new task for systematic studies of jetfinders
[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///////////////////////////////////////////////////////////////////////////////
4b189f98 28#include <TMatrixDSym.h>
d46683db 29#include <TPolyMarker3D.h>
30#include <TVector3.h>
cfdb62d4 31#include <TMatrixD.h>
d46683db 32
51ad6848 33#include "AliExternalTrackParam.h"
58e536c5 34#include "AliVVertex.h"
6c94f330 35#include "AliLog.h"
51ad6848 36
37ClassImp(AliExternalTrackParam)
38
ed5f2849 39Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
40
51ad6848 41//_____________________________________________________________________________
90e48c0c 42AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 43 AliVTrack(),
90e48c0c 44 fX(0),
c9ec41e8 45 fAlpha(0)
51ad6848 46{
90e48c0c 47 //
48 // default constructor
49 //
c9ec41e8 50 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
51 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 52}
53
6c94f330 54//_____________________________________________________________________________
55AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 56 AliVTrack(track),
6c94f330 57 fX(track.fX),
58 fAlpha(track.fAlpha)
59{
60 //
61 // copy constructor
62 //
63 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
64 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
65}
66
def9660e 67//_____________________________________________________________________________
68AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
69{
70 //
71 // assignment operator
72 //
73
74 if (this!=&trkPar) {
4f6e22bd 75 AliVTrack::operator=(trkPar);
def9660e 76 fX = trkPar.fX;
77 fAlpha = trkPar.fAlpha;
78
79 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
80 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
81 }
82
83 return *this;
84}
85
51ad6848 86//_____________________________________________________________________________
87AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
88 const Double_t param[5],
90e48c0c 89 const Double_t covar[15]) :
4f6e22bd 90 AliVTrack(),
90e48c0c 91 fX(x),
c9ec41e8 92 fAlpha(alpha)
51ad6848 93{
90e48c0c 94 //
95 // create external track parameters from given arguments
96 //
c9ec41e8 97 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
98 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 99}
100
4f6e22bd 101//_____________________________________________________________________________
102AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
103 AliVTrack(),
104 fX(0.),
105 fAlpha(0.)
106{
107 //
610e3088 108 // Constructor from virtual track,
109 // This is not a copy contructor !
4f6e22bd 110 //
610e3088 111
112 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
113 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
114 AliWarning("Calling the default constructor...");
115 AliExternalTrackParam();
116 return;
117 }
118
892be05f 119 Double_t xyz[3],pxpypz[3],cv[21];
120 vTrack->GetXYZ(xyz);
121 pxpypz[0]=vTrack->Px();
122 pxpypz[1]=vTrack->Py();
123 pxpypz[2]=vTrack->Pz();
4f6e22bd 124 vTrack->GetCovarianceXYZPxPyPz(cv);
125 Short_t sign = (Short_t)vTrack->Charge();
126
127 Set(xyz,pxpypz,cv,sign);
128}
129
90e48c0c 130//_____________________________________________________________________________
da4e3deb 131AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
132 Double_t cv[21],Short_t sign) :
4f6e22bd 133 AliVTrack(),
da4e3deb 134 fX(0.),
135 fAlpha(0.)
4f6e22bd 136{
137 //
138 // constructor from the global parameters
139 //
140
141 Set(xyz,pxpypz,cv,sign);
142}
143
144//_____________________________________________________________________________
145void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
146 Double_t cv[21],Short_t sign)
da4e3deb 147{
148 //
149 // create external track parameters from the global parameters
150 // x,y,z,px,py,pz and their 6x6 covariance matrix
151 // A.Dainese 10.10.08
152
aff56ff7 153 // Calculate alpha: the rotation angle of the corresponding local system.
154 //
155 // For global radial position inside the beam pipe, alpha is the
156 // azimuthal angle of the momentum projected on (x,y).
157 //
c99948ce 158 // For global radial position outside the ITS, alpha is the
aff56ff7 159 // azimuthal angle of the centre of the TPC sector in which the point
160 // xyz lies
161 //
162 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 163 Double_t radMax = 45.; // approximately ITS outer radius
164 if (radPos2 < radMax*radMax) { // inside the ITS
165
aff56ff7 166 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
c99948ce 167 } else { // outside the ITS
aff56ff7 168 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
169 fAlpha =
170 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
171 }
da4e3deb 172
173 // Get the vertex of origin and the momentum
174 TVector3 ver(xyz[0],xyz[1],xyz[2]);
175 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
176
177 // Rotate to the local coordinate system
178 ver.RotateZ(-fAlpha);
179 mom.RotateZ(-fAlpha);
180
181 // x of the reference plane
182 fX = ver.X();
183
184 Double_t charge = (Double_t)sign;
185
186 fP[0] = ver.Y();
187 fP[1] = ver.Z();
188 fP[2] = TMath::Sin(mom.Phi());
189 fP[3] = mom.Pz()/mom.Pt();
190 fP[4] = TMath::Sign(1/mom.Pt(),charge);
191
192 // Covariance matrix (formulas to be simplified)
193
194 Double_t pt=1./TMath::Abs(fP[4]);
195 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
196 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
197
198 Double_t m00=-sn;// m10=cs;
199 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
200 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
201 Double_t m35=pt, m45=-pt*pt*fP[3];
202
203 m43*=GetSign();
204 m44*=GetSign();
205 m45*=GetSign();
206
207 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
208 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
209 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
210 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
211 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
212 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
213 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
214
215 fC[0 ] = cv[0 ]+cv[2 ];
216 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
217 fC[2 ] = cv[5 ];
218 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
219 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
220 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
221 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
222 fC[11] = (cv[8]-fC[4]*m23)/m43;
223 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
224 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
225 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
226 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
227 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
228 Double_t b2=m23*m35;
229 Double_t b3=m43*m35;
230 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
231 Double_t b5=m24*m35;
232 Double_t b6=m44*m35;
233 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
234 fC[13] = b1/b3-b2*fC[8]/b3;
235 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 236
237 return;
da4e3deb 238}
239
51ad6848 240//_____________________________________________________________________________
c9ec41e8 241void AliExternalTrackParam::Reset() {
1530f89c 242 //
243 // Resets all the parameters to 0
244 //
c9ec41e8 245 fX=fAlpha=0.;
246 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
247 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 248}
249
3775b0ca 250//_____________________________________________________________________________
251void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
252 //
253 // Add "something" to the track covarince matrix.
254 // May be needed to account for unknown mis-calibration/mis-alignment
255 //
256 fC[0] +=c[0];
257 fC[1] +=c[1]; fC[2] +=c[2];
258 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
259 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
260 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
261}
262
263
c9ec41e8 264Double_t AliExternalTrackParam::GetP() const {
265 //---------------------------------------------------------------------
266 // This function returns the track momentum
267 // Results for (nearly) straight tracks are meaningless !
268 //---------------------------------------------------------------------
06fb4a2f 269 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 270 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 271}
272
1d99986f 273Double_t AliExternalTrackParam::Get1P() const {
274 //---------------------------------------------------------------------
275 // This function returns the 1/(track momentum)
276 //---------------------------------------------------------------------
277 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
278}
279
c9ec41e8 280//_______________________________________________________________________
c7bafca9 281Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 282 //------------------------------------------------------------------
283 // This function calculates the transverse impact parameter
284 // with respect to a point with global coordinates (x,y)
285 // in the magnetic field "b" (kG)
286 //------------------------------------------------------------------
5773defd 287 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 288 Double_t rp4=GetC(b);
c9ec41e8 289
290 Double_t xt=fX, yt=fP[0];
291
292 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
293 Double_t a = x*cs + y*sn;
294 y = -x*sn + y*cs; x=a;
295 xt-=x; yt-=y;
296
297 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
298 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 299 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
300}
301
302//_______________________________________________________________________
303void AliExternalTrackParam::
304GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
305 //------------------------------------------------------------------
306 // This function calculates the transverse and longitudinal impact parameters
307 // with respect to a point with global coordinates (x,y)
308 // in the magnetic field "b" (kG)
309 //------------------------------------------------------------------
310 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
311 Double_t xt=fX, yt=fP[0];
312 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
313 Double_t a = x*cs + y*sn;
314 y = -x*sn + y*cs; x=a;
315 xt-=x; yt-=y;
316
317 Double_t rp4=GetC(b);
318 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
319 dz[0] = -(xt*f1 - yt*r1);
320 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
321 return;
322 }
323
324 sn=rp4*xt - f1; cs=rp4*yt + r1;
325 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
326 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
327 dz[0] = -a/(1 + rr);
328 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
329 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 330}
331
49d13e89 332//_______________________________________________________________________
333Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
334 //------------------------------------------------------------------
335 // This function calculates the transverse impact parameter
336 // with respect to a point with global coordinates (xv,yv)
337 // neglecting the track curvature.
338 //------------------------------------------------------------------
339 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
340 Double_t x= xv*cs + yv*sn;
341 Double_t y=-xv*sn + yv*cs;
342
343 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
344
1530f89c 345 return -d;
49d13e89 346}
347
116b445b 348Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 349(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
350 Double_t (*Bethe)(Double_t)) {
116b445b 351 //------------------------------------------------------------------
352 // This function corrects the track parameters for the crossed material.
353 // "xOverX0" - X/X0, the thickness in units of the radiation length.
354 // "xTimesRho" - is the product length*density (g/cm^2).
355 // "mass" - the mass of this particle (GeV/c^2).
356 //------------------------------------------------------------------
357 Double_t &fP2=fP[2];
358 Double_t &fP3=fP[3];
359 Double_t &fP4=fP[4];
360
361 Double_t &fC22=fC[5];
362 Double_t &fC33=fC[9];
363 Double_t &fC43=fC[13];
364 Double_t &fC44=fC[14];
365
7dded1d5 366 //Apply angle correction, if requested
367 if(anglecorr) {
368 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
369 xOverX0 *=angle;
370 xTimesRho *=angle;
371 }
372
116b445b 373 Double_t p=GetP();
374 Double_t p2=p*p;
375 Double_t beta2=p2/(p2 + mass*mass);
116b445b 376
9f2bec63 377 //Calculating the multiple scattering corrections******************
378 Double_t cC22 = 0.;
379 Double_t cC33 = 0.;
380 Double_t cC43 = 0.;
381 Double_t cC44 = 0.;
116b445b 382 if (xOverX0 != 0) {
383 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
384 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 385 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
386 cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
387 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
388 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
389 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 390 }
391
9f2bec63 392 //Calculating the energy loss corrections************************
393 Double_t cP4=1.;
116b445b 394 if ((xTimesRho != 0.) && (beta2 < 1.)) {
d46683db 395 Double_t dE=Bethe(p/mass)*xTimesRho;
116b445b 396 Double_t e=TMath::Sqrt(p2 + mass*mass);
397 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
9f2bec63 398 cP4 = (1.- e/p2*dE);
399 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 400
116b445b 401
402 // Approximate energy loss fluctuation (M.Ivanov)
403 const Double_t knst=0.07; // To be tuned.
404 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 405 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 406
407 }
408
9f2bec63 409 //Applying the corrections*****************************
410 fC22 += cC22;
411 fC33 += cC33;
412 fC43 += cC43;
413 fC44 += cC44;
414 fP4 *= cP4;
415
116b445b 416 return kTRUE;
417}
418
419
ee5dba5e 420Bool_t AliExternalTrackParam::CorrectForMaterial
421(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 422 //------------------------------------------------------------------
116b445b 423 // Deprecated function !
424 // Better use CorrectForMeanMaterial instead of it.
425 //
c7bafca9 426 // This function corrects the track parameters for the crossed material
427 // "d" - the thickness (fraction of the radiation length)
428 // "x0" - the radiation length (g/cm^2)
429 // "mass" - the mass of this particle (GeV/c^2)
430 //------------------------------------------------------------------
431 Double_t &fP2=fP[2];
432 Double_t &fP3=fP[3];
433 Double_t &fP4=fP[4];
434
435 Double_t &fC22=fC[5];
436 Double_t &fC33=fC[9];
437 Double_t &fC43=fC[13];
438 Double_t &fC44=fC[14];
439
7b5ef2e6 440 Double_t p=GetP();
441 Double_t p2=p*p;
c7bafca9 442 Double_t beta2=p2/(p2 + mass*mass);
443 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
444
445 //Multiple scattering******************
9f2bec63 446 Double_t cC22 = 0.;
447 Double_t cC33 = 0.;
448 Double_t cC43 = 0.;
449 Double_t cC44 = 0.;
c7bafca9 450 if (d!=0) {
451 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
452 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 453 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
454 cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
455 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
456 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
457 cC44 = theta2*fP3*fP4*fP3*fP4;
c7bafca9 458 }
459
460 //Energy losses************************
9f2bec63 461 Double_t cP4=1.;
8fc1985d 462 if (x0!=0. && beta2<1) {
c7bafca9 463 d*=x0;
d46683db 464 Double_t dE=Bethe(p/mass)*d;
ee5dba5e 465 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 466 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
9f2bec63 467 cP4 = (1.- e/p2*dE);
ee5dba5e 468
469 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 470 const Double_t knst=0.07; // To be tuned.
471 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 472 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
ee5dba5e 473
c7bafca9 474 }
475
9f2bec63 476 fC22 += cC22;
477 fC33 += cC33;
478 fC43 += cC43;
479 fC44 += cC44;
480 fP4 *= cP4;
481
c7bafca9 482 return kTRUE;
483}
484
9c56b409 485Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
486 Double_t kp1,
487 Double_t kp2,
488 Double_t kp3,
489 Double_t kp4,
490 Double_t kp5) {
491 //
492 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
493 // It is normalized to 1 at the minimum.
494 //
495 // bg - beta*gamma
496 //
497 // The default values for the kp* parameters are for ALICE TPC.
498 // The returned value is in MIP units
499 //
500
501 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
502
503 Double_t aa = TMath::Power(beta,kp4);
504 Double_t bb = TMath::Power(1./bg,kp5);
505
506 bb=TMath::Log(kp3+bb);
507
508 return (kp2-aa-bb)*kp1/aa;
509}
510
511Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
512 Double_t kp0,
513 Double_t kp1,
514 Double_t kp2,
515 Double_t kp3,
516 Double_t kp4) {
517 //
518 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
519 //
520 // bg - beta*gamma
521 // kp0 - density [g/cm^3]
522 // kp1 - density effect first junction point
523 // kp2 - density effect second junction point
524 // kp3 - mean excitation energy [GeV]
525 // kp4 - mean Z/A
526 //
527 // The default values for the kp* parameters are for silicon.
528 // The returned value is in [GeV/(g/cm^2)].
529 //
530
531 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
532 const Double_t me = 0.511e-3; // [GeV/c^2]
533 const Double_t rho = kp0;
534 const Double_t x0 = kp1*2.303;
535 const Double_t x1 = kp2*2.303;
536 const Double_t mI = kp3;
537 const Double_t mZA = kp4;
538 const Double_t bg2 = bg*bg;
539 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
540
541 //*** Density effect
542 Double_t d2=0.;
543 const Double_t x=TMath::Log(bg);
544 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
545 if (x > x1) {
546 d2 = lhwI + x - 0.5;
547 } else if (x > x0) {
548 const Double_t r=(x1-x)/(x1-x0);
549 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
550 }
551
552 return mK*mZA*(1+bg2)/bg2*
553 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
554}
555
d46683db 556Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 557 //------------------------------------------------------------------
d46683db 558 // This is an approximation of the Bethe-Bloch formula,
559 // reasonable for solid materials.
560 // All the parameters are, in fact, for Si.
9b655cba 561 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 562 //------------------------------------------------------------------
a821848c 563
9c56b409 564 return BetheBlochGeant(bg);
d46683db 565}
ee5dba5e 566
d46683db 567Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
568 //------------------------------------------------------------------
569 // This is an approximation of the Bethe-Bloch formula,
570 // reasonable for gas materials.
571 // All the parameters are, in fact, for Ne.
9b655cba 572 // The returned value is in [GeV/(g/cm^2)]
d46683db 573 //------------------------------------------------------------------
574
575 const Double_t rho = 0.9e-3;
576 const Double_t x0 = 2.;
577 const Double_t x1 = 4.;
578 const Double_t mI = 140.e-9;
579 const Double_t mZA = 0.49555;
580
9c56b409 581 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 582}
583
49d13e89 584Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
585 //------------------------------------------------------------------
586 // Transform this track to the local coord. system rotated
587 // by angle "alpha" (rad) with respect to the global coord. system.
588 //------------------------------------------------------------------
dfcef74c 589 if (TMath::Abs(fP[2]) >= kAlmost1) {
590 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
591 return kFALSE;
592 }
593
49d13e89 594 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
595 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
596
597 Double_t &fP0=fP[0];
598 Double_t &fP2=fP[2];
599 Double_t &fC00=fC[0];
600 Double_t &fC10=fC[1];
601 Double_t &fC20=fC[3];
602 Double_t &fC21=fC[4];
603 Double_t &fC22=fC[5];
604 Double_t &fC30=fC[6];
605 Double_t &fC32=fC[8];
606 Double_t &fC40=fC[10];
607 Double_t &fC42=fC[12];
608
609 Double_t x=fX;
610 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
611 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
612
dfcef74c 613 Double_t tmp=sf*ca - cf*sa;
0b69bbb2 614 if (TMath::Abs(tmp) >= kAlmost1) {
615 AliError(Form("Rotation failed ! %.10e",tmp));
616 return kFALSE;
617 }
dfcef74c 618
49d13e89 619 fAlpha = alpha;
620 fX = x*ca + fP0*sa;
621 fP0= -x*sa + fP0*ca;
dfcef74c 622 fP2= tmp;
49d13e89 623
06fb4a2f 624 if (TMath::Abs(cf)<kAlmost0) {
625 AliError(Form("Too small cosine value %f",cf));
626 cf = kAlmost0;
627 }
628
49d13e89 629 Double_t rr=(ca+sf/cf*sa);
630
631 fC00 *= (ca*ca);
632 fC10 *= ca;
633 fC20 *= ca*rr;
634 fC21 *= rr;
635 fC22 *= rr*rr;
636 fC30 *= ca;
637 fC32 *= rr;
638 fC40 *= ca;
639 fC42 *= rr;
640
641 return kTRUE;
642}
643
644Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
645 //----------------------------------------------------------------
646 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
647 //----------------------------------------------------------------
49d13e89 648 Double_t dx=xk-fX;
e421f556 649 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 650
1530f89c 651 Double_t crv=GetC(b);
5773defd 652 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
653
49d13e89 654 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 655 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 656 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
657
658 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
659 Double_t
660 &fC00=fC[0],
661 &fC10=fC[1], &fC11=fC[2],
662 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
663 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
664 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
665
666 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
667
668 fX=xk;
669 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 670 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 671 fP2 += dx*crv;
672
673 //f = F - 1
674
675 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
676 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
677 Double_t f12= dx*fP3*f1/(r1*r1*r1);
678 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
679 Double_t f13= dx/r1;
680 Double_t f24= dx; f24*=cc;
681
682 //b = C*ft
683 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
684 Double_t b02=f24*fC40;
685 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
686 Double_t b12=f24*fC41;
687 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
688 Double_t b22=f24*fC42;
689 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
690 Double_t b42=f24*fC44;
691 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
692 Double_t b32=f24*fC43;
693
694 //a = f*b = f*C*ft
695 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
696 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
697 Double_t a22=f24*b42;
698
699 //F*C*Ft = C + (b + bt + a)
700 fC00 += b00 + b00 + a00;
701 fC10 += b10 + b01 + a01;
702 fC20 += b20 + b02 + a02;
703 fC30 += b30;
704 fC40 += b40;
705 fC11 += b11 + b11 + a11;
706 fC21 += b21 + b12 + a12;
707 fC31 += b31;
708 fC41 += b41;
709 fC22 += b22 + b22 + a22;
710 fC32 += b32;
711 fC42 += b42;
712
713 return kTRUE;
714}
715
9f2bec63 716Bool_t
717AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
718 //------------------------------------------------------------------
719 // Transform this track to the local coord. system rotated
720 // by angle "alpha" (rad) with respect to the global coord. system,
721 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
722 //------------------------------------------------------------------
723
724 //Save the parameters
725 Double_t as=fAlpha;
726 Double_t xs=fX;
727 Double_t ps[5], cs[15];
728 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
729 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
730
731 if (Rotate(alpha))
732 if (PropagateTo(x,b)) return kTRUE;
733
734 //Restore the parameters, if the operation failed
735 fAlpha=as;
736 fX=xs;
737 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
738 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
739 return kFALSE;
740}
741
742
052daaff 743void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
744Double_t p[3], Double_t bz) const {
745 //+++++++++++++++++++++++++++++++++++++++++
746 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
747 // Extrapolate track along simple helix in magnetic field
748 // Arguments: len -distance alogn helix, [cm]
749 // bz - mag field, [kGaus]
750 // Returns: x and p contain extrapolated positon and momentum
751 // The momentum returned for straight-line tracks is meaningless !
752 //+++++++++++++++++++++++++++++++++++++++++
753 GetXYZ(x);
754
2258e165 755 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 756 Double_t unit[3]; GetDirection(unit);
757 x[0]+=unit[0]*len;
758 x[1]+=unit[1]*len;
759 x[2]+=unit[2]*len;
760
761 p[0]=unit[0]/kAlmost0;
762 p[1]=unit[1]/kAlmost0;
763 p[2]=unit[2]/kAlmost0;
764 } else {
765 GetPxPyPz(p);
766 Double_t pp=GetP();
767 Double_t a = -kB2C*bz*GetSign();
768 Double_t rho = a/pp;
769 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
770 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
771 x[2] += p[2]*len/pp;
772
773 Double_t p0=p[0];
774 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
775 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
776 }
777}
778
779Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
780Double_t bz) const {
781 //+++++++++++++++++++++++++++++++++++++++++
782 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
783 // Finds point of intersection (if exists) of the helix with the plane.
784 // Stores result in fX and fP.
785 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
786 // and vector, normal to the plane
787 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
788 //+++++++++++++++++++++++++++++++++++++++++
789 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
790
791 //estimates initial helix length up to plane
792 Double_t s=
793 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
794 Double_t dist=99999,distPrev=dist;
795 Double_t x[3],p[3];
796 while(TMath::Abs(dist)>0.00001){
797 //calculates helix at the distance s from x0 ALONG the helix
798 Propagate(s,x,p,bz);
799
800 //distance between current helix position and plane
801 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
802
803 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
804 distPrev=dist;
805 s-=dist;
806 }
807 //on exit pnt is intersection point,norm is track vector at that point,
808 //all in MARS
809 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
810 return kTRUE;
811}
812
49d13e89 813Double_t
814AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
815 //----------------------------------------------------------------
816 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
817 //----------------------------------------------------------------
818 Double_t sdd = fC[0] + cov[0];
819 Double_t sdz = fC[1] + cov[1];
820 Double_t szz = fC[2] + cov[2];
821 Double_t det = sdd*szz - sdz*sdz;
822
823 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
824
825 Double_t d = fP[0] - p[0];
826 Double_t z = fP[1] - p[1];
827
828 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
829}
830
4b189f98 831Double_t AliExternalTrackParam::
832GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
833 //----------------------------------------------------------------
834 // Estimate the chi2 of the 3D space point "p" and
1e023a36 835 // the full covariance matrix "covyz" and "covxyz"
4b189f98 836 //
837 // Cov(x,x) ... : covxyz[0]
838 // Cov(y,x) ... : covxyz[1] covyz[0]
839 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
840 //----------------------------------------------------------------
841
842 Double_t res[3] = {
843 GetX() - p[0],
844 GetY() - p[1],
845 GetZ() - p[2]
846 };
847
848 Double_t f=GetSnp();
849 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
850 Double_t r=TMath::Sqrt(1.- f*f);
851 Double_t a=f/r, b=GetTgl()/r;
852
853 Double_t s2=333.*333.; //something reasonably big (cm^2)
854
855 TMatrixDSym v(3);
856 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
857 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
858 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
859
860 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
861 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
862 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
863
864 v.Invert();
865 if (!v.IsValid()) return kVeryBig;
866
867 Double_t chi2=0.;
868 for (Int_t i = 0; i < 3; i++)
869 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
870
871 return chi2;
872
873
874}
875
1e023a36 876Bool_t AliExternalTrackParam::
877PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
878 //----------------------------------------------------------------
879 // Propagate this track to the plane
880 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
881 // belongs to.
882 // The magnetic field is "bz" (kG)
883 //
884 // The track curvature and the change of the covariance matrix
885 // of the track parameters are negleted !
886 // (So the "step" should be small compared with 1/curvature)
887 //----------------------------------------------------------------
888
889 Double_t f=GetSnp();
890 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
891 Double_t r=TMath::Sqrt(1.- f*f);
892 Double_t a=f/r, b=GetTgl()/r;
893
894 Double_t s2=333.*333.; //something reasonably big (cm^2)
895
896 TMatrixDSym tV(3);
897 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
898 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
899 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
900
901 TMatrixDSym pV(3);
902 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
903 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
904 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
905
906 TMatrixDSym tpV(tV);
907 tpV+=pV;
908 tpV.Invert();
909 if (!tpV.IsValid()) return kFALSE;
910
911 TMatrixDSym pW(3),tW(3);
912 for (Int_t i=0; i<3; i++)
913 for (Int_t j=0; j<3; j++) {
914 pW(i,j)=tW(i,j)=0.;
915 for (Int_t k=0; k<3; k++) {
916 pW(i,j) += tV(i,k)*tpV(k,j);
917 tW(i,j) += pV(i,k)*tpV(k,j);
918 }
919 }
920
921 Double_t t[3] = {GetX(), GetY(), GetZ()};
922
923 Double_t x=0.;
924 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
925 Double_t crv=GetC(bz);
926 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
927 f += crv*(x-fX);
928 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
929 fX=x;
930
931 fP[0]=0.;
932 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
933 fP[1]=0.;
934 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
935
936 return kTRUE;
937}
938
e23a38cb 939Double_t *AliExternalTrackParam::GetResiduals(
940Double_t *p,Double_t *cov,Bool_t updated) const {
941 //------------------------------------------------------------------
942 // Returns the track residuals with the space point "p" having
943 // the covariance matrix "cov".
944 // If "updated" is kTRUE, the track parameters expected to be updated,
945 // otherwise they must be predicted.
946 //------------------------------------------------------------------
947 static Double_t res[2];
948
949 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
950 if (updated) {
951 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
952 } else {
953 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
954 }
955 Double_t det=r00*r11 - r01*r01;
956
957 if (TMath::Abs(det) < kAlmost0) return 0;
958
959 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 960
961 if (r00 < 0.) return 0;
962 if (r11 < 0.) return 0;
963
e23a38cb 964 Double_t dy = fP[0] - p[0];
965 Double_t dz = fP[1] - p[1];
966
967 res[0]=dy*TMath::Sqrt(r00);
968 res[1]=dz*TMath::Sqrt(r11);
969
970 return res;
971}
972
49d13e89 973Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
974 //------------------------------------------------------------------
975 // Update the track parameters with the space point "p" having
976 // the covariance matrix "cov"
977 //------------------------------------------------------------------
978 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
979 Double_t
980 &fC00=fC[0],
981 &fC10=fC[1], &fC11=fC[2],
982 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
983 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
984 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
985
986 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
987 r00+=fC00; r01+=fC10; r11+=fC11;
988 Double_t det=r00*r11 - r01*r01;
989
990 if (TMath::Abs(det) < kAlmost0) return kFALSE;
991
992
993 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
994
995 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
996 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
997 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
998 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
999 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
1000
1001 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1002 Double_t sf=fP2 + k20*dy + k21*dz;
1003 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1004
1005 fP0 += k00*dy + k01*dz;
1006 fP1 += k10*dy + k11*dz;
1007 fP2 = sf;
1008 fP3 += k30*dy + k31*dz;
1009 fP4 += k40*dy + k41*dz;
1010
1011 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1012 Double_t c12=fC21, c13=fC31, c14=fC41;
1013
1014 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1015 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1016 fC40-=k00*c04+k01*c14;
1017
1018 fC11-=k10*c01+k11*fC11;
1019 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1020 fC41-=k10*c04+k11*c14;
1021
1022 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1023 fC42-=k20*c04+k21*c14;
1024
1025 fC33-=k30*c03+k31*c13;
1026 fC43-=k30*c04+k31*c14;
1027
1028 fC44-=k40*c04+k41*c14;
1029
1030 return kTRUE;
1031}
1032
c7bafca9 1033void
1034AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1035 //--------------------------------------------------------------------
1036 // External track parameters -> helix parameters
1037 // "b" - magnetic field (kG)
1038 //--------------------------------------------------------------------
1039 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1040
1530f89c 1041 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1042
1043 hlx[5]=fX*cs - hlx[0]*sn; // x0
1044 hlx[0]=fX*sn + hlx[0]*cs; // y0
1045//hlx[1]= // z0
1046 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1047//hlx[3]= // tgl
1530f89c 1048 hlx[4]=GetC(b); // C
c7bafca9 1049}
1050
1051
1052static void Evaluate(const Double_t *h, Double_t t,
1053 Double_t r[3], //radius vector
1054 Double_t g[3], //first defivatives
1055 Double_t gg[3]) //second derivatives
1056{
1057 //--------------------------------------------------------------------
1058 // Calculate position of a point on a track and some derivatives
1059 //--------------------------------------------------------------------
1060 Double_t phase=h[4]*t+h[2];
1061 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1062
ba4550c4 1063 r[0] = h[5];
1064 r[1] = h[0];
1065 if (TMath::Abs(h[4])>kAlmost0) {
1066 r[0] += (sn - h[6])/h[4];
1067 r[1] -= (cs - h[7])/h[4];
1068 }
c7bafca9 1069 r[2] = h[1] + h[3]*t;
1070
1071 g[0] = cs; g[1]=sn; g[2]=h[3];
1072
1073 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1074}
1075
1076Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1077Double_t b, Double_t &xthis, Double_t &xp) const {
1078 //------------------------------------------------------------
1079 // Returns the (weighed !) distance of closest approach between
1080 // this track and the track "p".
1081 // Other returned values:
1082 // xthis, xt - coordinates of tracks' reference planes at the DCA
1083 //-----------------------------------------------------------
1084 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1085 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1086 Double_t dx2=dy2;
1087
c7bafca9 1088 Double_t p1[8]; GetHelixParameters(p1,b);
1089 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1090 Double_t p2[8]; p->GetHelixParameters(p2,b);
1091 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1092
1093
1094 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1095 Evaluate(p1,t1,r1,g1,gg1);
1096 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1097 Evaluate(p2,t2,r2,g2,gg2);
1098
1099 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1100 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1101
1102 Int_t max=27;
1103 while (max--) {
1104 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1105 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1106 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1107 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1108 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1109 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1110 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1111 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1112 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1113
1114 Double_t det=h11*h22-h12*h12;
1115
1116 Double_t dt1,dt2;
1117 if (TMath::Abs(det)<1.e-33) {
1118 //(quasi)singular Hessian
1119 dt1=-gt1; dt2=-gt2;
1120 } else {
1121 dt1=-(gt1*h22 - gt2*h12)/det;
1122 dt2=-(h11*gt2 - h12*gt1)/det;
1123 }
1124
1125 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1126
1127 //check delta(phase1) ?
1128 //check delta(phase2) ?
1129
1130 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1131 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1132 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1133 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1134 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1135 if (lmb < 0.)
358f16ae 1136 AliDebug(1," stopped at not a minimum !");
c7bafca9 1137 break;
1138 }
1139
1140 Double_t dd=dm;
1141 for (Int_t div=1 ; ; div*=2) {
1142 Evaluate(p1,t1+dt1,r1,g1,gg1);
1143 Evaluate(p2,t2+dt2,r2,g2,gg2);
1144 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1145 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1146 if (dd<dm) break;
1147 dt1*=0.5; dt2*=0.5;
1148 if (div>512) {
358f16ae 1149 AliDebug(1," overshoot !"); break;
c7bafca9 1150 }
1151 }
1152 dm=dd;
1153
1154 t1+=dt1;
1155 t2+=dt2;
1156
1157 }
1158
358f16ae 1159 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1160
1161 Double_t cs=TMath::Cos(GetAlpha());
1162 Double_t sn=TMath::Sin(GetAlpha());
1163 xthis=r1[0]*cs + r1[1]*sn;
1164
1165 cs=TMath::Cos(p->GetAlpha());
1166 sn=TMath::Sin(p->GetAlpha());
1167 xp=r2[0]*cs + r2[1]*sn;
1168
1169 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1170}
1171
1172Double_t AliExternalTrackParam::
1173PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1174 //--------------------------------------------------------------
1175 // Propagates this track and the argument track to the position of the
1176 // distance of closest approach.
1177 // Returns the (weighed !) distance of closest approach.
1178 //--------------------------------------------------------------
1179 Double_t xthis,xp;
1180 Double_t dca=GetDCA(p,b,xthis,xp);
1181
1182 if (!PropagateTo(xthis,b)) {
1183 //AliWarning(" propagation failed !");
1184 return 1e+33;
1185 }
1186
1187 if (!p->PropagateTo(xp,b)) {
1188 //AliWarning(" propagation failed !";
1189 return 1e+33;
1190 }
1191
1192 return dca;
1193}
1194
1195
58e536c5 1196Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1197Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1198 //
e99a34df 1199 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1200 // if the (rough) transverse impact parameter is not bigger then "maxd".
1201 // Magnetic field is "b" (kG).
1202 //
1203 // a) The track gets extapolated to the DCA to the vertex.
1204 // b) The impact parameters and their covariance matrix are calculated.
1205 //
1206 // In the case of success, the returned value is kTRUE
1207 // (otherwise, it's kFALSE)
1208 //
1209 Double_t alpha=GetAlpha();
1210 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1211 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1212 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1213 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1214 x-=xv; y-=yv;
1215
1216 //Estimate the impact parameter neglecting the track curvature
1217 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
1218 if (d > maxd) return kFALSE;
1219
1220 //Propagate to the DCA
2258e165 1221 Double_t crv=GetC(b);
e99a34df 1222 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1223
f76701bf 1224 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
1225 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 1226 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1227 else cs=1.;
f76701bf 1228
1229 x = xv*cs + yv*sn;
1230 yv=-xv*sn + yv*cs; xv=x;
1231
1232 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1233
1234 if (dz==0) return kTRUE;
1235 dz[0] = GetParameter()[0] - yv;
1236 dz[1] = GetParameter()[1] - zv;
1237
1238 if (covar==0) return kTRUE;
58e536c5 1239 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1240
1241 //***** Improvements by A.Dainese
1242 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1243 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1244 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1245 covar[1] = GetCovariance()[1]; // between (x,y) and z
1246 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1247 //*****
1248
29fbcc93 1249 return kTRUE;
f76701bf 1250}
1251
1252
b1149664 1253void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1254 //----------------------------------------------------------------
1255 // This function returns a unit vector along the track direction
1256 // in the global coordinate system.
1257 //----------------------------------------------------------------
1258 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1259 Double_t snp=fP[2];
92934324 1260 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 1261 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1262 d[0]=(csp*cs - snp*sn)/norm;
1263 d[1]=(snp*cs + csp*sn)/norm;
1264 d[2]=fP[3]/norm;
1265}
1266
c683ddc2 1267Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1268 //---------------------------------------------------------------------
1269 // This function returns the global track momentum components
1270 // Results for (nearly) straight tracks are meaningless !
1271 //---------------------------------------------------------------------
1272 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1273 return Local2GlobalMomentum(p,fAlpha);
1274}
a5e407e9 1275
def9660e 1276Double_t AliExternalTrackParam::Px() const {
957fb479 1277 //---------------------------------------------------------------------
1278 // Returns x-component of momentum
1279 // Result for (nearly) straight tracks is meaningless !
1280 //---------------------------------------------------------------------
def9660e 1281
957fb479 1282 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1283 GetPxPyPz(p);
1284
1285 return p[0];
1286}
1287
1288Double_t AliExternalTrackParam::Py() const {
957fb479 1289 //---------------------------------------------------------------------
1290 // Returns y-component of momentum
1291 // Result for (nearly) straight tracks is meaningless !
1292 //---------------------------------------------------------------------
def9660e 1293
957fb479 1294 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1295 GetPxPyPz(p);
1296
1297 return p[1];
1298}
1299
1300Double_t AliExternalTrackParam::Pz() const {
957fb479 1301 //---------------------------------------------------------------------
1302 // Returns z-component of momentum
1303 // Result for (nearly) straight tracks is meaningless !
1304 //---------------------------------------------------------------------
def9660e 1305
957fb479 1306 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1307 GetPxPyPz(p);
1308
1309 return p[2];
1310}
1311
c683ddc2 1312Double_t AliExternalTrackParam::Xv() const {
1313 //---------------------------------------------------------------------
1314 // Returns x-component of first track point
1315 //---------------------------------------------------------------------
1316
1317 Double_t r[3]={0.,0.,0.};
1318 GetXYZ(r);
1319
1320 return r[0];
1321}
1322
1323Double_t AliExternalTrackParam::Yv() const {
1324 //---------------------------------------------------------------------
1325 // Returns y-component of first track point
1326 //---------------------------------------------------------------------
1327
1328 Double_t r[3]={0.,0.,0.};
1329 GetXYZ(r);
1330
1331 return r[1];
1332}
1333
1334Double_t AliExternalTrackParam::Zv() const {
1335 //---------------------------------------------------------------------
1336 // Returns z-component of first track point
1337 //---------------------------------------------------------------------
1338
1339 Double_t r[3]={0.,0.,0.};
1340 GetXYZ(r);
1341
1342 return r[2];
1343}
1344
def9660e 1345Double_t AliExternalTrackParam::Theta() const {
1346 // return theta angle of momentum
1347
7cdd0c20 1348 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1349}
1350
1351Double_t AliExternalTrackParam::Phi() const {
957fb479 1352 //---------------------------------------------------------------------
1353 // Returns the azimuthal angle of momentum
1354 // 0 <= phi < 2*pi
1355 //---------------------------------------------------------------------
def9660e 1356
957fb479 1357 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1358 if (phi<0.) phi+=2.*TMath::Pi();
1359 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1360
1361 return phi;
def9660e 1362}
1363
1364Double_t AliExternalTrackParam::M() const {
1365 // return particle mass
1366
1367 // No mass information available so far.
1368 // Redifine in derived class!
1369
1370 return -999.;
1371}
1372
1373Double_t AliExternalTrackParam::E() const {
1374 // return particle energy
1375
1376 // No PID information available so far.
1377 // Redifine in derived class!
1378
1379 return -999.;
1380}
1381
1382Double_t AliExternalTrackParam::Eta() const {
1383 // return pseudorapidity
1384
1385 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1386}
1387
1388Double_t AliExternalTrackParam::Y() const {
1389 // return rapidity
1390
1391 // No PID information available so far.
1392 // Redifine in derived class!
1393
1394 return -999.;
1395}
1396
c9ec41e8 1397Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1398 //---------------------------------------------------------------------
1399 // This function returns the global track position
1400 //---------------------------------------------------------------------
1401 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1402 return Local2GlobalPosition(r,fAlpha);
51ad6848 1403}
1404
c9ec41e8 1405Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1406 //---------------------------------------------------------------------
1407 // This function returns the global covariance matrix of the track params
1408 //
1409 // Cov(x,x) ... : cv[0]
1410 // Cov(y,x) ... : cv[1] cv[2]
1411 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1412 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1413 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1414 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1415 //
c9ec41e8 1416 // Results for (nearly) straight tracks are meaningless !
1417 //---------------------------------------------------------------------
e421f556 1418 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1419 for (Int_t i=0; i<21; i++) cv[i]=0.;
1420 return kFALSE;
a5e407e9 1421 }
49d13e89 1422 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1423 for (Int_t i=0; i<21; i++) cv[i]=0.;
1424 return kFALSE;
1425 }
1426 Double_t pt=1./TMath::Abs(fP[4]);
1427 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1428 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1429
1430 Double_t m00=-sn, m10=cs;
1431 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1432 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1433 Double_t m35=pt, m45=-pt*pt*fP[3];
1434
854d5d49 1435 m43*=GetSign();
1436 m44*=GetSign();
1437 m45*=GetSign();
1438
c9ec41e8 1439 cv[0 ] = fC[0]*m00*m00;
1440 cv[1 ] = fC[0]*m00*m10;
1441 cv[2 ] = fC[0]*m10*m10;
1442 cv[3 ] = fC[1]*m00;
1443 cv[4 ] = fC[1]*m10;
1444 cv[5 ] = fC[2];
1445 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1446 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1447 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1448 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1449 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1450 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1451 cv[12] = fC[4]*m24 + fC[11]*m44;
1452 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1453 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1454 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1455 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1456 cv[17] = fC[7]*m35 + fC[11]*m45;
1457 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1458 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1459 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1460
c9ec41e8 1461 return kTRUE;
51ad6848 1462}
1463
51ad6848 1464
c9ec41e8 1465Bool_t
1466AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1467 //---------------------------------------------------------------------
1468 // This function returns the global track momentum extrapolated to
1469 // the radial position "x" (cm) in the magnetic field "b" (kG)
1470 //---------------------------------------------------------------------
c9ec41e8 1471 p[0]=fP[4];
1530f89c 1472 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1473 p[2]=fP[3];
1474 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1475}
1476
7cf7bb6c 1477Bool_t
1478AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1479 //---------------------------------------------------------------------
1480 // This function returns the local Y-coordinate of the intersection
1481 // point between this track and the reference plane "x" (cm).
1482 // Magnetic field "b" (kG)
1483 //---------------------------------------------------------------------
1484 Double_t dx=x-fX;
1485 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1486
1530f89c 1487 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1488
1489 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1490 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1491
60e55aee 1492 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 1493 y = fP[0] + dx*(f1+f2)/(r1+r2);
1494 return kTRUE;
1495}
1496
6c94f330 1497Bool_t
1498AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1499 //---------------------------------------------------------------------
1500 // This function returns the local Z-coordinate of the intersection
1501 // point between this track and the reference plane "x" (cm).
1502 // Magnetic field "b" (kG)
1503 //---------------------------------------------------------------------
1504 Double_t dx=x-fX;
1505 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1506
2258e165 1507 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1508
1509 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1510 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1511
60e55aee 1512 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
6c94f330 1513 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1514 return kTRUE;
1515}
1516
c9ec41e8 1517Bool_t
1518AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1519 //---------------------------------------------------------------------
1520 // This function returns the global track position extrapolated to
1521 // the radial position "x" (cm) in the magnetic field "b" (kG)
1522 //---------------------------------------------------------------------
c9ec41e8 1523 Double_t dx=x-fX;
e421f556 1524 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1525
1530f89c 1526 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1527
e421f556 1528 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1529 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1530
60e55aee 1531 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
c9ec41e8 1532 r[0] = x;
1533 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1534 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1535
c9ec41e8 1536 return Local2GlobalPosition(r,fAlpha);
51ad6848 1537}
1538
51ad6848 1539//_____________________________________________________________________________
1540void AliExternalTrackParam::Print(Option_t* /*option*/) const
1541{
1542// print the parameters and the covariance matrix
1543
1544 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1545 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1546 fP[0], fP[1], fP[2], fP[3], fP[4]);
1547 printf(" covariance: %12g\n", fC[0]);
1548 printf(" %12g %12g\n", fC[1], fC[2]);
1549 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1550 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1551 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1552 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1553 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1554}
5b77d93c 1555
c194ba83 1556Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1557 //
1558 // Get sinus at given x
1559 //
1530f89c 1560 Double_t crv=GetC(b);
c194ba83 1561 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1562 Double_t dx = x-fX;
1563 Double_t res = fP[2]+dx*crv;
1564 return res;
1565}
bf00ebb8 1566
1567Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1568 //------------------------------------------------------------------------
1569 // Get the distance between two tracks at the local position x
1570 // working in the local frame of this track.
1571 // Origin : Marian.Ivanov@cern.ch
1572 //-----------------------------------------------------------------------
1573 Double_t xyz[3];
1574 Double_t xyz2[3];
1575 xyz[0]=x;
1576 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1577 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1578 //
1579 //
1580 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1581 xyz2[0]=x;
1582 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1583 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1584 }else{
1585 //
1586 Double_t xyz1[3];
1587 Double_t dfi = param2->GetAlpha()-GetAlpha();
1588 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1589 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1590 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1591 //
1592 xyz1[0]=xyz2[0];
1593 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1594 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1595 //
1596 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1597 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1598 xyz2[2] = xyz1[2];
1599 }
1600 dist[0] = xyz[0]-xyz2[0];
1601 dist[1] = xyz[1]-xyz2[1];
1602 dist[2] = xyz[2]-xyz2[2];
1603
1604 return kTRUE;
1605}
0c19adf7 1606
1607
1608//
1609// Draw functionality.
1610// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1611//
1612
1613void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1614 //
1615 // Draw track line
1616 //
1617 if (minR>maxR) return ;
1618 if (stepR<=0) return ;
1619 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1620 if (npoints<1) return;
1621 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1622 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1623 polymarker->Draw();
1624}
1625
1626//
1627void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1628 //
1629 // Fill points in the polymarker
1630 //
1631 Int_t counter=0;
1632 for (Double_t r=minR; r<maxR; r+=stepR){
1633 Double_t point[3];
1634 GetXYZAt(r,magF,point);
1635 pol->SetPoint(counter,point[0],point[1], point[2]);
1636 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1637 counter++;
1638 }
1639}
0e8460af 1640
1641Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1642 //
1643 Int_t min = TMath::Min(i,j);
1644 Int_t max = TMath::Max(i,j);
1645
1646 return min+(max+1)*max/2;
1647}
8b6e3369 1648
1649
1650void AliExternalTrackParam::g3helx3(Double_t qfield,
1651 Double_t step,
1652 Double_t vect[7]) {
1653/******************************************************************
1654 * *
1655 * GEANT3 tracking routine in a constant field oriented *
1656 * along axis 3 *
1657 * Tracking is performed with a conventional *
1658 * helix step method *
1659 * *
1660 * Authors R.Brun, M.Hansroul ********* *
1661 * Rewritten V.Perevoztchikov *
1662 * *
1663 * Rewritten in C++ by I.Belikov *
1664 * *
1665 * qfield (kG) - particle charge times magnetic field *
1666 * step (cm) - step length along the helix *
1667 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
1668 * *
1669 ******************************************************************/
1670 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
1671
1672 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
1673
1674 Double_t rho = qfield*kB2C/vect[ipp];
1675 Double_t tet = rho*step;
1676
1677 Double_t tsint, sintt, sint, cos1t;
1678 if (TMath::Abs(tet) > 0.15) {
1679 sint = TMath::Sin(tet);
1680 sintt = sint/tet;
1681 tsint = (tet - sint)/tet;
1682 Double_t t=TMath::Sin(0.5*tet);
1683 cos1t = 2*t*t/tet;
1684 } else {
1685 tsint = tet*tet/6.;
1686 sintt = 1.- tsint;
1687 sint = tet*sintt;
1688 cos1t = 0.5*tet;
1689 }
1690
1691 Double_t f1 = step*sintt;
1692 Double_t f2 = step*cos1t;
1693 Double_t f3 = step*tsint*cosz;
1694 Double_t f4 = -tet*cos1t;
1695 Double_t f5 = sint;
1696
1697 vect[ix] += f1*cosx - f2*cosy;
1698 vect[iy] += f1*cosy + f2*cosx;
1699 vect[iz] += f1*cosz + f3;
1700
1701 vect[ipx] += f4*cosx - f5*cosy;
1702 vect[ipy] += f4*cosy + f5*cosx;
1703
1704}
1705
1706Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
1707 //----------------------------------------------------------------
1708 // Extrapolate this track to the plane X=xk in the field b[].
1709 //
1710 // X [cm] is in the "tracking coordinate system" of this track.
1711 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
1712 //----------------------------------------------------------------
1713
1714 Double_t dx=xk-fX;
1715 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
1716
1717 Double_t crv=GetC(b[2]);
1718 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
1719
1720 Double_t f1=fP[2], f2=f1 + crv*dx;
1721 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1722 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1723
1724
1725 // Estimate the covariance matrix
1726 Double_t &fP3=fP[3], &fP4=fP[4];
1727 Double_t
1728 &fC00=fC[0],
1729 &fC10=fC[1], &fC11=fC[2],
1730 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1731 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1732 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1733
1734 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1735
1736 //f = F - 1
1737 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
1738 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
1739 Double_t f12= dx*fP3*f1/(r1*r1*r1);
1740 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
1741 Double_t f13= dx/r1;
1742 Double_t f24= dx; f24*=cc;
1743
1744 //b = C*ft
1745 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
1746 Double_t b02=f24*fC40;
1747 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
1748 Double_t b12=f24*fC41;
1749 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
1750 Double_t b22=f24*fC42;
1751 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
1752 Double_t b42=f24*fC44;
1753 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
1754 Double_t b32=f24*fC43;
1755
1756 //a = f*b = f*C*ft
1757 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
1758 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
1759 Double_t a22=f24*b42;
1760
1761 //F*C*Ft = C + (b + bt + a)
1762 fC00 += b00 + b00 + a00;
1763 fC10 += b10 + b01 + a01;
1764 fC20 += b20 + b02 + a02;
1765 fC30 += b30;
1766 fC40 += b40;
1767 fC11 += b11 + b11 + a11;
1768 fC21 += b21 + b12 + a12;
1769 fC31 += b31;
1770 fC41 += b41;
1771 fC22 += b22 + b22 + a22;
1772 fC32 += b32;
1773 fC42 += b42;
1774
1775
1776 // Appoximate step length
1777 Double_t step=dx*TMath::Abs(r2 + f2*(f1+f2)/(r1+r2));
1778 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
1779
1780
1781 // Get the track's (x,y,z) and (px,py,pz) in the Global System
1782 Double_t r[3]; GetXYZ(r);
1783 Double_t p[3]; GetPxPyPz(p);
1784 Double_t pp=GetP();
1785 p[0] /= pp;
1786 p[1] /= pp;
1787 p[2] /= pp;
1788
1789
1790 // Rotate to the system where Bx=By=0.
1791 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
1792 Double_t cosphi=1., sinphi=0.;
1793 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
1794 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
1795 Double_t costet=1., sintet=0.;
1796 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
1797 Double_t vect[7];
1798
1799 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
1800 vect[1] = -sinphi*r[0] + cosphi*r[1];
1801 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
1802
1803 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
1804 vect[4] = -sinphi*p[0] + cosphi*p[1];
1805 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
1806
1807 vect[6] = pp;
1808
1809
1810 // Do the helix step
1811 g3helx3(GetSign()*bb,step,vect);
1812
1813
1814 // Rotate back to the Global System
1815 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
1816 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
1817 r[2] = -sintet*vect[0] + costet*vect[2];
1818
1819 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
1820 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
1821 p[2] = -sintet*vect[3] + costet*vect[5];
1822
1823
1824 // Rotate back to the Tracking System
1825 Double_t cosalp = TMath::Cos(fAlpha);
1826 Double_t sinalp =-TMath::Sin(fAlpha);
1827
1828 Double_t
1829 t = cosalp*r[0] - sinalp*r[1];
1830 r[1] = sinalp*r[0] + cosalp*r[1];
1831 r[0] = t;
1832
1833 t = cosalp*p[0] - sinalp*p[1];
1834 p[1] = sinalp*p[0] + cosalp*p[1];
1835 p[0] = t;
1836
1837
1838 // Do the final correcting step to the target plane (linear approximation)
1839 Double_t x=r[0], y=r[1], z=r[2];
1840 if (TMath::Abs(dx) > kAlmost0) {
1841 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
1842 dx = xk - r[0];
1843 x += dx;
1844 y += p[1]/p[0]*dx;
1845 z += p[2]/p[0]*dx;
1846 }
1847
1848
1849 // Calculate the track parameters
1850 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
1851 fX = x;
1852 fP[0] = y;
1853 fP[1] = z;
1854 fP[2] = p[1]/t;
1855 fP[3] = p[2]/t;
1856 fP[4] = GetSign()/(t*pp);
1857
1858 return kTRUE;
1859}
1860
cfdb62d4 1861Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
1862 //
1863 //Translation: in the event mixing, the tracks can be shifted
1864 //of the difference among primary vertices (vTrasl) and
1865 //the covariance matrix is changed accordingly
1866 //(covV = covariance of the primary vertex).
1867 //Origin: "Romita, Rossella" <R.Romita@gsi.de>
1868 //
1869 TVector3 translation;
1870 // vTrasl coordinates in the local system
1871 translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
1872 translation.RotateZ(-fAlpha);
1873 translation.GetXYZ(vTrasl);
1874
1875 //compute the new x,y,z of the track
5a87bb3d 1876 Double_t newX=fX-vTrasl[0];
1877 Double_t newY=fP[0]-vTrasl[1];
1878 Double_t newZ=fP[1]-vTrasl[2];
cfdb62d4 1879
1880 //define the new parameters
5a87bb3d 1881 Double_t newParam[5];
1882 newParam[0]=newY;
1883 newParam[1]=newZ;
1884 newParam[2]=fP[2];
1885 newParam[3]=fP[3];
1886 newParam[4]=fP[4];
cfdb62d4 1887
1888 // recompute the covariance matrix:
1889 // 1. covV in the local system
1890 Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
1891 TMatrixD qQi(3,3);
1892 qQi(0,0) = cosRot;
1893 qQi(0,1) = sinRot;
1894 qQi(0,2) = 0.;
1895 qQi(1,0) = -sinRot;
1896 qQi(1,1) = cosRot;
1897 qQi(1,2) = 0.;
1898 qQi(2,0) = 0.;
1899 qQi(2,1) = 0.;
1900 qQi(2,2) = 1.;
1901 TMatrixD uUi(3,3);
1902 uUi(0,0) = covV[0];
1903 uUi(0,0) = covV[0];
1904 uUi(1,0) = covV[1];
1905 uUi(0,1) = covV[1];
1906 uUi(2,0) = covV[3];
1907 uUi(0,2) = covV[3];
1908 uUi(1,1) = covV[2];
1909 uUi(2,2) = covV[5];
1910 uUi(1,2) = covV[4];
1911 if(uUi.Determinant() <= 0.) {return kFALSE;}
1912 TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
1913 TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
1914
1915 //2. compute the new covariance matrix of the track
1916 Double_t sigmaXX=m(0,0);
1917 Double_t sigmaXZ=m(2,0);
1918 Double_t sigmaXY=m(1,0);
1919 Double_t sigmaYY=GetSigmaY2()+m(1,1);
1920 Double_t sigmaYZ=fC[1]+m(1,2);
1921 Double_t sigmaZZ=fC[2]+m(2,2);
1922 Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
1923 Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
1924 Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
1925
1926 Double_t newCov[15];
1927 newCov[0]=covarianceYY;
1928 newCov[1]=covarianceYZ;
1929 newCov[2]=covarianceZZ;
1930 for(Int_t i=3;i<15;i++){
1931 newCov[i]=fC[i];
1932 }
1933
1934 // set the new parameters
1935
5a87bb3d 1936 Set(newX,fAlpha,newParam,newCov);
cfdb62d4 1937
1938 return kTRUE;
1939 }