Additional comment.
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
CommitLineData
51ad6848 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/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
86be8934 28#include <cassert>
29
30#include <TVectorD.h>
4b189f98 31#include <TMatrixDSym.h>
d46683db 32#include <TPolyMarker3D.h>
33#include <TVector3.h>
cfdb62d4 34#include <TMatrixD.h>
d46683db 35
51ad6848 36#include "AliExternalTrackParam.h"
58e536c5 37#include "AliVVertex.h"
6c94f330 38#include "AliLog.h"
51ad6848 39
40ClassImp(AliExternalTrackParam)
41
ed5f2849 42Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
f2cef1b5 43Bool_t AliExternalTrackParam::fgUseLogTermMS = kFALSE;;
51ad6848 44//_____________________________________________________________________________
90e48c0c 45AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 46 AliVTrack(),
90e48c0c 47 fX(0),
c9ec41e8 48 fAlpha(0)
51ad6848 49{
90e48c0c 50 //
51 // default constructor
52 //
c9ec41e8 53 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
54 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 55}
56
6c94f330 57//_____________________________________________________________________________
58AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 59 AliVTrack(track),
6c94f330 60 fX(track.fX),
61 fAlpha(track.fAlpha)
62{
63 //
64 // copy constructor
65 //
66 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
67 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
86be8934 68 CheckCovariance();
6c94f330 69}
70
def9660e 71//_____________________________________________________________________________
72AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
73{
74 //
75 // assignment operator
76 //
77
78 if (this!=&trkPar) {
4f6e22bd 79 AliVTrack::operator=(trkPar);
def9660e 80 fX = trkPar.fX;
81 fAlpha = trkPar.fAlpha;
82
83 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
84 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
86be8934 85 CheckCovariance();
def9660e 86 }
87
88 return *this;
89}
90
51ad6848 91//_____________________________________________________________________________
92AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
93 const Double_t param[5],
90e48c0c 94 const Double_t covar[15]) :
4f6e22bd 95 AliVTrack(),
90e48c0c 96 fX(x),
c9ec41e8 97 fAlpha(alpha)
51ad6848 98{
90e48c0c 99 //
100 // create external track parameters from given arguments
101 //
c9ec41e8 102 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
103 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
86be8934 104 CheckCovariance();
51ad6848 105}
106
4f6e22bd 107//_____________________________________________________________________________
108AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
109 AliVTrack(),
110 fX(0.),
111 fAlpha(0.)
112{
113 //
610e3088 114 // Constructor from virtual track,
115 // This is not a copy contructor !
4f6e22bd 116 //
610e3088 117
118 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
119 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
120 AliWarning("Calling the default constructor...");
121 AliExternalTrackParam();
122 return;
123 }
124
892be05f 125 Double_t xyz[3],pxpypz[3],cv[21];
126 vTrack->GetXYZ(xyz);
127 pxpypz[0]=vTrack->Px();
128 pxpypz[1]=vTrack->Py();
129 pxpypz[2]=vTrack->Pz();
4f6e22bd 130 vTrack->GetCovarianceXYZPxPyPz(cv);
131 Short_t sign = (Short_t)vTrack->Charge();
132
133 Set(xyz,pxpypz,cv,sign);
134}
135
90e48c0c 136//_____________________________________________________________________________
da4e3deb 137AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
138 Double_t cv[21],Short_t sign) :
4f6e22bd 139 AliVTrack(),
da4e3deb 140 fX(0.),
141 fAlpha(0.)
4f6e22bd 142{
143 //
144 // constructor from the global parameters
145 //
146
147 Set(xyz,pxpypz,cv,sign);
148}
149
150//_____________________________________________________________________________
151void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
152 Double_t cv[21],Short_t sign)
da4e3deb 153{
154 //
155 // create external track parameters from the global parameters
156 // x,y,z,px,py,pz and their 6x6 covariance matrix
157 // A.Dainese 10.10.08
158
aff56ff7 159 // Calculate alpha: the rotation angle of the corresponding local system.
160 //
161 // For global radial position inside the beam pipe, alpha is the
162 // azimuthal angle of the momentum projected on (x,y).
163 //
c99948ce 164 // For global radial position outside the ITS, alpha is the
aff56ff7 165 // azimuthal angle of the centre of the TPC sector in which the point
166 // xyz lies
167 //
4349f5a4 168 const double kSafe = 1e-5;
aff56ff7 169 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 170 Double_t radMax = 45.; // approximately ITS outer radius
4349f5a4 171 if (radPos2 < radMax*radMax) { // inside the ITS
aff56ff7 172 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
c99948ce 173 } else { // outside the ITS
aff56ff7 174 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
175 fAlpha =
176 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
177 }
4349f5a4 178 //
179 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
180 // protection: avoid alpha being too close to 0 or +-pi/2
181 if (TMath::Abs(sn)<kSafe) {
182 fAlpha = kSafe;
183 cs=TMath::Cos(fAlpha);
184 sn=TMath::Sin(fAlpha);
185 }
186 else if (cs<kSafe) {
187 fAlpha -= TMath::Sign(kSafe, fAlpha);
188 cs=TMath::Cos(fAlpha);
189 sn=TMath::Sin(fAlpha);
190 }
da4e3deb 191 // Get the vertex of origin and the momentum
192 TVector3 ver(xyz[0],xyz[1],xyz[2]);
193 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
4349f5a4 194 //
195 // avoid momenta along axis
196 if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]);
197 if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]);
da4e3deb 198
199 // Rotate to the local coordinate system
200 ver.RotateZ(-fAlpha);
201 mom.RotateZ(-fAlpha);
202
203 // x of the reference plane
204 fX = ver.X();
205
206 Double_t charge = (Double_t)sign;
207
208 fP[0] = ver.Y();
209 fP[1] = ver.Z();
210 fP[2] = TMath::Sin(mom.Phi());
211 fP[3] = mom.Pz()/mom.Pt();
212 fP[4] = TMath::Sign(1/mom.Pt(),charge);
213
214 // Covariance matrix (formulas to be simplified)
215
752303df 216 if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection
217 else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection
218
da4e3deb 219 Double_t pt=1./TMath::Abs(fP[4]);
da4e3deb 220 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
221
222 Double_t m00=-sn;// m10=cs;
223 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
224 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
225 Double_t m35=pt, m45=-pt*pt*fP[3];
226
227 m43*=GetSign();
228 m44*=GetSign();
229 m45*=GetSign();
230
231 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
232 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
233 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
234 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
235 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
236 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
237 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
238
239 fC[0 ] = cv[0 ]+cv[2 ];
240 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
241 fC[2 ] = cv[5 ];
242 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
243 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
244 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
245 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
246 fC[11] = (cv[8]-fC[4]*m23)/m43;
247 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
248 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
249 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
250 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
251 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
252 Double_t b2=m23*m35;
253 Double_t b3=m43*m35;
254 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
255 Double_t b5=m24*m35;
256 Double_t b6=m44*m35;
257 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
258 fC[13] = b1/b3-b2*fC[8]/b3;
259 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 260
86be8934 261 CheckCovariance();
262
4f6e22bd 263 return;
da4e3deb 264}
265
51ad6848 266//_____________________________________________________________________________
c9ec41e8 267void AliExternalTrackParam::Reset() {
1530f89c 268 //
269 // Resets all the parameters to 0
270 //
c9ec41e8 271 fX=fAlpha=0.;
272 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
273 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 274}
275
3775b0ca 276//_____________________________________________________________________________
277void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
278 //
279 // Add "something" to the track covarince matrix.
280 // May be needed to account for unknown mis-calibration/mis-alignment
281 //
282 fC[0] +=c[0];
283 fC[1] +=c[1]; fC[2] +=c[2];
284 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
285 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
286 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
86be8934 287 CheckCovariance();
3775b0ca 288}
289
290
c9ec41e8 291Double_t AliExternalTrackParam::GetP() const {
292 //---------------------------------------------------------------------
293 // This function returns the track momentum
294 // Results for (nearly) straight tracks are meaningless !
295 //---------------------------------------------------------------------
06fb4a2f 296 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 297 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 298}
299
1d99986f 300Double_t AliExternalTrackParam::Get1P() const {
301 //---------------------------------------------------------------------
302 // This function returns the 1/(track momentum)
303 //---------------------------------------------------------------------
304 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
305}
306
c9ec41e8 307//_______________________________________________________________________
c7bafca9 308Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 309 //------------------------------------------------------------------
310 // This function calculates the transverse impact parameter
311 // with respect to a point with global coordinates (x,y)
312 // in the magnetic field "b" (kG)
313 //------------------------------------------------------------------
5773defd 314 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 315 Double_t rp4=GetC(b);
c9ec41e8 316
317 Double_t xt=fX, yt=fP[0];
318
319 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
320 Double_t a = x*cs + y*sn;
321 y = -x*sn + y*cs; x=a;
322 xt-=x; yt-=y;
323
bfd20868 324 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2]));
325 a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
1530f89c 326 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
327}
328
329//_______________________________________________________________________
330void AliExternalTrackParam::
331GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
332 //------------------------------------------------------------------
333 // This function calculates the transverse and longitudinal impact parameters
334 // with respect to a point with global coordinates (x,y)
335 // in the magnetic field "b" (kG)
336 //------------------------------------------------------------------
bfd20868 337 Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1));
1530f89c 338 Double_t xt=fX, yt=fP[0];
339 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
340 Double_t a = x*cs + y*sn;
341 y = -x*sn + y*cs; x=a;
342 xt-=x; yt-=y;
343
344 Double_t rp4=GetC(b);
345 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
346 dz[0] = -(xt*f1 - yt*r1);
347 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
348 return;
349 }
350
351 sn=rp4*xt - f1; cs=rp4*yt + r1;
352 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
353 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
354 dz[0] = -a/(1 + rr);
bfd20868 355 Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2));
1530f89c 356 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 357}
358
49d13e89 359//_______________________________________________________________________
360Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
361 //------------------------------------------------------------------
362 // This function calculates the transverse impact parameter
363 // with respect to a point with global coordinates (xv,yv)
364 // neglecting the track curvature.
365 //------------------------------------------------------------------
366 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
367 Double_t x= xv*cs + yv*sn;
368 Double_t y=-xv*sn + yv*cs;
369
bfd20868 370 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
49d13e89 371
1530f89c 372 return -d;
49d13e89 373}
374
b8e07ed6 375Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx
376(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
377 Double_t dEdx,
378 Bool_t anglecorr) {
116b445b 379 //------------------------------------------------------------------
380 // This function corrects the track parameters for the crossed material.
381 // "xOverX0" - X/X0, the thickness in units of the radiation length.
2b99ff83 382 // "xTimesRho" - is the product length*density (g/cm^2).
383 // It should be passed as negative when propagating tracks
384 // from the intreaction point to the outside of the central barrel.
116b445b 385 // "mass" - the mass of this particle (GeV/c^2).
b8e07ed6 386 // "dEdx" - mean enery loss (GeV/(g/cm^2)
387 // "anglecorr" - switch for the angular correction
116b445b 388 //------------------------------------------------------------------
389 Double_t &fP2=fP[2];
390 Double_t &fP3=fP[3];
391 Double_t &fP4=fP[4];
392
393 Double_t &fC22=fC[5];
394 Double_t &fC33=fC[9];
395 Double_t &fC43=fC[13];
396 Double_t &fC44=fC[14];
397
7dded1d5 398 //Apply angle correction, if requested
399 if(anglecorr) {
bfd20868 400 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
7dded1d5 401 xOverX0 *=angle;
402 xTimesRho *=angle;
403 }
404
116b445b 405 Double_t p=GetP();
406 Double_t p2=p*p;
407 Double_t beta2=p2/(p2 + mass*mass);
116b445b 408
9f2bec63 409 //Calculating the multiple scattering corrections******************
410 Double_t cC22 = 0.;
411 Double_t cC33 = 0.;
412 Double_t cC43 = 0.;
413 Double_t cC44 = 0.;
116b445b 414 if (xOverX0 != 0) {
f2cef1b5 415 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
416 Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0);
417 if (GetUseLogTermMS()) {
418 double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0));
419 if (lt>0) theta2 *= lt*lt;
420 }
421 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
422 cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3);
423 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
424 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
425 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 426 }
427
9f2bec63 428 //Calculating the energy loss corrections************************
429 Double_t cP4=1.;
116b445b 430 if ((xTimesRho != 0.) && (beta2 < 1.)) {
b8e07ed6 431 Double_t dE=dEdx*xTimesRho;
116b445b 432 Double_t e=TMath::Sqrt(p2 + mass*mass);
433 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
c9038cae 434 //cP4 = (1.- e/p2*dE);
76ece3d8 435 if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE;
c9038cae 436 cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben !
9f2bec63 437 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 438
116b445b 439
440 // Approximate energy loss fluctuation (M.Ivanov)
441 const Double_t knst=0.07; // To be tuned.
442 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 443 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 444
445 }
446
9f2bec63 447 //Applying the corrections*****************************
448 fC22 += cC22;
449 fC33 += cC33;
450 fC43 += cC43;
451 fC44 += cC44;
452 fP4 *= cP4;
453
86be8934 454 CheckCovariance();
455
116b445b 456 return kTRUE;
457}
458
b8e07ed6 459Bool_t AliExternalTrackParam::CorrectForMeanMaterial
460(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
461 Bool_t anglecorr,
462 Double_t (*Bethe)(Double_t)) {
463 //------------------------------------------------------------------
464 // This function corrects the track parameters for the crossed material.
465 // "xOverX0" - X/X0, the thickness in units of the radiation length.
466 // "xTimesRho" - is the product length*density (g/cm^2).
2b99ff83 467 // It should be passed as negative when propagating tracks
468 // from the intreaction point to the outside of the central barrel.
b8e07ed6 469 // "mass" - the mass of this particle (GeV/c^2).
470 // "anglecorr" - switch for the angular correction
471 // "Bethe" - function calculating the energy loss (GeV/(g/cm^2))
472 //------------------------------------------------------------------
473
474 Double_t bg=GetP()/mass;
475 Double_t dEdx=Bethe(bg);
476
477 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
478}
479
480Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA
481(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
482 Double_t zOverA,
483 Double_t density,
484 Double_t exEnergy,
485 Double_t jp1,
486 Double_t jp2,
487 Bool_t anglecorr) {
488 //------------------------------------------------------------------
489 // This function corrects the track parameters for the crossed material
490 // using the full Geant-like Bethe-Bloch formula parameterization
491 // "xOverX0" - X/X0, the thickness in units of the radiation length.
492 // "xTimesRho" - is the product length*density (g/cm^2).
2b99ff83 493 // It should be passed as negative when propagating tracks
494 // from the intreaction point to the outside of the central barrel.
b8e07ed6 495 // "mass" - the mass of this particle (GeV/c^2).
496 // "density" - mean density (g/cm^3)
497 // "zOverA" - mean Z/A
498 // "exEnergy" - mean exitation energy (GeV)
499 // "jp1" - density effect first junction point
500 // "jp2" - density effect second junction point
501 // "anglecorr" - switch for the angular correction
502 //
503 // The default values of the parameters are for silicon
504 //
505 //------------------------------------------------------------------
506
507 Double_t bg=GetP()/mass;
508 Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA);
509
510 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
511}
512
513
116b445b 514
ee5dba5e 515Bool_t AliExternalTrackParam::CorrectForMaterial
516(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 517 //------------------------------------------------------------------
116b445b 518 // Deprecated function !
519 // Better use CorrectForMeanMaterial instead of it.
520 //
c7bafca9 521 // This function corrects the track parameters for the crossed material
522 // "d" - the thickness (fraction of the radiation length)
2b99ff83 523 // It should be passed as negative when propagating tracks
524 // from the intreaction point to the outside of the central barrel.
c7bafca9 525 // "x0" - the radiation length (g/cm^2)
526 // "mass" - the mass of this particle (GeV/c^2)
527 //------------------------------------------------------------------
c7bafca9 528
b8e07ed6 529 return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe);
c7bafca9 530
c7bafca9 531}
532
9c56b409 533Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
534 Double_t kp1,
535 Double_t kp2,
536 Double_t kp3,
537 Double_t kp4,
538 Double_t kp5) {
539 //
540 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
541 // It is normalized to 1 at the minimum.
542 //
543 // bg - beta*gamma
544 //
545 // The default values for the kp* parameters are for ALICE TPC.
546 // The returned value is in MIP units
547 //
548
549 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
550
551 Double_t aa = TMath::Power(beta,kp4);
552 Double_t bb = TMath::Power(1./bg,kp5);
553
554 bb=TMath::Log(kp3+bb);
555
556 return (kp2-aa-bb)*kp1/aa;
557}
558
559Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
560 Double_t kp0,
561 Double_t kp1,
562 Double_t kp2,
563 Double_t kp3,
564 Double_t kp4) {
565 //
566 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
567 //
568 // bg - beta*gamma
569 // kp0 - density [g/cm^3]
570 // kp1 - density effect first junction point
571 // kp2 - density effect second junction point
572 // kp3 - mean excitation energy [GeV]
573 // kp4 - mean Z/A
574 //
575 // The default values for the kp* parameters are for silicon.
576 // The returned value is in [GeV/(g/cm^2)].
577 //
578
579 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
580 const Double_t me = 0.511e-3; // [GeV/c^2]
581 const Double_t rho = kp0;
582 const Double_t x0 = kp1*2.303;
583 const Double_t x1 = kp2*2.303;
584 const Double_t mI = kp3;
585 const Double_t mZA = kp4;
586 const Double_t bg2 = bg*bg;
587 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
588
589 //*** Density effect
590 Double_t d2=0.;
591 const Double_t x=TMath::Log(bg);
592 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
593 if (x > x1) {
594 d2 = lhwI + x - 0.5;
595 } else if (x > x0) {
596 const Double_t r=(x1-x)/(x1-x0);
597 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
598 }
599
600 return mK*mZA*(1+bg2)/bg2*
601 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
602}
603
d46683db 604Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 605 //------------------------------------------------------------------
d46683db 606 // This is an approximation of the Bethe-Bloch formula,
607 // reasonable for solid materials.
608 // All the parameters are, in fact, for Si.
9b655cba 609 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 610 //------------------------------------------------------------------
a821848c 611
9c56b409 612 return BetheBlochGeant(bg);
d46683db 613}
ee5dba5e 614
d46683db 615Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
616 //------------------------------------------------------------------
617 // This is an approximation of the Bethe-Bloch formula,
618 // reasonable for gas materials.
619 // All the parameters are, in fact, for Ne.
9b655cba 620 // The returned value is in [GeV/(g/cm^2)]
d46683db 621 //------------------------------------------------------------------
622
623 const Double_t rho = 0.9e-3;
624 const Double_t x0 = 2.;
625 const Double_t x1 = 4.;
626 const Double_t mI = 140.e-9;
627 const Double_t mZA = 0.49555;
628
9c56b409 629 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 630}
631
49d13e89 632Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
633 //------------------------------------------------------------------
634 // Transform this track to the local coord. system rotated
635 // by angle "alpha" (rad) with respect to the global coord. system.
636 //------------------------------------------------------------------
dfcef74c 637 if (TMath::Abs(fP[2]) >= kAlmost1) {
638 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
639 return kFALSE;
640 }
641
49d13e89 642 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
643 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
644
645 Double_t &fP0=fP[0];
646 Double_t &fP2=fP[2];
647 Double_t &fC00=fC[0];
648 Double_t &fC10=fC[1];
649 Double_t &fC20=fC[3];
650 Double_t &fC21=fC[4];
651 Double_t &fC22=fC[5];
652 Double_t &fC30=fC[6];
653 Double_t &fC32=fC[8];
654 Double_t &fC40=fC[10];
655 Double_t &fC42=fC[12];
656
657 Double_t x=fX;
658 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
bfd20868 659 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
49d13e89 660
dfcef74c 661 Double_t tmp=sf*ca - cf*sa;
7248cf51 662 if (TMath::Abs(tmp) >= kAlmost1) {
663 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
664 AliWarning(Form("Rotation failed ! %.10e",tmp));
0b69bbb2 665 return kFALSE;
666 }
dfcef74c 667
49d13e89 668 fAlpha = alpha;
669 fX = x*ca + fP0*sa;
670 fP0= -x*sa + fP0*ca;
dfcef74c 671 fP2= tmp;
49d13e89 672
06fb4a2f 673 if (TMath::Abs(cf)<kAlmost0) {
674 AliError(Form("Too small cosine value %f",cf));
675 cf = kAlmost0;
676 }
677
49d13e89 678 Double_t rr=(ca+sf/cf*sa);
679
680 fC00 *= (ca*ca);
681 fC10 *= ca;
682 fC20 *= ca*rr;
683 fC21 *= rr;
684 fC22 *= rr*rr;
685 fC30 *= ca;
686 fC32 *= rr;
687 fC40 *= ca;
688 fC42 *= rr;
689
86be8934 690 CheckCovariance();
691
49d13e89 692 return kTRUE;
693}
694
695Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
696 //----------------------------------------------------------------
697 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
698 //----------------------------------------------------------------
49d13e89 699 Double_t dx=xk-fX;
e421f556 700 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 701
1530f89c 702 Double_t crv=GetC(b);
5773defd 703 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
704
2de63fc5 705 Double_t x2r = crv*dx;
706 Double_t f1=fP[2], f2=f1 + x2r;
bbefa4c4 707 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 708 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
4349f5a4 709 if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
49d13e89 710
711 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
712 Double_t
713 &fC00=fC[0],
714 &fC10=fC[1], &fC11=fC[2],
715 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
716 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
717 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
718
bfd20868 719 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
4349f5a4 720 if (TMath::Abs(r1)<kAlmost0) return kFALSE;
721 if (TMath::Abs(r2)<kAlmost0) return kFALSE;
49d13e89 722
723 fX=xk;
2de63fc5 724 double dy2dx = (f1+f2)/(r1+r2);
725 fP0 += dx*dy2dx;
726 if (TMath::Abs(x2r)<0.05) {
727 fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov !
728 fP2 += x2r;
729 }
730 else {
731 // for small dx/R the linear apporximation of the arc by the segment is OK,
732 // but at large dx/R the error is very large and leads to incorrect Z propagation
733 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
734 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
735 // Similarly, the rotation angle in linear in dx only for dx<<R
736 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
737 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
738 fP1 += rot/crv*fP3;
739 fP2 = TMath::Sin(rot + TMath::ASin(fP2));
740 }
49d13e89 741
742 //f = F - 1
743
744 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
745 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
746 Double_t f12= dx*fP3*f1/(r1*r1*r1);
747 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
748 Double_t f13= dx/r1;
749 Double_t f24= dx; f24*=cc;
750
751 //b = C*ft
752 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
753 Double_t b02=f24*fC40;
754 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
755 Double_t b12=f24*fC41;
756 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
757 Double_t b22=f24*fC42;
758 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
759 Double_t b42=f24*fC44;
760 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
761 Double_t b32=f24*fC43;
762
763 //a = f*b = f*C*ft
764 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
765 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
766 Double_t a22=f24*b42;
767
768 //F*C*Ft = C + (b + bt + a)
769 fC00 += b00 + b00 + a00;
770 fC10 += b10 + b01 + a01;
771 fC20 += b20 + b02 + a02;
772 fC30 += b30;
773 fC40 += b40;
774 fC11 += b11 + b11 + a11;
775 fC21 += b21 + b12 + a12;
776 fC31 += b31;
777 fC41 += b41;
778 fC22 += b22 + b22 + a22;
779 fC32 += b32;
780 fC42 += b42;
781
86be8934 782 CheckCovariance();
783
49d13e89 784 return kTRUE;
785}
786
9f2bec63 787Bool_t
788AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
789 //------------------------------------------------------------------
790 // Transform this track to the local coord. system rotated
791 // by angle "alpha" (rad) with respect to the global coord. system,
792 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
793 //------------------------------------------------------------------
794
795 //Save the parameters
796 Double_t as=fAlpha;
797 Double_t xs=fX;
798 Double_t ps[5], cs[15];
799 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
800 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
801
802 if (Rotate(alpha))
803 if (PropagateTo(x,b)) return kTRUE;
804
805 //Restore the parameters, if the operation failed
806 fAlpha=as;
807 fX=xs;
808 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
809 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
810 return kFALSE;
811}
812
266a0f9b 813Bool_t AliExternalTrackParam::PropagateBxByBz
814(Double_t alpha, Double_t x, Double_t b[3]) {
815 //------------------------------------------------------------------
816 // Transform this track to the local coord. system rotated
817 // by angle "alpha" (rad) with respect to the global coord. system,
818 // and propagate this track to the plane X=xk (cm),
819 // taking into account all three components of the B field, "b[3]" (kG)
820 //------------------------------------------------------------------
821
822 //Save the parameters
823 Double_t as=fAlpha;
824 Double_t xs=fX;
825 Double_t ps[5], cs[15];
826 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
827 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
828
829 if (Rotate(alpha))
830 if (PropagateToBxByBz(x,b)) return kTRUE;
831
832 //Restore the parameters, if the operation failed
833 fAlpha=as;
834 fX=xs;
835 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
836 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
837 return kFALSE;
838}
839
9f2bec63 840
052daaff 841void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
842Double_t p[3], Double_t bz) const {
843 //+++++++++++++++++++++++++++++++++++++++++
844 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
845 // Extrapolate track along simple helix in magnetic field
846 // Arguments: len -distance alogn helix, [cm]
847 // bz - mag field, [kGaus]
848 // Returns: x and p contain extrapolated positon and momentum
849 // The momentum returned for straight-line tracks is meaningless !
850 //+++++++++++++++++++++++++++++++++++++++++
851 GetXYZ(x);
852
2258e165 853 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 854 Double_t unit[3]; GetDirection(unit);
855 x[0]+=unit[0]*len;
856 x[1]+=unit[1]*len;
857 x[2]+=unit[2]*len;
858
859 p[0]=unit[0]/kAlmost0;
860 p[1]=unit[1]/kAlmost0;
861 p[2]=unit[2]/kAlmost0;
862 } else {
863 GetPxPyPz(p);
864 Double_t pp=GetP();
865 Double_t a = -kB2C*bz*GetSign();
866 Double_t rho = a/pp;
867 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
868 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
869 x[2] += p[2]*len/pp;
870
871 Double_t p0=p[0];
872 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
873 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
874 }
875}
876
877Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
878Double_t bz) const {
879 //+++++++++++++++++++++++++++++++++++++++++
880 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
881 // Finds point of intersection (if exists) of the helix with the plane.
882 // Stores result in fX and fP.
883 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
884 // and vector, normal to the plane
885 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
886 //+++++++++++++++++++++++++++++++++++++++++
887 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
888
889 //estimates initial helix length up to plane
890 Double_t s=
891 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
892 Double_t dist=99999,distPrev=dist;
893 Double_t x[3],p[3];
894 while(TMath::Abs(dist)>0.00001){
895 //calculates helix at the distance s from x0 ALONG the helix
896 Propagate(s,x,p,bz);
897
898 //distance between current helix position and plane
899 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
900
901 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
902 distPrev=dist;
903 s-=dist;
904 }
905 //on exit pnt is intersection point,norm is track vector at that point,
906 //all in MARS
907 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
908 return kTRUE;
909}
910
49d13e89 911Double_t
912AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
913 //----------------------------------------------------------------
914 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
915 //----------------------------------------------------------------
916 Double_t sdd = fC[0] + cov[0];
917 Double_t sdz = fC[1] + cov[1];
918 Double_t szz = fC[2] + cov[2];
919 Double_t det = sdd*szz - sdz*sdz;
920
921 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
922
923 Double_t d = fP[0] - p[0];
924 Double_t z = fP[1] - p[1];
925
926 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
927}
928
4b189f98 929Double_t AliExternalTrackParam::
930GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
931 //----------------------------------------------------------------
932 // Estimate the chi2 of the 3D space point "p" and
1e023a36 933 // the full covariance matrix "covyz" and "covxyz"
4b189f98 934 //
935 // Cov(x,x) ... : covxyz[0]
936 // Cov(y,x) ... : covxyz[1] covyz[0]
937 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
938 //----------------------------------------------------------------
939
940 Double_t res[3] = {
941 GetX() - p[0],
942 GetY() - p[1],
943 GetZ() - p[2]
944 };
945
946 Double_t f=GetSnp();
947 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
bfd20868 948 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
4b189f98 949 Double_t a=f/r, b=GetTgl()/r;
950
951 Double_t s2=333.*333.; //something reasonably big (cm^2)
952
953 TMatrixDSym v(3);
954 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
955 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
956 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
957
958 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
959 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
960 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
961
962 v.Invert();
963 if (!v.IsValid()) return kVeryBig;
964
965 Double_t chi2=0.;
966 for (Int_t i = 0; i < 3; i++)
967 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
968
969 return chi2;
acdfbc78 970}
971
972Double_t AliExternalTrackParam::
973GetPredictedChi2(const AliExternalTrackParam *t) const {
974 //----------------------------------------------------------------
975 // Estimate the chi2 (5 dof) of this track with respect to the track
976 // given by the argument.
977 // The two tracks must be in the same reference system
978 // and estimated at the same reference plane.
979 //----------------------------------------------------------------
980
981 if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) {
982 AliError("The reference systems of the tracks differ !");
983 return kVeryBig;
984 }
985 if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) {
986 AliError("The reference of the tracks planes differ !");
987 return kVeryBig;
988 }
989
990 TMatrixDSym c(5);
991 c(0,0)=GetSigmaY2();
992 c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
993 c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
994 c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
995 c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
996
997 c(0,0)+=t->GetSigmaY2();
998 c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
999 c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
1000 c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
1001 c(4,0)+=t->GetSigma1PtY();c(4,1)+=t->GetSigma1PtZ();c(4,2)+=t->GetSigma1PtSnp();c(4,3)+=t->GetSigma1PtTgl();c(4,4)+=t->GetSigma1Pt2();
1002 c(0,1)=c(1,0);
1003 c(0,2)=c(2,0); c(1,2)=c(2,1);
1004 c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
1005 c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
1006
1007 c.Invert();
1008 if (!c.IsValid()) return kVeryBig;
1009
1010
1011 Double_t res[5] = {
1012 GetY() - t->GetY(),
1013 GetZ() - t->GetZ(),
1014 GetSnp() - t->GetSnp(),
1015 GetTgl() - t->GetTgl(),
1016 GetSigned1Pt() - t->GetSigned1Pt()
1017 };
4b189f98 1018
acdfbc78 1019 Double_t chi2=0.;
1020 for (Int_t i = 0; i < 5; i++)
1021 for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
4b189f98 1022
acdfbc78 1023 return chi2;
4b189f98 1024}
1025
1e023a36 1026Bool_t AliExternalTrackParam::
1027PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
1028 //----------------------------------------------------------------
1029 // Propagate this track to the plane
1030 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
1031 // belongs to.
1032 // The magnetic field is "bz" (kG)
1033 //
1034 // The track curvature and the change of the covariance matrix
1035 // of the track parameters are negleted !
1036 // (So the "step" should be small compared with 1/curvature)
1037 //----------------------------------------------------------------
1038
1039 Double_t f=GetSnp();
1040 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
bfd20868 1041 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
1e023a36 1042 Double_t a=f/r, b=GetTgl()/r;
1043
1044 Double_t s2=333.*333.; //something reasonably big (cm^2)
1045
1046 TMatrixDSym tV(3);
1047 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
1048 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
1049 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
1050
1051 TMatrixDSym pV(3);
1052 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
1053 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
1054 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
1055
1056 TMatrixDSym tpV(tV);
1057 tpV+=pV;
1058 tpV.Invert();
1059 if (!tpV.IsValid()) return kFALSE;
1060
1061 TMatrixDSym pW(3),tW(3);
1062 for (Int_t i=0; i<3; i++)
1063 for (Int_t j=0; j<3; j++) {
1064 pW(i,j)=tW(i,j)=0.;
1065 for (Int_t k=0; k<3; k++) {
1066 pW(i,j) += tV(i,k)*tpV(k,j);
1067 tW(i,j) += pV(i,k)*tpV(k,j);
1068 }
1069 }
1070
1071 Double_t t[3] = {GetX(), GetY(), GetZ()};
1072
1073 Double_t x=0.;
1074 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
1075 Double_t crv=GetC(bz);
1076 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1077 f += crv*(x-fX);
1078 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
1079 fX=x;
1080
1081 fP[0]=0.;
1082 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
1083 fP[1]=0.;
1084 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
1085
1086 return kTRUE;
1087}
1088
e23a38cb 1089Double_t *AliExternalTrackParam::GetResiduals(
1090Double_t *p,Double_t *cov,Bool_t updated) const {
1091 //------------------------------------------------------------------
1092 // Returns the track residuals with the space point "p" having
1093 // the covariance matrix "cov".
1094 // If "updated" is kTRUE, the track parameters expected to be updated,
1095 // otherwise they must be predicted.
1096 //------------------------------------------------------------------
1097 static Double_t res[2];
1098
1099 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1100 if (updated) {
1101 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
1102 } else {
1103 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
1104 }
1105 Double_t det=r00*r11 - r01*r01;
1106
1107 if (TMath::Abs(det) < kAlmost0) return 0;
1108
1109 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 1110
1111 if (r00 < 0.) return 0;
1112 if (r11 < 0.) return 0;
1113
e23a38cb 1114 Double_t dy = fP[0] - p[0];
1115 Double_t dz = fP[1] - p[1];
1116
1117 res[0]=dy*TMath::Sqrt(r00);
1118 res[1]=dz*TMath::Sqrt(r11);
1119
1120 return res;
1121}
1122
49d13e89 1123Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
1124 //------------------------------------------------------------------
1125 // Update the track parameters with the space point "p" having
1126 // the covariance matrix "cov"
1127 //------------------------------------------------------------------
1128 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
1129 Double_t
1130 &fC00=fC[0],
1131 &fC10=fC[1], &fC11=fC[2],
1132 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1133 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1134 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1135
1136 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1137 r00+=fC00; r01+=fC10; r11+=fC11;
1138 Double_t det=r00*r11 - r01*r01;
1139
1140 if (TMath::Abs(det) < kAlmost0) return kFALSE;
1141
1142
1143 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
1144
1145 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
1146 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
1147 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
1148 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
1149 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
1150
1151 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1152 Double_t sf=fP2 + k20*dy + k21*dz;
1153 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1154
1155 fP0 += k00*dy + k01*dz;
1156 fP1 += k10*dy + k11*dz;
1157 fP2 = sf;
1158 fP3 += k30*dy + k31*dz;
1159 fP4 += k40*dy + k41*dz;
1160
1161 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1162 Double_t c12=fC21, c13=fC31, c14=fC41;
1163
1164 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1165 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1166 fC40-=k00*c04+k01*c14;
1167
1168 fC11-=k10*c01+k11*fC11;
1169 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1170 fC41-=k10*c04+k11*c14;
1171
1172 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1173 fC42-=k20*c04+k21*c14;
1174
1175 fC33-=k30*c03+k31*c13;
1176 fC43-=k30*c04+k31*c14;
1177
1178 fC44-=k40*c04+k41*c14;
1179
86be8934 1180 CheckCovariance();
1181
49d13e89 1182 return kTRUE;
1183}
1184
c7bafca9 1185void
1186AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1187 //--------------------------------------------------------------------
1188 // External track parameters -> helix parameters
1189 // "b" - magnetic field (kG)
1190 //--------------------------------------------------------------------
1191 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1192
1530f89c 1193 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1194
1195 hlx[5]=fX*cs - hlx[0]*sn; // x0
1196 hlx[0]=fX*sn + hlx[0]*cs; // y0
1197//hlx[1]= // z0
1198 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1199//hlx[3]= // tgl
1530f89c 1200 hlx[4]=GetC(b); // C
c7bafca9 1201}
1202
1203
1204static void Evaluate(const Double_t *h, Double_t t,
1205 Double_t r[3], //radius vector
1206 Double_t g[3], //first defivatives
1207 Double_t gg[3]) //second derivatives
1208{
1209 //--------------------------------------------------------------------
1210 // Calculate position of a point on a track and some derivatives
1211 //--------------------------------------------------------------------
1212 Double_t phase=h[4]*t+h[2];
1213 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1214
ba4550c4 1215 r[0] = h[5];
1216 r[1] = h[0];
1217 if (TMath::Abs(h[4])>kAlmost0) {
1218 r[0] += (sn - h[6])/h[4];
1219 r[1] -= (cs - h[7])/h[4];
1220 }
c7bafca9 1221 r[2] = h[1] + h[3]*t;
1222
1223 g[0] = cs; g[1]=sn; g[2]=h[3];
1224
1225 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1226}
1227
1228Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1229Double_t b, Double_t &xthis, Double_t &xp) const {
1230 //------------------------------------------------------------
1231 // Returns the (weighed !) distance of closest approach between
1232 // this track and the track "p".
1233 // Other returned values:
1234 // xthis, xt - coordinates of tracks' reference planes at the DCA
1235 //-----------------------------------------------------------
1236 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1237 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1238 Double_t dx2=dy2;
1239
c7bafca9 1240 Double_t p1[8]; GetHelixParameters(p1,b);
1241 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1242 Double_t p2[8]; p->GetHelixParameters(p2,b);
1243 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1244
1245
1246 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1247 Evaluate(p1,t1,r1,g1,gg1);
1248 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1249 Evaluate(p2,t2,r2,g2,gg2);
1250
1251 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1252 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1253
1254 Int_t max=27;
1255 while (max--) {
1256 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1257 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1258 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1259 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1260 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1261 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1262 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1263 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1264 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1265
1266 Double_t det=h11*h22-h12*h12;
1267
1268 Double_t dt1,dt2;
1269 if (TMath::Abs(det)<1.e-33) {
1270 //(quasi)singular Hessian
1271 dt1=-gt1; dt2=-gt2;
1272 } else {
1273 dt1=-(gt1*h22 - gt2*h12)/det;
1274 dt2=-(h11*gt2 - h12*gt1)/det;
1275 }
1276
1277 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1278
1279 //check delta(phase1) ?
1280 //check delta(phase2) ?
1281
1282 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1283 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1284 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1285 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1286 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1287 if (lmb < 0.)
358f16ae 1288 AliDebug(1," stopped at not a minimum !");
c7bafca9 1289 break;
1290 }
1291
1292 Double_t dd=dm;
1293 for (Int_t div=1 ; ; div*=2) {
1294 Evaluate(p1,t1+dt1,r1,g1,gg1);
1295 Evaluate(p2,t2+dt2,r2,g2,gg2);
1296 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1297 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1298 if (dd<dm) break;
1299 dt1*=0.5; dt2*=0.5;
1300 if (div>512) {
358f16ae 1301 AliDebug(1," overshoot !"); break;
c7bafca9 1302 }
1303 }
1304 dm=dd;
1305
1306 t1+=dt1;
1307 t2+=dt2;
1308
1309 }
1310
358f16ae 1311 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1312
1313 Double_t cs=TMath::Cos(GetAlpha());
1314 Double_t sn=TMath::Sin(GetAlpha());
1315 xthis=r1[0]*cs + r1[1]*sn;
1316
1317 cs=TMath::Cos(p->GetAlpha());
1318 sn=TMath::Sin(p->GetAlpha());
1319 xp=r2[0]*cs + r2[1]*sn;
1320
1321 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1322}
1323
1324Double_t AliExternalTrackParam::
1325PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1326 //--------------------------------------------------------------
1327 // Propagates this track and the argument track to the position of the
1328 // distance of closest approach.
1329 // Returns the (weighed !) distance of closest approach.
1330 //--------------------------------------------------------------
1331 Double_t xthis,xp;
1332 Double_t dca=GetDCA(p,b,xthis,xp);
1333
1334 if (!PropagateTo(xthis,b)) {
1335 //AliWarning(" propagation failed !");
1336 return 1e+33;
1337 }
1338
1339 if (!p->PropagateTo(xp,b)) {
1340 //AliWarning(" propagation failed !";
1341 return 1e+33;
1342 }
1343
1344 return dca;
1345}
1346
1347
58e536c5 1348Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1349Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1350 //
e99a34df 1351 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1352 // if the (rough) transverse impact parameter is not bigger then "maxd".
1353 // Magnetic field is "b" (kG).
1354 //
1355 // a) The track gets extapolated to the DCA to the vertex.
1356 // b) The impact parameters and their covariance matrix are calculated.
1357 //
1358 // In the case of success, the returned value is kTRUE
1359 // (otherwise, it's kFALSE)
1360 //
1361 Double_t alpha=GetAlpha();
1362 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1363 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1364 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1365 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1366 x-=xv; y-=yv;
1367
1368 //Estimate the impact parameter neglecting the track curvature
bfd20868 1369 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
f76701bf 1370 if (d > maxd) return kFALSE;
1371
1372 //Propagate to the DCA
2258e165 1373 Double_t crv=GetC(b);
e99a34df 1374 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1375
bfd20868 1376 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1377 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
e99a34df 1378 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1379 else cs=1.;
f76701bf 1380
1381 x = xv*cs + yv*sn;
1382 yv=-xv*sn + yv*cs; xv=x;
1383
1384 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
266a0f9b 1385
1386 if (dz==0) return kTRUE;
1387 dz[0] = GetParameter()[0] - yv;
1388 dz[1] = GetParameter()[1] - zv;
1389
1390 if (covar==0) return kTRUE;
1391 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
1392
1393 //***** Improvements by A.Dainese
1394 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1395 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1396 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1397 covar[1] = GetCovariance()[1]; // between (x,y) and z
1398 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1399 //*****
1400
1401 return kTRUE;
1402}
1403
1404Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
1405Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
1406 //
1407 // Propagate this track to the DCA to vertex "vtx",
1408 // if the (rough) transverse impact parameter is not bigger then "maxd".
1409 //
1410 // This function takes into account all three components of the magnetic
1411 // field given by the b[3] arument (kG)
1412 //
1413 // a) The track gets extapolated to the DCA to the vertex.
1414 // b) The impact parameters and their covariance matrix are calculated.
1415 //
1416 // In the case of success, the returned value is kTRUE
1417 // (otherwise, it's kFALSE)
1418 //
1419 Double_t alpha=GetAlpha();
1420 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1421 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
1422 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1423 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
1424 x-=xv; y-=yv;
1425
1426 //Estimate the impact parameter neglecting the track curvature
bfd20868 1427 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
266a0f9b 1428 if (d > maxd) return kFALSE;
1429
1430 //Propagate to the DCA
8567bf39 1431 Double_t crv=GetC(b[2]);
1432 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
266a0f9b 1433
bfd20868 1434 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1435 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
266a0f9b 1436 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1437 else cs=1.;
1438
1439 x = xv*cs + yv*sn;
1440 yv=-xv*sn + yv*cs; xv=x;
1441
1442 if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1443
1444 if (dz==0) return kTRUE;
1445 dz[0] = GetParameter()[0] - yv;
1446 dz[1] = GetParameter()[1] - zv;
1447
1448 if (covar==0) return kTRUE;
58e536c5 1449 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1450
1451 //***** Improvements by A.Dainese
1452 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1453 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1454 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1455 covar[1] = GetCovariance()[1]; // between (x,y) and z
1456 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1457 //*****
1458
29fbcc93 1459 return kTRUE;
f76701bf 1460}
1461
b1149664 1462void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1463 //----------------------------------------------------------------
1464 // This function returns a unit vector along the track direction
1465 // in the global coordinate system.
1466 //----------------------------------------------------------------
1467 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1468 Double_t snp=fP[2];
bfd20868 1469 Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp));
b1149664 1470 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1471 d[0]=(csp*cs - snp*sn)/norm;
1472 d[1]=(snp*cs + csp*sn)/norm;
1473 d[2]=fP[3]/norm;
1474}
1475
c683ddc2 1476Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1477 //---------------------------------------------------------------------
1478 // This function returns the global track momentum components
1479 // Results for (nearly) straight tracks are meaningless !
1480 //---------------------------------------------------------------------
1481 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1482 return Local2GlobalMomentum(p,fAlpha);
1483}
a5e407e9 1484
def9660e 1485Double_t AliExternalTrackParam::Px() const {
957fb479 1486 //---------------------------------------------------------------------
1487 // Returns x-component of momentum
1488 // Result for (nearly) straight tracks is meaningless !
1489 //---------------------------------------------------------------------
def9660e 1490
957fb479 1491 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1492 GetPxPyPz(p);
1493
1494 return p[0];
1495}
1496
1497Double_t AliExternalTrackParam::Py() const {
957fb479 1498 //---------------------------------------------------------------------
1499 // Returns y-component of momentum
1500 // Result for (nearly) straight tracks is meaningless !
1501 //---------------------------------------------------------------------
def9660e 1502
957fb479 1503 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1504 GetPxPyPz(p);
1505
1506 return p[1];
1507}
1508
c683ddc2 1509Double_t AliExternalTrackParam::Xv() const {
1510 //---------------------------------------------------------------------
1511 // Returns x-component of first track point
1512 //---------------------------------------------------------------------
1513
1514 Double_t r[3]={0.,0.,0.};
1515 GetXYZ(r);
1516
1517 return r[0];
1518}
1519
1520Double_t AliExternalTrackParam::Yv() const {
1521 //---------------------------------------------------------------------
1522 // Returns y-component of first track point
1523 //---------------------------------------------------------------------
1524
1525 Double_t r[3]={0.,0.,0.};
1526 GetXYZ(r);
1527
1528 return r[1];
1529}
1530
def9660e 1531Double_t AliExternalTrackParam::Theta() const {
1532 // return theta angle of momentum
1533
7cdd0c20 1534 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1535}
1536
1537Double_t AliExternalTrackParam::Phi() const {
957fb479 1538 //---------------------------------------------------------------------
1539 // Returns the azimuthal angle of momentum
1540 // 0 <= phi < 2*pi
1541 //---------------------------------------------------------------------
def9660e 1542
957fb479 1543 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1544 if (phi<0.) phi+=2.*TMath::Pi();
1545 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1546
1547 return phi;
def9660e 1548}
1549
1550Double_t AliExternalTrackParam::M() const {
1551 // return particle mass
1552
1553 // No mass information available so far.
1554 // Redifine in derived class!
1555
1556 return -999.;
1557}
1558
1559Double_t AliExternalTrackParam::E() const {
1560 // return particle energy
1561
1562 // No PID information available so far.
1563 // Redifine in derived class!
1564
1565 return -999.;
1566}
1567
1568Double_t AliExternalTrackParam::Eta() const {
1569 // return pseudorapidity
1570
1571 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1572}
1573
1574Double_t AliExternalTrackParam::Y() const {
1575 // return rapidity
1576
1577 // No PID information available so far.
1578 // Redifine in derived class!
1579
1580 return -999.;
1581}
1582
c9ec41e8 1583Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1584 //---------------------------------------------------------------------
1585 // This function returns the global track position
1586 //---------------------------------------------------------------------
1587 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1588 return Local2GlobalPosition(r,fAlpha);
51ad6848 1589}
1590
c9ec41e8 1591Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1592 //---------------------------------------------------------------------
1593 // This function returns the global covariance matrix of the track params
1594 //
1595 // Cov(x,x) ... : cv[0]
1596 // Cov(y,x) ... : cv[1] cv[2]
1597 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1598 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1599 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1600 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1601 //
c9ec41e8 1602 // Results for (nearly) straight tracks are meaningless !
1603 //---------------------------------------------------------------------
e421f556 1604 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1605 for (Int_t i=0; i<21; i++) cv[i]=0.;
1606 return kFALSE;
a5e407e9 1607 }
49d13e89 1608 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1609 for (Int_t i=0; i<21; i++) cv[i]=0.;
1610 return kFALSE;
1611 }
1612 Double_t pt=1./TMath::Abs(fP[4]);
1613 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1614 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1615
1616 Double_t m00=-sn, m10=cs;
1617 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1618 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1619 Double_t m35=pt, m45=-pt*pt*fP[3];
1620
854d5d49 1621 m43*=GetSign();
1622 m44*=GetSign();
1623 m45*=GetSign();
1624
c9ec41e8 1625 cv[0 ] = fC[0]*m00*m00;
1626 cv[1 ] = fC[0]*m00*m10;
1627 cv[2 ] = fC[0]*m10*m10;
1628 cv[3 ] = fC[1]*m00;
1629 cv[4 ] = fC[1]*m10;
1630 cv[5 ] = fC[2];
1631 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1632 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1633 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1634 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1635 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1636 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1637 cv[12] = fC[4]*m24 + fC[11]*m44;
1638 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1639 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1640 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1641 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1642 cv[17] = fC[7]*m35 + fC[11]*m45;
1643 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1644 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1645 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1646
c9ec41e8 1647 return kTRUE;
51ad6848 1648}
1649
51ad6848 1650
c9ec41e8 1651Bool_t
1652AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1653 //---------------------------------------------------------------------
1654 // This function returns the global track momentum extrapolated to
1655 // the radial position "x" (cm) in the magnetic field "b" (kG)
1656 //---------------------------------------------------------------------
c9ec41e8 1657 p[0]=fP[4];
1530f89c 1658 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1659 p[2]=fP[3];
1660 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1661}
1662
7cf7bb6c 1663Bool_t
1664AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1665 //---------------------------------------------------------------------
1666 // This function returns the local Y-coordinate of the intersection
1667 // point between this track and the reference plane "x" (cm).
1668 // Magnetic field "b" (kG)
1669 //---------------------------------------------------------------------
1670 Double_t dx=x-fX;
1671 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1672
1530f89c 1673 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1674
1675 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1676 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1677
60e55aee 1678 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 1679 y = fP[0] + dx*(f1+f2)/(r1+r2);
1680 return kTRUE;
1681}
1682
6c94f330 1683Bool_t
1684AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1685 //---------------------------------------------------------------------
1686 // This function returns the local Z-coordinate of the intersection
1687 // point between this track and the reference plane "x" (cm).
1688 // Magnetic field "b" (kG)
1689 //---------------------------------------------------------------------
1690 Double_t dx=x-fX;
1691 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1692
2258e165 1693 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1694
1695 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1696 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1697
60e55aee 1698 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
6c94f330 1699 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1700 return kTRUE;
1701}
1702
c9ec41e8 1703Bool_t
1704AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1705 //---------------------------------------------------------------------
1706 // This function returns the global track position extrapolated to
1707 // the radial position "x" (cm) in the magnetic field "b" (kG)
1708 //---------------------------------------------------------------------
c9ec41e8 1709 Double_t dx=x-fX;
e421f556 1710 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1711
1530f89c 1712 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1713
e421f556 1714 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1715 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1716
60e55aee 1717 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
c9ec41e8 1718 r[0] = x;
1719 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1720 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1721
c9ec41e8 1722 return Local2GlobalPosition(r,fAlpha);
51ad6848 1723}
1724
51ad6848 1725//_____________________________________________________________________________
1726void AliExternalTrackParam::Print(Option_t* /*option*/) const
1727{
1728// print the parameters and the covariance matrix
1729
1730 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1731 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1732 fP[0], fP[1], fP[2], fP[3], fP[4]);
1733 printf(" covariance: %12g\n", fC[0]);
1734 printf(" %12g %12g\n", fC[1], fC[2]);
1735 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1736 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1737 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1738 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1739 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1740}
5b77d93c 1741
c194ba83 1742Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1743 //
1744 // Get sinus at given x
1745 //
1530f89c 1746 Double_t crv=GetC(b);
c194ba83 1747 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1748 Double_t dx = x-fX;
1749 Double_t res = fP[2]+dx*crv;
1750 return res;
1751}
bf00ebb8 1752
1753Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1754 //------------------------------------------------------------------------
1755 // Get the distance between two tracks at the local position x
1756 // working in the local frame of this track.
1757 // Origin : Marian.Ivanov@cern.ch
1758 //-----------------------------------------------------------------------
1759 Double_t xyz[3];
1760 Double_t xyz2[3];
1761 xyz[0]=x;
1762 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1763 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1764 //
1765 //
1766 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1767 xyz2[0]=x;
1768 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1769 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1770 }else{
1771 //
1772 Double_t xyz1[3];
1773 Double_t dfi = param2->GetAlpha()-GetAlpha();
1774 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1775 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1776 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1777 //
1778 xyz1[0]=xyz2[0];
1779 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1780 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1781 //
1782 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1783 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1784 xyz2[2] = xyz1[2];
1785 }
1786 dist[0] = xyz[0]-xyz2[0];
1787 dist[1] = xyz[1]-xyz2[1];
1788 dist[2] = xyz[2]-xyz2[2];
1789
1790 return kTRUE;
1791}
0c19adf7 1792
1793
1794//
1795// Draw functionality.
1796// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1797//
1798
1799void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1800 //
1801 // Draw track line
1802 //
1803 if (minR>maxR) return ;
1804 if (stepR<=0) return ;
1805 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1806 if (npoints<1) return;
1807 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1808 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1809 polymarker->Draw();
1810}
1811
1812//
1813void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1814 //
1815 // Fill points in the polymarker
1816 //
1817 Int_t counter=0;
1818 for (Double_t r=minR; r<maxR; r+=stepR){
1819 Double_t point[3];
1820 GetXYZAt(r,magF,point);
1821 pol->SetPoint(counter,point[0],point[1], point[2]);
1822 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1823 counter++;
1824 }
1825}
0e8460af 1826
1827Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1828 //
1829 Int_t min = TMath::Min(i,j);
1830 Int_t max = TMath::Max(i,j);
1831
1832 return min+(max+1)*max/2;
1833}
8b6e3369 1834
1835
1836void AliExternalTrackParam::g3helx3(Double_t qfield,
1837 Double_t step,
1838 Double_t vect[7]) {
1839/******************************************************************
1840 * *
1841 * GEANT3 tracking routine in a constant field oriented *
1842 * along axis 3 *
1843 * Tracking is performed with a conventional *
1844 * helix step method *
1845 * *
1846 * Authors R.Brun, M.Hansroul ********* *
1847 * Rewritten V.Perevoztchikov *
1848 * *
1849 * Rewritten in C++ by I.Belikov *
1850 * *
1851 * qfield (kG) - particle charge times magnetic field *
1852 * step (cm) - step length along the helix *
1853 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
1854 * *
1855 ******************************************************************/
1856 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
bfd20868 1857 const Double_t kOvSqSix=TMath::Sqrt(1./6.);
8b6e3369 1858
1859 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
1860
1861 Double_t rho = qfield*kB2C/vect[ipp];
1862 Double_t tet = rho*step;
1863
1864 Double_t tsint, sintt, sint, cos1t;
2de63fc5 1865 if (TMath::Abs(tet) > 0.03) {
8b6e3369 1866 sint = TMath::Sin(tet);
1867 sintt = sint/tet;
1868 tsint = (tet - sint)/tet;
1869 Double_t t=TMath::Sin(0.5*tet);
1870 cos1t = 2*t*t/tet;
1871 } else {
1872 tsint = tet*tet/6.;
bfd20868 1873 sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint;
8b6e3369 1874 sint = tet*sintt;
1875 cos1t = 0.5*tet;
1876 }
1877
1878 Double_t f1 = step*sintt;
1879 Double_t f2 = step*cos1t;
1880 Double_t f3 = step*tsint*cosz;
1881 Double_t f4 = -tet*cos1t;
1882 Double_t f5 = sint;
1883
1884 vect[ix] += f1*cosx - f2*cosy;
1885 vect[iy] += f1*cosy + f2*cosx;
1886 vect[iz] += f1*cosz + f3;
1887
1888 vect[ipx] += f4*cosx - f5*cosy;
1889 vect[ipy] += f4*cosy + f5*cosx;
1890
1891}
1892
1893Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
1894 //----------------------------------------------------------------
1895 // Extrapolate this track to the plane X=xk in the field b[].
1896 //
1897 // X [cm] is in the "tracking coordinate system" of this track.
1898 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
1899 //----------------------------------------------------------------
1900
1901 Double_t dx=xk-fX;
1902 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
7e1b73dd 1903 if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
ef3508c5 1904 // Do not propagate tracks outside the ALICE detector
1905 if (TMath::Abs(dx)>1e5 ||
1906 TMath::Abs(GetY())>1e5 ||
1907 TMath::Abs(GetZ())>1e5) {
1908 AliWarning(Form("Anomalous track, target X:%f",xk));
1909 Print();
1910 return kFALSE;
1911 }
8b6e3369 1912
1913 Double_t crv=GetC(b[2]);
1914 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
1915
2de63fc5 1916 Double_t x2r = crv*dx;
1917 Double_t f1=fP[2], f2=f1 + x2r;
8b6e3369 1918 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1919 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1920
1921
1922 // Estimate the covariance matrix
1923 Double_t &fP3=fP[3], &fP4=fP[4];
1924 Double_t
1925 &fC00=fC[0],
1926 &fC10=fC[1], &fC11=fC[2],
1927 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1928 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1929 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1930
bfd20868 1931 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
8b6e3369 1932
1933 //f = F - 1
1934 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
1935 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
1936 Double_t f12= dx*fP3*f1/(r1*r1*r1);
1937 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
1938 Double_t f13= dx/r1;
1939 Double_t f24= dx; f24*=cc;
1940
1941 //b = C*ft
1942 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
1943 Double_t b02=f24*fC40;
1944 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
1945 Double_t b12=f24*fC41;
1946 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
1947 Double_t b22=f24*fC42;
1948 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
1949 Double_t b42=f24*fC44;
1950 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
1951 Double_t b32=f24*fC43;
1952
1953 //a = f*b = f*C*ft
1954 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
1955 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
1956 Double_t a22=f24*b42;
1957
1958 //F*C*Ft = C + (b + bt + a)
1959 fC00 += b00 + b00 + a00;
1960 fC10 += b10 + b01 + a01;
1961 fC20 += b20 + b02 + a02;
1962 fC30 += b30;
1963 fC40 += b40;
1964 fC11 += b11 + b11 + a11;
1965 fC21 += b21 + b12 + a12;
1966 fC31 += b31;
1967 fC41 += b41;
1968 fC22 += b22 + b22 + a22;
1969 fC32 += b32;
1970 fC42 += b42;
1971
86be8934 1972 CheckCovariance();
8b6e3369 1973
1974 // Appoximate step length
2de63fc5 1975 double dy2dx = (f1+f2)/(r1+r2);
1976 Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord
1977 : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc
8b6e3369 1978 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
1979
8b6e3369 1980 // Get the track's (x,y,z) and (px,py,pz) in the Global System
1981 Double_t r[3]; GetXYZ(r);
1982 Double_t p[3]; GetPxPyPz(p);
1983 Double_t pp=GetP();
1984 p[0] /= pp;
1985 p[1] /= pp;
1986 p[2] /= pp;
1987
1988
1989 // Rotate to the system where Bx=By=0.
1990 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
1991 Double_t cosphi=1., sinphi=0.;
1992 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
1993 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
1994 Double_t costet=1., sintet=0.;
1995 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
1996 Double_t vect[7];
1997
1998 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
1999 vect[1] = -sinphi*r[0] + cosphi*r[1];
2000 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
2001
2002 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
2003 vect[4] = -sinphi*p[0] + cosphi*p[1];
2004 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
2005
2006 vect[6] = pp;
2007
2008
2009 // Do the helix step
2010 g3helx3(GetSign()*bb,step,vect);
2011
2012
2013 // Rotate back to the Global System
2014 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
2015 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
2016 r[2] = -sintet*vect[0] + costet*vect[2];
2017
2018 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
2019 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
2020 p[2] = -sintet*vect[3] + costet*vect[5];
2021
2022
2023 // Rotate back to the Tracking System
2024 Double_t cosalp = TMath::Cos(fAlpha);
2025 Double_t sinalp =-TMath::Sin(fAlpha);
2026
2027 Double_t
2028 t = cosalp*r[0] - sinalp*r[1];
2029 r[1] = sinalp*r[0] + cosalp*r[1];
2030 r[0] = t;
2031
2032 t = cosalp*p[0] - sinalp*p[1];
2033 p[1] = sinalp*p[0] + cosalp*p[1];
2034 p[0] = t;
2035
2036
2037 // Do the final correcting step to the target plane (linear approximation)
2038 Double_t x=r[0], y=r[1], z=r[2];
2039 if (TMath::Abs(dx) > kAlmost0) {
2040 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
2041 dx = xk - r[0];
2042 x += dx;
2043 y += p[1]/p[0]*dx;
2044 z += p[2]/p[0]*dx;
2045 }
2046
2047
2048 // Calculate the track parameters
2049 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
2050 fX = x;
2051 fP[0] = y;
2052 fP[1] = z;
2053 fP[2] = p[1]/t;
2054 fP[3] = p[2]/t;
2055 fP[4] = GetSign()/(t*pp);
2056
2057 return kTRUE;
2058}
2059
cfdb62d4 2060Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
2061 //
2062 //Translation: in the event mixing, the tracks can be shifted
2063 //of the difference among primary vertices (vTrasl) and
2064 //the covariance matrix is changed accordingly
2065 //(covV = covariance of the primary vertex).
2066 //Origin: "Romita, Rossella" <R.Romita@gsi.de>
2067 //
2068 TVector3 translation;
2069 // vTrasl coordinates in the local system
2070 translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
2071 translation.RotateZ(-fAlpha);
2072 translation.GetXYZ(vTrasl);
2073
2074 //compute the new x,y,z of the track
5a87bb3d 2075 Double_t newX=fX-vTrasl[0];
2076 Double_t newY=fP[0]-vTrasl[1];
2077 Double_t newZ=fP[1]-vTrasl[2];
cfdb62d4 2078
2079 //define the new parameters
5a87bb3d 2080 Double_t newParam[5];
2081 newParam[0]=newY;
2082 newParam[1]=newZ;
2083 newParam[2]=fP[2];
2084 newParam[3]=fP[3];
2085 newParam[4]=fP[4];
cfdb62d4 2086
2087 // recompute the covariance matrix:
2088 // 1. covV in the local system
2089 Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
2090 TMatrixD qQi(3,3);
2091 qQi(0,0) = cosRot;
2092 qQi(0,1) = sinRot;
2093 qQi(0,2) = 0.;
2094 qQi(1,0) = -sinRot;
2095 qQi(1,1) = cosRot;
2096 qQi(1,2) = 0.;
2097 qQi(2,0) = 0.;
2098 qQi(2,1) = 0.;
2099 qQi(2,2) = 1.;
2100 TMatrixD uUi(3,3);
2101 uUi(0,0) = covV[0];
2102 uUi(0,0) = covV[0];
2103 uUi(1,0) = covV[1];
2104 uUi(0,1) = covV[1];
2105 uUi(2,0) = covV[3];
2106 uUi(0,2) = covV[3];
2107 uUi(1,1) = covV[2];
2108 uUi(2,2) = covV[5];
2109 uUi(1,2) = covV[4];
2110 if(uUi.Determinant() <= 0.) {return kFALSE;}
2111 TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
2112 TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
2113
2114 //2. compute the new covariance matrix of the track
2115 Double_t sigmaXX=m(0,0);
2116 Double_t sigmaXZ=m(2,0);
2117 Double_t sigmaXY=m(1,0);
2118 Double_t sigmaYY=GetSigmaY2()+m(1,1);
2119 Double_t sigmaYZ=fC[1]+m(1,2);
2120 Double_t sigmaZZ=fC[2]+m(2,2);
2121 Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
2122 Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
2123 Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
2124
2125 Double_t newCov[15];
2126 newCov[0]=covarianceYY;
2127 newCov[1]=covarianceYZ;
2128 newCov[2]=covarianceZZ;
2129 for(Int_t i=3;i<15;i++){
2130 newCov[i]=fC[i];
2131 }
2132
2133 // set the new parameters
2134
5a87bb3d 2135 Set(newX,fAlpha,newParam,newCov);
cfdb62d4 2136
2137 return kTRUE;
2138 }
86be8934 2139
2140void AliExternalTrackParam::CheckCovariance() {
2141
2142 // This function forces the diagonal elements of the covariance matrix to be positive.
2143 // In case the diagonal element is bigger than the maximal allowed value, it is set to
2144 // the limit and the off-diagonal elements that correspond to it are set to zero.
2145
2146 fC[0] = TMath::Abs(fC[0]);
2147 if (fC[0]>kC0max) {
2148 fC[0] = kC0max;
2149 fC[1] = 0;
2150 fC[3] = 0;
2151 fC[6] = 0;
2152 fC[10] = 0;
2153 }
2154 fC[2] = TMath::Abs(fC[2]);
2155 if (fC[2]>kC2max) {
2156 fC[2] = kC2max;
2157 fC[1] = 0;
2158 fC[4] = 0;
2159 fC[7] = 0;
2160 fC[11] = 0;
2161 }
2162 fC[5] = TMath::Abs(fC[5]);
2163 if (fC[5]>kC5max) {
2164 fC[5] = kC5max;
2165 fC[3] = 0;
2166 fC[4] = 0;
2167 fC[8] = 0;
2168 fC[12] = 0;
2169 }
2170 fC[9] = TMath::Abs(fC[9]);
2171 if (fC[9]>kC9max) {
2172 fC[9] = kC9max;
2173 fC[6] = 0;
2174 fC[7] = 0;
2175 fC[8] = 0;
2176 fC[13] = 0;
2177 }
2178 fC[14] = TMath::Abs(fC[14]);
2179 if (fC[14]>kC14max) {
2180 fC[14] = kC14max;
2181 fC[10] = 0;
2182 fC[11] = 0;
2183 fC[12] = 0;
2184 fC[13] = 0;
2185 }
2186
2187 // The part below is used for tests and normally is commented out
2188// TMatrixDSym m(5);
2189// TVectorD eig(5);
2190
2191// m(0,0)=fC[0];
2192// m(1,0)=fC[1]; m(1,1)=fC[2];
2193// m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5];
2194// m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9];
2195// m(4,0)=fC[10]; m(4,1)=fC[11]; m(4,2)=fC[12]; m(4,3)=fC[13]; m(4,4)=fC[14];
2196
2197// m(0,1)=m(1,0);
2198// m(0,2)=m(2,0); m(1,2)=m(2,1);
2199// m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2);
2200// m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3);
2201// m.EigenVectors(eig);
2202
2203// // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0);
2204// if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) {
2205// AliWarning("Negative eigenvalues of the covariance matrix!");
2206// this->Print();
2207// eig.Print();
2208// }
2209}