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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
23#include <TMatrixD.h>
24
25#include <TMath.h>
26
27#include "AliCluster.h"
28#include "AliTPCtrack.h"
29#include "AliESDtrack.h"
30#include "AliITStrackV2.h"
31
32ClassImp(AliITStrackV2)
33
34const Int_t kWARN=5;
35
36//____________________________________________________________________________
37AliITStrackV2::AliITStrackV2():AliKalmanTrack(),
38 fX(0),
39 fAlpha(0),
40 fdEdx(0),
41 fP0(0),
42 fP1(0),
43 fP2(0),
44 fP3(0),
45 fP4(0),
46 fC00(0),
47 fC10(0),
48 fC11(0),
49 fC20(0),
50 fC21(0),
51 fC22(0),
52 fC30(0),
53 fC31(0),
54 fC32(0),
55 fC33(0),
56 fC40(0),
57 fC41(0),
58 fC42(0),
59 fC43(0),
60 fC44(0),
61 fESDtrack(0)
62 {
63 for(Int_t i=0; i<kMaxLayer; i++) fIndex[i]=0;
64 for(Int_t i=0; i<4; i++) fdEdxSample[i]=0;
65}
66
67//____________________________________________________________________________
68AliITStrackV2::AliITStrackV2(const AliTPCtrack& t) throw (const Char_t *) :
69AliKalmanTrack(t) {
70 //------------------------------------------------------------------
71 //Conversion TPC track -> ITS track
72 //------------------------------------------------------------------
73 SetChi2(0.);
74 SetNumberOfClusters(0);
75
76 fdEdx = t.GetdEdx();
77 SetMass(t.GetMass());
78
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]; t.GetExternalParameters(x,p);
85 fX=x; x=GetConvConst();
86 fP0=p[0];
87 fP1=p[1];
88 fP2=p[2];
89 fP3=p[3];
90 fP4=p[4]/x;
91
92 //Conversion of the covariance matrix
93 Double_t c[15]; t.GetExternalCovariance(c);
94
95 fC00=c[0 ];
96 fC10=c[1 ]; fC11=c[2 ];
97 fC20=c[3 ]; fC21=c[4 ]; fC22=c[5 ];
98 fC30=c[6 ]; fC31=c[7 ]; fC32=c[8 ]; fC33=c[9 ];
99 fC40=c[10]/x; fC41=c[11]/x; fC42=c[12]/x; fC43=c[13]/x; fC44=c[14]/x/x;
100
101 if (!Invariant()) throw "AliITStrackV2: conversion failed !\n";
102
103}
104
105//____________________________________________________________________________
106AliITStrackV2::AliITStrackV2(AliESDtrack& t) throw (const Char_t *) :
107AliKalmanTrack() {
108 //------------------------------------------------------------------
109 //Conversion ESD track -> ITS track
110 //------------------------------------------------------------------
111 SetNumberOfClusters(t.GetITSclusters(fIndex));
112 SetLabel(t.GetLabel());
113 SetMass(t.GetMass());
114
115 fdEdx=t.GetITSsignal();
116 fAlpha = t.GetAlpha();
117 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
118 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
119
120 //Conversion of the track parameters
121 Double_t x,p[5]; t.GetExternalParameters(x,p);
122 fX=x; x=GetConvConst();
123 fP0=p[0];
124 fP1=p[1];
125 fP2=p[2];
126 fP3=p[3];
127 fP4=p[4]/x;
128
129 //Conversion of the covariance matrix
130 Double_t c[15]; t.GetExternalCovariance(c);
131
132 fC00=c[0 ];
133 fC10=c[1 ]; fC11=c[2 ];
134 fC20=c[3 ]; fC21=c[4 ]; fC22=c[5 ];
135 fC30=c[6 ]; fC31=c[7 ]; fC32=c[8 ]; fC33=c[9 ];
136 fC40=c[10]/x; fC41=c[11]/x; fC42=c[12]/x; fC43=c[13]/x; fC44=c[14]/x/x;
137
138 if (t.GetStatus()&AliESDtrack::kTIME) {
139 StartTimeIntegral();
140 Double_t times[10]; t.GetIntegratedTimes(times); SetIntegratedTimes(times);
141 SetIntegratedLength(t.GetIntegratedLength());
142 }
143 fESDtrack=&t;
144
145 if (!Invariant()) throw "AliITStrackV2: conversion failed !\n";
146
147}
148
149void AliITStrackV2::UpdateESDtrack(ULong_t flags) {
150 fESDtrack->UpdateTrackParams(this,flags);
151}
152
153//____________________________________________________________________________
154AliITStrackV2::AliITStrackV2(const AliITStrackV2& t) : AliKalmanTrack(t) {
155 //------------------------------------------------------------------
156 //Copy constructor
157 //------------------------------------------------------------------
158 fX=t.fX;
159 fAlpha=t.fAlpha;
160 fdEdx=t.fdEdx;
161
162 fP0=t.fP0; fP1=t.fP1; fP2=t.fP2; fP3=t.fP3; fP4=t.fP4;
163
164 fC00=t.fC00;
165 fC10=t.fC10; fC11=t.fC11;
166 fC20=t.fC20; fC21=t.fC21; fC22=t.fC22;
167 fC30=t.fC30; fC31=t.fC31; fC32=t.fC32; fC33=t.fC33;
168 fC40=t.fC40; fC41=t.fC41; fC42=t.fC42; fC43=t.fC43; fC44=t.fC44;
169
170 Int_t n=GetNumberOfClusters();
171 for (Int_t i=0; i<n; i++) {
172 fIndex[i]=t.fIndex[i];
173 if (i<4) fdEdxSample[i]=t.fdEdxSample[i];
174 }
175 fESDtrack=t.fESDtrack;
176}
177
178//_____________________________________________________________________________
179Int_t AliITStrackV2::Compare(const TObject *o) const {
180 //-----------------------------------------------------------------
181 // This function compares tracks according to the their curvature
182 //-----------------------------------------------------------------
183 AliITStrackV2 *t=(AliITStrackV2*)o;
184 //Double_t co=TMath::Abs(t->Get1Pt());
185 //Double_t c =TMath::Abs(Get1Pt());
186 Double_t co=t->GetSigmaY2()*t->GetSigmaZ2();
187 Double_t c =GetSigmaY2()*GetSigmaZ2();
188 if (c>co) return 1;
189 else if (c<co) return -1;
190 return 0;
191}
192
193//_____________________________________________________________________________
194void AliITStrackV2::GetExternalCovariance(Double_t cc[15]) const {
195 //-------------------------------------------------------------------------
196 // This function returns an external representation of the covriance matrix.
197 // (See comments in AliTPCtrack.h about external track representation)
198 //-------------------------------------------------------------------------
199 Double_t a=GetConvConst();
200
201 cc[0 ]=fC00;
202 cc[1 ]=fC10; cc[2 ]=fC11;
203 cc[3 ]=fC20; cc[4 ]=fC21; cc[5 ]=fC22;
204 cc[6 ]=fC30; cc[7 ]=fC31; cc[8 ]=fC32; cc[9 ]=fC33;
205 cc[10]=fC40*a; cc[11]=fC41*a; cc[12]=fC42*a; cc[13]=fC43*a; cc[14]=fC44*a*a;
206}
207
208//____________________________________________________________________________
209Int_t AliITStrackV2::PropagateToVertex(Double_t d,Double_t x0) {
210 //------------------------------------------------------------------
211 //This function propagates a track to the minimal distance from the origin
212 //------------------------------------------------------------------
213 //Double_t xv=fP2*(fX*fP2 - fP0*TMath::Sqrt(1.- fP2*fP2)); //linear approxim.
214 Double_t tgf=-(fP4*fX - fP2)/(fP4*fP0 + TMath::Sqrt(1 - fP2*fP2));
215 Double_t snf=tgf/TMath::Sqrt(1.+ tgf*tgf);
216 Double_t xv=(snf - fP2)/fP4 + fX;
217 return PropagateTo(xv,d,x0);
218}
219
220//____________________________________________________________________________
221Int_t AliITStrackV2::
222GetGlobalXYZat(Double_t xk, Double_t &x, Double_t &y, Double_t &z) const {
223 //------------------------------------------------------------------
224 //This function returns a track position in the global system
225 //------------------------------------------------------------------
226 Double_t dx=xk-fX;
227 Double_t f1=fP2, f2=f1 + fP4*dx;
228 if (TMath::Abs(f2) >= 0.9999) {
229 Int_t n=GetNumberOfClusters();
230 if (n>kWARN)
231 Warning("GetGlobalXYZat","Propagation failed (%d) !\n",n);
232 return 0;
233 }
234
235 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
236
237 Double_t yk = fP0 + dx*(f1+f2)/(r1+r2);
238 Double_t zk = fP1 + dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
239
240 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
241 x = xk*cs - yk*sn;
242 y = xk*sn + yk*cs;
243 z = zk;
244
245 return 1;
246}
247
248//_____________________________________________________________________________
249Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c) const
250{
251 //-----------------------------------------------------------------
252 // This function calculates a predicted chi2 increment.
253 //-----------------------------------------------------------------
254 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
255 r00+=fC00; r01+=fC10; r11+=fC11;
256
257 Double_t det=r00*r11 - r01*r01;
258 if (TMath::Abs(det) < 1.e-30) {
259 Int_t n=GetNumberOfClusters();
260 if (n>kWARN)
261 Warning("GetPredictedChi2","Singular matrix (%d) !\n",n);
262 return 1e10;
263 }
264 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
265
266 Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1;
267
268 return (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
269}
270
271//____________________________________________________________________________
272Int_t AliITStrackV2::CorrectForMaterial(Double_t d, Double_t x0) {
273 //------------------------------------------------------------------
274 //This function corrects the track parameters for crossed material
275 //------------------------------------------------------------------
276 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
277 Double_t beta2=p2/(p2 + GetMass()*GetMass());
278 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
279
280 //Multiple scattering******************
281 if (d!=0) {
282 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
283 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
284 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
285 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
286 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
287 fC44 += theta2*fP3*fP4*fP3*fP4;
288 }
289
290 //Energy losses************************
291 if (x0!=0.) {
292 d*=x0;
293 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
294 if (beta2/(1-beta2)>3.5*3.5)
295 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
296 fP4*=(1.- sqrt(p2+GetMass()*GetMass())/p2*dE);
297 }
298
299 if (!Invariant()) return 0;
300
301 return 1;
302}
303
304//____________________________________________________________________________
305Int_t AliITStrackV2::PropagateTo(Double_t xk, Double_t d, Double_t x0) {
306 //------------------------------------------------------------------
307 //This function propagates a track
308 //------------------------------------------------------------------
309 Double_t x1=fX, x2=xk, dx=x2-x1;
310 Double_t f1=fP2, f2=f1 + fP4*dx;
311 if (TMath::Abs(f2) >= 0.9999) {
312 Int_t n=GetNumberOfClusters();
313 if (n>kWARN)
314 Warning("PropagateTo","Propagation failed !\n",n);
315 return 0;
316 }
317
318 // old position [SR, GSI, 17.02.2003]
319 Double_t oldX = fX, oldY = fP0, oldZ = fP1;
320
321 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
322
323 fP0 += dx*(f1+f2)/(r1+r2);
324 fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
325 fP2 += dx*fP4;
326
327 //f = F - 1
328
329 Double_t f02= dx/(r1*r1*r1);
330 Double_t f04=0.5*dx*dx/(r1*r1*r1);
331 Double_t f12= dx*fP3*f1/(r1*r1*r1);
332 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1);
333 Double_t f13= dx/r1;
334 Double_t f24= dx;
335
336 //b = C*ft
337 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
338 Double_t b02=f24*fC40;
339 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
340 Double_t b12=f24*fC41;
341 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
342 Double_t b22=f24*fC42;
343 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
344 Double_t b42=f24*fC44;
345 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
346 Double_t b32=f24*fC43;
347
348 //a = f*b = f*C*ft
349 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
350 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
351 Double_t a22=f24*b42;
352
353 //F*C*Ft = C + (b + bt + a)
354 fC00 += b00 + b00 + a00;
355 fC10 += b10 + b01 + a01;
356 fC20 += b20 + b02 + a02;
357 fC30 += b30;
358 fC40 += b40;
359 fC11 += b11 + b11 + a11;
360 fC21 += b21 + b12 + a12;
361 fC31 += b31;
362 fC41 += b41;
363 fC22 += b22 + b22 + a22;
364 fC32 += b32;
365 fC42 += b42;
366
367 fX=x2;
368
369 if (!CorrectForMaterial(d,x0)) return 0;
370
371 // Integrated Time [SR, GSI, 17.02.2003]
372 if (IsStartedTimeIntegral() && fX>oldX) {
373 Double_t l2 = (fX-oldX)*(fX-oldX)+(fP0-oldY)*(fP0-oldY)+
374 (fP1-oldZ)*(fP1-oldZ);
375 AddTimeStep(TMath::Sqrt(l2));
376 }
377 //
378
379 return 1;
380}
381
382//____________________________________________________________________________
383Int_t AliITStrackV2::Update(const AliCluster* c, Double_t chi2, UInt_t index) {
384 //------------------------------------------------------------------
385 //This function updates track parameters
386 //------------------------------------------------------------------
387 Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4;
388 Double_t c00=fC00;
389 Double_t c10=fC10, c11=fC11;
390 Double_t c20=fC20, c21=fC21, c22=fC22;
391 Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33;
392 Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44;
393
394
395 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
396 r00+=fC00; r01+=fC10; r11+=fC11;
397 Double_t det=r00*r11 - r01*r01;
398 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
399
400 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
401 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
402 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
403 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
404 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
405
406 Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1;
407 Double_t sf=fP2 + k20*dy + k21*dz;
408
409 fP0 += k00*dy + k01*dz;
410 fP1 += k10*dy + k11*dz;
411 fP2 = sf;
412 fP3 += k30*dy + k31*dz;
413 fP4 += k40*dy + k41*dz;
414
415 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
416 Double_t c12=fC21, c13=fC31, c14=fC41;
417
418 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
419 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
420 fC40-=k00*c04+k01*c14;
421
422 fC11-=k10*c01+k11*fC11;
423 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
424 fC41-=k10*c04+k11*c14;
425
426 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
427 fC42-=k20*c04+k21*c14;
428
429 fC33-=k30*c03+k31*c13;
430 fC43-=k30*c04+k31*c14;
431
432 fC44-=k40*c04+k41*c14;
433
434 if (!Invariant()) {
435 fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4;
436 fC00=c00;
437 fC10=c10; fC11=c11;
438 fC20=c20; fC21=c21; fC22=c22;
439 fC30=c30; fC31=c31; fC32=c32; fC33=c33;
440 fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44;
441 return 0;
442 }
443
444 Int_t n=GetNumberOfClusters();
445 fIndex[n]=index;
446 SetNumberOfClusters(n+1);
447 SetChi2(GetChi2()+chi2);
448
449 return 1;
450}
451
452Int_t AliITStrackV2::Invariant() const {
453 //------------------------------------------------------------------
454 // This function is for debugging purpose only
455 //------------------------------------------------------------------
456 Int_t n=GetNumberOfClusters();
457
458 if (TMath::Abs(fP2)>=0.9999){
459 if (n>kWARN) Warning("Invariant","fP2=%f\n",fP2);
460 return 0;
461 }
462 if (fC00<=0 || fC00>9.) {
463 if (n>kWARN) Warning("Invariant","fC00=%f\n",fC00);
464 return 0;
465 }
466 if (fC11<=0 || fC11>9.) {
467 if (n>kWARN) Warning("Invariant","fC11=%f\n",fC11);
468 return 0;
469 }
470 if (fC22<=0 || fC22>1.) {
471 if (n>kWARN) Warning("Invariant","fC22=%f\n",fC22);
472 return 0;
473 }
474 if (fC33<=0 || fC33>1.) {
475 if (n>kWARN) Warning("Invariant","fC33=%f\n",fC33);
476 return 0;
477 }
478 if (fC44<=0 || fC44>6e-5) {
479 if (n>kWARN) Warning("Invariant","fC44=%f\n",fC44);
480 return 0;
481 }
482 return 1;
483}
484
485//____________________________________________________________________________
486Int_t AliITStrackV2::Propagate(Double_t alp,Double_t xk) {
487 //------------------------------------------------------------------
488 //This function propagates a track
489 //------------------------------------------------------------------
490 Double_t alpha=fAlpha, x=fX;
491 Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4;
492 Double_t c00=fC00;
493 Double_t c10=fC10, c11=fC11;
494 Double_t c20=fC20, c21=fC21, c22=fC22;
495 Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33;
496 Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44;
497
498 if (alp < -TMath::Pi()) alp += 2*TMath::Pi();
499 else if (alp >= TMath::Pi()) alp -= 2*TMath::Pi();
500 Double_t ca=TMath::Cos(alp-fAlpha), sa=TMath::Sin(alp-fAlpha);
501 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
502
503 TMatrixD *T=0;
504 // **** rotation **********************
505 {
506 fAlpha = alp;
507 fX = x*ca + p0*sa;
508 fP0= -x*sa + p0*ca;
509 fP2= sf*ca - cf*sa;
510
511 TMatrixD C(5,5);
512 C(0,0)=c00;
513 C(1,0)=c10; C(1,1)=c11;
514 C(2,0)=c20; C(2,1)=c21; C(2,2)=c22;
515 C(3,0)=c30; C(3,1)=c31; C(3,2)=c32; C(3,3)=c33;
516 C(4,0)=c40; C(4,1)=c41; C(4,2)=c42; C(4,3)=c43; C(4,4)=c44;
517 C(0,1)=C(1,0);
518 C(0,2)=C(2,0); C(1,2)=C(2,1);
519 C(0,3)=C(3,0); C(1,3)=C(3,1); C(2,3)=C(3,2);
520 C(0,4)=C(4,0); C(1,4)=C(4,1); C(2,4)=C(4,2); C(3,4)=C(4,3);
521
522 TMatrixD F(6,5);
523 F(0,0)=sa;
524 F(1,0)=ca;
525 F(2,1)=F(4,3)=F(5,4)=1;
526 F(3,2)=ca + sf/cf*sa;
527
528 TMatrixD tmp(C,TMatrixD::kMult,TMatrixD(TMatrixD::kTransposed, F));
529 T=new TMatrixD(F,TMatrixD::kMult,tmp);
530 }
531
532 // **** translation ******************
533 {
534 Double_t dx=xk-fX;
535 Double_t f1=fP2, f2=f1 + fP4*dx;
536 if (TMath::Abs(f2) >= 0.9999) {
537 Int_t n=GetNumberOfClusters();
538 if (n>kWARN)
539 Warning("Propagate","Propagation failed (%d) !\n",n);
540 return 0;
541 }
542 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
543
544 fX=xk;
545 fP0 += dx*(f1+f2)/(r1+r2);
546 fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
547 fP2 += dx*fP4;
548
549 TMatrixD F(5,6);
550 F(0,1)=F(1,2)=F(2,3)=F(3,4)=F(4,5)=1;
551 F(0,3)=dx/(r1+r2)*(2+(f1+f2)*(f2/r2+f1/r1)/(r1+r2));
552 F(0,5)=dx*dx/(r1+r2)*(1+(f1+f2)*f2/(r1+r2));
553 F(1,3)=dx*fP3/(f1*r2 + f2*r1)*(2-(f1+f2)*(r2-f1*f2/r2+r1-f2*f1/r1)/(f1*r2 + f2*r1));
554 F(1,4)=dx*(f1+f2)/(f1*r2 + f2*r1);
555 F(1,5)=dx*dx*fP3/(f1*r2 + f2*r1)*(1-(f1+f2)*(-f1*f2/r2+r1)/(f1*r2 + f2*r1));
556 F(2,5)=dx;
557 F(0,0)=-1/(r1+r2)*((f1+f2)+dx*fP4*(1+(f1+f2)/(r1+r2)*f2/r2));
558 F(1,0)=-fP3/(f1*r2 + f2*r1)*((f1+f2)+dx*fP4*(1+(f1+f2)/(f1*r2 + f2*r1)*(f1*f2/r2-r1)));
559 F(2,0)=-fP4;
560
561 TMatrixD tmp(*T,TMatrixD::kMult,TMatrixD(TMatrixD::kTransposed, F));
562 delete T;
563 TMatrixD C(F,TMatrixD::kMult,tmp);
564
565 fC00=C(0,0);
566 fC10=C(1,0); fC11=C(1,1);
567 fC20=C(2,0); fC21=C(2,1); fC22=C(2,2);
568 fC30=C(3,0); fC31=C(3,1); fC32=C(3,2); fC33=C(3,3);
569 fC40=C(4,0); fC41=C(4,1); fC42=C(4,2); fC43=C(4,3); fC44=C(4,4);
570
571 if (!Invariant()) {
572 fAlpha=alpha;
573 fX=x;
574 fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4;
575 fC00=c00;
576 fC10=c10; fC11=c11;
577 fC20=c20; fC21=c21; fC22=c22;
578 fC30=c30; fC31=c31; fC32=c32; fC33=c33;
579 fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44;
580 return 0;
581 }
582 }
583
584 return 1;
585}
586
587Double_t AliITStrackV2::GetD(Double_t x, Double_t y) const {
588 //------------------------------------------------------------------
589 // This function calculates the transverse impact parameter
590 // with respect to a point with global coordinates (x,y)
591 //------------------------------------------------------------------
592 Double_t xt=fX, yt=fP0;
593
594 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
595 Double_t a = x*cs + y*sn;
596 y = -x*sn + y*cs; x=a;
597 xt-=x; yt-=y;
598
599 sn=fP4*xt - fP2; cs=fP4*yt + TMath::Sqrt(1.- fP2*fP2);
600 a=2*(xt*fP2 - yt*TMath::Sqrt(1.- fP2*fP2))-fP4*(xt*xt + yt*yt);
601 if (fP4<0) a=-a;
602 return a/(1 + TMath::Sqrt(sn*sn + cs*cs));
603}
604
605Int_t AliITStrackV2::Improve(Double_t x0,Double_t xyz[3],Double_t ers[3]) {
606 //------------------------------------------------------------------
607 //This function improves angular track parameters
608 //------------------------------------------------------------------
609 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
610 //Double_t xv = xyz[0]*cs + xyz[1]*sn; // vertex
611 Double_t yv =-xyz[0]*sn + xyz[1]*cs; // in the
612 Double_t zv = xyz[2]; // local frame
613 Double_t dy=fP0-yv, dz=fP1-zv;
614 Double_t r2=fX*fX+dy*dy;
615 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
616 Double_t beta2=p2/(p2 + GetMass()*GetMass());
617 x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp()));
618 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0;
619 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*x0*9.36*2.33;
620 {
621 Double_t parp=0.5*(fP4*fX + dy*TMath::Sqrt(4/r2-fP4*fP4));
622 Double_t sigma2p = theta2*(1.- GetSnp()*GetSnp())*(1. + GetTgl()*GetTgl());
623 sigma2p += fC00/r2*(1.- dy*dy/r2)*(1.- dy*dy/r2);
624 sigma2p += ers[1]*ers[1]/r2;
625 sigma2p += 0.25*fC44*fX*fX;
626 Double_t eps2p=sigma2p/(fC22+sigma2p);
627 fP0 += fC20/(fC22+sigma2p)*(parp-fP2);
628 fP2 = eps2p*fP2 + (1-eps2p)*parp;
629 fC22 *= eps2p;
630 fC20 *= eps2p;
631 }
632 {
633 Double_t parl=0.5*fP4*dz/TMath::ASin(0.5*fP4*TMath::Sqrt(r2));
634 Double_t sigma2l=theta2;
635 sigma2l += fC11/r2+fC00*dy*dy*dz*dz/(r2*r2*r2);
636 sigma2l += ers[2]*ers[2]/r2;
637 Double_t eps2l=sigma2l/(fC33+sigma2l);
638 fP1 += fC31/(fC33+sigma2l)*(parl-fP3);
639 fP4 += fC43/(fC33+sigma2l)*(parl-fP3);
640 fP3 = eps2l*fP3 + (1-eps2l)*parl;
641 fC33 *= eps2l; fC43 *= eps2l;
642 fC31 *= eps2l;
643 }
644 if (!Invariant()) return 0;
645 return 1;
646}
647
648/*
649Int_t AliITStrackV2::Improve(Double_t x0,Double_t yv,Double_t zv) {
650 //------------------------------------------------------------------
651 //This function improves angular track parameters
652 //------------------------------------------------------------------
653 Double_t dy=fP0-yv, dz=fP1-zv;
654 Double_t r2=fX*fX+dy*dy;
655 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
656 Double_t beta2=p2/(p2 + GetMass()*GetMass());
657 x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp()));
658 //Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0;
659 Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*x0*9.36*2.33;
660
661 Double_t par=0.5*(fP4*fX + dy*TMath::Sqrt(4/r2-fP4*fP4));
662 Double_t sigma2 = theta2*(1.- GetSnp()*GetSnp())*(1. + GetTgl()*GetTgl());
663 sigma2 += fC00/r2*(1.- dy*dy/r2)*(1.- dy*dy/r2);
664 sigma2 += kSigmaYV*kSigmaYV/r2;
665 sigma2 += 0.25*fC44*fX*fX;
666 Double_t eps2=sigma2/(fC22+sigma2), eps=TMath::Sqrt(eps2);
667 if (10*r2*fC44<fC22) {
668 fP2 = eps2*fP2 + (1-eps2)*par;
669 fC22*=eps2; fC21*=eps; fC20*=eps; fC32*=eps; fC42*=eps;
670 }
671
672 par=0.5*fP4*dz/TMath::ASin(0.5*fP4*TMath::Sqrt(r2));
673 sigma2=theta2;
674 sigma2 += fC11/r2+fC00*dy*dy*dz*dz/(r2*r2*r2);
675 sigma2 += kSigmaZV*kSigmaZV/r2;
676 eps2=sigma2/(fC33+sigma2); eps=TMath::Sqrt(eps2);
677 Double_t tgl=fP3;
678 fP3 = eps2*fP3 + (1-eps2)*par;
679 fC33*=eps2; fC32*=eps; fC31*=eps; fC30*=eps; fC43*=eps;
680
681 eps=TMath::Sqrt((1+fP3*fP3)/(1+tgl*tgl));
682 fP4*=eps;
683 fC44*=eps*eps; fC43*=eps;fC42*=eps; fC41*=eps; fC40*=eps;
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}