Modifications needed to use PID framework based mass during tracking and
[u/mrichter/AliRoot.git] / STEER / STEERBase / AliExternalTrackParam.cxx
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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. *
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8 * documentation strictly for non-commercial purposes is hereby granted *
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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
4ec1ca0f 107//_____________________________________________________________________________
108void AliExternalTrackParam::CopyFromVTrack(const AliVTrack *vTrack)
109{
110 //
111 // Recreate TrackParams from VTrack
112 // This is not a copy contructor !
113 //
114 if (!vTrack) {
115 AliError("Source VTrack is NULL");
116 return;
117 }
118 if (this==vTrack) {
119 AliError("Copy of itself is requested");
120 return;
121 }
122 //
123 if (vTrack->InheritsFrom(AliExternalTrackParam::Class())) {
124 AliDebug(1,"Source itself is AliExternalTrackParam, using assignment operator");
125 *this = *(AliExternalTrackParam*)vTrack;
126 return;
127 }
128 //
129 AliVTrack::operator=( *vTrack );
130 //
131 Double_t xyz[3],pxpypz[3],cv[21];
132 vTrack->GetXYZ(xyz);
133 pxpypz[0]=vTrack->Px();
134 pxpypz[1]=vTrack->Py();
135 pxpypz[2]=vTrack->Pz();
136 vTrack->GetCovarianceXYZPxPyPz(cv);
137 Short_t sign = (Short_t)vTrack->Charge();
138 Set(xyz,pxpypz,cv,sign);
139}
140
4f6e22bd 141//_____________________________________________________________________________
142AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
143 AliVTrack(),
144 fX(0.),
145 fAlpha(0.)
146{
147 //
610e3088 148 // Constructor from virtual track,
149 // This is not a copy contructor !
4f6e22bd 150 //
610e3088 151
152 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
153 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
154 AliWarning("Calling the default constructor...");
155 AliExternalTrackParam();
156 return;
157 }
158
892be05f 159 Double_t xyz[3],pxpypz[3],cv[21];
160 vTrack->GetXYZ(xyz);
161 pxpypz[0]=vTrack->Px();
162 pxpypz[1]=vTrack->Py();
163 pxpypz[2]=vTrack->Pz();
4f6e22bd 164 vTrack->GetCovarianceXYZPxPyPz(cv);
165 Short_t sign = (Short_t)vTrack->Charge();
166
167 Set(xyz,pxpypz,cv,sign);
168}
169
90e48c0c 170//_____________________________________________________________________________
da4e3deb 171AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
172 Double_t cv[21],Short_t sign) :
4f6e22bd 173 AliVTrack(),
da4e3deb 174 fX(0.),
175 fAlpha(0.)
4f6e22bd 176{
177 //
178 // constructor from the global parameters
179 //
180
181 Set(xyz,pxpypz,cv,sign);
182}
183
184//_____________________________________________________________________________
185void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
186 Double_t cv[21],Short_t sign)
da4e3deb 187{
188 //
189 // create external track parameters from the global parameters
190 // x,y,z,px,py,pz and their 6x6 covariance matrix
191 // A.Dainese 10.10.08
192
aff56ff7 193 // Calculate alpha: the rotation angle of the corresponding local system.
194 //
195 // For global radial position inside the beam pipe, alpha is the
196 // azimuthal angle of the momentum projected on (x,y).
197 //
c99948ce 198 // For global radial position outside the ITS, alpha is the
aff56ff7 199 // azimuthal angle of the centre of the TPC sector in which the point
200 // xyz lies
201 //
4349f5a4 202 const double kSafe = 1e-5;
aff56ff7 203 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 204 Double_t radMax = 45.; // approximately ITS outer radius
4349f5a4 205 if (radPos2 < radMax*radMax) { // inside the ITS
aff56ff7 206 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
c99948ce 207 } else { // outside the ITS
aff56ff7 208 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
209 fAlpha =
210 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
211 }
4349f5a4 212 //
213 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
214 // protection: avoid alpha being too close to 0 or +-pi/2
5123be3b 215 if (TMath::Abs(sn)<2*kSafe) {
216 if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
217 else fAlpha += fAlpha>-TMath::Pi()/2. ? -2*kSafe : 2*kSafe;
4349f5a4 218 cs=TMath::Cos(fAlpha);
219 sn=TMath::Sin(fAlpha);
220 }
5123be3b 221 else if (TMath::Abs(cs)<2*kSafe) {
222 if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
223 else fAlpha += fAlpha>-TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
4349f5a4 224 cs=TMath::Cos(fAlpha);
8defb4a0 225 sn=TMath::Sin(fAlpha);
4349f5a4 226 }
da4e3deb 227 // Get the vertex of origin and the momentum
228 TVector3 ver(xyz[0],xyz[1],xyz[2]);
229 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
4349f5a4 230 //
231 // avoid momenta along axis
232 if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]);
233 if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]);
da4e3deb 234
235 // Rotate to the local coordinate system
236 ver.RotateZ(-fAlpha);
237 mom.RotateZ(-fAlpha);
238
239 // x of the reference plane
240 fX = ver.X();
241
242 Double_t charge = (Double_t)sign;
243
244 fP[0] = ver.Y();
245 fP[1] = ver.Z();
246 fP[2] = TMath::Sin(mom.Phi());
247 fP[3] = mom.Pz()/mom.Pt();
248 fP[4] = TMath::Sign(1/mom.Pt(),charge);
249
250 // Covariance matrix (formulas to be simplified)
251
752303df 252 if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection
253 else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection
254
da4e3deb 255 Double_t pt=1./TMath::Abs(fP[4]);
da4e3deb 256 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
257
258 Double_t m00=-sn;// m10=cs;
259 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
260 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
261 Double_t m35=pt, m45=-pt*pt*fP[3];
262
263 m43*=GetSign();
264 m44*=GetSign();
265 m45*=GetSign();
266
267 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
268 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
269 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
270 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
271 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
272 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
273 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
274
275 fC[0 ] = cv[0 ]+cv[2 ];
276 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
277 fC[2 ] = cv[5 ];
5123be3b 278 fC[3 ] = (cv[10]*m43-cv[6]*m44)/(m24*m43-m23*m44)/m00;
da4e3deb 279 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
280 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
5123be3b 281 fC[4 ] = (cv[12]*m43-cv[8]*m44)/(m24*m43-m23*m44);
da4e3deb 282 fC[11] = (cv[8]-fC[4]*m23)/m43;
283 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
5123be3b 284 fC[5 ] = TMath::Abs((a4*a3-a6*a1)/(a5*a3-a6*a2));
285 fC[14] = TMath::Abs((a1-a2*fC[5])/a3);
da4e3deb 286 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
287 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
288 Double_t b2=m23*m35;
289 Double_t b3=m43*m35;
290 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
291 Double_t b5=m24*m35;
292 Double_t b6=m44*m35;
293 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
294 fC[13] = b1/b3-b2*fC[8]/b3;
295 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 296
86be8934 297 CheckCovariance();
298
4f6e22bd 299 return;
da4e3deb 300}
301
51ad6848 302//_____________________________________________________________________________
c9ec41e8 303void AliExternalTrackParam::Reset() {
1530f89c 304 //
305 // Resets all the parameters to 0
306 //
c9ec41e8 307 fX=fAlpha=0.;
308 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
309 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 310}
311
3775b0ca 312//_____________________________________________________________________________
313void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
314 //
315 // Add "something" to the track covarince matrix.
316 // May be needed to account for unknown mis-calibration/mis-alignment
317 //
318 fC[0] +=c[0];
319 fC[1] +=c[1]; fC[2] +=c[2];
320 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
321 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
322 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
86be8934 323 CheckCovariance();
3775b0ca 324}
325
326
c9ec41e8 327Double_t AliExternalTrackParam::GetP() const {
328 //---------------------------------------------------------------------
329 // This function returns the track momentum
330 // Results for (nearly) straight tracks are meaningless !
331 //---------------------------------------------------------------------
06fb4a2f 332 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 333 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 334}
335
1d99986f 336Double_t AliExternalTrackParam::Get1P() const {
337 //---------------------------------------------------------------------
338 // This function returns the 1/(track momentum)
339 //---------------------------------------------------------------------
340 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
341}
342
c9ec41e8 343//_______________________________________________________________________
c7bafca9 344Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 345 //------------------------------------------------------------------
346 // This function calculates the transverse impact parameter
347 // with respect to a point with global coordinates (x,y)
348 // in the magnetic field "b" (kG)
349 //------------------------------------------------------------------
5773defd 350 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 351 Double_t rp4=GetC(b);
c9ec41e8 352
353 Double_t xt=fX, yt=fP[0];
354
355 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
356 Double_t a = x*cs + y*sn;
357 y = -x*sn + y*cs; x=a;
358 xt-=x; yt-=y;
359
bfd20868 360 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2]));
361 a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
1530f89c 362 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
363}
364
365//_______________________________________________________________________
366void AliExternalTrackParam::
367GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
368 //------------------------------------------------------------------
369 // This function calculates the transverse and longitudinal impact parameters
370 // with respect to a point with global coordinates (x,y)
371 // in the magnetic field "b" (kG)
372 //------------------------------------------------------------------
bfd20868 373 Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1));
1530f89c 374 Double_t xt=fX, yt=fP[0];
375 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
376 Double_t a = x*cs + y*sn;
377 y = -x*sn + y*cs; x=a;
378 xt-=x; yt-=y;
379
380 Double_t rp4=GetC(b);
381 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
382 dz[0] = -(xt*f1 - yt*r1);
383 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
384 return;
385 }
386
387 sn=rp4*xt - f1; cs=rp4*yt + r1;
388 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
389 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
390 dz[0] = -a/(1 + rr);
bfd20868 391 Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2));
1530f89c 392 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 393}
394
49d13e89 395//_______________________________________________________________________
396Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
397 //------------------------------------------------------------------
398 // This function calculates the transverse impact parameter
399 // with respect to a point with global coordinates (xv,yv)
400 // neglecting the track curvature.
401 //------------------------------------------------------------------
402 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
403 Double_t x= xv*cs + yv*sn;
404 Double_t y=-xv*sn + yv*cs;
405
bfd20868 406 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
49d13e89 407
1530f89c 408 return -d;
49d13e89 409}
410
b8e07ed6 411Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx
412(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
413 Double_t dEdx,
414 Bool_t anglecorr) {
116b445b 415 //------------------------------------------------------------------
416 // This function corrects the track parameters for the crossed material.
417 // "xOverX0" - X/X0, the thickness in units of the radiation length.
2b99ff83 418 // "xTimesRho" - is the product length*density (g/cm^2).
419 // It should be passed as negative when propagating tracks
420 // from the intreaction point to the outside of the central barrel.
1d26da6d 421 // "mass" - the mass of this particle (GeV/c^2). Negative mass means charge=2 particle
b8e07ed6 422 // "dEdx" - mean enery loss (GeV/(g/cm^2)
423 // "anglecorr" - switch for the angular correction
116b445b 424 //------------------------------------------------------------------
425 Double_t &fP2=fP[2];
426 Double_t &fP3=fP[3];
427 Double_t &fP4=fP[4];
428
429 Double_t &fC22=fC[5];
430 Double_t &fC33=fC[9];
431 Double_t &fC43=fC[13];
432 Double_t &fC44=fC[14];
433
7dded1d5 434 //Apply angle correction, if requested
435 if(anglecorr) {
bfd20868 436 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
7dded1d5 437 xOverX0 *=angle;
438 xTimesRho *=angle;
439 }
440
116b445b 441 Double_t p=GetP();
1d26da6d 442 if (mass<0) p += p; // q=2 particle
116b445b 443 Double_t p2=p*p;
444 Double_t beta2=p2/(p2 + mass*mass);
116b445b 445
9f2bec63 446 //Calculating the multiple scattering corrections******************
447 Double_t cC22 = 0.;
448 Double_t cC33 = 0.;
449 Double_t cC43 = 0.;
450 Double_t cC44 = 0.;
116b445b 451 if (xOverX0 != 0) {
f2cef1b5 452 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
453 Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0);
454 if (GetUseLogTermMS()) {
455 double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0));
456 if (lt>0) theta2 *= lt*lt;
457 }
1d26da6d 458 if (mass<0) theta2 *= 4; // q=2 particle
f2cef1b5 459 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
460 cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3);
461 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
462 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
463 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 464 }
465
9f2bec63 466 //Calculating the energy loss corrections************************
467 Double_t cP4=1.;
116b445b 468 if ((xTimesRho != 0.) && (beta2 < 1.)) {
b8e07ed6 469 Double_t dE=dEdx*xTimesRho;
116b445b 470 Double_t e=TMath::Sqrt(p2 + mass*mass);
471 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
76ece3d8 472 if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE;
c9038cae 473 cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben !
9f2bec63 474 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 475
116b445b 476
477 // Approximate energy loss fluctuation (M.Ivanov)
478 const Double_t knst=0.07; // To be tuned.
479 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 480 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 481
482 }
483
9f2bec63 484 //Applying the corrections*****************************
485 fC22 += cC22;
486 fC33 += cC33;
487 fC43 += cC43;
488 fC44 += cC44;
489 fP4 *= cP4;
490
86be8934 491 CheckCovariance();
492
116b445b 493 return kTRUE;
494}
495
b8e07ed6 496Bool_t AliExternalTrackParam::CorrectForMeanMaterial
497(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
498 Bool_t anglecorr,
499 Double_t (*Bethe)(Double_t)) {
500 //------------------------------------------------------------------
501 // This function corrects the track parameters for the crossed material.
502 // "xOverX0" - X/X0, the thickness in units of the radiation length.
503 // "xTimesRho" - is the product length*density (g/cm^2).
2b99ff83 504 // It should be passed as negative when propagating tracks
505 // from the intreaction point to the outside of the central barrel.
1d26da6d 506 // "mass" - the mass of this particle (GeV/c^2). mass<0 means charge=2
b8e07ed6 507 // "anglecorr" - switch for the angular correction
508 // "Bethe" - function calculating the energy loss (GeV/(g/cm^2))
509 //------------------------------------------------------------------
b8e07ed6 510 Double_t bg=GetP()/mass;
1d26da6d 511 if (mass<0) {
512 if (mass<-990) {
513 AliDebug(2,Form("Mass %f corresponds to unknown PID particle = %e",mass));
514 return kFALSE;
515 }
516 bg = -2*bg;
937a4c16 517 }
b8e07ed6 518 Double_t dEdx=Bethe(bg);
1d26da6d 519 if (mass<0) dEdx *= 4;
b8e07ed6 520
521 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
522}
523
524Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA
525(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
526 Double_t zOverA,
527 Double_t density,
528 Double_t exEnergy,
529 Double_t jp1,
530 Double_t jp2,
531 Bool_t anglecorr) {
532 //------------------------------------------------------------------
533 // This function corrects the track parameters for the crossed material
534 // using the full Geant-like Bethe-Bloch formula parameterization
535 // "xOverX0" - X/X0, the thickness in units of the radiation length.
536 // "xTimesRho" - is the product length*density (g/cm^2).
2b99ff83 537 // It should be passed as negative when propagating tracks
538 // from the intreaction point to the outside of the central barrel.
1d26da6d 539 // "mass" - the mass of this particle (GeV/c^2). mass<0 means charge=2 particle
b8e07ed6 540 // "density" - mean density (g/cm^3)
541 // "zOverA" - mean Z/A
542 // "exEnergy" - mean exitation energy (GeV)
543 // "jp1" - density effect first junction point
544 // "jp2" - density effect second junction point
545 // "anglecorr" - switch for the angular correction
546 //
547 // The default values of the parameters are for silicon
548 //
549 //------------------------------------------------------------------
550
551 Double_t bg=GetP()/mass;
1d26da6d 552 if (mass<0) {
553 if (mass<-990) {
554 AliDebug(2,Form("Mass %f corresponds to unknown PID particle = %e",mass));
555 return kFALSE;
556 }
557 bg = -2*bg;
558 }
b8e07ed6 559 Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA);
1d26da6d 560 if (mass<0) dEdx *= 4;
b8e07ed6 561 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
562}
563
564
116b445b 565
ee5dba5e 566Bool_t AliExternalTrackParam::CorrectForMaterial
567(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 568 //------------------------------------------------------------------
116b445b 569 // Deprecated function !
570 // Better use CorrectForMeanMaterial instead of it.
571 //
c7bafca9 572 // This function corrects the track parameters for the crossed material
573 // "d" - the thickness (fraction of the radiation length)
2b99ff83 574 // It should be passed as negative when propagating tracks
575 // from the intreaction point to the outside of the central barrel.
c7bafca9 576 // "x0" - the radiation length (g/cm^2)
577 // "mass" - the mass of this particle (GeV/c^2)
578 //------------------------------------------------------------------
c7bafca9 579
b8e07ed6 580 return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe);
c7bafca9 581
c7bafca9 582}
583
9c56b409 584Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
585 Double_t kp1,
586 Double_t kp2,
587 Double_t kp3,
588 Double_t kp4,
589 Double_t kp5) {
590 //
591 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
592 // It is normalized to 1 at the minimum.
593 //
594 // bg - beta*gamma
595 //
596 // The default values for the kp* parameters are for ALICE TPC.
597 // The returned value is in MIP units
598 //
599
600 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
601
602 Double_t aa = TMath::Power(beta,kp4);
603 Double_t bb = TMath::Power(1./bg,kp5);
604
605 bb=TMath::Log(kp3+bb);
606
607 return (kp2-aa-bb)*kp1/aa;
608}
609
610Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
611 Double_t kp0,
612 Double_t kp1,
613 Double_t kp2,
614 Double_t kp3,
615 Double_t kp4) {
616 //
617 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
618 //
619 // bg - beta*gamma
620 // kp0 - density [g/cm^3]
621 // kp1 - density effect first junction point
622 // kp2 - density effect second junction point
623 // kp3 - mean excitation energy [GeV]
624 // kp4 - mean Z/A
625 //
626 // The default values for the kp* parameters are for silicon.
627 // The returned value is in [GeV/(g/cm^2)].
628 //
629
630 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
631 const Double_t me = 0.511e-3; // [GeV/c^2]
632 const Double_t rho = kp0;
633 const Double_t x0 = kp1*2.303;
634 const Double_t x1 = kp2*2.303;
635 const Double_t mI = kp3;
636 const Double_t mZA = kp4;
637 const Double_t bg2 = bg*bg;
638 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
639
640 //*** Density effect
641 Double_t d2=0.;
642 const Double_t x=TMath::Log(bg);
643 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
644 if (x > x1) {
645 d2 = lhwI + x - 0.5;
646 } else if (x > x0) {
647 const Double_t r=(x1-x)/(x1-x0);
648 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
649 }
650
651 return mK*mZA*(1+bg2)/bg2*
652 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
653}
654
d46683db 655Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 656 //------------------------------------------------------------------
d46683db 657 // This is an approximation of the Bethe-Bloch formula,
658 // reasonable for solid materials.
659 // All the parameters are, in fact, for Si.
9b655cba 660 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 661 //------------------------------------------------------------------
a821848c 662
9c56b409 663 return BetheBlochGeant(bg);
d46683db 664}
ee5dba5e 665
d46683db 666Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
667 //------------------------------------------------------------------
668 // This is an approximation of the Bethe-Bloch formula,
669 // reasonable for gas materials.
670 // All the parameters are, in fact, for Ne.
9b655cba 671 // The returned value is in [GeV/(g/cm^2)]
d46683db 672 //------------------------------------------------------------------
673
674 const Double_t rho = 0.9e-3;
675 const Double_t x0 = 2.;
676 const Double_t x1 = 4.;
677 const Double_t mI = 140.e-9;
678 const Double_t mZA = 0.49555;
679
9c56b409 680 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 681}
682
49d13e89 683Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
684 //------------------------------------------------------------------
685 // Transform this track to the local coord. system rotated
686 // by angle "alpha" (rad) with respect to the global coord. system.
687 //------------------------------------------------------------------
dfcef74c 688 if (TMath::Abs(fP[2]) >= kAlmost1) {
689 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
690 return kFALSE;
691 }
692
49d13e89 693 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
694 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
695
696 Double_t &fP0=fP[0];
697 Double_t &fP2=fP[2];
698 Double_t &fC00=fC[0];
699 Double_t &fC10=fC[1];
700 Double_t &fC20=fC[3];
701 Double_t &fC21=fC[4];
702 Double_t &fC22=fC[5];
703 Double_t &fC30=fC[6];
704 Double_t &fC32=fC[8];
705 Double_t &fC40=fC[10];
706 Double_t &fC42=fC[12];
707
708 Double_t x=fX;
709 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
bfd20868 710 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
07dfd570 711 // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle
712 // direction in local frame is along the X axis
713 if ((cf*ca+sf*sa)<0) {
1450dc8a 714 AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa));
07dfd570 715 return kFALSE;
716 }
717 //
dfcef74c 718 Double_t tmp=sf*ca - cf*sa;
6e50abb1 719
7248cf51 720 if (TMath::Abs(tmp) >= kAlmost1) {
721 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
722 AliWarning(Form("Rotation failed ! %.10e",tmp));
0b69bbb2 723 return kFALSE;
724 }
49d13e89 725 fAlpha = alpha;
726 fX = x*ca + fP0*sa;
727 fP0= -x*sa + fP0*ca;
dfcef74c 728 fP2= tmp;
49d13e89 729
06fb4a2f 730 if (TMath::Abs(cf)<kAlmost0) {
731 AliError(Form("Too small cosine value %f",cf));
732 cf = kAlmost0;
733 }
734
49d13e89 735 Double_t rr=(ca+sf/cf*sa);
736
737 fC00 *= (ca*ca);
738 fC10 *= ca;
739 fC20 *= ca*rr;
740 fC21 *= rr;
741 fC22 *= rr*rr;
742 fC30 *= ca;
743 fC32 *= rr;
744 fC40 *= ca;
745 fC42 *= rr;
746
86be8934 747 CheckCovariance();
748
49d13e89 749 return kTRUE;
750}
751
2d2fd909 752Bool_t AliExternalTrackParam::Invert() {
753 //------------------------------------------------------------------
754 // Transform this track to the local coord. system rotated by 180 deg.
755 //------------------------------------------------------------------
756 fX = -fX;
757 fAlpha += TMath::Pi();
758 while (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
759 while (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
760 //
761 fP[0] = -fP[0];
6e50abb1 762 //fP[2] = -fP[2];
2d2fd909 763 fP[3] = -fP[3];
764 fP[4] = -fP[4];
765 //
6e50abb1 766 fC[1] = -fC[1]; // since the fP1 and fP2 are not inverted, their covariances with others change sign
767 fC[3] = -fC[3];
2d2fd909 768 fC[7] = -fC[7];
6e50abb1 769 fC[8] = -fC[8];
2d2fd909 770 fC[11] = -fC[11];
6e50abb1 771 fC[12] = -fC[12];
2d2fd909 772 //
773 return kTRUE;
774}
775
49d13e89 776Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
777 //----------------------------------------------------------------
778 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
779 //----------------------------------------------------------------
49d13e89 780 Double_t dx=xk-fX;
e421f556 781 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 782
1530f89c 783 Double_t crv=GetC(b);
5773defd 784 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
785
2de63fc5 786 Double_t x2r = crv*dx;
787 Double_t f1=fP[2], f2=f1 + x2r;
bbefa4c4 788 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 789 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
4349f5a4 790 if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
49d13e89 791
792 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
793 Double_t
794 &fC00=fC[0],
795 &fC10=fC[1], &fC11=fC[2],
796 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
797 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
798 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
799
bfd20868 800 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
4349f5a4 801 if (TMath::Abs(r1)<kAlmost0) return kFALSE;
802 if (TMath::Abs(r2)<kAlmost0) return kFALSE;
49d13e89 803
804 fX=xk;
2de63fc5 805 double dy2dx = (f1+f2)/(r1+r2);
806 fP0 += dx*dy2dx;
807 if (TMath::Abs(x2r)<0.05) {
808 fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov !
809 fP2 += x2r;
810 }
811 else {
812 // for small dx/R the linear apporximation of the arc by the segment is OK,
813 // but at large dx/R the error is very large and leads to incorrect Z propagation
814 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
815 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
816 // Similarly, the rotation angle in linear in dx only for dx<<R
817 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
818 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
819 fP1 += rot/crv*fP3;
820 fP2 = TMath::Sin(rot + TMath::ASin(fP2));
821 }
49d13e89 822
823 //f = F - 1
e804766b 824 /*
49d13e89 825 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
826 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
827 Double_t f12= dx*fP3*f1/(r1*r1*r1);
828 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
829 Double_t f13= dx/r1;
830 Double_t f24= dx; f24*=cc;
e804766b 831 */
832 Double_t rinv = 1./r1;
833 Double_t r3inv = rinv*rinv*rinv;
834 Double_t f24= x2r/fP4;
835 Double_t f02= dx*r3inv;
836 Double_t f04=0.5*f24*f02;
837 Double_t f12= f02*fP3*f1;
838 Double_t f14=0.5*f24*f02*fP3*f1;
839 Double_t f13= dx*rinv;
840
49d13e89 841 //b = C*ft
842 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
843 Double_t b02=f24*fC40;
844 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
845 Double_t b12=f24*fC41;
846 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
847 Double_t b22=f24*fC42;
848 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
849 Double_t b42=f24*fC44;
850 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
851 Double_t b32=f24*fC43;
852
853 //a = f*b = f*C*ft
854 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
855 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
856 Double_t a22=f24*b42;
857
858 //F*C*Ft = C + (b + bt + a)
859 fC00 += b00 + b00 + a00;
860 fC10 += b10 + b01 + a01;
861 fC20 += b20 + b02 + a02;
862 fC30 += b30;
863 fC40 += b40;
864 fC11 += b11 + b11 + a11;
865 fC21 += b21 + b12 + a12;
866 fC31 += b31;
867 fC41 += b41;
868 fC22 += b22 + b22 + a22;
869 fC32 += b32;
870 fC42 += b42;
871
86be8934 872 CheckCovariance();
873
49d13e89 874 return kTRUE;
875}
876
599b440e 877Bool_t AliExternalTrackParam::PropagateParamOnlyTo(Double_t xk, Double_t b) {
878 //----------------------------------------------------------------
879 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
880 // Only parameters are propagated, not the matrix. To be used for small
881 // distances only (<mm, i.e. misalignment)
882 //----------------------------------------------------------------
883 Double_t dx=xk-fX;
884 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
885
886 Double_t crv=GetC(b);
887 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
888
889 Double_t x2r = crv*dx;
890 Double_t f1=fP[2], f2=f1 + x2r;
891 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
892 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
893 if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
894
895 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
896 if (TMath::Abs(r1)<kAlmost0) return kFALSE;
897 if (TMath::Abs(r2)<kAlmost0) return kFALSE;
898
899 fX=xk;
900 double dy2dx = (f1+f2)/(r1+r2);
901 fP[0] += dx*dy2dx;
902 fP[1] += dx*(r2 + f2*dy2dx)*fP[3]; // Many thanks to P.Hristov !
903 fP[2] += x2r;
904
905 return kTRUE;
906}
907
9f2bec63 908Bool_t
909AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
910 //------------------------------------------------------------------
911 // Transform this track to the local coord. system rotated
912 // by angle "alpha" (rad) with respect to the global coord. system,
913 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
914 //------------------------------------------------------------------
915
916 //Save the parameters
917 Double_t as=fAlpha;
918 Double_t xs=fX;
919 Double_t ps[5], cs[15];
920 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
921 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
922
923 if (Rotate(alpha))
924 if (PropagateTo(x,b)) return kTRUE;
925
926 //Restore the parameters, if the operation failed
927 fAlpha=as;
928 fX=xs;
929 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
930 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
931 return kFALSE;
932}
933
266a0f9b 934Bool_t AliExternalTrackParam::PropagateBxByBz
935(Double_t alpha, Double_t x, Double_t b[3]) {
936 //------------------------------------------------------------------
937 // Transform this track to the local coord. system rotated
938 // by angle "alpha" (rad) with respect to the global coord. system,
939 // and propagate this track to the plane X=xk (cm),
940 // taking into account all three components of the B field, "b[3]" (kG)
941 //------------------------------------------------------------------
942
943 //Save the parameters
944 Double_t as=fAlpha;
945 Double_t xs=fX;
946 Double_t ps[5], cs[15];
947 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
948 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
949
950 if (Rotate(alpha))
951 if (PropagateToBxByBz(x,b)) return kTRUE;
952
953 //Restore the parameters, if the operation failed
954 fAlpha=as;
955 fX=xs;
956 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
957 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
958 return kFALSE;
959}
960
9f2bec63 961
052daaff 962void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
963Double_t p[3], Double_t bz) const {
964 //+++++++++++++++++++++++++++++++++++++++++
965 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
966 // Extrapolate track along simple helix in magnetic field
967 // Arguments: len -distance alogn helix, [cm]
968 // bz - mag field, [kGaus]
969 // Returns: x and p contain extrapolated positon and momentum
970 // The momentum returned for straight-line tracks is meaningless !
971 //+++++++++++++++++++++++++++++++++++++++++
972 GetXYZ(x);
973
2258e165 974 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 975 Double_t unit[3]; GetDirection(unit);
976 x[0]+=unit[0]*len;
977 x[1]+=unit[1]*len;
978 x[2]+=unit[2]*len;
979
980 p[0]=unit[0]/kAlmost0;
981 p[1]=unit[1]/kAlmost0;
982 p[2]=unit[2]/kAlmost0;
983 } else {
984 GetPxPyPz(p);
985 Double_t pp=GetP();
986 Double_t a = -kB2C*bz*GetSign();
987 Double_t rho = a/pp;
988 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
989 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
990 x[2] += p[2]*len/pp;
991
992 Double_t p0=p[0];
993 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
994 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
995 }
996}
997
998Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
999Double_t bz) const {
1000 //+++++++++++++++++++++++++++++++++++++++++
1001 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
1002 // Finds point of intersection (if exists) of the helix with the plane.
1003 // Stores result in fX and fP.
1004 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
1005 // and vector, normal to the plane
1006 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
1007 //+++++++++++++++++++++++++++++++++++++++++
1008 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
1009
1010 //estimates initial helix length up to plane
1011 Double_t s=
1012 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
1013 Double_t dist=99999,distPrev=dist;
1014 Double_t x[3],p[3];
1015 while(TMath::Abs(dist)>0.00001){
1016 //calculates helix at the distance s from x0 ALONG the helix
1017 Propagate(s,x,p,bz);
1018
1019 //distance between current helix position and plane
1020 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
1021
1022 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
1023 distPrev=dist;
1024 s-=dist;
1025 }
1026 //on exit pnt is intersection point,norm is track vector at that point,
1027 //all in MARS
1028 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
1029 return kTRUE;
1030}
1031
49d13e89 1032Double_t
1033AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
1034 //----------------------------------------------------------------
1035 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
1036 //----------------------------------------------------------------
1037 Double_t sdd = fC[0] + cov[0];
1038 Double_t sdz = fC[1] + cov[1];
1039 Double_t szz = fC[2] + cov[2];
1040 Double_t det = sdd*szz - sdz*sdz;
1041
1042 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
1043
1044 Double_t d = fP[0] - p[0];
1045 Double_t z = fP[1] - p[1];
1046
1047 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
1048}
1049
4b189f98 1050Double_t AliExternalTrackParam::
1051GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
1052 //----------------------------------------------------------------
1053 // Estimate the chi2 of the 3D space point "p" and
1e023a36 1054 // the full covariance matrix "covyz" and "covxyz"
4b189f98 1055 //
1056 // Cov(x,x) ... : covxyz[0]
1057 // Cov(y,x) ... : covxyz[1] covyz[0]
1058 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
1059 //----------------------------------------------------------------
1060
1061 Double_t res[3] = {
1062 GetX() - p[0],
1063 GetY() - p[1],
1064 GetZ() - p[2]
1065 };
1066
1067 Double_t f=GetSnp();
1068 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
bfd20868 1069 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
4b189f98 1070 Double_t a=f/r, b=GetTgl()/r;
1071
1072 Double_t s2=333.*333.; //something reasonably big (cm^2)
1073
1074 TMatrixDSym v(3);
1075 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
1076 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
1077 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
1078
1079 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
1080 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
1081 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
1082
1083 v.Invert();
1084 if (!v.IsValid()) return kVeryBig;
1085
1086 Double_t chi2=0.;
1087 for (Int_t i = 0; i < 3; i++)
1088 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
1089
1090 return chi2;
acdfbc78 1091}
1092
1093Double_t AliExternalTrackParam::
1094GetPredictedChi2(const AliExternalTrackParam *t) const {
1095 //----------------------------------------------------------------
1096 // Estimate the chi2 (5 dof) of this track with respect to the track
1097 // given by the argument.
1098 // The two tracks must be in the same reference system
1099 // and estimated at the same reference plane.
1100 //----------------------------------------------------------------
1101
1102 if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) {
1103 AliError("The reference systems of the tracks differ !");
1104 return kVeryBig;
1105 }
1106 if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) {
1107 AliError("The reference of the tracks planes differ !");
1108 return kVeryBig;
1109 }
1110
1111 TMatrixDSym c(5);
1112 c(0,0)=GetSigmaY2();
1113 c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
1114 c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
1115 c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
1116 c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
1117
1118 c(0,0)+=t->GetSigmaY2();
1119 c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
1120 c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
1121 c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
1122 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();
1123 c(0,1)=c(1,0);
1124 c(0,2)=c(2,0); c(1,2)=c(2,1);
1125 c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
1126 c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
1127
1128 c.Invert();
1129 if (!c.IsValid()) return kVeryBig;
1130
1131
1132 Double_t res[5] = {
1133 GetY() - t->GetY(),
1134 GetZ() - t->GetZ(),
1135 GetSnp() - t->GetSnp(),
1136 GetTgl() - t->GetTgl(),
1137 GetSigned1Pt() - t->GetSigned1Pt()
1138 };
4b189f98 1139
acdfbc78 1140 Double_t chi2=0.;
1141 for (Int_t i = 0; i < 5; i++)
1142 for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
4b189f98 1143
acdfbc78 1144 return chi2;
4b189f98 1145}
1146
1e023a36 1147Bool_t AliExternalTrackParam::
1148PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
1149 //----------------------------------------------------------------
1150 // Propagate this track to the plane
1151 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
1152 // belongs to.
1153 // The magnetic field is "bz" (kG)
1154 //
1155 // The track curvature and the change of the covariance matrix
1156 // of the track parameters are negleted !
1157 // (So the "step" should be small compared with 1/curvature)
1158 //----------------------------------------------------------------
1159
1160 Double_t f=GetSnp();
1161 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
bfd20868 1162 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
1e023a36 1163 Double_t a=f/r, b=GetTgl()/r;
1164
1165 Double_t s2=333.*333.; //something reasonably big (cm^2)
1166
1167 TMatrixDSym tV(3);
1168 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
1169 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
1170 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
1171
1172 TMatrixDSym pV(3);
1173 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
1174 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
1175 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
1176
1177 TMatrixDSym tpV(tV);
1178 tpV+=pV;
1179 tpV.Invert();
1180 if (!tpV.IsValid()) return kFALSE;
1181
1182 TMatrixDSym pW(3),tW(3);
1183 for (Int_t i=0; i<3; i++)
1184 for (Int_t j=0; j<3; j++) {
1185 pW(i,j)=tW(i,j)=0.;
1186 for (Int_t k=0; k<3; k++) {
1187 pW(i,j) += tV(i,k)*tpV(k,j);
1188 tW(i,j) += pV(i,k)*tpV(k,j);
1189 }
1190 }
1191
1192 Double_t t[3] = {GetX(), GetY(), GetZ()};
1193
1194 Double_t x=0.;
1195 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
1196 Double_t crv=GetC(bz);
1197 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1198 f += crv*(x-fX);
1199 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
1200 fX=x;
1201
1202 fP[0]=0.;
1203 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
1204 fP[1]=0.;
1205 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
1206
1207 return kTRUE;
1208}
1209
e23a38cb 1210Double_t *AliExternalTrackParam::GetResiduals(
1211Double_t *p,Double_t *cov,Bool_t updated) const {
1212 //------------------------------------------------------------------
1213 // Returns the track residuals with the space point "p" having
1214 // the covariance matrix "cov".
1215 // If "updated" is kTRUE, the track parameters expected to be updated,
1216 // otherwise they must be predicted.
1217 //------------------------------------------------------------------
1218 static Double_t res[2];
1219
1220 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1221 if (updated) {
1222 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
1223 } else {
1224 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
1225 }
1226 Double_t det=r00*r11 - r01*r01;
1227
1228 if (TMath::Abs(det) < kAlmost0) return 0;
1229
1230 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 1231
1232 if (r00 < 0.) return 0;
1233 if (r11 < 0.) return 0;
1234
e23a38cb 1235 Double_t dy = fP[0] - p[0];
1236 Double_t dz = fP[1] - p[1];
1237
1238 res[0]=dy*TMath::Sqrt(r00);
1239 res[1]=dz*TMath::Sqrt(r11);
1240
1241 return res;
1242}
1243
49d13e89 1244Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
1245 //------------------------------------------------------------------
1246 // Update the track parameters with the space point "p" having
1247 // the covariance matrix "cov"
1248 //------------------------------------------------------------------
1249 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
1250 Double_t
1251 &fC00=fC[0],
1252 &fC10=fC[1], &fC11=fC[2],
1253 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1254 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1255 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1256
1257 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1258 r00+=fC00; r01+=fC10; r11+=fC11;
1259 Double_t det=r00*r11 - r01*r01;
1260
1261 if (TMath::Abs(det) < kAlmost0) return kFALSE;
1262
1263
1264 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
1265
1266 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
1267 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
1268 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
1269 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
1270 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
1271
1272 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1273 Double_t sf=fP2 + k20*dy + k21*dz;
1274 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1275
1276 fP0 += k00*dy + k01*dz;
1277 fP1 += k10*dy + k11*dz;
1278 fP2 = sf;
1279 fP3 += k30*dy + k31*dz;
1280 fP4 += k40*dy + k41*dz;
1281
1282 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1283 Double_t c12=fC21, c13=fC31, c14=fC41;
1284
1285 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1286 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1287 fC40-=k00*c04+k01*c14;
1288
1289 fC11-=k10*c01+k11*fC11;
1290 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1291 fC41-=k10*c04+k11*c14;
1292
1293 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1294 fC42-=k20*c04+k21*c14;
1295
1296 fC33-=k30*c03+k31*c13;
1297 fC43-=k30*c04+k31*c14;
599b440e 1298
49d13e89 1299 fC44-=k40*c04+k41*c14;
1300
86be8934 1301 CheckCovariance();
1302
49d13e89 1303 return kTRUE;
1304}
1305
c7bafca9 1306void
1307AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1308 //--------------------------------------------------------------------
1309 // External track parameters -> helix parameters
1310 // "b" - magnetic field (kG)
1311 //--------------------------------------------------------------------
1312 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1313
1530f89c 1314 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1315
1316 hlx[5]=fX*cs - hlx[0]*sn; // x0
1317 hlx[0]=fX*sn + hlx[0]*cs; // y0
1318//hlx[1]= // z0
1319 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1320//hlx[3]= // tgl
1530f89c 1321 hlx[4]=GetC(b); // C
c7bafca9 1322}
1323
1324
1325static void Evaluate(const Double_t *h, Double_t t,
1326 Double_t r[3], //radius vector
1327 Double_t g[3], //first defivatives
1328 Double_t gg[3]) //second derivatives
1329{
1330 //--------------------------------------------------------------------
1331 // Calculate position of a point on a track and some derivatives
1332 //--------------------------------------------------------------------
1333 Double_t phase=h[4]*t+h[2];
1334 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1335
ba4550c4 1336 r[0] = h[5];
1337 r[1] = h[0];
1338 if (TMath::Abs(h[4])>kAlmost0) {
1339 r[0] += (sn - h[6])/h[4];
1340 r[1] -= (cs - h[7])/h[4];
1341 }
c7bafca9 1342 r[2] = h[1] + h[3]*t;
1343
1344 g[0] = cs; g[1]=sn; g[2]=h[3];
1345
1346 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1347}
1348
1349Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1350Double_t b, Double_t &xthis, Double_t &xp) const {
1351 //------------------------------------------------------------
1352 // Returns the (weighed !) distance of closest approach between
1353 // this track and the track "p".
1354 // Other returned values:
1355 // xthis, xt - coordinates of tracks' reference planes at the DCA
1356 //-----------------------------------------------------------
1357 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1358 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1359 Double_t dx2=dy2;
1360
c7bafca9 1361 Double_t p1[8]; GetHelixParameters(p1,b);
1362 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1363 Double_t p2[8]; p->GetHelixParameters(p2,b);
1364 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1365
1366
1367 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1368 Evaluate(p1,t1,r1,g1,gg1);
1369 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1370 Evaluate(p2,t2,r2,g2,gg2);
1371
1372 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1373 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1374
1375 Int_t max=27;
1376 while (max--) {
1377 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1378 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1379 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1380 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1381 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1382 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1383 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1384 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1385 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1386
1387 Double_t det=h11*h22-h12*h12;
1388
1389 Double_t dt1,dt2;
1390 if (TMath::Abs(det)<1.e-33) {
1391 //(quasi)singular Hessian
1392 dt1=-gt1; dt2=-gt2;
1393 } else {
1394 dt1=-(gt1*h22 - gt2*h12)/det;
1395 dt2=-(h11*gt2 - h12*gt1)/det;
1396 }
1397
1398 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1399
1400 //check delta(phase1) ?
1401 //check delta(phase2) ?
1402
1403 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1404 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1405 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1406 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1407 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1408 if (lmb < 0.)
358f16ae 1409 AliDebug(1," stopped at not a minimum !");
c7bafca9 1410 break;
1411 }
1412
1413 Double_t dd=dm;
1414 for (Int_t div=1 ; ; div*=2) {
1415 Evaluate(p1,t1+dt1,r1,g1,gg1);
1416 Evaluate(p2,t2+dt2,r2,g2,gg2);
1417 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1418 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1419 if (dd<dm) break;
1420 dt1*=0.5; dt2*=0.5;
1421 if (div>512) {
358f16ae 1422 AliDebug(1," overshoot !"); break;
c7bafca9 1423 }
1424 }
1425 dm=dd;
1426
1427 t1+=dt1;
1428 t2+=dt2;
1429
1430 }
1431
358f16ae 1432 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1433
1434 Double_t cs=TMath::Cos(GetAlpha());
1435 Double_t sn=TMath::Sin(GetAlpha());
1436 xthis=r1[0]*cs + r1[1]*sn;
1437
1438 cs=TMath::Cos(p->GetAlpha());
1439 sn=TMath::Sin(p->GetAlpha());
1440 xp=r2[0]*cs + r2[1]*sn;
1441
1442 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1443}
1444
1445Double_t AliExternalTrackParam::
1446PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1447 //--------------------------------------------------------------
1448 // Propagates this track and the argument track to the position of the
1449 // distance of closest approach.
1450 // Returns the (weighed !) distance of closest approach.
1451 //--------------------------------------------------------------
1452 Double_t xthis,xp;
1453 Double_t dca=GetDCA(p,b,xthis,xp);
1454
1455 if (!PropagateTo(xthis,b)) {
1456 //AliWarning(" propagation failed !");
1457 return 1e+33;
1458 }
1459
1460 if (!p->PropagateTo(xp,b)) {
1461 //AliWarning(" propagation failed !";
1462 return 1e+33;
1463 }
1464
1465 return dca;
1466}
1467
1468
58e536c5 1469Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1470Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1471 //
e99a34df 1472 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1473 // if the (rough) transverse impact parameter is not bigger then "maxd".
1474 // Magnetic field is "b" (kG).
1475 //
1476 // a) The track gets extapolated to the DCA to the vertex.
1477 // b) The impact parameters and their covariance matrix are calculated.
1478 //
1479 // In the case of success, the returned value is kTRUE
1480 // (otherwise, it's kFALSE)
1481 //
1482 Double_t alpha=GetAlpha();
1483 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1484 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1485 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1486 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1487 x-=xv; y-=yv;
1488
1489 //Estimate the impact parameter neglecting the track curvature
bfd20868 1490 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
f76701bf 1491 if (d > maxd) return kFALSE;
1492
1493 //Propagate to the DCA
2258e165 1494 Double_t crv=GetC(b);
e99a34df 1495 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1496
bfd20868 1497 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1498 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
e99a34df 1499 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1500 else cs=1.;
f76701bf 1501
1502 x = xv*cs + yv*sn;
1503 yv=-xv*sn + yv*cs; xv=x;
1504
1505 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
266a0f9b 1506
1507 if (dz==0) return kTRUE;
1508 dz[0] = GetParameter()[0] - yv;
1509 dz[1] = GetParameter()[1] - zv;
1510
1511 if (covar==0) return kTRUE;
1512 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
1513
1514 //***** Improvements by A.Dainese
1515 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1516 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1517 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1518 covar[1] = GetCovariance()[1]; // between (x,y) and z
1519 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1520 //*****
1521
1522 return kTRUE;
1523}
1524
1525Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
1526Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
1527 //
1528 // Propagate this track to the DCA to vertex "vtx",
1529 // if the (rough) transverse impact parameter is not bigger then "maxd".
1530 //
1531 // This function takes into account all three components of the magnetic
1532 // field given by the b[3] arument (kG)
1533 //
1534 // a) The track gets extapolated to the DCA to the vertex.
1535 // b) The impact parameters and their covariance matrix are calculated.
1536 //
1537 // In the case of success, the returned value is kTRUE
1538 // (otherwise, it's kFALSE)
1539 //
1540 Double_t alpha=GetAlpha();
1541 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1542 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
1543 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1544 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
1545 x-=xv; y-=yv;
1546
1547 //Estimate the impact parameter neglecting the track curvature
bfd20868 1548 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
266a0f9b 1549 if (d > maxd) return kFALSE;
1550
1551 //Propagate to the DCA
8567bf39 1552 Double_t crv=GetC(b[2]);
1553 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
266a0f9b 1554
bfd20868 1555 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1556 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
266a0f9b 1557 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1558 else cs=1.;
1559
1560 x = xv*cs + yv*sn;
1561 yv=-xv*sn + yv*cs; xv=x;
1562
1563 if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1564
1565 if (dz==0) return kTRUE;
1566 dz[0] = GetParameter()[0] - yv;
1567 dz[1] = GetParameter()[1] - zv;
1568
1569 if (covar==0) return kTRUE;
58e536c5 1570 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1571
1572 //***** Improvements by A.Dainese
1573 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1574 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1575 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1576 covar[1] = GetCovariance()[1]; // between (x,y) and z
1577 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1578 //*****
1579
29fbcc93 1580 return kTRUE;
f76701bf 1581}
1582
b1149664 1583void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1584 //----------------------------------------------------------------
1585 // This function returns a unit vector along the track direction
1586 // in the global coordinate system.
1587 //----------------------------------------------------------------
1588 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1589 Double_t snp=fP[2];
bfd20868 1590 Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp));
b1149664 1591 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1592 d[0]=(csp*cs - snp*sn)/norm;
1593 d[1]=(snp*cs + csp*sn)/norm;
1594 d[2]=fP[3]/norm;
1595}
1596
c683ddc2 1597Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1598 //---------------------------------------------------------------------
1599 // This function returns the global track momentum components
1600 // Results for (nearly) straight tracks are meaningless !
1601 //---------------------------------------------------------------------
1602 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1603 return Local2GlobalMomentum(p,fAlpha);
1604}
a5e407e9 1605
def9660e 1606Double_t AliExternalTrackParam::Px() const {
957fb479 1607 //---------------------------------------------------------------------
1608 // Returns x-component of momentum
1609 // Result for (nearly) straight tracks is meaningless !
1610 //---------------------------------------------------------------------
def9660e 1611
957fb479 1612 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1613 GetPxPyPz(p);
1614
1615 return p[0];
1616}
1617
1618Double_t AliExternalTrackParam::Py() const {
957fb479 1619 //---------------------------------------------------------------------
1620 // Returns y-component of momentum
1621 // Result for (nearly) straight tracks is meaningless !
1622 //---------------------------------------------------------------------
def9660e 1623
957fb479 1624 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1625 GetPxPyPz(p);
1626
1627 return p[1];
1628}
1629
c683ddc2 1630Double_t AliExternalTrackParam::Xv() const {
1631 //---------------------------------------------------------------------
1632 // Returns x-component of first track point
1633 //---------------------------------------------------------------------
1634
1635 Double_t r[3]={0.,0.,0.};
1636 GetXYZ(r);
1637
1638 return r[0];
1639}
1640
1641Double_t AliExternalTrackParam::Yv() const {
1642 //---------------------------------------------------------------------
1643 // Returns y-component of first track point
1644 //---------------------------------------------------------------------
1645
1646 Double_t r[3]={0.,0.,0.};
1647 GetXYZ(r);
1648
1649 return r[1];
1650}
1651
def9660e 1652Double_t AliExternalTrackParam::Theta() const {
1653 // return theta angle of momentum
1654
7cdd0c20 1655 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1656}
1657
1658Double_t AliExternalTrackParam::Phi() const {
957fb479 1659 //---------------------------------------------------------------------
1660 // Returns the azimuthal angle of momentum
1661 // 0 <= phi < 2*pi
1662 //---------------------------------------------------------------------
def9660e 1663
957fb479 1664 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1665 if (phi<0.) phi+=2.*TMath::Pi();
1666 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1667
1668 return phi;
def9660e 1669}
1670
1671Double_t AliExternalTrackParam::M() const {
1672 // return particle mass
1673
1674 // No mass information available so far.
1675 // Redifine in derived class!
1676
1677 return -999.;
1678}
1679
1680Double_t AliExternalTrackParam::E() const {
1681 // return particle energy
1682
1683 // No PID information available so far.
1684 // Redifine in derived class!
1685
1686 return -999.;
1687}
1688
1689Double_t AliExternalTrackParam::Eta() const {
1690 // return pseudorapidity
1691
1692 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1693}
1694
1695Double_t AliExternalTrackParam::Y() const {
1696 // return rapidity
1697
1698 // No PID information available so far.
1699 // Redifine in derived class!
1700
1701 return -999.;
1702}
1703
c9ec41e8 1704Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1705 //---------------------------------------------------------------------
1706 // This function returns the global track position
1707 //---------------------------------------------------------------------
1708 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1709 return Local2GlobalPosition(r,fAlpha);
51ad6848 1710}
1711
c9ec41e8 1712Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1713 //---------------------------------------------------------------------
1714 // This function returns the global covariance matrix of the track params
1715 //
1716 // Cov(x,x) ... : cv[0]
1717 // Cov(y,x) ... : cv[1] cv[2]
1718 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1719 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1720 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1721 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1722 //
c9ec41e8 1723 // Results for (nearly) straight tracks are meaningless !
1724 //---------------------------------------------------------------------
e421f556 1725 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1726 for (Int_t i=0; i<21; i++) cv[i]=0.;
1727 return kFALSE;
a5e407e9 1728 }
49d13e89 1729 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1730 for (Int_t i=0; i<21; i++) cv[i]=0.;
1731 return kFALSE;
1732 }
1733 Double_t pt=1./TMath::Abs(fP[4]);
1734 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1735 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1736
1737 Double_t m00=-sn, m10=cs;
1738 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1739 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1740 Double_t m35=pt, m45=-pt*pt*fP[3];
1741
854d5d49 1742 m43*=GetSign();
1743 m44*=GetSign();
1744 m45*=GetSign();
1745
c9ec41e8 1746 cv[0 ] = fC[0]*m00*m00;
1747 cv[1 ] = fC[0]*m00*m10;
1748 cv[2 ] = fC[0]*m10*m10;
1749 cv[3 ] = fC[1]*m00;
1750 cv[4 ] = fC[1]*m10;
1751 cv[5 ] = fC[2];
1752 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1753 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1754 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1755 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1756 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1757 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1758 cv[12] = fC[4]*m24 + fC[11]*m44;
1759 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1760 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1761 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1762 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1763 cv[17] = fC[7]*m35 + fC[11]*m45;
1764 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1765 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1766 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1767
c9ec41e8 1768 return kTRUE;
51ad6848 1769}
1770
51ad6848 1771
c9ec41e8 1772Bool_t
1773AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1774 //---------------------------------------------------------------------
1775 // This function returns the global track momentum extrapolated to
1776 // the radial position "x" (cm) in the magnetic field "b" (kG)
1777 //---------------------------------------------------------------------
c9ec41e8 1778 p[0]=fP[4];
1530f89c 1779 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1780 p[2]=fP[3];
1781 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1782}
1783
7cf7bb6c 1784Bool_t
1785AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1786 //---------------------------------------------------------------------
1787 // This function returns the local Y-coordinate of the intersection
1788 // point between this track and the reference plane "x" (cm).
1789 // Magnetic field "b" (kG)
1790 //---------------------------------------------------------------------
1791 Double_t dx=x-fX;
1792 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1793
1530f89c 1794 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1795
1796 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1797 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1798
60e55aee 1799 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 1800 y = fP[0] + dx*(f1+f2)/(r1+r2);
1801 return kTRUE;
1802}
1803
6c94f330 1804Bool_t
1805AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1806 //---------------------------------------------------------------------
1807 // This function returns the local Z-coordinate of the intersection
1808 // point between this track and the reference plane "x" (cm).
1809 // Magnetic field "b" (kG)
1810 //---------------------------------------------------------------------
1811 Double_t dx=x-fX;
1812 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1813
2258e165 1814 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1815
1816 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1817 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1818
60e55aee 1819 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
6c94f330 1820 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1821 return kTRUE;
1822}
1823
c9ec41e8 1824Bool_t
1825AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1826 //---------------------------------------------------------------------
1827 // This function returns the global track position extrapolated to
1828 // the radial position "x" (cm) in the magnetic field "b" (kG)
1829 //---------------------------------------------------------------------
c9ec41e8 1830 Double_t dx=x-fX;
e421f556 1831 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1832
1530f89c 1833 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1834
e421f556 1835 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1836 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1837
60e55aee 1838 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
c9ec41e8 1839 r[0] = x;
1840 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1841 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1842
c9ec41e8 1843 return Local2GlobalPosition(r,fAlpha);
51ad6848 1844}
1845
51ad6848 1846//_____________________________________________________________________________
1847void AliExternalTrackParam::Print(Option_t* /*option*/) const
1848{
1849// print the parameters and the covariance matrix
1850
1851 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1852 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1853 fP[0], fP[1], fP[2], fP[3], fP[4]);
1854 printf(" covariance: %12g\n", fC[0]);
1855 printf(" %12g %12g\n", fC[1], fC[2]);
1856 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1857 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1858 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1859 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1860 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1861}
5b77d93c 1862
c194ba83 1863Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1864 //
1865 // Get sinus at given x
1866 //
1530f89c 1867 Double_t crv=GetC(b);
c194ba83 1868 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1869 Double_t dx = x-fX;
1870 Double_t res = fP[2]+dx*crv;
1871 return res;
1872}
bf00ebb8 1873
1874Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1875 //------------------------------------------------------------------------
1876 // Get the distance between two tracks at the local position x
1877 // working in the local frame of this track.
1878 // Origin : Marian.Ivanov@cern.ch
1879 //-----------------------------------------------------------------------
1880 Double_t xyz[3];
1881 Double_t xyz2[3];
1882 xyz[0]=x;
1883 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1884 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1885 //
1886 //
1887 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1888 xyz2[0]=x;
1889 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1890 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1891 }else{
1892 //
1893 Double_t xyz1[3];
1894 Double_t dfi = param2->GetAlpha()-GetAlpha();
1895 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1896 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1897 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1898 //
1899 xyz1[0]=xyz2[0];
1900 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1901 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1902 //
1903 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1904 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1905 xyz2[2] = xyz1[2];
1906 }
1907 dist[0] = xyz[0]-xyz2[0];
1908 dist[1] = xyz[1]-xyz2[1];
1909 dist[2] = xyz[2]-xyz2[2];
1910
1911 return kTRUE;
1912}
0c19adf7 1913
1914
1915//
1916// Draw functionality.
1917// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1918//
1919
1920void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1921 //
1922 // Draw track line
1923 //
1924 if (minR>maxR) return ;
1925 if (stepR<=0) return ;
1926 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1927 if (npoints<1) return;
1928 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1929 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1930 polymarker->Draw();
1931}
1932
1933//
1934void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1935 //
1936 // Fill points in the polymarker
1937 //
1938 Int_t counter=0;
1939 for (Double_t r=minR; r<maxR; r+=stepR){
1940 Double_t point[3];
1941 GetXYZAt(r,magF,point);
1942 pol->SetPoint(counter,point[0],point[1], point[2]);
047640da 1943 // printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
0c19adf7 1944 counter++;
1945 }
1946}
0e8460af 1947
1948Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1949 //
1950 Int_t min = TMath::Min(i,j);
1951 Int_t max = TMath::Max(i,j);
1952
1953 return min+(max+1)*max/2;
1954}
8b6e3369 1955
1956
1957void AliExternalTrackParam::g3helx3(Double_t qfield,
1958 Double_t step,
1959 Double_t vect[7]) {
1960/******************************************************************
1961 * *
1962 * GEANT3 tracking routine in a constant field oriented *
1963 * along axis 3 *
1964 * Tracking is performed with a conventional *
1965 * helix step method *
1966 * *
1967 * Authors R.Brun, M.Hansroul ********* *
1968 * Rewritten V.Perevoztchikov *
1969 * *
1970 * Rewritten in C++ by I.Belikov *
1971 * *
1972 * qfield (kG) - particle charge times magnetic field *
1973 * step (cm) - step length along the helix *
1974 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
1975 * *
1976 ******************************************************************/
1977 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
bfd20868 1978 const Double_t kOvSqSix=TMath::Sqrt(1./6.);
8b6e3369 1979
1980 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
1981
1982 Double_t rho = qfield*kB2C/vect[ipp];
1983 Double_t tet = rho*step;
1984
1985 Double_t tsint, sintt, sint, cos1t;
2de63fc5 1986 if (TMath::Abs(tet) > 0.03) {
8b6e3369 1987 sint = TMath::Sin(tet);
1988 sintt = sint/tet;
1989 tsint = (tet - sint)/tet;
1990 Double_t t=TMath::Sin(0.5*tet);
1991 cos1t = 2*t*t/tet;
1992 } else {
1993 tsint = tet*tet/6.;
bfd20868 1994 sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint;
8b6e3369 1995 sint = tet*sintt;
1996 cos1t = 0.5*tet;
1997 }
1998
1999 Double_t f1 = step*sintt;
2000 Double_t f2 = step*cos1t;
2001 Double_t f3 = step*tsint*cosz;
2002 Double_t f4 = -tet*cos1t;
2003 Double_t f5 = sint;
2004
2005 vect[ix] += f1*cosx - f2*cosy;
2006 vect[iy] += f1*cosy + f2*cosx;
2007 vect[iz] += f1*cosz + f3;
2008
2009 vect[ipx] += f4*cosx - f5*cosy;
2010 vect[ipy] += f4*cosy + f5*cosx;
2011
2012}
2013
2014Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
2015 //----------------------------------------------------------------
2016 // Extrapolate this track to the plane X=xk in the field b[].
2017 //
2018 // X [cm] is in the "tracking coordinate system" of this track.
2019 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
2020 //----------------------------------------------------------------
2021
2022 Double_t dx=xk-fX;
2023 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
7e1b73dd 2024 if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
ef3508c5 2025 // Do not propagate tracks outside the ALICE detector
2026 if (TMath::Abs(dx)>1e5 ||
2027 TMath::Abs(GetY())>1e5 ||
2028 TMath::Abs(GetZ())>1e5) {
2029 AliWarning(Form("Anomalous track, target X:%f",xk));
2030 Print();
2031 return kFALSE;
2032 }
8b6e3369 2033
2034 Double_t crv=GetC(b[2]);
2035 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
2036
2de63fc5 2037 Double_t x2r = crv*dx;
2038 Double_t f1=fP[2], f2=f1 + x2r;
8b6e3369 2039 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
2040 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
2041
2042
2043 // Estimate the covariance matrix
2044 Double_t &fP3=fP[3], &fP4=fP[4];
2045 Double_t
2046 &fC00=fC[0],
2047 &fC10=fC[1], &fC11=fC[2],
2048 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
2049 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
2050 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
2051
bfd20868 2052 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
8b6e3369 2053
2054 //f = F - 1
e804766b 2055 /*
8b6e3369 2056 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
2057 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
2058 Double_t f12= dx*fP3*f1/(r1*r1*r1);
2059 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
2060 Double_t f13= dx/r1;
2061 Double_t f24= dx; f24*=cc;
e804766b 2062 */
2063 Double_t rinv = 1./r1;
2064 Double_t r3inv = rinv*rinv*rinv;
2065 Double_t f24= x2r/fP4;
2066 Double_t f02= dx*r3inv;
2067 Double_t f04=0.5*f24*f02;
2068 Double_t f12= f02*fP3*f1;
2069 Double_t f14=0.5*f24*f02*fP3*f1;
2070 Double_t f13= dx*rinv;
2071
8b6e3369 2072 //b = C*ft
2073 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
2074 Double_t b02=f24*fC40;
2075 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
2076 Double_t b12=f24*fC41;
2077 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
2078 Double_t b22=f24*fC42;
2079 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
2080 Double_t b42=f24*fC44;
2081 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
2082 Double_t b32=f24*fC43;
2083
2084 //a = f*b = f*C*ft
2085 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
2086 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
2087 Double_t a22=f24*b42;
2088
2089 //F*C*Ft = C + (b + bt + a)
2090 fC00 += b00 + b00 + a00;
2091 fC10 += b10 + b01 + a01;
2092 fC20 += b20 + b02 + a02;
2093 fC30 += b30;
2094 fC40 += b40;
2095 fC11 += b11 + b11 + a11;
2096 fC21 += b21 + b12 + a12;
2097 fC31 += b31;
2098 fC41 += b41;
2099 fC22 += b22 + b22 + a22;
2100 fC32 += b32;
2101 fC42 += b42;
2102
86be8934 2103 CheckCovariance();
8b6e3369 2104
2105 // Appoximate step length
2de63fc5 2106 double dy2dx = (f1+f2)/(r1+r2);
2107 Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord
2108 : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc
8b6e3369 2109 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
2110
8b6e3369 2111 // Get the track's (x,y,z) and (px,py,pz) in the Global System
2112 Double_t r[3]; GetXYZ(r);
2113 Double_t p[3]; GetPxPyPz(p);
2114 Double_t pp=GetP();
2115 p[0] /= pp;
2116 p[1] /= pp;
2117 p[2] /= pp;
2118
2119
2120 // Rotate to the system where Bx=By=0.
2121 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
2122 Double_t cosphi=1., sinphi=0.;
2123 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
2124 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
2125 Double_t costet=1., sintet=0.;
2126 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
2127 Double_t vect[7];
2128
2129 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
2130 vect[1] = -sinphi*r[0] + cosphi*r[1];
2131 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
2132
2133 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
2134 vect[4] = -sinphi*p[0] + cosphi*p[1];
2135 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
2136
2137 vect[6] = pp;
2138
2139
2140 // Do the helix step
2141 g3helx3(GetSign()*bb,step,vect);
2142
2143
2144 // Rotate back to the Global System
2145 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
2146 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
2147 r[2] = -sintet*vect[0] + costet*vect[2];
2148
2149 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
2150 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
2151 p[2] = -sintet*vect[3] + costet*vect[5];
2152
2153
2154 // Rotate back to the Tracking System
2155 Double_t cosalp = TMath::Cos(fAlpha);
2156 Double_t sinalp =-TMath::Sin(fAlpha);
2157
2158 Double_t
2159 t = cosalp*r[0] - sinalp*r[1];
2160 r[1] = sinalp*r[0] + cosalp*r[1];
2161 r[0] = t;
2162
2163 t = cosalp*p[0] - sinalp*p[1];
2164 p[1] = sinalp*p[0] + cosalp*p[1];
2165 p[0] = t;
2166
2167
2168 // Do the final correcting step to the target plane (linear approximation)
2169 Double_t x=r[0], y=r[1], z=r[2];
2170 if (TMath::Abs(dx) > kAlmost0) {
2171 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
2172 dx = xk - r[0];
2173 x += dx;
2174 y += p[1]/p[0]*dx;
2175 z += p[2]/p[0]*dx;
2176 }
2177
2178
2179 // Calculate the track parameters
2180 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
2181 fX = x;
2182 fP[0] = y;
2183 fP[1] = z;
2184 fP[2] = p[1]/t;
2185 fP[3] = p[2]/t;
2186 fP[4] = GetSign()/(t*pp);
2187
2188 return kTRUE;
2189}
2190
cfdb62d4 2191Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
2192 //
2193 //Translation: in the event mixing, the tracks can be shifted
2194 //of the difference among primary vertices (vTrasl) and
2195 //the covariance matrix is changed accordingly
2196 //(covV = covariance of the primary vertex).
2197 //Origin: "Romita, Rossella" <R.Romita@gsi.de>
2198 //
2199 TVector3 translation;
2200 // vTrasl coordinates in the local system
2201 translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
2202 translation.RotateZ(-fAlpha);
2203 translation.GetXYZ(vTrasl);
2204
2205 //compute the new x,y,z of the track
5a87bb3d 2206 Double_t newX=fX-vTrasl[0];
2207 Double_t newY=fP[0]-vTrasl[1];
2208 Double_t newZ=fP[1]-vTrasl[2];
cfdb62d4 2209
2210 //define the new parameters
5a87bb3d 2211 Double_t newParam[5];
2212 newParam[0]=newY;
2213 newParam[1]=newZ;
2214 newParam[2]=fP[2];
2215 newParam[3]=fP[3];
2216 newParam[4]=fP[4];
cfdb62d4 2217
2218 // recompute the covariance matrix:
2219 // 1. covV in the local system
2220 Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
2221 TMatrixD qQi(3,3);
2222 qQi(0,0) = cosRot;
2223 qQi(0,1) = sinRot;
2224 qQi(0,2) = 0.;
2225 qQi(1,0) = -sinRot;
2226 qQi(1,1) = cosRot;
2227 qQi(1,2) = 0.;
2228 qQi(2,0) = 0.;
2229 qQi(2,1) = 0.;
2230 qQi(2,2) = 1.;
2231 TMatrixD uUi(3,3);
2232 uUi(0,0) = covV[0];
2233 uUi(0,0) = covV[0];
2234 uUi(1,0) = covV[1];
2235 uUi(0,1) = covV[1];
2236 uUi(2,0) = covV[3];
2237 uUi(0,2) = covV[3];
2238 uUi(1,1) = covV[2];
2239 uUi(2,2) = covV[5];
2240 uUi(1,2) = covV[4];
2241 if(uUi.Determinant() <= 0.) {return kFALSE;}
2242 TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
2243 TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
2244
2245 //2. compute the new covariance matrix of the track
2246 Double_t sigmaXX=m(0,0);
2247 Double_t sigmaXZ=m(2,0);
2248 Double_t sigmaXY=m(1,0);
2249 Double_t sigmaYY=GetSigmaY2()+m(1,1);
2250 Double_t sigmaYZ=fC[1]+m(1,2);
2251 Double_t sigmaZZ=fC[2]+m(2,2);
2252 Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
2253 Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
2254 Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
2255
2256 Double_t newCov[15];
2257 newCov[0]=covarianceYY;
2258 newCov[1]=covarianceYZ;
2259 newCov[2]=covarianceZZ;
2260 for(Int_t i=3;i<15;i++){
2261 newCov[i]=fC[i];
2262 }
2263
2264 // set the new parameters
2265
5a87bb3d 2266 Set(newX,fAlpha,newParam,newCov);
cfdb62d4 2267
2268 return kTRUE;
2269 }
86be8934 2270
2271void AliExternalTrackParam::CheckCovariance() {
2272
2273 // This function forces the diagonal elements of the covariance matrix to be positive.
2274 // In case the diagonal element is bigger than the maximal allowed value, it is set to
2275 // the limit and the off-diagonal elements that correspond to it are set to zero.
32e55f82 2276 fC[0] = TMath::Abs(fC[0]);
2277 if (fC[0]>kC0max) {
2278 double scl = TMath::Sqrt(kC0max/fC[0]);
2279 fC[0] = kC0max;
2280 fC[1] *= scl;
2281 fC[3] *= scl;
2282 fC[6] *= scl;
2283 fC[10] *= scl;
2284 }
2285 fC[2] = TMath::Abs(fC[2]);
2286 if (fC[2]>kC2max) {
2287 double scl = TMath::Sqrt(kC2max/fC[2]);
2288 fC[2] = kC2max;
2289 fC[1] *= scl;
2290 fC[4] *= scl;
2291 fC[7] *= scl;
2292 fC[11] *= scl;
2293 }
2294 fC[5] = TMath::Abs(fC[5]);
2295 if (fC[5]>kC5max) {
2296 double scl = TMath::Sqrt(kC5max/fC[5]);
2297 fC[5] = kC5max;
2298 fC[3] *= scl;
2299 fC[4] *= scl;
2300 fC[8] *= scl;
2301 fC[12] *= scl;
2302 }
2303 fC[9] = TMath::Abs(fC[9]);
2304 if (fC[9]>kC9max) {
2305 double scl = TMath::Sqrt(kC9max/fC[9]);
2306 fC[9] = kC9max;
2307 fC[6] *= scl;
2308 fC[7] *= scl;
2309 fC[8] *= scl;
2310 fC[13] *= scl;
2311 }
2312 fC[14] = TMath::Abs(fC[14]);
2313 if (fC[14]>kC14max) {
2314 double scl = TMath::Sqrt(kC14max/fC[14]);
2315 fC[14] = kC14max;
2316 fC[10] *= scl;
2317 fC[11] *= scl;
2318 fC[12] *= scl;
2319 fC[13] *= scl;
2320 }
2321
86be8934 2322 // The part below is used for tests and normally is commented out
2323// TMatrixDSym m(5);
2324// TVectorD eig(5);
2325
2326// m(0,0)=fC[0];
2327// m(1,0)=fC[1]; m(1,1)=fC[2];
2328// m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5];
2329// m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9];
2330// 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];
2331
2332// m(0,1)=m(1,0);
2333// m(0,2)=m(2,0); m(1,2)=m(2,1);
2334// m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2);
2335// m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3);
2336// m.EigenVectors(eig);
2337
2338// // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0);
2339// if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) {
2340// AliWarning("Negative eigenvalues of the covariance matrix!");
2341// this->Print();
2342// eig.Print();
2343// }
2344}
4c3dc2a0 2345
2346Bool_t AliExternalTrackParam::ConstrainToVertex(const AliVVertex* vtx, Double_t b[3])
2347{
2348 // Constrain TPC inner params constrained
2349 //
2350 if (!vtx)
2351 return kFALSE;
2352
2353 Double_t dz[2], cov[3];
2354 if (!PropagateToDCABxByBz(vtx, b, 3, dz, cov))
2355 return kFALSE;
2356
2357 Double_t covar[6];
2358 vtx->GetCovarianceMatrix(covar);
2359
2360 Double_t p[2]= { fP[0] - dz[0], fP[1] - dz[1] };
2361 Double_t c[3]= { covar[2], 0., covar[5] };
2362
2363 Double_t chi2C = GetPredictedChi2(p,c);
2364 if (chi2C>kVeryBig)
2365 return kFALSE;
2366
2367 if (!Update(p,c))
2368 return kFALSE;
2369
2370 return kTRUE;
2371}
70580f26 2372
2373//___________________________________________________________________________________________
2374Bool_t AliExternalTrackParam::GetXatLabR(Double_t r,Double_t &x, Double_t bz, Int_t dir) const
2375{
2376 // Get local X of the track position estimated at the radius lab radius r.
2377 // The track curvature is accounted exactly
2378 //
2379 // The flag "dir" can be used to remove the ambiguity of which intersection to take (out of 2 possible)
2380 // 0 - take the intersection closest to the current track position
2381 // >0 - go along the track (increasing fX)
2382 // <0 - go backward (decreasing fX)
2383 //
2384 const Double_t &fy=fP[0], &sn = fP[2];
2385 //
2386 double crv = GetC(bz);
2387 if (TMath::Abs(crv)<=kAlmost0) { // this is a straight track
2388 if (TMath::Abs(sn)>=kAlmost1) { // || to Y axis
2389 double det = (r-fX)*(r+fX);
2390 if (det<0) return kFALSE; // does not reach raduis r
2391 x = fX;
2392 if (dir==0) return kTRUE;
2393 det = TMath::Sqrt(det);
2394 if (dir>0) { // along the track direction
2395 if (sn>0) {if (fy>det) return kFALSE;} // track is along Y axis and above the circle
2396 else {if (fy<-det) return kFALSE;} // track is against Y axis amd belo the circle
2397 }
e804766b 2398 else { // agains track direction
70580f26 2399 if (sn>0) {if (fy<-det) return kFALSE;} // track is along Y axis
2400 else if (fy>det) return kFALSE; // track is against Y axis
2401 }
2402 }
2403 else if (TMath::Abs(sn)<=kAlmost0) { // || to X axis
2404 double det = (r-fy)*(r+fy);
2405 if (det<0) return kFALSE; // does not reach raduis r
2406 det = TMath::Sqrt(det);
2407 if (!dir) {
2408 x = fX>0 ? det : -det; // choose the solution requiring the smalest step
2409 return kTRUE;
2410 }
2411 else if (dir>0) { // along the track direction
2412 if (fX > det) return kFALSE; // current point is in on the right from the circle
2413 else if (fX <-det) x = -det; // on the left
2414 else x = det; // within the circle
2415 }
2416 else { // against the track direction
2417 if (fX <-det) return kFALSE;
2418 else if (fX > det) x = det;
2419 else x = -det;
2420 }
2421 }
2422 else { // general case of straight line
2423 double cs = TMath::Sqrt((1-sn)*(1+sn));
2424 double xsyc = fX*sn-fy*cs;
2425 double det = (r-xsyc)*(r+xsyc);
2426 if (det<0) return kFALSE; // does not reach raduis r
2427 det = TMath::Sqrt(det);
2428 double xcys = fX*cs+fy*sn;
2429 double t = -xcys;
2430 if (dir==0) t += t>0 ? -det:det; // chose the solution requiring the smalest step
2431 else if (dir>0) { // go in increasing fX direction. ( t+-det > 0)
2432 if (t>=-det) t += -det; // take minimal step giving t>0
2433 else return kFALSE; // both solutions have negative t
2434 }
2435 else { // go in increasing fX direction. (t+-det < 0)
2436 if (t<det) t -= det; // take minimal step giving t<0
2437 else return kFALSE; // both solutions have positive t
2438 }
2439 x = fX + cs*t;
2440 }
2441 }
2442 else { // helix
2443 // get center of the track circle
2444 double tR = 1./crv; // track radius (for the moment signed)
2445 double cs = TMath::Sqrt((1-sn)*(1+sn));
2446 double x0 = fX - sn*tR;
2447 double y0 = fy + cs*tR;
2448 double r0 = TMath::Sqrt(x0*x0+y0*y0);
2449 // printf("Xc:%+e Yc:%+e\n",x0,y0);
2450 //
2451 if (r0<=kAlmost0) return kFALSE; // the track is concentric to circle
2452 tR = TMath::Abs(tR);
2453 double tR2r0 = tR/r0;
2454 double g = 0.5*(r*r/(r0*tR) - tR2r0 - 1./tR2r0);
2455 double det = (1.-g)*(1.+g);
2456 if (det<0) return kFALSE; // does not reach raduis r
2457 det = TMath::Sqrt(det);
2458 //
2459 // the intersection happens in 2 points: {x0+tR*C,y0+tR*S}
2460 // with C=f*c0+-|s0|*det and S=f*s0-+c0 sign(s0)*det
2461 // where s0 and c0 make direction for the circle center (=x0/r0 and y0/r0)
2462 //
2463 double tmp = 1.+g*tR2r0;
2464 x = x0*tmp;
2465 double y = y0*tmp;
2466 if (TMath::Abs(y0)>kAlmost0) { // when y0==0 the x,y is unique
2467 double dfx = tR2r0*TMath::Abs(y0)*det;
2468 double dfy = tR2r0*x0*TMath::Sign(det,y0);
2469 if (dir==0) { // chose the one which corresponds to smallest step
2470 double delta = (x-fX)*dfx-(y-fy)*dfy; // the choice of + in C will lead to smaller step if delta<0
2471 if (delta<0) x += dfx;
2472 else x -= dfx;
2473 }
2474 else if (dir>0) { // along track direction: x must be > fX
2475 x -= dfx; // try the smallest step (dfx is positive)
2476 if (x<fX && (x+=dfx+dfx)<fX) return kFALSE;
2477 }
2478 else { // backward: x must be < fX
2479 x += dfx; // try the smallest step (dfx is positive)
2480 if (x>fX && (x-=dfx+dfx)>fX) return kFALSE;
2481 }
2482 }
2483 else { // special case: track touching the circle just in 1 point
2484 if ( (dir>0&&x<fX) || (dir<0&&x>fX) ) return kFALSE;
2485 }
2486 }
2487 //
2488 return kTRUE;
2489}