Bug corrected.
[u/mrichter/AliRoot.git] / STEER / 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. *
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;
43
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
57//_____________________________________________________________________________
6c94f330 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
71//_____________________________________________________________________________
def9660e 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
91//_____________________________________________________________________________
51ad6848 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
90e48c0c 107//_____________________________________________________________________________
4f6e22bd 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
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.)
142{
143 //
4f6e22bd 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)
153{
154 //
da4e3deb 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 //
168 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 169 Double_t radMax = 45.; // approximately ITS outer radius
170 if (radPos2 < radMax*radMax) { // inside the ITS
171
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 }
da4e3deb 178
179 // Get the vertex of origin and the momentum
180 TVector3 ver(xyz[0],xyz[1],xyz[2]);
181 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
182
183 // Rotate to the local coordinate system
184 ver.RotateZ(-fAlpha);
185 mom.RotateZ(-fAlpha);
186
187 // x of the reference plane
188 fX = ver.X();
189
190 Double_t charge = (Double_t)sign;
191
192 fP[0] = ver.Y();
193 fP[1] = ver.Z();
194 fP[2] = TMath::Sin(mom.Phi());
195 fP[3] = mom.Pz()/mom.Pt();
196 fP[4] = TMath::Sign(1/mom.Pt(),charge);
197
198 // Covariance matrix (formulas to be simplified)
199
200 Double_t pt=1./TMath::Abs(fP[4]);
201 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
202 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
203
204 Double_t m00=-sn;// m10=cs;
205 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
206 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
207 Double_t m35=pt, m45=-pt*pt*fP[3];
208
209 m43*=GetSign();
210 m44*=GetSign();
211 m45*=GetSign();
212
213 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
214 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
215 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
216 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
217 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
218 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
219 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
220
221 fC[0 ] = cv[0 ]+cv[2 ];
222 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
223 fC[2 ] = cv[5 ];
224 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
225 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
226 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
227 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
228 fC[11] = (cv[8]-fC[4]*m23)/m43;
229 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
230 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
231 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
232 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
233 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
234 Double_t b2=m23*m35;
235 Double_t b3=m43*m35;
236 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
237 Double_t b5=m24*m35;
238 Double_t b6=m44*m35;
239 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
240 fC[13] = b1/b3-b2*fC[8]/b3;
241 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 242
86be8934 243 CheckCovariance();
244
4f6e22bd 245 return;
da4e3deb 246}
247
248//_____________________________________________________________________________
c9ec41e8 249void AliExternalTrackParam::Reset() {
1530f89c 250 //
251 // Resets all the parameters to 0
252 //
c9ec41e8 253 fX=fAlpha=0.;
254 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
255 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 256}
257
3775b0ca 258//_____________________________________________________________________________
259void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
260 //
261 // Add "something" to the track covarince matrix.
262 // May be needed to account for unknown mis-calibration/mis-alignment
263 //
264 fC[0] +=c[0];
265 fC[1] +=c[1]; fC[2] +=c[2];
266 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
267 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
268 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
86be8934 269 CheckCovariance();
3775b0ca 270}
271
272
c9ec41e8 273Double_t AliExternalTrackParam::GetP() const {
274 //---------------------------------------------------------------------
275 // This function returns the track momentum
276 // Results for (nearly) straight tracks are meaningless !
277 //---------------------------------------------------------------------
06fb4a2f 278 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 279 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 280}
281
1d99986f 282Double_t AliExternalTrackParam::Get1P() const {
283 //---------------------------------------------------------------------
284 // This function returns the 1/(track momentum)
285 //---------------------------------------------------------------------
286 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
287}
288
c9ec41e8 289//_______________________________________________________________________
c7bafca9 290Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 291 //------------------------------------------------------------------
292 // This function calculates the transverse impact parameter
293 // with respect to a point with global coordinates (x,y)
294 // in the magnetic field "b" (kG)
295 //------------------------------------------------------------------
5773defd 296 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 297 Double_t rp4=GetC(b);
c9ec41e8 298
299 Double_t xt=fX, yt=fP[0];
300
301 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
302 Double_t a = x*cs + y*sn;
303 y = -x*sn + y*cs; x=a;
304 xt-=x; yt-=y;
305
bfd20868 306 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2]));
307 a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
1530f89c 308 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
309}
310
311//_______________________________________________________________________
312void AliExternalTrackParam::
313GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
314 //------------------------------------------------------------------
315 // This function calculates the transverse and longitudinal impact parameters
316 // with respect to a point with global coordinates (x,y)
317 // in the magnetic field "b" (kG)
318 //------------------------------------------------------------------
bfd20868 319 Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1));
1530f89c 320 Double_t xt=fX, yt=fP[0];
321 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
322 Double_t a = x*cs + y*sn;
323 y = -x*sn + y*cs; x=a;
324 xt-=x; yt-=y;
325
326 Double_t rp4=GetC(b);
327 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
328 dz[0] = -(xt*f1 - yt*r1);
329 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
330 return;
331 }
332
333 sn=rp4*xt - f1; cs=rp4*yt + r1;
334 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
335 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
336 dz[0] = -a/(1 + rr);
bfd20868 337 Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2));
1530f89c 338 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 339}
340
49d13e89 341//_______________________________________________________________________
342Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
343 //------------------------------------------------------------------
344 // This function calculates the transverse impact parameter
345 // with respect to a point with global coordinates (xv,yv)
346 // neglecting the track curvature.
347 //------------------------------------------------------------------
348 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
349 Double_t x= xv*cs + yv*sn;
350 Double_t y=-xv*sn + yv*cs;
351
bfd20868 352 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
49d13e89 353
1530f89c 354 return -d;
49d13e89 355}
356
b8e07ed6 357Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx
358(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
359 Double_t dEdx,
360 Bool_t anglecorr) {
116b445b 361 //------------------------------------------------------------------
362 // This function corrects the track parameters for the crossed material.
363 // "xOverX0" - X/X0, the thickness in units of the radiation length.
364 // "xTimesRho" - is the product length*density (g/cm^2).
365 // "mass" - the mass of this particle (GeV/c^2).
b8e07ed6 366 // "dEdx" - mean enery loss (GeV/(g/cm^2)
367 // "anglecorr" - switch for the angular correction
116b445b 368 //------------------------------------------------------------------
369 Double_t &fP2=fP[2];
370 Double_t &fP3=fP[3];
371 Double_t &fP4=fP[4];
372
373 Double_t &fC22=fC[5];
374 Double_t &fC33=fC[9];
375 Double_t &fC43=fC[13];
376 Double_t &fC44=fC[14];
377
7dded1d5 378 //Apply angle correction, if requested
379 if(anglecorr) {
bfd20868 380 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
7dded1d5 381 xOverX0 *=angle;
382 xTimesRho *=angle;
383 }
384
116b445b 385 Double_t p=GetP();
386 Double_t p2=p*p;
387 Double_t beta2=p2/(p2 + mass*mass);
116b445b 388
9f2bec63 389 //Calculating the multiple scattering corrections******************
390 Double_t cC22 = 0.;
391 Double_t cC33 = 0.;
392 Double_t cC43 = 0.;
393 Double_t cC44 = 0.;
116b445b 394 if (xOverX0 != 0) {
395 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
396 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 397 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
bfd20868 398 cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3);
9f2bec63 399 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
400 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
401 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 402 }
403
9f2bec63 404 //Calculating the energy loss corrections************************
405 Double_t cP4=1.;
116b445b 406 if ((xTimesRho != 0.) && (beta2 < 1.)) {
b8e07ed6 407 Double_t dE=dEdx*xTimesRho;
116b445b 408 Double_t e=TMath::Sqrt(p2 + mass*mass);
409 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
c9038cae 410 //cP4 = (1.- e/p2*dE);
76ece3d8 411 if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE;
c9038cae 412 cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben !
9f2bec63 413 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 414
116b445b 415
416 // Approximate energy loss fluctuation (M.Ivanov)
417 const Double_t knst=0.07; // To be tuned.
418 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 419 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 420
421 }
422
9f2bec63 423 //Applying the corrections*****************************
424 fC22 += cC22;
425 fC33 += cC33;
426 fC43 += cC43;
427 fC44 += cC44;
428 fP4 *= cP4;
429
86be8934 430 CheckCovariance();
431
116b445b 432 return kTRUE;
433}
434
b8e07ed6 435Bool_t AliExternalTrackParam::CorrectForMeanMaterial
436(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
437 Bool_t anglecorr,
438 Double_t (*Bethe)(Double_t)) {
439 //------------------------------------------------------------------
440 // This function corrects the track parameters for the crossed material.
441 // "xOverX0" - X/X0, the thickness in units of the radiation length.
442 // "xTimesRho" - is the product length*density (g/cm^2).
443 // "mass" - the mass of this particle (GeV/c^2).
444 // "anglecorr" - switch for the angular correction
445 // "Bethe" - function calculating the energy loss (GeV/(g/cm^2))
446 //------------------------------------------------------------------
447
448 Double_t bg=GetP()/mass;
449 Double_t dEdx=Bethe(bg);
450
451 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
452}
453
454Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA
455(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
456 Double_t zOverA,
457 Double_t density,
458 Double_t exEnergy,
459 Double_t jp1,
460 Double_t jp2,
461 Bool_t anglecorr) {
462 //------------------------------------------------------------------
463 // This function corrects the track parameters for the crossed material
464 // using the full Geant-like Bethe-Bloch formula parameterization
465 // "xOverX0" - X/X0, the thickness in units of the radiation length.
466 // "xTimesRho" - is the product length*density (g/cm^2).
467 // "mass" - the mass of this particle (GeV/c^2).
468 // "density" - mean density (g/cm^3)
469 // "zOverA" - mean Z/A
470 // "exEnergy" - mean exitation energy (GeV)
471 // "jp1" - density effect first junction point
472 // "jp2" - density effect second junction point
473 // "anglecorr" - switch for the angular correction
474 //
475 // The default values of the parameters are for silicon
476 //
477 //------------------------------------------------------------------
478
479 Double_t bg=GetP()/mass;
480 Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA);
481
482 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
483}
484
485
116b445b 486
ee5dba5e 487Bool_t AliExternalTrackParam::CorrectForMaterial
488(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 489 //------------------------------------------------------------------
116b445b 490 // Deprecated function !
491 // Better use CorrectForMeanMaterial instead of it.
492 //
c7bafca9 493 // This function corrects the track parameters for the crossed material
494 // "d" - the thickness (fraction of the radiation length)
495 // "x0" - the radiation length (g/cm^2)
496 // "mass" - the mass of this particle (GeV/c^2)
497 //------------------------------------------------------------------
c7bafca9 498
b8e07ed6 499 return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe);
c7bafca9 500
c7bafca9 501}
502
9c56b409 503Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
504 Double_t kp1,
505 Double_t kp2,
506 Double_t kp3,
507 Double_t kp4,
508 Double_t kp5) {
509 //
510 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
511 // It is normalized to 1 at the minimum.
512 //
513 // bg - beta*gamma
514 //
515 // The default values for the kp* parameters are for ALICE TPC.
516 // The returned value is in MIP units
517 //
518
519 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
520
521 Double_t aa = TMath::Power(beta,kp4);
522 Double_t bb = TMath::Power(1./bg,kp5);
523
524 bb=TMath::Log(kp3+bb);
525
526 return (kp2-aa-bb)*kp1/aa;
527}
528
529Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
530 Double_t kp0,
531 Double_t kp1,
532 Double_t kp2,
533 Double_t kp3,
534 Double_t kp4) {
535 //
536 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
537 //
538 // bg - beta*gamma
539 // kp0 - density [g/cm^3]
540 // kp1 - density effect first junction point
541 // kp2 - density effect second junction point
542 // kp3 - mean excitation energy [GeV]
543 // kp4 - mean Z/A
544 //
545 // The default values for the kp* parameters are for silicon.
546 // The returned value is in [GeV/(g/cm^2)].
547 //
548
549 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
550 const Double_t me = 0.511e-3; // [GeV/c^2]
551 const Double_t rho = kp0;
552 const Double_t x0 = kp1*2.303;
553 const Double_t x1 = kp2*2.303;
554 const Double_t mI = kp3;
555 const Double_t mZA = kp4;
556 const Double_t bg2 = bg*bg;
557 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
558
559 //*** Density effect
560 Double_t d2=0.;
561 const Double_t x=TMath::Log(bg);
562 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
563 if (x > x1) {
564 d2 = lhwI + x - 0.5;
565 } else if (x > x0) {
566 const Double_t r=(x1-x)/(x1-x0);
567 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
568 }
569
570 return mK*mZA*(1+bg2)/bg2*
571 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
572}
573
d46683db 574Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 575 //------------------------------------------------------------------
d46683db 576 // This is an approximation of the Bethe-Bloch formula,
577 // reasonable for solid materials.
578 // All the parameters are, in fact, for Si.
9b655cba 579 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 580 //------------------------------------------------------------------
a821848c 581
9c56b409 582 return BetheBlochGeant(bg);
d46683db 583}
ee5dba5e 584
d46683db 585Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
586 //------------------------------------------------------------------
587 // This is an approximation of the Bethe-Bloch formula,
588 // reasonable for gas materials.
589 // All the parameters are, in fact, for Ne.
9b655cba 590 // The returned value is in [GeV/(g/cm^2)]
d46683db 591 //------------------------------------------------------------------
592
593 const Double_t rho = 0.9e-3;
594 const Double_t x0 = 2.;
595 const Double_t x1 = 4.;
596 const Double_t mI = 140.e-9;
597 const Double_t mZA = 0.49555;
598
9c56b409 599 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 600}
601
49d13e89 602Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
603 //------------------------------------------------------------------
604 // Transform this track to the local coord. system rotated
605 // by angle "alpha" (rad) with respect to the global coord. system.
606 //------------------------------------------------------------------
dfcef74c 607 if (TMath::Abs(fP[2]) >= kAlmost1) {
608 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
609 return kFALSE;
610 }
611
49d13e89 612 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
613 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
614
615 Double_t &fP0=fP[0];
616 Double_t &fP2=fP[2];
617 Double_t &fC00=fC[0];
618 Double_t &fC10=fC[1];
619 Double_t &fC20=fC[3];
620 Double_t &fC21=fC[4];
621 Double_t &fC22=fC[5];
622 Double_t &fC30=fC[6];
623 Double_t &fC32=fC[8];
624 Double_t &fC40=fC[10];
625 Double_t &fC42=fC[12];
626
627 Double_t x=fX;
628 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
bfd20868 629 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
49d13e89 630
dfcef74c 631 Double_t tmp=sf*ca - cf*sa;
7248cf51 632 if (TMath::Abs(tmp) >= kAlmost1) {
633 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
634 AliWarning(Form("Rotation failed ! %.10e",tmp));
0b69bbb2 635 return kFALSE;
636 }
dfcef74c 637
49d13e89 638 fAlpha = alpha;
639 fX = x*ca + fP0*sa;
640 fP0= -x*sa + fP0*ca;
dfcef74c 641 fP2= tmp;
49d13e89 642
06fb4a2f 643 if (TMath::Abs(cf)<kAlmost0) {
644 AliError(Form("Too small cosine value %f",cf));
645 cf = kAlmost0;
646 }
647
49d13e89 648 Double_t rr=(ca+sf/cf*sa);
649
650 fC00 *= (ca*ca);
651 fC10 *= ca;
652 fC20 *= ca*rr;
653 fC21 *= rr;
654 fC22 *= rr*rr;
655 fC30 *= ca;
656 fC32 *= rr;
657 fC40 *= ca;
658 fC42 *= rr;
659
86be8934 660 CheckCovariance();
661
49d13e89 662 return kTRUE;
663}
664
665Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
666 //----------------------------------------------------------------
667 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
668 //----------------------------------------------------------------
49d13e89 669 Double_t dx=xk-fX;
e421f556 670 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 671
1530f89c 672 Double_t crv=GetC(b);
5773defd 673 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
674
2de63fc5 675 Double_t x2r = crv*dx;
676 Double_t f1=fP[2], f2=f1 + x2r;
bbefa4c4 677 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 678 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
679
680 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
681 Double_t
682 &fC00=fC[0],
683 &fC10=fC[1], &fC11=fC[2],
684 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
685 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
686 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
687
bfd20868 688 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
49d13e89 689
690 fX=xk;
2de63fc5 691 double dy2dx = (f1+f2)/(r1+r2);
692 fP0 += dx*dy2dx;
693 if (TMath::Abs(x2r)<0.05) {
694 fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov !
695 fP2 += x2r;
696 }
697 else {
698 // for small dx/R the linear apporximation of the arc by the segment is OK,
699 // but at large dx/R the error is very large and leads to incorrect Z propagation
700 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
701 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
702 // Similarly, the rotation angle in linear in dx only for dx<<R
703 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
704 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
705 fP1 += rot/crv*fP3;
706 fP2 = TMath::Sin(rot + TMath::ASin(fP2));
707 }
49d13e89 708
709 //f = F - 1
710
711 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
712 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
713 Double_t f12= dx*fP3*f1/(r1*r1*r1);
714 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
715 Double_t f13= dx/r1;
716 Double_t f24= dx; f24*=cc;
717
718 //b = C*ft
719 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
720 Double_t b02=f24*fC40;
721 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
722 Double_t b12=f24*fC41;
723 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
724 Double_t b22=f24*fC42;
725 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
726 Double_t b42=f24*fC44;
727 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
728 Double_t b32=f24*fC43;
729
730 //a = f*b = f*C*ft
731 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
732 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
733 Double_t a22=f24*b42;
734
735 //F*C*Ft = C + (b + bt + a)
736 fC00 += b00 + b00 + a00;
737 fC10 += b10 + b01 + a01;
738 fC20 += b20 + b02 + a02;
739 fC30 += b30;
740 fC40 += b40;
741 fC11 += b11 + b11 + a11;
742 fC21 += b21 + b12 + a12;
743 fC31 += b31;
744 fC41 += b41;
745 fC22 += b22 + b22 + a22;
746 fC32 += b32;
747 fC42 += b42;
748
86be8934 749 CheckCovariance();
750
49d13e89 751 return kTRUE;
752}
753
9f2bec63 754Bool_t
755AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
756 //------------------------------------------------------------------
757 // Transform this track to the local coord. system rotated
758 // by angle "alpha" (rad) with respect to the global coord. system,
759 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
760 //------------------------------------------------------------------
761
762 //Save the parameters
763 Double_t as=fAlpha;
764 Double_t xs=fX;
765 Double_t ps[5], cs[15];
766 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
767 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
768
769 if (Rotate(alpha))
770 if (PropagateTo(x,b)) return kTRUE;
771
772 //Restore the parameters, if the operation failed
773 fAlpha=as;
774 fX=xs;
775 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
776 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
777 return kFALSE;
778}
779
266a0f9b 780Bool_t AliExternalTrackParam::PropagateBxByBz
781(Double_t alpha, Double_t x, Double_t b[3]) {
782 //------------------------------------------------------------------
783 // Transform this track to the local coord. system rotated
784 // by angle "alpha" (rad) with respect to the global coord. system,
785 // and propagate this track to the plane X=xk (cm),
786 // taking into account all three components of the B field, "b[3]" (kG)
787 //------------------------------------------------------------------
788
789 //Save the parameters
790 Double_t as=fAlpha;
791 Double_t xs=fX;
792 Double_t ps[5], cs[15];
793 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
794 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
795
796 if (Rotate(alpha))
797 if (PropagateToBxByBz(x,b)) return kTRUE;
798
799 //Restore the parameters, if the operation failed
800 fAlpha=as;
801 fX=xs;
802 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
803 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
804 return kFALSE;
805}
806
9f2bec63 807
052daaff 808void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
809Double_t p[3], Double_t bz) const {
810 //+++++++++++++++++++++++++++++++++++++++++
811 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
812 // Extrapolate track along simple helix in magnetic field
813 // Arguments: len -distance alogn helix, [cm]
814 // bz - mag field, [kGaus]
815 // Returns: x and p contain extrapolated positon and momentum
816 // The momentum returned for straight-line tracks is meaningless !
817 //+++++++++++++++++++++++++++++++++++++++++
818 GetXYZ(x);
819
2258e165 820 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 821 Double_t unit[3]; GetDirection(unit);
822 x[0]+=unit[0]*len;
823 x[1]+=unit[1]*len;
824 x[2]+=unit[2]*len;
825
826 p[0]=unit[0]/kAlmost0;
827 p[1]=unit[1]/kAlmost0;
828 p[2]=unit[2]/kAlmost0;
829 } else {
830 GetPxPyPz(p);
831 Double_t pp=GetP();
832 Double_t a = -kB2C*bz*GetSign();
833 Double_t rho = a/pp;
834 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
835 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
836 x[2] += p[2]*len/pp;
837
838 Double_t p0=p[0];
839 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
840 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
841 }
842}
843
844Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
845Double_t bz) const {
846 //+++++++++++++++++++++++++++++++++++++++++
847 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
848 // Finds point of intersection (if exists) of the helix with the plane.
849 // Stores result in fX and fP.
850 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
851 // and vector, normal to the plane
852 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
853 //+++++++++++++++++++++++++++++++++++++++++
854 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
855
856 //estimates initial helix length up to plane
857 Double_t s=
858 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
859 Double_t dist=99999,distPrev=dist;
860 Double_t x[3],p[3];
861 while(TMath::Abs(dist)>0.00001){
862 //calculates helix at the distance s from x0 ALONG the helix
863 Propagate(s,x,p,bz);
864
865 //distance between current helix position and plane
866 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
867
868 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
869 distPrev=dist;
870 s-=dist;
871 }
872 //on exit pnt is intersection point,norm is track vector at that point,
873 //all in MARS
874 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
875 return kTRUE;
876}
877
49d13e89 878Double_t
879AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
880 //----------------------------------------------------------------
881 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
882 //----------------------------------------------------------------
883 Double_t sdd = fC[0] + cov[0];
884 Double_t sdz = fC[1] + cov[1];
885 Double_t szz = fC[2] + cov[2];
886 Double_t det = sdd*szz - sdz*sdz;
887
888 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
889
890 Double_t d = fP[0] - p[0];
891 Double_t z = fP[1] - p[1];
892
893 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
894}
895
4b189f98 896Double_t AliExternalTrackParam::
897GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
898 //----------------------------------------------------------------
899 // Estimate the chi2 of the 3D space point "p" and
1e023a36 900 // the full covariance matrix "covyz" and "covxyz"
4b189f98 901 //
902 // Cov(x,x) ... : covxyz[0]
903 // Cov(y,x) ... : covxyz[1] covyz[0]
904 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
905 //----------------------------------------------------------------
906
907 Double_t res[3] = {
908 GetX() - p[0],
909 GetY() - p[1],
910 GetZ() - p[2]
911 };
912
913 Double_t f=GetSnp();
914 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
bfd20868 915 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
4b189f98 916 Double_t a=f/r, b=GetTgl()/r;
917
918 Double_t s2=333.*333.; //something reasonably big (cm^2)
919
920 TMatrixDSym v(3);
921 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
922 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
923 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
924
925 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
926 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
927 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
928
929 v.Invert();
930 if (!v.IsValid()) return kVeryBig;
931
932 Double_t chi2=0.;
933 for (Int_t i = 0; i < 3; i++)
934 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
935
936 return chi2;
acdfbc78 937}
938
939Double_t AliExternalTrackParam::
940GetPredictedChi2(const AliExternalTrackParam *t) const {
941 //----------------------------------------------------------------
942 // Estimate the chi2 (5 dof) of this track with respect to the track
943 // given by the argument.
944 // The two tracks must be in the same reference system
945 // and estimated at the same reference plane.
946 //----------------------------------------------------------------
947
948 if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) {
949 AliError("The reference systems of the tracks differ !");
950 return kVeryBig;
951 }
952 if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) {
953 AliError("The reference of the tracks planes differ !");
954 return kVeryBig;
955 }
956
957 TMatrixDSym c(5);
958 c(0,0)=GetSigmaY2();
959 c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
960 c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
961 c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
962 c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
963
964 c(0,0)+=t->GetSigmaY2();
965 c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
966 c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
967 c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
968 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();
969 c(0,1)=c(1,0);
970 c(0,2)=c(2,0); c(1,2)=c(2,1);
971 c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
972 c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
973
974 c.Invert();
975 if (!c.IsValid()) return kVeryBig;
976
977
978 Double_t res[5] = {
979 GetY() - t->GetY(),
980 GetZ() - t->GetZ(),
981 GetSnp() - t->GetSnp(),
982 GetTgl() - t->GetTgl(),
983 GetSigned1Pt() - t->GetSigned1Pt()
984 };
4b189f98 985
acdfbc78 986 Double_t chi2=0.;
987 for (Int_t i = 0; i < 5; i++)
988 for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
4b189f98 989
acdfbc78 990 return chi2;
4b189f98 991}
992
1e023a36 993Bool_t AliExternalTrackParam::
994PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
995 //----------------------------------------------------------------
996 // Propagate this track to the plane
997 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
998 // belongs to.
999 // The magnetic field is "bz" (kG)
1000 //
1001 // The track curvature and the change of the covariance matrix
1002 // of the track parameters are negleted !
1003 // (So the "step" should be small compared with 1/curvature)
1004 //----------------------------------------------------------------
1005
1006 Double_t f=GetSnp();
1007 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
bfd20868 1008 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
1e023a36 1009 Double_t a=f/r, b=GetTgl()/r;
1010
1011 Double_t s2=333.*333.; //something reasonably big (cm^2)
1012
1013 TMatrixDSym tV(3);
1014 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
1015 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
1016 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
1017
1018 TMatrixDSym pV(3);
1019 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
1020 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
1021 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
1022
1023 TMatrixDSym tpV(tV);
1024 tpV+=pV;
1025 tpV.Invert();
1026 if (!tpV.IsValid()) return kFALSE;
1027
1028 TMatrixDSym pW(3),tW(3);
1029 for (Int_t i=0; i<3; i++)
1030 for (Int_t j=0; j<3; j++) {
1031 pW(i,j)=tW(i,j)=0.;
1032 for (Int_t k=0; k<3; k++) {
1033 pW(i,j) += tV(i,k)*tpV(k,j);
1034 tW(i,j) += pV(i,k)*tpV(k,j);
1035 }
1036 }
1037
1038 Double_t t[3] = {GetX(), GetY(), GetZ()};
1039
1040 Double_t x=0.;
1041 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
1042 Double_t crv=GetC(bz);
1043 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1044 f += crv*(x-fX);
1045 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
1046 fX=x;
1047
1048 fP[0]=0.;
1049 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
1050 fP[1]=0.;
1051 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
1052
1053 return kTRUE;
1054}
1055
e23a38cb 1056Double_t *AliExternalTrackParam::GetResiduals(
1057Double_t *p,Double_t *cov,Bool_t updated) const {
1058 //------------------------------------------------------------------
1059 // Returns the track residuals with the space point "p" having
1060 // the covariance matrix "cov".
1061 // If "updated" is kTRUE, the track parameters expected to be updated,
1062 // otherwise they must be predicted.
1063 //------------------------------------------------------------------
1064 static Double_t res[2];
1065
1066 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1067 if (updated) {
1068 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
1069 } else {
1070 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
1071 }
1072 Double_t det=r00*r11 - r01*r01;
1073
1074 if (TMath::Abs(det) < kAlmost0) return 0;
1075
1076 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 1077
1078 if (r00 < 0.) return 0;
1079 if (r11 < 0.) return 0;
1080
e23a38cb 1081 Double_t dy = fP[0] - p[0];
1082 Double_t dz = fP[1] - p[1];
1083
1084 res[0]=dy*TMath::Sqrt(r00);
1085 res[1]=dz*TMath::Sqrt(r11);
1086
1087 return res;
1088}
1089
49d13e89 1090Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
1091 //------------------------------------------------------------------
1092 // Update the track parameters with the space point "p" having
1093 // the covariance matrix "cov"
1094 //------------------------------------------------------------------
1095 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
1096 Double_t
1097 &fC00=fC[0],
1098 &fC10=fC[1], &fC11=fC[2],
1099 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1100 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1101 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1102
1103 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1104 r00+=fC00; r01+=fC10; r11+=fC11;
1105 Double_t det=r00*r11 - r01*r01;
1106
1107 if (TMath::Abs(det) < kAlmost0) return kFALSE;
1108
1109
1110 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
1111
1112 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
1113 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
1114 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
1115 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
1116 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
1117
1118 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1119 Double_t sf=fP2 + k20*dy + k21*dz;
1120 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1121
1122 fP0 += k00*dy + k01*dz;
1123 fP1 += k10*dy + k11*dz;
1124 fP2 = sf;
1125 fP3 += k30*dy + k31*dz;
1126 fP4 += k40*dy + k41*dz;
1127
1128 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1129 Double_t c12=fC21, c13=fC31, c14=fC41;
1130
1131 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1132 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1133 fC40-=k00*c04+k01*c14;
1134
1135 fC11-=k10*c01+k11*fC11;
1136 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1137 fC41-=k10*c04+k11*c14;
1138
1139 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1140 fC42-=k20*c04+k21*c14;
1141
1142 fC33-=k30*c03+k31*c13;
1143 fC43-=k30*c04+k31*c14;
1144
1145 fC44-=k40*c04+k41*c14;
1146
86be8934 1147 CheckCovariance();
1148
49d13e89 1149 return kTRUE;
1150}
1151
c7bafca9 1152void
1153AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1154 //--------------------------------------------------------------------
1155 // External track parameters -> helix parameters
1156 // "b" - magnetic field (kG)
1157 //--------------------------------------------------------------------
1158 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1159
1530f89c 1160 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1161
1162 hlx[5]=fX*cs - hlx[0]*sn; // x0
1163 hlx[0]=fX*sn + hlx[0]*cs; // y0
1164//hlx[1]= // z0
1165 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1166//hlx[3]= // tgl
1530f89c 1167 hlx[4]=GetC(b); // C
c7bafca9 1168}
1169
1170
1171static void Evaluate(const Double_t *h, Double_t t,
1172 Double_t r[3], //radius vector
1173 Double_t g[3], //first defivatives
1174 Double_t gg[3]) //second derivatives
1175{
1176 //--------------------------------------------------------------------
1177 // Calculate position of a point on a track and some derivatives
1178 //--------------------------------------------------------------------
1179 Double_t phase=h[4]*t+h[2];
1180 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1181
ba4550c4 1182 r[0] = h[5];
1183 r[1] = h[0];
1184 if (TMath::Abs(h[4])>kAlmost0) {
1185 r[0] += (sn - h[6])/h[4];
1186 r[1] -= (cs - h[7])/h[4];
1187 }
c7bafca9 1188 r[2] = h[1] + h[3]*t;
1189
1190 g[0] = cs; g[1]=sn; g[2]=h[3];
1191
1192 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1193}
1194
1195Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1196Double_t b, Double_t &xthis, Double_t &xp) const {
1197 //------------------------------------------------------------
1198 // Returns the (weighed !) distance of closest approach between
1199 // this track and the track "p".
1200 // Other returned values:
1201 // xthis, xt - coordinates of tracks' reference planes at the DCA
1202 //-----------------------------------------------------------
1203 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1204 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1205 Double_t dx2=dy2;
1206
c7bafca9 1207 Double_t p1[8]; GetHelixParameters(p1,b);
1208 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1209 Double_t p2[8]; p->GetHelixParameters(p2,b);
1210 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1211
1212
1213 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1214 Evaluate(p1,t1,r1,g1,gg1);
1215 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1216 Evaluate(p2,t2,r2,g2,gg2);
1217
1218 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1219 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1220
1221 Int_t max=27;
1222 while (max--) {
1223 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1224 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1225 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1226 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1227 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1228 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1229 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1230 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1231 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1232
1233 Double_t det=h11*h22-h12*h12;
1234
1235 Double_t dt1,dt2;
1236 if (TMath::Abs(det)<1.e-33) {
1237 //(quasi)singular Hessian
1238 dt1=-gt1; dt2=-gt2;
1239 } else {
1240 dt1=-(gt1*h22 - gt2*h12)/det;
1241 dt2=-(h11*gt2 - h12*gt1)/det;
1242 }
1243
1244 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1245
1246 //check delta(phase1) ?
1247 //check delta(phase2) ?
1248
1249 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1250 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1251 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1252 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1253 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1254 if (lmb < 0.)
358f16ae 1255 AliDebug(1," stopped at not a minimum !");
c7bafca9 1256 break;
1257 }
1258
1259 Double_t dd=dm;
1260 for (Int_t div=1 ; ; div*=2) {
1261 Evaluate(p1,t1+dt1,r1,g1,gg1);
1262 Evaluate(p2,t2+dt2,r2,g2,gg2);
1263 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1264 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1265 if (dd<dm) break;
1266 dt1*=0.5; dt2*=0.5;
1267 if (div>512) {
358f16ae 1268 AliDebug(1," overshoot !"); break;
c7bafca9 1269 }
1270 }
1271 dm=dd;
1272
1273 t1+=dt1;
1274 t2+=dt2;
1275
1276 }
1277
358f16ae 1278 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1279
1280 Double_t cs=TMath::Cos(GetAlpha());
1281 Double_t sn=TMath::Sin(GetAlpha());
1282 xthis=r1[0]*cs + r1[1]*sn;
1283
1284 cs=TMath::Cos(p->GetAlpha());
1285 sn=TMath::Sin(p->GetAlpha());
1286 xp=r2[0]*cs + r2[1]*sn;
1287
1288 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1289}
1290
1291Double_t AliExternalTrackParam::
1292PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1293 //--------------------------------------------------------------
1294 // Propagates this track and the argument track to the position of the
1295 // distance of closest approach.
1296 // Returns the (weighed !) distance of closest approach.
1297 //--------------------------------------------------------------
1298 Double_t xthis,xp;
1299 Double_t dca=GetDCA(p,b,xthis,xp);
1300
1301 if (!PropagateTo(xthis,b)) {
1302 //AliWarning(" propagation failed !");
1303 return 1e+33;
1304 }
1305
1306 if (!p->PropagateTo(xp,b)) {
1307 //AliWarning(" propagation failed !";
1308 return 1e+33;
1309 }
1310
1311 return dca;
1312}
1313
1314
58e536c5 1315Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1316Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1317 //
e99a34df 1318 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1319 // if the (rough) transverse impact parameter is not bigger then "maxd".
1320 // Magnetic field is "b" (kG).
1321 //
1322 // a) The track gets extapolated to the DCA to the vertex.
1323 // b) The impact parameters and their covariance matrix are calculated.
1324 //
1325 // In the case of success, the returned value is kTRUE
1326 // (otherwise, it's kFALSE)
1327 //
1328 Double_t alpha=GetAlpha();
1329 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1330 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1331 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1332 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1333 x-=xv; y-=yv;
1334
1335 //Estimate the impact parameter neglecting the track curvature
bfd20868 1336 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
f76701bf 1337 if (d > maxd) return kFALSE;
1338
1339 //Propagate to the DCA
2258e165 1340 Double_t crv=GetC(b);
e99a34df 1341 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1342
bfd20868 1343 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1344 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
e99a34df 1345 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1346 else cs=1.;
f76701bf 1347
1348 x = xv*cs + yv*sn;
1349 yv=-xv*sn + yv*cs; xv=x;
1350
1351 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
266a0f9b 1352
1353 if (dz==0) return kTRUE;
1354 dz[0] = GetParameter()[0] - yv;
1355 dz[1] = GetParameter()[1] - zv;
1356
1357 if (covar==0) return kTRUE;
1358 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
1359
1360 //***** Improvements by A.Dainese
1361 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1362 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1363 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1364 covar[1] = GetCovariance()[1]; // between (x,y) and z
1365 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1366 //*****
1367
1368 return kTRUE;
1369}
1370
1371Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
1372Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
1373 //
1374 // Propagate this track to the DCA to vertex "vtx",
1375 // if the (rough) transverse impact parameter is not bigger then "maxd".
1376 //
1377 // This function takes into account all three components of the magnetic
1378 // field given by the b[3] arument (kG)
1379 //
1380 // a) The track gets extapolated to the DCA to the vertex.
1381 // b) The impact parameters and their covariance matrix are calculated.
1382 //
1383 // In the case of success, the returned value is kTRUE
1384 // (otherwise, it's kFALSE)
1385 //
1386 Double_t alpha=GetAlpha();
1387 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1388 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
1389 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1390 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
1391 x-=xv; y-=yv;
1392
1393 //Estimate the impact parameter neglecting the track curvature
bfd20868 1394 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
266a0f9b 1395 if (d > maxd) return kFALSE;
1396
1397 //Propagate to the DCA
8567bf39 1398 Double_t crv=GetC(b[2]);
1399 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
266a0f9b 1400
bfd20868 1401 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1402 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
266a0f9b 1403 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1404 else cs=1.;
1405
1406 x = xv*cs + yv*sn;
1407 yv=-xv*sn + yv*cs; xv=x;
1408
1409 if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1410
1411 if (dz==0) return kTRUE;
1412 dz[0] = GetParameter()[0] - yv;
1413 dz[1] = GetParameter()[1] - zv;
1414
1415 if (covar==0) return kTRUE;
58e536c5 1416 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1417
1418 //***** Improvements by A.Dainese
1419 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1420 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1421 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1422 covar[1] = GetCovariance()[1]; // between (x,y) and z
1423 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1424 //*****
1425
29fbcc93 1426 return kTRUE;
f76701bf 1427}
1428
b1149664 1429void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1430 //----------------------------------------------------------------
1431 // This function returns a unit vector along the track direction
1432 // in the global coordinate system.
1433 //----------------------------------------------------------------
1434 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1435 Double_t snp=fP[2];
bfd20868 1436 Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp));
b1149664 1437 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1438 d[0]=(csp*cs - snp*sn)/norm;
1439 d[1]=(snp*cs + csp*sn)/norm;
1440 d[2]=fP[3]/norm;
1441}
1442
c683ddc2 1443Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1444 //---------------------------------------------------------------------
1445 // This function returns the global track momentum components
1446 // Results for (nearly) straight tracks are meaningless !
1447 //---------------------------------------------------------------------
1448 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1449 return Local2GlobalMomentum(p,fAlpha);
1450}
a5e407e9 1451
def9660e 1452Double_t AliExternalTrackParam::Px() const {
957fb479 1453 //---------------------------------------------------------------------
1454 // Returns x-component of momentum
1455 // Result for (nearly) straight tracks is meaningless !
1456 //---------------------------------------------------------------------
def9660e 1457
957fb479 1458 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1459 GetPxPyPz(p);
1460
1461 return p[0];
1462}
1463
1464Double_t AliExternalTrackParam::Py() const {
957fb479 1465 //---------------------------------------------------------------------
1466 // Returns y-component of momentum
1467 // Result for (nearly) straight tracks is meaningless !
1468 //---------------------------------------------------------------------
def9660e 1469
957fb479 1470 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1471 GetPxPyPz(p);
1472
1473 return p[1];
1474}
1475
c683ddc2 1476Double_t AliExternalTrackParam::Xv() const {
1477 //---------------------------------------------------------------------
1478 // Returns x-component of first track point
1479 //---------------------------------------------------------------------
1480
1481 Double_t r[3]={0.,0.,0.};
1482 GetXYZ(r);
1483
1484 return r[0];
1485}
1486
1487Double_t AliExternalTrackParam::Yv() const {
1488 //---------------------------------------------------------------------
1489 // Returns y-component of first track point
1490 //---------------------------------------------------------------------
1491
1492 Double_t r[3]={0.,0.,0.};
1493 GetXYZ(r);
1494
1495 return r[1];
1496}
1497
def9660e 1498Double_t AliExternalTrackParam::Theta() const {
1499 // return theta angle of momentum
1500
7cdd0c20 1501 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1502}
1503
1504Double_t AliExternalTrackParam::Phi() const {
957fb479 1505 //---------------------------------------------------------------------
1506 // Returns the azimuthal angle of momentum
1507 // 0 <= phi < 2*pi
1508 //---------------------------------------------------------------------
def9660e 1509
957fb479 1510 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1511 if (phi<0.) phi+=2.*TMath::Pi();
1512 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1513
1514 return phi;
def9660e 1515}
1516
1517Double_t AliExternalTrackParam::M() const {
1518 // return particle mass
1519
1520 // No mass information available so far.
1521 // Redifine in derived class!
1522
1523 return -999.;
1524}
1525
1526Double_t AliExternalTrackParam::E() const {
1527 // return particle energy
1528
1529 // No PID information available so far.
1530 // Redifine in derived class!
1531
1532 return -999.;
1533}
1534
1535Double_t AliExternalTrackParam::Eta() const {
1536 // return pseudorapidity
1537
1538 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1539}
1540
1541Double_t AliExternalTrackParam::Y() const {
1542 // return rapidity
1543
1544 // No PID information available so far.
1545 // Redifine in derived class!
1546
1547 return -999.;
1548}
1549
c9ec41e8 1550Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1551 //---------------------------------------------------------------------
1552 // This function returns the global track position
1553 //---------------------------------------------------------------------
1554 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1555 return Local2GlobalPosition(r,fAlpha);
51ad6848 1556}
1557
c9ec41e8 1558Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1559 //---------------------------------------------------------------------
1560 // This function returns the global covariance matrix of the track params
1561 //
1562 // Cov(x,x) ... : cv[0]
1563 // Cov(y,x) ... : cv[1] cv[2]
1564 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1565 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1566 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1567 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1568 //
c9ec41e8 1569 // Results for (nearly) straight tracks are meaningless !
1570 //---------------------------------------------------------------------
e421f556 1571 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1572 for (Int_t i=0; i<21; i++) cv[i]=0.;
1573 return kFALSE;
a5e407e9 1574 }
49d13e89 1575 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1576 for (Int_t i=0; i<21; i++) cv[i]=0.;
1577 return kFALSE;
1578 }
1579 Double_t pt=1./TMath::Abs(fP[4]);
1580 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1581 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1582
1583 Double_t m00=-sn, m10=cs;
1584 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1585 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1586 Double_t m35=pt, m45=-pt*pt*fP[3];
1587
854d5d49 1588 m43*=GetSign();
1589 m44*=GetSign();
1590 m45*=GetSign();
1591
c9ec41e8 1592 cv[0 ] = fC[0]*m00*m00;
1593 cv[1 ] = fC[0]*m00*m10;
1594 cv[2 ] = fC[0]*m10*m10;
1595 cv[3 ] = fC[1]*m00;
1596 cv[4 ] = fC[1]*m10;
1597 cv[5 ] = fC[2];
1598 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1599 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1600 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1601 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1602 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1603 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1604 cv[12] = fC[4]*m24 + fC[11]*m44;
1605 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1606 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1607 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1608 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1609 cv[17] = fC[7]*m35 + fC[11]*m45;
1610 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1611 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1612 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1613
c9ec41e8 1614 return kTRUE;
51ad6848 1615}
1616
51ad6848 1617
c9ec41e8 1618Bool_t
1619AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1620 //---------------------------------------------------------------------
1621 // This function returns the global track momentum extrapolated to
1622 // the radial position "x" (cm) in the magnetic field "b" (kG)
1623 //---------------------------------------------------------------------
c9ec41e8 1624 p[0]=fP[4];
1530f89c 1625 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1626 p[2]=fP[3];
1627 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1628}
1629
c9ec41e8 1630Bool_t
7cf7bb6c 1631AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1632 //---------------------------------------------------------------------
1633 // This function returns the local Y-coordinate of the intersection
1634 // point between this track and the reference plane "x" (cm).
1635 // Magnetic field "b" (kG)
1636 //---------------------------------------------------------------------
1637 Double_t dx=x-fX;
1638 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1639
1530f89c 1640 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1641
1642 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1643 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1644
60e55aee 1645 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 1646 y = fP[0] + dx*(f1+f2)/(r1+r2);
1647 return kTRUE;
1648}
1649
1650Bool_t
6c94f330 1651AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1652 //---------------------------------------------------------------------
1653 // This function returns the local Z-coordinate of the intersection
1654 // point between this track and the reference plane "x" (cm).
1655 // Magnetic field "b" (kG)
1656 //---------------------------------------------------------------------
1657 Double_t dx=x-fX;
1658 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1659
2258e165 1660 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1661
1662 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1663 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1664
60e55aee 1665 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
6c94f330 1666 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1667 return kTRUE;
1668}
1669
1670Bool_t
c9ec41e8 1671AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1672 //---------------------------------------------------------------------
1673 // This function returns the global track position extrapolated to
1674 // the radial position "x" (cm) in the magnetic field "b" (kG)
1675 //---------------------------------------------------------------------
c9ec41e8 1676 Double_t dx=x-fX;
e421f556 1677 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1678
1530f89c 1679 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1680
e421f556 1681 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1682 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1683
60e55aee 1684 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
c9ec41e8 1685 r[0] = x;
1686 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1687 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1688
c9ec41e8 1689 return Local2GlobalPosition(r,fAlpha);
51ad6848 1690}
1691
edc97986 1692//_____________________________________________________________________________
51ad6848 1693void AliExternalTrackParam::Print(Option_t* /*option*/) const
1694{
1695// print the parameters and the covariance matrix
1696
1697 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1698 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1699 fP[0], fP[1], fP[2], fP[3], fP[4]);
1700 printf(" covariance: %12g\n", fC[0]);
1701 printf(" %12g %12g\n", fC[1], fC[2]);
1702 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1703 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1704 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1705 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1706 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1707}
5b77d93c 1708
c194ba83 1709Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1710 //
1711 // Get sinus at given x
1712 //
1530f89c 1713 Double_t crv=GetC(b);
c194ba83 1714 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1715 Double_t dx = x-fX;
1716 Double_t res = fP[2]+dx*crv;
1717 return res;
1718}
bf00ebb8 1719
1720Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1721 //------------------------------------------------------------------------
1722 // Get the distance between two tracks at the local position x
1723 // working in the local frame of this track.
1724 // Origin : Marian.Ivanov@cern.ch
1725 //-----------------------------------------------------------------------
1726 Double_t xyz[3];
1727 Double_t xyz2[3];
1728 xyz[0]=x;
1729 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1730 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1731 //
1732 //
1733 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1734 xyz2[0]=x;
1735 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1736 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1737 }else{
1738 //
1739 Double_t xyz1[3];
1740 Double_t dfi = param2->GetAlpha()-GetAlpha();
1741 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1742 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1743 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1744 //
1745 xyz1[0]=xyz2[0];
1746 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1747 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1748 //
1749 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1750 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1751 xyz2[2] = xyz1[2];
1752 }
1753 dist[0] = xyz[0]-xyz2[0];
1754 dist[1] = xyz[1]-xyz2[1];
1755 dist[2] = xyz[2]-xyz2[2];
1756
1757 return kTRUE;
1758}
0c19adf7 1759
1760
1761//
1762// Draw functionality.
1763// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1764//
1765
1766void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1767 //
1768 // Draw track line
1769 //
1770 if (minR>maxR) return ;
1771 if (stepR<=0) return ;
1772 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1773 if (npoints<1) return;
1774 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1775 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1776 polymarker->Draw();
1777}
1778
1779//
1780void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1781 //
1782 // Fill points in the polymarker
1783 //
1784 Int_t counter=0;
1785 for (Double_t r=minR; r<maxR; r+=stepR){
1786 Double_t point[3];
1787 GetXYZAt(r,magF,point);
1788 pol->SetPoint(counter,point[0],point[1], point[2]);
1789 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1790 counter++;
1791 }
1792}
0e8460af 1793
1794Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1795 //
1796 Int_t min = TMath::Min(i,j);
1797 Int_t max = TMath::Max(i,j);
1798
1799 return min+(max+1)*max/2;
1800}
8b6e3369 1801
1802
1803void AliExternalTrackParam::g3helx3(Double_t qfield,
1804 Double_t step,
1805 Double_t vect[7]) {
1806/******************************************************************
1807 * *
1808 * GEANT3 tracking routine in a constant field oriented *
1809 * along axis 3 *
1810 * Tracking is performed with a conventional *
1811 * helix step method *
1812 * *
1813 * Authors R.Brun, M.Hansroul ********* *
1814 * Rewritten V.Perevoztchikov *
1815 * *
1816 * Rewritten in C++ by I.Belikov *
1817 * *
1818 * qfield (kG) - particle charge times magnetic field *
1819 * step (cm) - step length along the helix *
1820 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
1821 * *
1822 ******************************************************************/
1823 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
bfd20868 1824 const Double_t kOvSqSix=TMath::Sqrt(1./6.);
8b6e3369 1825
1826 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
1827
1828 Double_t rho = qfield*kB2C/vect[ipp];
1829 Double_t tet = rho*step;
1830
1831 Double_t tsint, sintt, sint, cos1t;
2de63fc5 1832 if (TMath::Abs(tet) > 0.03) {
8b6e3369 1833 sint = TMath::Sin(tet);
1834 sintt = sint/tet;
1835 tsint = (tet - sint)/tet;
1836 Double_t t=TMath::Sin(0.5*tet);
1837 cos1t = 2*t*t/tet;
1838 } else {
1839 tsint = tet*tet/6.;
bfd20868 1840 sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint;
8b6e3369 1841 sint = tet*sintt;
1842 cos1t = 0.5*tet;
1843 }
1844
1845 Double_t f1 = step*sintt;
1846 Double_t f2 = step*cos1t;
1847 Double_t f3 = step*tsint*cosz;
1848 Double_t f4 = -tet*cos1t;
1849 Double_t f5 = sint;
1850
1851 vect[ix] += f1*cosx - f2*cosy;
1852 vect[iy] += f1*cosy + f2*cosx;
1853 vect[iz] += f1*cosz + f3;
1854
1855 vect[ipx] += f4*cosx - f5*cosy;
1856 vect[ipy] += f4*cosy + f5*cosx;
1857
1858}
1859
1860Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
1861 //----------------------------------------------------------------
1862 // Extrapolate this track to the plane X=xk in the field b[].
1863 //
1864 // X [cm] is in the "tracking coordinate system" of this track.
1865 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
1866 //----------------------------------------------------------------
1867
1868 Double_t dx=xk-fX;
1869 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
7e1b73dd 1870 if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
8b6e3369 1871
1872 Double_t crv=GetC(b[2]);
1873 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
1874
2de63fc5 1875 Double_t x2r = crv*dx;
1876 Double_t f1=fP[2], f2=f1 + x2r;
8b6e3369 1877 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1878 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1879
1880
1881 // Estimate the covariance matrix
1882 Double_t &fP3=fP[3], &fP4=fP[4];
1883 Double_t
1884 &fC00=fC[0],
1885 &fC10=fC[1], &fC11=fC[2],
1886 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1887 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1888 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1889
bfd20868 1890 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
8b6e3369 1891
1892 //f = F - 1
1893 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
1894 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
1895 Double_t f12= dx*fP3*f1/(r1*r1*r1);
1896 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
1897 Double_t f13= dx/r1;
1898 Double_t f24= dx; f24*=cc;
1899
1900 //b = C*ft
1901 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
1902 Double_t b02=f24*fC40;
1903 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
1904 Double_t b12=f24*fC41;
1905 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
1906 Double_t b22=f24*fC42;
1907 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
1908 Double_t b42=f24*fC44;
1909 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
1910 Double_t b32=f24*fC43;
1911
1912 //a = f*b = f*C*ft
1913 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
1914 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
1915 Double_t a22=f24*b42;
1916
1917 //F*C*Ft = C + (b + bt + a)
1918 fC00 += b00 + b00 + a00;
1919 fC10 += b10 + b01 + a01;
1920 fC20 += b20 + b02 + a02;
1921 fC30 += b30;
1922 fC40 += b40;
1923 fC11 += b11 + b11 + a11;
1924 fC21 += b21 + b12 + a12;
1925 fC31 += b31;
1926 fC41 += b41;
1927 fC22 += b22 + b22 + a22;
1928 fC32 += b32;
1929 fC42 += b42;
1930
86be8934 1931 CheckCovariance();
8b6e3369 1932
1933 // Appoximate step length
2de63fc5 1934 double dy2dx = (f1+f2)/(r1+r2);
1935 Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord
1936 : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc
8b6e3369 1937 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
1938
8b6e3369 1939 // Get the track's (x,y,z) and (px,py,pz) in the Global System
1940 Double_t r[3]; GetXYZ(r);
1941 Double_t p[3]; GetPxPyPz(p);
1942 Double_t pp=GetP();
1943 p[0] /= pp;
1944 p[1] /= pp;
1945 p[2] /= pp;
1946
1947
1948 // Rotate to the system where Bx=By=0.
1949 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
1950 Double_t cosphi=1., sinphi=0.;
1951 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
1952 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
1953 Double_t costet=1., sintet=0.;
1954 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
1955 Double_t vect[7];
1956
1957 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
1958 vect[1] = -sinphi*r[0] + cosphi*r[1];
1959 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
1960
1961 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
1962 vect[4] = -sinphi*p[0] + cosphi*p[1];
1963 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
1964
1965 vect[6] = pp;
1966
1967
1968 // Do the helix step
1969 g3helx3(GetSign()*bb,step,vect);
1970
1971
1972 // Rotate back to the Global System
1973 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
1974 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
1975 r[2] = -sintet*vect[0] + costet*vect[2];
1976
1977 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
1978 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
1979 p[2] = -sintet*vect[3] + costet*vect[5];
1980
1981
1982 // Rotate back to the Tracking System
1983 Double_t cosalp = TMath::Cos(fAlpha);
1984 Double_t sinalp =-TMath::Sin(fAlpha);
1985
1986 Double_t
1987 t = cosalp*r[0] - sinalp*r[1];
1988 r[1] = sinalp*r[0] + cosalp*r[1];
1989 r[0] = t;
1990
1991 t = cosalp*p[0] - sinalp*p[1];
1992 p[1] = sinalp*p[0] + cosalp*p[1];
1993 p[0] = t;
1994
1995
1996 // Do the final correcting step to the target plane (linear approximation)
1997 Double_t x=r[0], y=r[1], z=r[2];
1998 if (TMath::Abs(dx) > kAlmost0) {
1999 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
2000 dx = xk - r[0];
2001 x += dx;
2002 y += p[1]/p[0]*dx;
2003 z += p[2]/p[0]*dx;
2004 }
2005
2006
2007 // Calculate the track parameters
2008 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
2009 fX = x;
2010 fP[0] = y;
2011 fP[1] = z;
2012 fP[2] = p[1]/t;
2013 fP[3] = p[2]/t;
2014 fP[4] = GetSign()/(t*pp);
2015
2016 return kTRUE;
2017}
2018
cfdb62d4 2019Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
2020 //
2021 //Translation: in the event mixing, the tracks can be shifted
2022 //of the difference among primary vertices (vTrasl) and
2023 //the covariance matrix is changed accordingly
2024 //(covV = covariance of the primary vertex).
2025 //Origin: "Romita, Rossella" <R.Romita@gsi.de>
2026 //
2027 TVector3 translation;
2028 // vTrasl coordinates in the local system
2029 translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
2030 translation.RotateZ(-fAlpha);
2031 translation.GetXYZ(vTrasl);
2032
2033 //compute the new x,y,z of the track
5a87bb3d 2034 Double_t newX=fX-vTrasl[0];
2035 Double_t newY=fP[0]-vTrasl[1];
2036 Double_t newZ=fP[1]-vTrasl[2];
cfdb62d4 2037
2038 //define the new parameters
5a87bb3d 2039 Double_t newParam[5];
2040 newParam[0]=newY;
2041 newParam[1]=newZ;
2042 newParam[2]=fP[2];
2043 newParam[3]=fP[3];
2044 newParam[4]=fP[4];
cfdb62d4 2045
2046 // recompute the covariance matrix:
2047 // 1. covV in the local system
2048 Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
2049 TMatrixD qQi(3,3);
2050 qQi(0,0) = cosRot;
2051 qQi(0,1) = sinRot;
2052 qQi(0,2) = 0.;
2053 qQi(1,0) = -sinRot;
2054 qQi(1,1) = cosRot;
2055 qQi(1,2) = 0.;
2056 qQi(2,0) = 0.;
2057 qQi(2,1) = 0.;
2058 qQi(2,2) = 1.;
2059 TMatrixD uUi(3,3);
2060 uUi(0,0) = covV[0];
2061 uUi(0,0) = covV[0];
2062 uUi(1,0) = covV[1];
2063 uUi(0,1) = covV[1];
2064 uUi(2,0) = covV[3];
2065 uUi(0,2) = covV[3];
2066 uUi(1,1) = covV[2];
2067 uUi(2,2) = covV[5];
2068 uUi(1,2) = covV[4];
2069 if(uUi.Determinant() <= 0.) {return kFALSE;}
2070 TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
2071 TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
2072
2073 //2. compute the new covariance matrix of the track
2074 Double_t sigmaXX=m(0,0);
2075 Double_t sigmaXZ=m(2,0);
2076 Double_t sigmaXY=m(1,0);
2077 Double_t sigmaYY=GetSigmaY2()+m(1,1);
2078 Double_t sigmaYZ=fC[1]+m(1,2);
2079 Double_t sigmaZZ=fC[2]+m(2,2);
2080 Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
2081 Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
2082 Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
2083
2084 Double_t newCov[15];
2085 newCov[0]=covarianceYY;
2086 newCov[1]=covarianceYZ;
2087 newCov[2]=covarianceZZ;
2088 for(Int_t i=3;i<15;i++){
2089 newCov[i]=fC[i];
2090 }
2091
2092 // set the new parameters
2093
5a87bb3d 2094 Set(newX,fAlpha,newParam,newCov);
cfdb62d4 2095
2096 return kTRUE;
2097 }
86be8934 2098
2099void AliExternalTrackParam::CheckCovariance() {
2100
2101 // This function forces the diagonal elements of the covariance matrix to be positive.
2102 // In case the diagonal element is bigger than the maximal allowed value, it is set to
2103 // the limit and the off-diagonal elements that correspond to it are set to zero.
2104
2105 fC[0] = TMath::Abs(fC[0]);
2106 if (fC[0]>kC0max) {
2107 fC[0] = kC0max;
2108 fC[1] = 0;
2109 fC[3] = 0;
2110 fC[6] = 0;
2111 fC[10] = 0;
2112 }
2113 fC[2] = TMath::Abs(fC[2]);
2114 if (fC[2]>kC2max) {
2115 fC[2] = kC2max;
2116 fC[1] = 0;
2117 fC[4] = 0;
2118 fC[7] = 0;
2119 fC[11] = 0;
2120 }
2121 fC[5] = TMath::Abs(fC[5]);
2122 if (fC[5]>kC5max) {
2123 fC[5] = kC5max;
2124 fC[3] = 0;
2125 fC[4] = 0;
2126 fC[8] = 0;
2127 fC[12] = 0;
2128 }
2129 fC[9] = TMath::Abs(fC[9]);
2130 if (fC[9]>kC9max) {
2131 fC[9] = kC9max;
2132 fC[6] = 0;
2133 fC[7] = 0;
2134 fC[8] = 0;
2135 fC[13] = 0;
2136 }
2137 fC[14] = TMath::Abs(fC[14]);
2138 if (fC[14]>kC14max) {
2139 fC[14] = kC14max;
2140 fC[10] = 0;
2141 fC[11] = 0;
2142 fC[12] = 0;
2143 fC[13] = 0;
2144 }
2145
2146 // The part below is used for tests and normally is commented out
2147// TMatrixDSym m(5);
2148// TVectorD eig(5);
2149
2150// m(0,0)=fC[0];
2151// m(1,0)=fC[1]; m(1,1)=fC[2];
2152// m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5];
2153// m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9];
2154// 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];
2155
2156// m(0,1)=m(1,0);
2157// m(0,2)=m(2,0); m(1,2)=m(2,1);
2158// m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2);
2159// m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3);
2160// m.EigenVectors(eig);
2161
2162// // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0);
2163// if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) {
2164// AliWarning("Negative eigenvalues of the covariance matrix!");
2165// this->Print();
2166// eig.Print();
2167// }
2168}