eps2l; fC43 *= eps2l;
683 fC31 *= eps2l;
684 }
685 if (!Invariant()) return 0;
686 return 1;
687}
688
689void AliITStrackV2::ResetCovariance() {
690 //------------------------------------------------------------------
691 //This function makes a track forget its history :)
692 //------------------------------------------------------------------
693
694 fC00*=10.;
695 fC10=0.; fC11*=10.;
696 fC20=0.; fC21=0.; fC22*=10.;
697 fC30=0.; fC31=0.; fC32=0.; fC33*=10.;
698 fC40=0.; fC41=0.; fC42=0.; fC43=0.; fC44*=10.;
699
700}
701
702void AliITStrackV2::CookdEdx(Double_t low, Double_t up) {
703 //-----------------------------------------------------------------
704 // This function calculates dE/dX within the "low" and "up" cuts.
705 // Origin: Boris Batyunya, JINR, Boris.Batiounia@cern.ch
706 //-----------------------------------------------------------------
707 // The clusters order is: SSD-2, SSD-1, SDD-2, SDD-1, SPD-2, SPD-1
708
709 Int_t i;
710 Int_t nc=0;
711 for (i=0; i<GetNumberOfClusters(); i++) {
712 Int_t idx=GetClusterIndex(i);
713 idx=(idx&0xf0000000)>>28;
714 if (idx>1) nc++; // Take only SSD and SDD
715 }
716
717 Int_t swap;//stupid sorting
718 do {
719 swap=0;
720 for (i=0; i<nc-1; i++) {
721 if (fdEdxSample[i]<=fdEdxSample[i+1]) continue;
722 Float_t tmp=fdEdxSample[i];
723 fdEdxSample[i]=fdEdxSample[i+1]; fdEdxSample[i+1]=tmp;
724 swap++;
725 }
726 } while (swap);
727
728 Int_t nl=Int_t(low*nc), nu=Int_t(up*nc); //b.b. to take two lowest dEdX
729 // values from four ones choose
730 // nu=2
731 Float_t dedx=0;
732 for (i=nl; i<nu; i++) dedx += fdEdxSample[i];
733 if (nu-nl>0) dedx /= (nu-nl);
734
735 SetdEdx(dedx);
736}
737
738Double_t AliITStrackV2::
739PropagateToDCA(AliKalmanTrack *p, Double_t d, Double_t x0) {
740 //--------------------------------------------------------------
741 // Propagates this track and the argument track to the position of the
742 // distance of closest approach.
743 // Returns the (weighed !) distance of closest approach.
744 //--------------------------------------------------------------
745 Double_t xthis, xp, dca;
746 {
747 //Temporary solution
748 Double_t b=1./GetLocalConvConst()/kB2C;
749 AliExternalTrackParam dummy1(*this), dummy2(*p);
750 dca=dummy1.GetDCA(&dummy2,b,xthis,xp);
751 }
752 if (!PropagateTo(xthis,d,x0)) {
753 //AliWarning(" propagation failed !");
754 return 1e+33;
755 }
756
757 if (!p->PropagateTo(xp,d,x0)) {
758 //AliWarning(" propagation failed !";
759 return 1e+33;
760 }
761
762 return dca;
763}