- Three classes by MinJung Kweon AliHFEpriVtx, AliHFEsecVtx and AliHFEmcQA for primar...
[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>
31
51ad6848 32#include "AliExternalTrackParam.h"
58e536c5 33#include "AliVVertex.h"
6c94f330 34#include "AliLog.h"
51ad6848 35
36ClassImp(AliExternalTrackParam)
37
ed5f2849 38Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
39
51ad6848 40//_____________________________________________________________________________
90e48c0c 41AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 42 AliVTrack(),
90e48c0c 43 fX(0),
c9ec41e8 44 fAlpha(0)
51ad6848 45{
90e48c0c 46 //
47 // default constructor
48 //
c9ec41e8 49 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
50 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 51}
52
53//_____________________________________________________________________________
6c94f330 54AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 55 AliVTrack(track),
6c94f330 56 fX(track.fX),
57 fAlpha(track.fAlpha)
58{
59 //
60 // copy constructor
61 //
62 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
63 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
64}
65
66//_____________________________________________________________________________
def9660e 67AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
68{
69 //
70 // assignment operator
71 //
72
73 if (this!=&trkPar) {
4f6e22bd 74 AliVTrack::operator=(trkPar);
def9660e 75 fX = trkPar.fX;
76 fAlpha = trkPar.fAlpha;
77
78 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
79 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
80 }
81
82 return *this;
83}
84
85//_____________________________________________________________________________
51ad6848 86AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
87 const Double_t param[5],
90e48c0c 88 const Double_t covar[15]) :
4f6e22bd 89 AliVTrack(),
90e48c0c 90 fX(x),
c9ec41e8 91 fAlpha(alpha)
51ad6848 92{
90e48c0c 93 //
94 // create external track parameters from given arguments
95 //
c9ec41e8 96 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
97 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 98}
99
90e48c0c 100//_____________________________________________________________________________
4f6e22bd 101AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
102 AliVTrack(),
103 fX(0.),
104 fAlpha(0.)
105{
106 //
610e3088 107 // Constructor from virtual track,
108 // This is not a copy contructor !
4f6e22bd 109 //
610e3088 110
111 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
112 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
113 AliWarning("Calling the default constructor...");
114 AliExternalTrackParam();
115 return;
116 }
117
892be05f 118 Double_t xyz[3],pxpypz[3],cv[21];
119 vTrack->GetXYZ(xyz);
120 pxpypz[0]=vTrack->Px();
121 pxpypz[1]=vTrack->Py();
122 pxpypz[2]=vTrack->Pz();
4f6e22bd 123 vTrack->GetCovarianceXYZPxPyPz(cv);
124 Short_t sign = (Short_t)vTrack->Charge();
125
126 Set(xyz,pxpypz,cv,sign);
127}
128
129//_____________________________________________________________________________
da4e3deb 130AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
131 Double_t cv[21],Short_t sign) :
4f6e22bd 132 AliVTrack(),
da4e3deb 133 fX(0.),
134 fAlpha(0.)
135{
136 //
4f6e22bd 137 // constructor from the global parameters
138 //
139
140 Set(xyz,pxpypz,cv,sign);
141}
142
143//_____________________________________________________________________________
144void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
145 Double_t cv[21],Short_t sign)
146{
147 //
da4e3deb 148 // create external track parameters from the global parameters
149 // x,y,z,px,py,pz and their 6x6 covariance matrix
150 // A.Dainese 10.10.08
151
aff56ff7 152 // Calculate alpha: the rotation angle of the corresponding local system.
153 //
154 // For global radial position inside the beam pipe, alpha is the
155 // azimuthal angle of the momentum projected on (x,y).
156 //
c99948ce 157 // For global radial position outside the ITS, alpha is the
aff56ff7 158 // azimuthal angle of the centre of the TPC sector in which the point
159 // xyz lies
160 //
161 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 162 Double_t radMax = 45.; // approximately ITS outer radius
163 if (radPos2 < radMax*radMax) { // inside the ITS
164
aff56ff7 165 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
c99948ce 166 } else { // outside the ITS
aff56ff7 167 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
168 fAlpha =
169 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
170 }
da4e3deb 171
172 // Get the vertex of origin and the momentum
173 TVector3 ver(xyz[0],xyz[1],xyz[2]);
174 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
175
176 // Rotate to the local coordinate system
177 ver.RotateZ(-fAlpha);
178 mom.RotateZ(-fAlpha);
179
180 // x of the reference plane
181 fX = ver.X();
182
183 Double_t charge = (Double_t)sign;
184
185 fP[0] = ver.Y();
186 fP[1] = ver.Z();
187 fP[2] = TMath::Sin(mom.Phi());
188 fP[3] = mom.Pz()/mom.Pt();
189 fP[4] = TMath::Sign(1/mom.Pt(),charge);
190
191 // Covariance matrix (formulas to be simplified)
192
193 Double_t pt=1./TMath::Abs(fP[4]);
194 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
195 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
196
197 Double_t m00=-sn;// m10=cs;
198 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
199 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
200 Double_t m35=pt, m45=-pt*pt*fP[3];
201
202 m43*=GetSign();
203 m44*=GetSign();
204 m45*=GetSign();
205
206 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
207 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
208 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
209 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
210 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
211 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
212 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
213
214 fC[0 ] = cv[0 ]+cv[2 ];
215 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
216 fC[2 ] = cv[5 ];
217 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
218 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
219 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
220 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
221 fC[11] = (cv[8]-fC[4]*m23)/m43;
222 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
223 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
224 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
225 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
226 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
227 Double_t b2=m23*m35;
228 Double_t b3=m43*m35;
229 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
230 Double_t b5=m24*m35;
231 Double_t b6=m44*m35;
232 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
233 fC[13] = b1/b3-b2*fC[8]/b3;
234 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 235
236 return;
da4e3deb 237}
238
239//_____________________________________________________________________________
c9ec41e8 240void AliExternalTrackParam::Reset() {
1530f89c 241 //
242 // Resets all the parameters to 0
243 //
c9ec41e8 244 fX=fAlpha=0.;
245 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
246 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 247}
248
3775b0ca 249//_____________________________________________________________________________
250void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
251 //
252 // Add "something" to the track covarince matrix.
253 // May be needed to account for unknown mis-calibration/mis-alignment
254 //
255 fC[0] +=c[0];
256 fC[1] +=c[1]; fC[2] +=c[2];
257 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
258 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
259 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
260}
261
262
c9ec41e8 263Double_t AliExternalTrackParam::GetP() const {
264 //---------------------------------------------------------------------
265 // This function returns the track momentum
266 // Results for (nearly) straight tracks are meaningless !
267 //---------------------------------------------------------------------
06fb4a2f 268 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 269 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 270}
271
1d99986f 272Double_t AliExternalTrackParam::Get1P() const {
273 //---------------------------------------------------------------------
274 // This function returns the 1/(track momentum)
275 //---------------------------------------------------------------------
276 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
277}
278
c9ec41e8 279//_______________________________________________________________________
c7bafca9 280Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 281 //------------------------------------------------------------------
282 // This function calculates the transverse impact parameter
283 // with respect to a point with global coordinates (x,y)
284 // in the magnetic field "b" (kG)
285 //------------------------------------------------------------------
5773defd 286 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 287 Double_t rp4=GetC(b);
c9ec41e8 288
289 Double_t xt=fX, yt=fP[0];
290
291 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
292 Double_t a = x*cs + y*sn;
293 y = -x*sn + y*cs; x=a;
294 xt-=x; yt-=y;
295
296 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
297 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 298 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
299}
300
301//_______________________________________________________________________
302void AliExternalTrackParam::
303GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
304 //------------------------------------------------------------------
305 // This function calculates the transverse and longitudinal impact parameters
306 // with respect to a point with global coordinates (x,y)
307 // in the magnetic field "b" (kG)
308 //------------------------------------------------------------------
309 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
310 Double_t xt=fX, yt=fP[0];
311 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
312 Double_t a = x*cs + y*sn;
313 y = -x*sn + y*cs; x=a;
314 xt-=x; yt-=y;
315
316 Double_t rp4=GetC(b);
317 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
318 dz[0] = -(xt*f1 - yt*r1);
319 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
320 return;
321 }
322
323 sn=rp4*xt - f1; cs=rp4*yt + r1;
324 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
325 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
326 dz[0] = -a/(1 + rr);
327 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
328 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 329}
330
49d13e89 331//_______________________________________________________________________
332Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
333 //------------------------------------------------------------------
334 // This function calculates the transverse impact parameter
335 // with respect to a point with global coordinates (xv,yv)
336 // neglecting the track curvature.
337 //------------------------------------------------------------------
338 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
339 Double_t x= xv*cs + yv*sn;
340 Double_t y=-xv*sn + yv*cs;
341
342 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
343
1530f89c 344 return -d;
49d13e89 345}
346
116b445b 347Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 348(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
349 Double_t (*Bethe)(Double_t)) {
116b445b 350 //------------------------------------------------------------------
351 // This function corrects the track parameters for the crossed material.
352 // "xOverX0" - X/X0, the thickness in units of the radiation length.
353 // "xTimesRho" - is the product length*density (g/cm^2).
354 // "mass" - the mass of this particle (GeV/c^2).
355 //------------------------------------------------------------------
356 Double_t &fP2=fP[2];
357 Double_t &fP3=fP[3];
358 Double_t &fP4=fP[4];
359
360 Double_t &fC22=fC[5];
361 Double_t &fC33=fC[9];
362 Double_t &fC43=fC[13];
363 Double_t &fC44=fC[14];
364
7dded1d5 365 //Apply angle correction, if requested
366 if(anglecorr) {
367 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
368 xOverX0 *=angle;
369 xTimesRho *=angle;
370 }
371
116b445b 372 Double_t p=GetP();
373 Double_t p2=p*p;
374 Double_t beta2=p2/(p2 + mass*mass);
116b445b 375
9f2bec63 376 //Calculating the multiple scattering corrections******************
377 Double_t cC22 = 0.;
378 Double_t cC33 = 0.;
379 Double_t cC43 = 0.;
380 Double_t cC44 = 0.;
116b445b 381 if (xOverX0 != 0) {
382 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
383 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 384 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
385 cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
386 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
387 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
388 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 389 }
390
9f2bec63 391 //Calculating the energy loss corrections************************
392 Double_t cP4=1.;
116b445b 393 if ((xTimesRho != 0.) && (beta2 < 1.)) {
d46683db 394 Double_t dE=Bethe(p/mass)*xTimesRho;
116b445b 395 Double_t e=TMath::Sqrt(p2 + mass*mass);
396 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
9f2bec63 397 cP4 = (1.- e/p2*dE);
398 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 399
116b445b 400
401 // Approximate energy loss fluctuation (M.Ivanov)
402 const Double_t knst=0.07; // To be tuned.
403 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 404 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 405
406 }
407
9f2bec63 408 //Applying the corrections*****************************
409 fC22 += cC22;
410 fC33 += cC33;
411 fC43 += cC43;
412 fC44 += cC44;
413 fP4 *= cP4;
414
116b445b 415 return kTRUE;
416}
417
418
ee5dba5e 419Bool_t AliExternalTrackParam::CorrectForMaterial
420(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 421 //------------------------------------------------------------------
116b445b 422 // Deprecated function !
423 // Better use CorrectForMeanMaterial instead of it.
424 //
c7bafca9 425 // This function corrects the track parameters for the crossed material
426 // "d" - the thickness (fraction of the radiation length)
427 // "x0" - the radiation length (g/cm^2)
428 // "mass" - the mass of this particle (GeV/c^2)
429 //------------------------------------------------------------------
430 Double_t &fP2=fP[2];
431 Double_t &fP3=fP[3];
432 Double_t &fP4=fP[4];
433
434 Double_t &fC22=fC[5];
435 Double_t &fC33=fC[9];
436 Double_t &fC43=fC[13];
437 Double_t &fC44=fC[14];
438
7b5ef2e6 439 Double_t p=GetP();
440 Double_t p2=p*p;
c7bafca9 441 Double_t beta2=p2/(p2 + mass*mass);
442 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
443
444 //Multiple scattering******************
9f2bec63 445 Double_t cC22 = 0.;
446 Double_t cC33 = 0.;
447 Double_t cC43 = 0.;
448 Double_t cC44 = 0.;
c7bafca9 449 if (d!=0) {
450 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
451 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
9f2bec63 452 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
453 cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
454 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
455 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
456 cC44 = theta2*fP3*fP4*fP3*fP4;
c7bafca9 457 }
458
459 //Energy losses************************
9f2bec63 460 Double_t cP4=1.;
8fc1985d 461 if (x0!=0. && beta2<1) {
c7bafca9 462 d*=x0;
d46683db 463 Double_t dE=Bethe(p/mass)*d;
ee5dba5e 464 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 465 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
9f2bec63 466 cP4 = (1.- e/p2*dE);
ee5dba5e 467
468 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 469 const Double_t knst=0.07; // To be tuned.
470 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 471 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
ee5dba5e 472
c7bafca9 473 }
474
9f2bec63 475 fC22 += cC22;
476 fC33 += cC33;
477 fC43 += cC43;
478 fC44 += cC44;
479 fP4 *= cP4;
480
c7bafca9 481 return kTRUE;
482}
483
9c56b409 484Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
485 Double_t kp1,
486 Double_t kp2,
487 Double_t kp3,
488 Double_t kp4,
489 Double_t kp5) {
490 //
491 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
492 // It is normalized to 1 at the minimum.
493 //
494 // bg - beta*gamma
495 //
496 // The default values for the kp* parameters are for ALICE TPC.
497 // The returned value is in MIP units
498 //
499
500 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
501
502 Double_t aa = TMath::Power(beta,kp4);
503 Double_t bb = TMath::Power(1./bg,kp5);
504
505 bb=TMath::Log(kp3+bb);
506
507 return (kp2-aa-bb)*kp1/aa;
508}
509
510Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
511 Double_t kp0,
512 Double_t kp1,
513 Double_t kp2,
514 Double_t kp3,
515 Double_t kp4) {
516 //
517 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
518 //
519 // bg - beta*gamma
520 // kp0 - density [g/cm^3]
521 // kp1 - density effect first junction point
522 // kp2 - density effect second junction point
523 // kp3 - mean excitation energy [GeV]
524 // kp4 - mean Z/A
525 //
526 // The default values for the kp* parameters are for silicon.
527 // The returned value is in [GeV/(g/cm^2)].
528 //
529
530 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
531 const Double_t me = 0.511e-3; // [GeV/c^2]
532 const Double_t rho = kp0;
533 const Double_t x0 = kp1*2.303;
534 const Double_t x1 = kp2*2.303;
535 const Double_t mI = kp3;
536 const Double_t mZA = kp4;
537 const Double_t bg2 = bg*bg;
538 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
539
540 //*** Density effect
541 Double_t d2=0.;
542 const Double_t x=TMath::Log(bg);
543 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
544 if (x > x1) {
545 d2 = lhwI + x - 0.5;
546 } else if (x > x0) {
547 const Double_t r=(x1-x)/(x1-x0);
548 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
549 }
550
551 return mK*mZA*(1+bg2)/bg2*
552 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
553}
554
d46683db 555Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 556 //------------------------------------------------------------------
d46683db 557 // This is an approximation of the Bethe-Bloch formula,
558 // reasonable for solid materials.
559 // All the parameters are, in fact, for Si.
9b655cba 560 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 561 //------------------------------------------------------------------
a821848c 562
9c56b409 563 return BetheBlochGeant(bg);
d46683db 564}
ee5dba5e 565
d46683db 566Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
567 //------------------------------------------------------------------
568 // This is an approximation of the Bethe-Bloch formula,
569 // reasonable for gas materials.
570 // All the parameters are, in fact, for Ne.
9b655cba 571 // The returned value is in [GeV/(g/cm^2)]
d46683db 572 //------------------------------------------------------------------
573
574 const Double_t rho = 0.9e-3;
575 const Double_t x0 = 2.;
576 const Double_t x1 = 4.;
577 const Double_t mI = 140.e-9;
578 const Double_t mZA = 0.49555;
579
9c56b409 580 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 581}
582
49d13e89 583Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
584 //------------------------------------------------------------------
585 // Transform this track to the local coord. system rotated
586 // by angle "alpha" (rad) with respect to the global coord. system.
587 //------------------------------------------------------------------
dfcef74c 588 if (TMath::Abs(fP[2]) >= kAlmost1) {
589 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
590 return kFALSE;
591 }
592
49d13e89 593 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
594 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
595
596 Double_t &fP0=fP[0];
597 Double_t &fP2=fP[2];
598 Double_t &fC00=fC[0];
599 Double_t &fC10=fC[1];
600 Double_t &fC20=fC[3];
601 Double_t &fC21=fC[4];
602 Double_t &fC22=fC[5];
603 Double_t &fC30=fC[6];
604 Double_t &fC32=fC[8];
605 Double_t &fC40=fC[10];
606 Double_t &fC42=fC[12];
607
608 Double_t x=fX;
609 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
610 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
611
dfcef74c 612 Double_t tmp=sf*ca - cf*sa;
0b69bbb2 613 if (TMath::Abs(tmp) >= kAlmost1) {
614 AliError(Form("Rotation failed ! %.10e",tmp));
615 return kFALSE;
616 }
dfcef74c 617
49d13e89 618 fAlpha = alpha;
619 fX = x*ca + fP0*sa;
620 fP0= -x*sa + fP0*ca;
dfcef74c 621 fP2= tmp;
49d13e89 622
06fb4a2f 623 if (TMath::Abs(cf)<kAlmost0) {
624 AliError(Form("Too small cosine value %f",cf));
625 cf = kAlmost0;
626 }
627
49d13e89 628 Double_t rr=(ca+sf/cf*sa);
629
630 fC00 *= (ca*ca);
631 fC10 *= ca;
632 fC20 *= ca*rr;
633 fC21 *= rr;
634 fC22 *= rr*rr;
635 fC30 *= ca;
636 fC32 *= rr;
637 fC40 *= ca;
638 fC42 *= rr;
639
640 return kTRUE;
641}
642
643Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
644 //----------------------------------------------------------------
645 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
646 //----------------------------------------------------------------
49d13e89 647 Double_t dx=xk-fX;
e421f556 648 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 649
1530f89c 650 Double_t crv=GetC(b);
5773defd 651 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
652
49d13e89 653 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 654 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 655 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
656
657 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
658 Double_t
659 &fC00=fC[0],
660 &fC10=fC[1], &fC11=fC[2],
661 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
662 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
663 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
664
665 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
666
667 fX=xk;
668 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 669 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 670 fP2 += dx*crv;
671
672 //f = F - 1
673
674 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
675 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
676 Double_t f12= dx*fP3*f1/(r1*r1*r1);
677 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
678 Double_t f13= dx/r1;
679 Double_t f24= dx; f24*=cc;
680
681 //b = C*ft
682 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
683 Double_t b02=f24*fC40;
684 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
685 Double_t b12=f24*fC41;
686 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
687 Double_t b22=f24*fC42;
688 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
689 Double_t b42=f24*fC44;
690 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
691 Double_t b32=f24*fC43;
692
693 //a = f*b = f*C*ft
694 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
695 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
696 Double_t a22=f24*b42;
697
698 //F*C*Ft = C + (b + bt + a)
699 fC00 += b00 + b00 + a00;
700 fC10 += b10 + b01 + a01;
701 fC20 += b20 + b02 + a02;
702 fC30 += b30;
703 fC40 += b40;
704 fC11 += b11 + b11 + a11;
705 fC21 += b21 + b12 + a12;
706 fC31 += b31;
707 fC41 += b41;
708 fC22 += b22 + b22 + a22;
709 fC32 += b32;
710 fC42 += b42;
711
712 return kTRUE;
713}
714
9f2bec63 715Bool_t
716AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
717 //------------------------------------------------------------------
718 // Transform this track to the local coord. system rotated
719 // by angle "alpha" (rad) with respect to the global coord. system,
720 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
721 //------------------------------------------------------------------
722
723 //Save the parameters
724 Double_t as=fAlpha;
725 Double_t xs=fX;
726 Double_t ps[5], cs[15];
727 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
728 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
729
730 if (Rotate(alpha))
731 if (PropagateTo(x,b)) return kTRUE;
732
733 //Restore the parameters, if the operation failed
734 fAlpha=as;
735 fX=xs;
736 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
737 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
738 return kFALSE;
739}
740
741
052daaff 742void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
743Double_t p[3], Double_t bz) const {
744 //+++++++++++++++++++++++++++++++++++++++++
745 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
746 // Extrapolate track along simple helix in magnetic field
747 // Arguments: len -distance alogn helix, [cm]
748 // bz - mag field, [kGaus]
749 // Returns: x and p contain extrapolated positon and momentum
750 // The momentum returned for straight-line tracks is meaningless !
751 //+++++++++++++++++++++++++++++++++++++++++
752 GetXYZ(x);
753
2258e165 754 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 755 Double_t unit[3]; GetDirection(unit);
756 x[0]+=unit[0]*len;
757 x[1]+=unit[1]*len;
758 x[2]+=unit[2]*len;
759
760 p[0]=unit[0]/kAlmost0;
761 p[1]=unit[1]/kAlmost0;
762 p[2]=unit[2]/kAlmost0;
763 } else {
764 GetPxPyPz(p);
765 Double_t pp=GetP();
766 Double_t a = -kB2C*bz*GetSign();
767 Double_t rho = a/pp;
768 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
769 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
770 x[2] += p[2]*len/pp;
771
772 Double_t p0=p[0];
773 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
774 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
775 }
776}
777
778Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
779Double_t bz) const {
780 //+++++++++++++++++++++++++++++++++++++++++
781 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
782 // Finds point of intersection (if exists) of the helix with the plane.
783 // Stores result in fX and fP.
784 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
785 // and vector, normal to the plane
786 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
787 //+++++++++++++++++++++++++++++++++++++++++
788 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
789
790 //estimates initial helix length up to plane
791 Double_t s=
792 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
793 Double_t dist=99999,distPrev=dist;
794 Double_t x[3],p[3];
795 while(TMath::Abs(dist)>0.00001){
796 //calculates helix at the distance s from x0 ALONG the helix
797 Propagate(s,x,p,bz);
798
799 //distance between current helix position and plane
800 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
801
802 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
803 distPrev=dist;
804 s-=dist;
805 }
806 //on exit pnt is intersection point,norm is track vector at that point,
807 //all in MARS
808 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
809 return kTRUE;
810}
811
49d13e89 812Double_t
813AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
814 //----------------------------------------------------------------
815 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
816 //----------------------------------------------------------------
817 Double_t sdd = fC[0] + cov[0];
818 Double_t sdz = fC[1] + cov[1];
819 Double_t szz = fC[2] + cov[2];
820 Double_t det = sdd*szz - sdz*sdz;
821
822 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
823
824 Double_t d = fP[0] - p[0];
825 Double_t z = fP[1] - p[1];
826
827 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
828}
829
4b189f98 830Double_t AliExternalTrackParam::
831GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
832 //----------------------------------------------------------------
833 // Estimate the chi2 of the 3D space point "p" and
1e023a36 834 // the full covariance matrix "covyz" and "covxyz"
4b189f98 835 //
836 // Cov(x,x) ... : covxyz[0]
837 // Cov(y,x) ... : covxyz[1] covyz[0]
838 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
839 //----------------------------------------------------------------
840
841 Double_t res[3] = {
842 GetX() - p[0],
843 GetY() - p[1],
844 GetZ() - p[2]
845 };
846
847 Double_t f=GetSnp();
848 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
849 Double_t r=TMath::Sqrt(1.- f*f);
850 Double_t a=f/r, b=GetTgl()/r;
851
852 Double_t s2=333.*333.; //something reasonably big (cm^2)
853
854 TMatrixDSym v(3);
855 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
856 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
857 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
858
859 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
860 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
861 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
862
863 v.Invert();
864 if (!v.IsValid()) return kVeryBig;
865
866 Double_t chi2=0.;
867 for (Int_t i = 0; i < 3; i++)
868 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
869
870 return chi2;
871
872
873}
874
1e023a36 875Bool_t AliExternalTrackParam::
876PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
877 //----------------------------------------------------------------
878 // Propagate this track to the plane
879 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
880 // belongs to.
881 // The magnetic field is "bz" (kG)
882 //
883 // The track curvature and the change of the covariance matrix
884 // of the track parameters are negleted !
885 // (So the "step" should be small compared with 1/curvature)
886 //----------------------------------------------------------------
887
888 Double_t f=GetSnp();
889 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
890 Double_t r=TMath::Sqrt(1.- f*f);
891 Double_t a=f/r, b=GetTgl()/r;
892
893 Double_t s2=333.*333.; //something reasonably big (cm^2)
894
895 TMatrixDSym tV(3);
896 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
897 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
898 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
899
900 TMatrixDSym pV(3);
901 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
902 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
903 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
904
905 TMatrixDSym tpV(tV);
906 tpV+=pV;
907 tpV.Invert();
908 if (!tpV.IsValid()) return kFALSE;
909
910 TMatrixDSym pW(3),tW(3);
911 for (Int_t i=0; i<3; i++)
912 for (Int_t j=0; j<3; j++) {
913 pW(i,j)=tW(i,j)=0.;
914 for (Int_t k=0; k<3; k++) {
915 pW(i,j) += tV(i,k)*tpV(k,j);
916 tW(i,j) += pV(i,k)*tpV(k,j);
917 }
918 }
919
920 Double_t t[3] = {GetX(), GetY(), GetZ()};
921
922 Double_t x=0.;
923 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
924 Double_t crv=GetC(bz);
925 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
926 f += crv*(x-fX);
927 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
928 fX=x;
929
930 fP[0]=0.;
931 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
932 fP[1]=0.;
933 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
934
935 return kTRUE;
936}
937
e23a38cb 938Double_t *AliExternalTrackParam::GetResiduals(
939Double_t *p,Double_t *cov,Bool_t updated) const {
940 //------------------------------------------------------------------
941 // Returns the track residuals with the space point "p" having
942 // the covariance matrix "cov".
943 // If "updated" is kTRUE, the track parameters expected to be updated,
944 // otherwise they must be predicted.
945 //------------------------------------------------------------------
946 static Double_t res[2];
947
948 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
949 if (updated) {
950 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
951 } else {
952 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
953 }
954 Double_t det=r00*r11 - r01*r01;
955
956 if (TMath::Abs(det) < kAlmost0) return 0;
957
958 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 959
960 if (r00 < 0.) return 0;
961 if (r11 < 0.) return 0;
962
e23a38cb 963 Double_t dy = fP[0] - p[0];
964 Double_t dz = fP[1] - p[1];
965
966 res[0]=dy*TMath::Sqrt(r00);
967 res[1]=dz*TMath::Sqrt(r11);
968
969 return res;
970}
971
49d13e89 972Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
973 //------------------------------------------------------------------
974 // Update the track parameters with the space point "p" having
975 // the covariance matrix "cov"
976 //------------------------------------------------------------------
977 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
978 Double_t
979 &fC00=fC[0],
980 &fC10=fC[1], &fC11=fC[2],
981 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
982 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
983 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
984
985 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
986 r00+=fC00; r01+=fC10; r11+=fC11;
987 Double_t det=r00*r11 - r01*r01;
988
989 if (TMath::Abs(det) < kAlmost0) return kFALSE;
990
991
992 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
993
994 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
995 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
996 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
997 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
998 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
999
1000 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1001 Double_t sf=fP2 + k20*dy + k21*dz;
1002 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1003
1004 fP0 += k00*dy + k01*dz;
1005 fP1 += k10*dy + k11*dz;
1006 fP2 = sf;
1007 fP3 += k30*dy + k31*dz;
1008 fP4 += k40*dy + k41*dz;
1009
1010 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1011 Double_t c12=fC21, c13=fC31, c14=fC41;
1012
1013 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1014 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1015 fC40-=k00*c04+k01*c14;
1016
1017 fC11-=k10*c01+k11*fC11;
1018 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1019 fC41-=k10*c04+k11*c14;
1020
1021 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1022 fC42-=k20*c04+k21*c14;
1023
1024 fC33-=k30*c03+k31*c13;
1025 fC43-=k30*c04+k31*c14;
1026
1027 fC44-=k40*c04+k41*c14;
1028
1029 return kTRUE;
1030}
1031
c7bafca9 1032void
1033AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1034 //--------------------------------------------------------------------
1035 // External track parameters -> helix parameters
1036 // "b" - magnetic field (kG)
1037 //--------------------------------------------------------------------
1038 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1039
1530f89c 1040 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1041
1042 hlx[5]=fX*cs - hlx[0]*sn; // x0
1043 hlx[0]=fX*sn + hlx[0]*cs; // y0
1044//hlx[1]= // z0
1045 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1046//hlx[3]= // tgl
1530f89c 1047 hlx[4]=GetC(b); // C
c7bafca9 1048}
1049
1050
1051static void Evaluate(const Double_t *h, Double_t t,
1052 Double_t r[3], //radius vector
1053 Double_t g[3], //first defivatives
1054 Double_t gg[3]) //second derivatives
1055{
1056 //--------------------------------------------------------------------
1057 // Calculate position of a point on a track and some derivatives
1058 //--------------------------------------------------------------------
1059 Double_t phase=h[4]*t+h[2];
1060 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1061
ba4550c4 1062 r[0] = h[5];
1063 r[1] = h[0];
1064 if (TMath::Abs(h[4])>kAlmost0) {
1065 r[0] += (sn - h[6])/h[4];
1066 r[1] -= (cs - h[7])/h[4];
1067 }
c7bafca9 1068 r[2] = h[1] + h[3]*t;
1069
1070 g[0] = cs; g[1]=sn; g[2]=h[3];
1071
1072 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1073}
1074
1075Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1076Double_t b, Double_t &xthis, Double_t &xp) const {
1077 //------------------------------------------------------------
1078 // Returns the (weighed !) distance of closest approach between
1079 // this track and the track "p".
1080 // Other returned values:
1081 // xthis, xt - coordinates of tracks' reference planes at the DCA
1082 //-----------------------------------------------------------
1083 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1084 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1085 Double_t dx2=dy2;
1086
c7bafca9 1087 Double_t p1[8]; GetHelixParameters(p1,b);
1088 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1089 Double_t p2[8]; p->GetHelixParameters(p2,b);
1090 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1091
1092
1093 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1094 Evaluate(p1,t1,r1,g1,gg1);
1095 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1096 Evaluate(p2,t2,r2,g2,gg2);
1097
1098 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1099 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1100
1101 Int_t max=27;
1102 while (max--) {
1103 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1104 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1105 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1106 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1107 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1108 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1109 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1110 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1111 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1112
1113 Double_t det=h11*h22-h12*h12;
1114
1115 Double_t dt1,dt2;
1116 if (TMath::Abs(det)<1.e-33) {
1117 //(quasi)singular Hessian
1118 dt1=-gt1; dt2=-gt2;
1119 } else {
1120 dt1=-(gt1*h22 - gt2*h12)/det;
1121 dt2=-(h11*gt2 - h12*gt1)/det;
1122 }
1123
1124 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1125
1126 //check delta(phase1) ?
1127 //check delta(phase2) ?
1128
1129 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1130 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1131 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1132 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1133 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1134 if (lmb < 0.)
358f16ae 1135 AliDebug(1," stopped at not a minimum !");
c7bafca9 1136 break;
1137 }
1138
1139 Double_t dd=dm;
1140 for (Int_t div=1 ; ; div*=2) {
1141 Evaluate(p1,t1+dt1,r1,g1,gg1);
1142 Evaluate(p2,t2+dt2,r2,g2,gg2);
1143 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1144 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1145 if (dd<dm) break;
1146 dt1*=0.5; dt2*=0.5;
1147 if (div>512) {
358f16ae 1148 AliDebug(1," overshoot !"); break;
c7bafca9 1149 }
1150 }
1151 dm=dd;
1152
1153 t1+=dt1;
1154 t2+=dt2;
1155
1156 }
1157
358f16ae 1158 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1159
1160 Double_t cs=TMath::Cos(GetAlpha());
1161 Double_t sn=TMath::Sin(GetAlpha());
1162 xthis=r1[0]*cs + r1[1]*sn;
1163
1164 cs=TMath::Cos(p->GetAlpha());
1165 sn=TMath::Sin(p->GetAlpha());
1166 xp=r2[0]*cs + r2[1]*sn;
1167
1168 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1169}
1170
1171Double_t AliExternalTrackParam::
1172PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1173 //--------------------------------------------------------------
1174 // Propagates this track and the argument track to the position of the
1175 // distance of closest approach.
1176 // Returns the (weighed !) distance of closest approach.
1177 //--------------------------------------------------------------
1178 Double_t xthis,xp;
1179 Double_t dca=GetDCA(p,b,xthis,xp);
1180
1181 if (!PropagateTo(xthis,b)) {
1182 //AliWarning(" propagation failed !");
1183 return 1e+33;
1184 }
1185
1186 if (!p->PropagateTo(xp,b)) {
1187 //AliWarning(" propagation failed !";
1188 return 1e+33;
1189 }
1190
1191 return dca;
1192}
1193
1194
58e536c5 1195Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1196Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1197 //
e99a34df 1198 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1199 // if the (rough) transverse impact parameter is not bigger then "maxd".
1200 // Magnetic field is "b" (kG).
1201 //
1202 // a) The track gets extapolated to the DCA to the vertex.
1203 // b) The impact parameters and their covariance matrix are calculated.
1204 //
1205 // In the case of success, the returned value is kTRUE
1206 // (otherwise, it's kFALSE)
1207 //
1208 Double_t alpha=GetAlpha();
1209 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1210 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1211 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1212 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1213 x-=xv; y-=yv;
1214
1215 //Estimate the impact parameter neglecting the track curvature
1216 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
1217 if (d > maxd) return kFALSE;
1218
1219 //Propagate to the DCA
2258e165 1220 Double_t crv=GetC(b);
e99a34df 1221 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1222
f76701bf 1223 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
1224 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 1225 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1226 else cs=1.;
f76701bf 1227
1228 x = xv*cs + yv*sn;
1229 yv=-xv*sn + yv*cs; xv=x;
1230
1231 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1232
1233 if (dz==0) return kTRUE;
1234 dz[0] = GetParameter()[0] - yv;
1235 dz[1] = GetParameter()[1] - zv;
1236
1237 if (covar==0) return kTRUE;
58e536c5 1238 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1239
1240 //***** Improvements by A.Dainese
1241 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1242 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1243 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1244 covar[1] = GetCovariance()[1]; // between (x,y) and z
1245 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1246 //*****
1247
29fbcc93 1248 return kTRUE;
f76701bf 1249}
1250
1251
b1149664 1252void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1253 //----------------------------------------------------------------
1254 // This function returns a unit vector along the track direction
1255 // in the global coordinate system.
1256 //----------------------------------------------------------------
1257 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1258 Double_t snp=fP[2];
92934324 1259 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 1260 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1261 d[0]=(csp*cs - snp*sn)/norm;
1262 d[1]=(snp*cs + csp*sn)/norm;
1263 d[2]=fP[3]/norm;
1264}
1265
c683ddc2 1266Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1267 //---------------------------------------------------------------------
1268 // This function returns the global track momentum components
1269 // Results for (nearly) straight tracks are meaningless !
1270 //---------------------------------------------------------------------
1271 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1272 return Local2GlobalMomentum(p,fAlpha);
1273}
a5e407e9 1274
def9660e 1275Double_t AliExternalTrackParam::Px() const {
957fb479 1276 //---------------------------------------------------------------------
1277 // Returns x-component of momentum
1278 // Result for (nearly) straight tracks is meaningless !
1279 //---------------------------------------------------------------------
def9660e 1280
957fb479 1281 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1282 GetPxPyPz(p);
1283
1284 return p[0];
1285}
1286
1287Double_t AliExternalTrackParam::Py() const {
957fb479 1288 //---------------------------------------------------------------------
1289 // Returns y-component of momentum
1290 // Result for (nearly) straight tracks is meaningless !
1291 //---------------------------------------------------------------------
def9660e 1292
957fb479 1293 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1294 GetPxPyPz(p);
1295
1296 return p[1];
1297}
1298
1299Double_t AliExternalTrackParam::Pz() const {
957fb479 1300 //---------------------------------------------------------------------
1301 // Returns z-component of momentum
1302 // Result for (nearly) straight tracks is meaningless !
1303 //---------------------------------------------------------------------
def9660e 1304
957fb479 1305 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1306 GetPxPyPz(p);
1307
1308 return p[2];
1309}
1310
c683ddc2 1311Double_t AliExternalTrackParam::Xv() const {
1312 //---------------------------------------------------------------------
1313 // Returns x-component of first track point
1314 //---------------------------------------------------------------------
1315
1316 Double_t r[3]={0.,0.,0.};
1317 GetXYZ(r);
1318
1319 return r[0];
1320}
1321
1322Double_t AliExternalTrackParam::Yv() const {
1323 //---------------------------------------------------------------------
1324 // Returns y-component of first track point
1325 //---------------------------------------------------------------------
1326
1327 Double_t r[3]={0.,0.,0.};
1328 GetXYZ(r);
1329
1330 return r[1];
1331}
1332
1333Double_t AliExternalTrackParam::Zv() const {
1334 //---------------------------------------------------------------------
1335 // Returns z-component of first track point
1336 //---------------------------------------------------------------------
1337
1338 Double_t r[3]={0.,0.,0.};
1339 GetXYZ(r);
1340
1341 return r[2];
1342}
1343
def9660e 1344Double_t AliExternalTrackParam::Theta() const {
1345 // return theta angle of momentum
1346
7cdd0c20 1347 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1348}
1349
1350Double_t AliExternalTrackParam::Phi() const {
957fb479 1351 //---------------------------------------------------------------------
1352 // Returns the azimuthal angle of momentum
1353 // 0 <= phi < 2*pi
1354 //---------------------------------------------------------------------
def9660e 1355
957fb479 1356 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1357 if (phi<0.) phi+=2.*TMath::Pi();
1358 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1359
1360 return phi;
def9660e 1361}
1362
1363Double_t AliExternalTrackParam::M() const {
1364 // return particle mass
1365
1366 // No mass information available so far.
1367 // Redifine in derived class!
1368
1369 return -999.;
1370}
1371
1372Double_t AliExternalTrackParam::E() const {
1373 // return particle energy
1374
1375 // No PID information available so far.
1376 // Redifine in derived class!
1377
1378 return -999.;
1379}
1380
1381Double_t AliExternalTrackParam::Eta() const {
1382 // return pseudorapidity
1383
1384 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1385}
1386
1387Double_t AliExternalTrackParam::Y() const {
1388 // return rapidity
1389
1390 // No PID information available so far.
1391 // Redifine in derived class!
1392
1393 return -999.;
1394}
1395
c9ec41e8 1396Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1397 //---------------------------------------------------------------------
1398 // This function returns the global track position
1399 //---------------------------------------------------------------------
1400 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1401 return Local2GlobalPosition(r,fAlpha);
51ad6848 1402}
1403
c9ec41e8 1404Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1405 //---------------------------------------------------------------------
1406 // This function returns the global covariance matrix of the track params
1407 //
1408 // Cov(x,x) ... : cv[0]
1409 // Cov(y,x) ... : cv[1] cv[2]
1410 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1411 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1412 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1413 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1414 //
c9ec41e8 1415 // Results for (nearly) straight tracks are meaningless !
1416 //---------------------------------------------------------------------
e421f556 1417 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1418 for (Int_t i=0; i<21; i++) cv[i]=0.;
1419 return kFALSE;
a5e407e9 1420 }
49d13e89 1421 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1422 for (Int_t i=0; i<21; i++) cv[i]=0.;
1423 return kFALSE;
1424 }
1425 Double_t pt=1./TMath::Abs(fP[4]);
1426 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1427 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1428
1429 Double_t m00=-sn, m10=cs;
1430 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1431 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1432 Double_t m35=pt, m45=-pt*pt*fP[3];
1433
854d5d49 1434 m43*=GetSign();
1435 m44*=GetSign();
1436 m45*=GetSign();
1437
c9ec41e8 1438 cv[0 ] = fC[0]*m00*m00;
1439 cv[1 ] = fC[0]*m00*m10;
1440 cv[2 ] = fC[0]*m10*m10;
1441 cv[3 ] = fC[1]*m00;
1442 cv[4 ] = fC[1]*m10;
1443 cv[5 ] = fC[2];
1444 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1445 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1446 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1447 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1448 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1449 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1450 cv[12] = fC[4]*m24 + fC[11]*m44;
1451 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1452 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1453 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1454 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1455 cv[17] = fC[7]*m35 + fC[11]*m45;
1456 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1457 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1458 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1459
c9ec41e8 1460 return kTRUE;
51ad6848 1461}
1462
51ad6848 1463
c9ec41e8 1464Bool_t
1465AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1466 //---------------------------------------------------------------------
1467 // This function returns the global track momentum extrapolated to
1468 // the radial position "x" (cm) in the magnetic field "b" (kG)
1469 //---------------------------------------------------------------------
c9ec41e8 1470 p[0]=fP[4];
1530f89c 1471 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1472 p[2]=fP[3];
1473 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1474}
1475
c9ec41e8 1476Bool_t
7cf7bb6c 1477AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1478 //---------------------------------------------------------------------
1479 // This function returns the local Y-coordinate of the intersection
1480 // point between this track and the reference plane "x" (cm).
1481 // Magnetic field "b" (kG)
1482 //---------------------------------------------------------------------
1483 Double_t dx=x-fX;
1484 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1485
1530f89c 1486 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1487
1488 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1489 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1490
60e55aee 1491 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 1492 y = fP[0] + dx*(f1+f2)/(r1+r2);
1493 return kTRUE;
1494}
1495
1496Bool_t
6c94f330 1497AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1498 //---------------------------------------------------------------------
1499 // This function returns the local Z-coordinate of the intersection
1500 // point between this track and the reference plane "x" (cm).
1501 // Magnetic field "b" (kG)
1502 //---------------------------------------------------------------------
1503 Double_t dx=x-fX;
1504 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1505
2258e165 1506 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1507
1508 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1509 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1510
60e55aee 1511 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
6c94f330 1512 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1513 return kTRUE;
1514}
1515
1516Bool_t
c9ec41e8 1517AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1518 //---------------------------------------------------------------------
1519 // This function returns the global track position extrapolated to
1520 // the radial position "x" (cm) in the magnetic field "b" (kG)
1521 //---------------------------------------------------------------------
c9ec41e8 1522 Double_t dx=x-fX;
e421f556 1523 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1524
1530f89c 1525 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1526
e421f556 1527 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1528 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1529
60e55aee 1530 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
c9ec41e8 1531 r[0] = x;
1532 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1533 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1534
c9ec41e8 1535 return Local2GlobalPosition(r,fAlpha);
51ad6848 1536}
1537
edc97986 1538//_____________________________________________________________________________
51ad6848 1539void AliExternalTrackParam::Print(Option_t* /*option*/) const
1540{
1541// print the parameters and the covariance matrix
1542
1543 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1544 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1545 fP[0], fP[1], fP[2], fP[3], fP[4]);
1546 printf(" covariance: %12g\n", fC[0]);
1547 printf(" %12g %12g\n", fC[1], fC[2]);
1548 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1549 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1550 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1551 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1552 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1553}
5b77d93c 1554
c194ba83 1555Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1556 //
1557 // Get sinus at given x
1558 //
1530f89c 1559 Double_t crv=GetC(b);
c194ba83 1560 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1561 Double_t dx = x-fX;
1562 Double_t res = fP[2]+dx*crv;
1563 return res;
1564}
bf00ebb8 1565
1566Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1567 //------------------------------------------------------------------------
1568 // Get the distance between two tracks at the local position x
1569 // working in the local frame of this track.
1570 // Origin : Marian.Ivanov@cern.ch
1571 //-----------------------------------------------------------------------
1572 Double_t xyz[3];
1573 Double_t xyz2[3];
1574 xyz[0]=x;
1575 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1576 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1577 //
1578 //
1579 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1580 xyz2[0]=x;
1581 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1582 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1583 }else{
1584 //
1585 Double_t xyz1[3];
1586 Double_t dfi = param2->GetAlpha()-GetAlpha();
1587 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1588 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1589 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1590 //
1591 xyz1[0]=xyz2[0];
1592 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1593 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1594 //
1595 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1596 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1597 xyz2[2] = xyz1[2];
1598 }
1599 dist[0] = xyz[0]-xyz2[0];
1600 dist[1] = xyz[1]-xyz2[1];
1601 dist[2] = xyz[2]-xyz2[2];
1602
1603 return kTRUE;
1604}
0c19adf7 1605
1606
1607//
1608// Draw functionality.
1609// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1610//
1611
1612void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1613 //
1614 // Draw track line
1615 //
1616 if (minR>maxR) return ;
1617 if (stepR<=0) return ;
1618 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1619 if (npoints<1) return;
1620 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1621 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1622 polymarker->Draw();
1623}
1624
1625//
1626void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1627 //
1628 // Fill points in the polymarker
1629 //
1630 Int_t counter=0;
1631 for (Double_t r=minR; r<maxR; r+=stepR){
1632 Double_t point[3];
1633 GetXYZAt(r,magF,point);
1634 pol->SetPoint(counter,point[0],point[1], point[2]);
1635 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1636 counter++;
1637 }
1638}
0e8460af 1639
1640Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1641 //
1642 Int_t min = TMath::Min(i,j);
1643 Int_t max = TMath::Max(i,j);
1644
1645 return min+(max+1)*max/2;
1646}
8b6e3369 1647
1648
1649void AliExternalTrackParam::g3helx3(Double_t qfield,
1650 Double_t step,
1651 Double_t vect[7]) {
1652/******************************************************************
1653 * *
1654 * GEANT3 tracking routine in a constant field oriented *
1655 * along axis 3 *
1656 * Tracking is performed with a conventional *
1657 * helix step method *
1658 * *
1659 * Authors R.Brun, M.Hansroul ********* *
1660 * Rewritten V.Perevoztchikov *
1661 * *
1662 * Rewritten in C++ by I.Belikov *
1663 * *
1664 * qfield (kG) - particle charge times magnetic field *
1665 * step (cm) - step length along the helix *
1666 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
1667 * *
1668 ******************************************************************/
1669 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
1670
1671 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
1672
1673 Double_t rho = qfield*kB2C/vect[ipp];
1674 Double_t tet = rho*step;
1675
1676 Double_t tsint, sintt, sint, cos1t;
1677 if (TMath::Abs(tet) > 0.15) {
1678 sint = TMath::Sin(tet);
1679 sintt = sint/tet;
1680 tsint = (tet - sint)/tet;
1681 Double_t t=TMath::Sin(0.5*tet);
1682 cos1t = 2*t*t/tet;
1683 } else {
1684 tsint = tet*tet/6.;
1685 sintt = 1.- tsint;
1686 sint = tet*sintt;
1687 cos1t = 0.5*tet;
1688 }
1689
1690 Double_t f1 = step*sintt;
1691 Double_t f2 = step*cos1t;
1692 Double_t f3 = step*tsint*cosz;
1693 Double_t f4 = -tet*cos1t;
1694 Double_t f5 = sint;
1695
1696 vect[ix] += f1*cosx - f2*cosy;
1697 vect[iy] += f1*cosy + f2*cosx;
1698 vect[iz] += f1*cosz + f3;
1699
1700 vect[ipx] += f4*cosx - f5*cosy;
1701 vect[ipy] += f4*cosy + f5*cosx;
1702
1703}
1704
1705Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
1706 //----------------------------------------------------------------
1707 // Extrapolate this track to the plane X=xk in the field b[].
1708 //
1709 // X [cm] is in the "tracking coordinate system" of this track.
1710 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
1711 //----------------------------------------------------------------
1712
1713 Double_t dx=xk-fX;
1714 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
1715
1716 Double_t crv=GetC(b[2]);
1717 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
1718
1719 Double_t f1=fP[2], f2=f1 + crv*dx;
1720 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1721 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1722
1723
1724 // Estimate the covariance matrix
1725 Double_t &fP3=fP[3], &fP4=fP[4];
1726 Double_t
1727 &fC00=fC[0],
1728 &fC10=fC[1], &fC11=fC[2],
1729 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1730 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1731 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1732
1733 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1734
1735 //f = F - 1
1736 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
1737 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
1738 Double_t f12= dx*fP3*f1/(r1*r1*r1);
1739 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
1740 Double_t f13= dx/r1;
1741 Double_t f24= dx; f24*=cc;
1742
1743 //b = C*ft
1744 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
1745 Double_t b02=f24*fC40;
1746 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
1747 Double_t b12=f24*fC41;
1748 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
1749 Double_t b22=f24*fC42;
1750 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
1751 Double_t b42=f24*fC44;
1752 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
1753 Double_t b32=f24*fC43;
1754
1755 //a = f*b = f*C*ft
1756 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
1757 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
1758 Double_t a22=f24*b42;
1759
1760 //F*C*Ft = C + (b + bt + a)
1761 fC00 += b00 + b00 + a00;
1762 fC10 += b10 + b01 + a01;
1763 fC20 += b20 + b02 + a02;
1764 fC30 += b30;
1765 fC40 += b40;
1766 fC11 += b11 + b11 + a11;
1767 fC21 += b21 + b12 + a12;
1768 fC31 += b31;
1769 fC41 += b41;
1770 fC22 += b22 + b22 + a22;
1771 fC32 += b32;
1772 fC42 += b42;
1773
1774
1775 // Appoximate step length
1776 Double_t step=dx*TMath::Abs(r2 + f2*(f1+f2)/(r1+r2));
1777 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
1778
1779
1780 // Get the track's (x,y,z) and (px,py,pz) in the Global System
1781 Double_t r[3]; GetXYZ(r);
1782 Double_t p[3]; GetPxPyPz(p);
1783 Double_t pp=GetP();
1784 p[0] /= pp;
1785 p[1] /= pp;
1786 p[2] /= pp;
1787
1788
1789 // Rotate to the system where Bx=By=0.
1790 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
1791 Double_t cosphi=1., sinphi=0.;
1792 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
1793 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
1794 Double_t costet=1., sintet=0.;
1795 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
1796 Double_t vect[7];
1797
1798 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
1799 vect[1] = -sinphi*r[0] + cosphi*r[1];
1800 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
1801
1802 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
1803 vect[4] = -sinphi*p[0] + cosphi*p[1];
1804 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
1805
1806 vect[6] = pp;
1807
1808
1809 // Do the helix step
1810 g3helx3(GetSign()*bb,step,vect);
1811
1812
1813 // Rotate back to the Global System
1814 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
1815 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
1816 r[2] = -sintet*vect[0] + costet*vect[2];
1817
1818 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
1819 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
1820 p[2] = -sintet*vect[3] + costet*vect[5];
1821
1822
1823 // Rotate back to the Tracking System
1824 Double_t cosalp = TMath::Cos(fAlpha);
1825 Double_t sinalp =-TMath::Sin(fAlpha);
1826
1827 Double_t
1828 t = cosalp*r[0] - sinalp*r[1];
1829 r[1] = sinalp*r[0] + cosalp*r[1];
1830 r[0] = t;
1831
1832 t = cosalp*p[0] - sinalp*p[1];
1833 p[1] = sinalp*p[0] + cosalp*p[1];
1834 p[0] = t;
1835
1836
1837 // Do the final correcting step to the target plane (linear approximation)
1838 Double_t x=r[0], y=r[1], z=r[2];
1839 if (TMath::Abs(dx) > kAlmost0) {
1840 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
1841 dx = xk - r[0];
1842 x += dx;
1843 y += p[1]/p[0]*dx;
1844 z += p[2]/p[0]*dx;
1845 }
1846
1847
1848 // Calculate the track parameters
1849 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
1850 fX = x;
1851 fP[0] = y;
1852 fP[1] = z;
1853 fP[2] = p[1]/t;
1854 fP[3] = p[2]/t;
1855 fP[4] = GetSign()/(t*pp);
1856
1857 return kTRUE;
1858}
1859