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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>
51ad6848 29#include "AliExternalTrackParam.h"
f76701bf 30#include "AliESDVertex.h"
0c19adf7 31#include "TPolyMarker3D.h"
6c94f330 32#include "AliLog.h"
51ad6848 33
34ClassImp(AliExternalTrackParam)
35
ed5f2849 36Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
37
51ad6848 38//_____________________________________________________________________________
90e48c0c 39AliExternalTrackParam::AliExternalTrackParam() :
def9660e 40 AliVParticle(),
90e48c0c 41 fX(0),
c9ec41e8 42 fAlpha(0)
51ad6848 43{
90e48c0c 44 //
45 // default constructor
46 //
c9ec41e8 47 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
48 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 49}
50
6c94f330 51//_____________________________________________________________________________
52AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
def9660e 53 AliVParticle(track),
6c94f330 54 fX(track.fX),
55 fAlpha(track.fAlpha)
56{
57 //
58 // copy constructor
59 //
60 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
61 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
62}
63
def9660e 64//_____________________________________________________________________________
65AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
66{
67 //
68 // assignment operator
69 //
70
71 if (this!=&trkPar) {
72 AliVParticle::operator=(trkPar);
73 fX = trkPar.fX;
74 fAlpha = trkPar.fAlpha;
75
76 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
77 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
78 }
79
80 return *this;
81}
82
51ad6848 83//_____________________________________________________________________________
84AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
85 const Double_t param[5],
90e48c0c 86 const Double_t covar[15]) :
def9660e 87 AliVParticle(),
90e48c0c 88 fX(x),
c9ec41e8 89 fAlpha(alpha)
51ad6848 90{
90e48c0c 91 //
92 // create external track parameters from given arguments
93 //
c9ec41e8 94 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
95 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 96}
97
90e48c0c 98//_____________________________________________________________________________
6c94f330 99void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
100 const Double_t p[5], const Double_t cov[15]) {
c9ec41e8 101 //
6c94f330 102 // Sets the parameters
c9ec41e8 103 //
6c94f330 104 fX=x;
105 fAlpha=alpha;
106 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
107 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
51ad6848 108}
109
110//_____________________________________________________________________________
c9ec41e8 111void AliExternalTrackParam::Reset() {
1530f89c 112 //
113 // Resets all the parameters to 0
114 //
c9ec41e8 115 fX=fAlpha=0.;
116 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
117 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 118}
119
3775b0ca 120//_____________________________________________________________________________
121void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
122 //
123 // Add "something" to the track covarince matrix.
124 // May be needed to account for unknown mis-calibration/mis-alignment
125 //
126 fC[0] +=c[0];
127 fC[1] +=c[1]; fC[2] +=c[2];
128 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
129 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
130 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
131}
132
133
c9ec41e8 134Double_t AliExternalTrackParam::GetP() const {
135 //---------------------------------------------------------------------
136 // This function returns the track momentum
137 // Results for (nearly) straight tracks are meaningless !
138 //---------------------------------------------------------------------
06fb4a2f 139 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 140 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 141}
142
1d99986f 143Double_t AliExternalTrackParam::Get1P() const {
144 //---------------------------------------------------------------------
145 // This function returns the 1/(track momentum)
146 //---------------------------------------------------------------------
147 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
148}
149
c9ec41e8 150//_______________________________________________________________________
c7bafca9 151Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 152 //------------------------------------------------------------------
153 // This function calculates the transverse impact parameter
154 // with respect to a point with global coordinates (x,y)
155 // in the magnetic field "b" (kG)
156 //------------------------------------------------------------------
5773defd 157 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 158 Double_t rp4=GetC(b);
c9ec41e8 159
160 Double_t xt=fX, yt=fP[0];
161
162 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
163 Double_t a = x*cs + y*sn;
164 y = -x*sn + y*cs; x=a;
165 xt-=x; yt-=y;
166
167 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
168 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 169 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
170}
171
172//_______________________________________________________________________
173void AliExternalTrackParam::
174GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
175 //------------------------------------------------------------------
176 // This function calculates the transverse and longitudinal impact parameters
177 // with respect to a point with global coordinates (x,y)
178 // in the magnetic field "b" (kG)
179 //------------------------------------------------------------------
180 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
181 Double_t xt=fX, yt=fP[0];
182 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
183 Double_t a = x*cs + y*sn;
184 y = -x*sn + y*cs; x=a;
185 xt-=x; yt-=y;
186
187 Double_t rp4=GetC(b);
188 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
189 dz[0] = -(xt*f1 - yt*r1);
190 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
191 return;
192 }
193
194 sn=rp4*xt - f1; cs=rp4*yt + r1;
195 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
196 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
197 dz[0] = -a/(1 + rr);
198 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
199 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 200}
201
49d13e89 202//_______________________________________________________________________
203Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
204 //------------------------------------------------------------------
205 // This function calculates the transverse impact parameter
206 // with respect to a point with global coordinates (xv,yv)
207 // neglecting the track curvature.
208 //------------------------------------------------------------------
209 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
210 Double_t x= xv*cs + yv*sn;
211 Double_t y=-xv*sn + yv*cs;
212
213 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
214
1530f89c 215 return -d;
49d13e89 216}
217
116b445b 218Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 219(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
220 Double_t (*Bethe)(Double_t)) {
116b445b 221 //------------------------------------------------------------------
222 // This function corrects the track parameters for the crossed material.
223 // "xOverX0" - X/X0, the thickness in units of the radiation length.
224 // "xTimesRho" - is the product length*density (g/cm^2).
225 // "mass" - the mass of this particle (GeV/c^2).
226 //------------------------------------------------------------------
227 Double_t &fP2=fP[2];
228 Double_t &fP3=fP[3];
229 Double_t &fP4=fP[4];
230
231 Double_t &fC22=fC[5];
232 Double_t &fC33=fC[9];
233 Double_t &fC43=fC[13];
234 Double_t &fC44=fC[14];
235
7dded1d5 236 //Apply angle correction, if requested
237 if(anglecorr) {
238 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
239 xOverX0 *=angle;
240 xTimesRho *=angle;
241 }
242
116b445b 243 Double_t p=GetP();
244 Double_t p2=p*p;
245 Double_t beta2=p2/(p2 + mass*mass);
116b445b 246
247 //Multiple scattering******************
248 if (xOverX0 != 0) {
249 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
9a53dcc6 250 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
116b445b 251 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
252 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
253 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
254 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
255 fC44 += theta2*fP3*fP4*fP3*fP4;
256 }
257
258 //Energy losses************************
259 if ((xTimesRho != 0.) && (beta2 < 1.)) {
260 Double_t dE=Bethe(beta2)*xTimesRho;
261 Double_t e=TMath::Sqrt(p2 + mass*mass);
262 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
263 fP4*=(1.- e/p2*dE);
4b2fa3ce 264 if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c
265
116b445b 266
267 // Approximate energy loss fluctuation (M.Ivanov)
268 const Double_t knst=0.07; // To be tuned.
269 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
270 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
271
272 }
273
274 return kTRUE;
275}
276
277
ee5dba5e 278Bool_t AliExternalTrackParam::CorrectForMaterial
279(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 280 //------------------------------------------------------------------
116b445b 281 // Deprecated function !
282 // Better use CorrectForMeanMaterial instead of it.
283 //
c7bafca9 284 // This function corrects the track parameters for the crossed material
285 // "d" - the thickness (fraction of the radiation length)
286 // "x0" - the radiation length (g/cm^2)
287 // "mass" - the mass of this particle (GeV/c^2)
288 //------------------------------------------------------------------
289 Double_t &fP2=fP[2];
290 Double_t &fP3=fP[3];
291 Double_t &fP4=fP[4];
292
293 Double_t &fC22=fC[5];
294 Double_t &fC33=fC[9];
295 Double_t &fC43=fC[13];
296 Double_t &fC44=fC[14];
297
7b5ef2e6 298 Double_t p=GetP();
299 Double_t p2=p*p;
c7bafca9 300 Double_t beta2=p2/(p2 + mass*mass);
301 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
302
303 //Multiple scattering******************
304 if (d!=0) {
305 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
9a53dcc6 306 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
c7bafca9 307 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
308 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
309 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
310 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
311 fC44 += theta2*fP3*fP4*fP3*fP4;
312 }
313
314 //Energy losses************************
8fc1985d 315 if (x0!=0. && beta2<1) {
c7bafca9 316 d*=x0;
ee5dba5e 317 Double_t dE=Bethe(beta2)*d;
318 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 319 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 320 fP4*=(1.- e/p2*dE);
321
322 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 323 const Double_t knst=0.07; // To be tuned.
324 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 325 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
326
c7bafca9 327 }
328
329 return kTRUE;
330}
331
ee5dba5e 332Double_t ApproximateBetheBloch(Double_t beta2) {
333 //------------------------------------------------------------------
334 // This is an approximation of the Bethe-Bloch formula with
335 // the density effect taken into account at beta*gamma > 3.5
336 // (the approximation is reasonable only for solid materials)
337 //------------------------------------------------------------------
a821848c 338 if (beta2 >= 1) return kVeryBig;
339
ee5dba5e 340 if (beta2/(1-beta2)>3.5*3.5)
341 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
342
343 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
344}
345
49d13e89 346Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
347 //------------------------------------------------------------------
348 // Transform this track to the local coord. system rotated
349 // by angle "alpha" (rad) with respect to the global coord. system.
350 //------------------------------------------------------------------
dfcef74c 351 if (TMath::Abs(fP[2]) >= kAlmost1) {
352 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
353 return kFALSE;
354 }
355
49d13e89 356 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
357 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
358
359 Double_t &fP0=fP[0];
360 Double_t &fP2=fP[2];
361 Double_t &fC00=fC[0];
362 Double_t &fC10=fC[1];
363 Double_t &fC20=fC[3];
364 Double_t &fC21=fC[4];
365 Double_t &fC22=fC[5];
366 Double_t &fC30=fC[6];
367 Double_t &fC32=fC[8];
368 Double_t &fC40=fC[10];
369 Double_t &fC42=fC[12];
370
371 Double_t x=fX;
372 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
373 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
374
dfcef74c 375 Double_t tmp=sf*ca - cf*sa;
376 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
377
49d13e89 378 fAlpha = alpha;
379 fX = x*ca + fP0*sa;
380 fP0= -x*sa + fP0*ca;
dfcef74c 381 fP2= tmp;
49d13e89 382
06fb4a2f 383 if (TMath::Abs(cf)<kAlmost0) {
384 AliError(Form("Too small cosine value %f",cf));
385 cf = kAlmost0;
386 }
387
49d13e89 388 Double_t rr=(ca+sf/cf*sa);
389
390 fC00 *= (ca*ca);
391 fC10 *= ca;
392 fC20 *= ca*rr;
393 fC21 *= rr;
394 fC22 *= rr*rr;
395 fC30 *= ca;
396 fC32 *= rr;
397 fC40 *= ca;
398 fC42 *= rr;
399
400 return kTRUE;
401}
402
403Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
404 //----------------------------------------------------------------
405 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
406 //----------------------------------------------------------------
49d13e89 407 Double_t dx=xk-fX;
e421f556 408 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 409
1530f89c 410 Double_t crv=GetC(b);
5773defd 411 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
412
49d13e89 413 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 414 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 415 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
416
417 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
418 Double_t
419 &fC00=fC[0],
420 &fC10=fC[1], &fC11=fC[2],
421 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
422 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
423 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
424
425 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
426
427 fX=xk;
428 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 429 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 430 fP2 += dx*crv;
431
432 //f = F - 1
433
434 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
435 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
436 Double_t f12= dx*fP3*f1/(r1*r1*r1);
437 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
438 Double_t f13= dx/r1;
439 Double_t f24= dx; f24*=cc;
440
441 //b = C*ft
442 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
443 Double_t b02=f24*fC40;
444 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
445 Double_t b12=f24*fC41;
446 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
447 Double_t b22=f24*fC42;
448 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
449 Double_t b42=f24*fC44;
450 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
451 Double_t b32=f24*fC43;
452
453 //a = f*b = f*C*ft
454 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
455 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
456 Double_t a22=f24*b42;
457
458 //F*C*Ft = C + (b + bt + a)
459 fC00 += b00 + b00 + a00;
460 fC10 += b10 + b01 + a01;
461 fC20 += b20 + b02 + a02;
462 fC30 += b30;
463 fC40 += b40;
464 fC11 += b11 + b11 + a11;
465 fC21 += b21 + b12 + a12;
466 fC31 += b31;
467 fC41 += b41;
468 fC22 += b22 + b22 + a22;
469 fC32 += b32;
470 fC42 += b42;
471
472 return kTRUE;
473}
474
052daaff 475void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
476Double_t p[3], Double_t bz) const {
477 //+++++++++++++++++++++++++++++++++++++++++
478 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
479 // Extrapolate track along simple helix in magnetic field
480 // Arguments: len -distance alogn helix, [cm]
481 // bz - mag field, [kGaus]
482 // Returns: x and p contain extrapolated positon and momentum
483 // The momentum returned for straight-line tracks is meaningless !
484 //+++++++++++++++++++++++++++++++++++++++++
485 GetXYZ(x);
486
def9660e 487 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 488 Double_t unit[3]; GetDirection(unit);
489 x[0]+=unit[0]*len;
490 x[1]+=unit[1]*len;
491 x[2]+=unit[2]*len;
492
493 p[0]=unit[0]/kAlmost0;
494 p[1]=unit[1]/kAlmost0;
495 p[2]=unit[2]/kAlmost0;
496 } else {
497 GetPxPyPz(p);
498 Double_t pp=GetP();
499 Double_t a = -kB2C*bz*GetSign();
500 Double_t rho = a/pp;
501 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
502 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
503 x[2] += p[2]*len/pp;
504
505 Double_t p0=p[0];
506 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
507 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
508 }
509}
510
511Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
512Double_t bz) const {
513 //+++++++++++++++++++++++++++++++++++++++++
514 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
515 // Finds point of intersection (if exists) of the helix with the plane.
516 // Stores result in fX and fP.
517 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
518 // and vector, normal to the plane
519 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
520 //+++++++++++++++++++++++++++++++++++++++++
521 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
522
523 //estimates initial helix length up to plane
524 Double_t s=
525 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
526 Double_t dist=99999,distPrev=dist;
527 Double_t x[3],p[3];
528 while(TMath::Abs(dist)>0.00001){
529 //calculates helix at the distance s from x0 ALONG the helix
530 Propagate(s,x,p,bz);
531
532 //distance between current helix position and plane
533 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
534
535 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
536 distPrev=dist;
537 s-=dist;
538 }
539 //on exit pnt is intersection point,norm is track vector at that point,
540 //all in MARS
541 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
542 return kTRUE;
543}
544
49d13e89 545Double_t
546AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
547 //----------------------------------------------------------------
548 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
549 //----------------------------------------------------------------
550 Double_t sdd = fC[0] + cov[0];
551 Double_t sdz = fC[1] + cov[1];
552 Double_t szz = fC[2] + cov[2];
553 Double_t det = sdd*szz - sdz*sdz;
554
555 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
556
557 Double_t d = fP[0] - p[0];
558 Double_t z = fP[1] - p[1];
559
560 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
561}
562
4b189f98 563Double_t AliExternalTrackParam::
564GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
565 //----------------------------------------------------------------
566 // Estimate the chi2 of the 3D space point "p" and
1e023a36 567 // the full covariance matrix "covyz" and "covxyz"
4b189f98 568 //
569 // Cov(x,x) ... : covxyz[0]
570 // Cov(y,x) ... : covxyz[1] covyz[0]
571 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
572 //----------------------------------------------------------------
573
574 Double_t res[3] = {
575 GetX() - p[0],
576 GetY() - p[1],
577 GetZ() - p[2]
578 };
579
580 Double_t f=GetSnp();
581 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
582 Double_t r=TMath::Sqrt(1.- f*f);
583 Double_t a=f/r, b=GetTgl()/r;
584
585 Double_t s2=333.*333.; //something reasonably big (cm^2)
586
587 TMatrixDSym v(3);
588 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
589 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
590 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
591
592 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
593 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
594 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
595
596 v.Invert();
597 if (!v.IsValid()) return kVeryBig;
598
599 Double_t chi2=0.;
600 for (Int_t i = 0; i < 3; i++)
601 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
602
603 return chi2;
604
605
606}
607
1e023a36 608Bool_t AliExternalTrackParam::
609PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
610 //----------------------------------------------------------------
611 // Propagate this track to the plane
612 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
613 // belongs to.
614 // The magnetic field is "bz" (kG)
615 //
616 // The track curvature and the change of the covariance matrix
617 // of the track parameters are negleted !
618 // (So the "step" should be small compared with 1/curvature)
619 //----------------------------------------------------------------
620
621 Double_t f=GetSnp();
622 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
623 Double_t r=TMath::Sqrt(1.- f*f);
624 Double_t a=f/r, b=GetTgl()/r;
625
626 Double_t s2=333.*333.; //something reasonably big (cm^2)
627
628 TMatrixDSym tV(3);
629 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
630 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
631 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
632
633 TMatrixDSym pV(3);
634 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
635 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
636 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
637
638 TMatrixDSym tpV(tV);
639 tpV+=pV;
640 tpV.Invert();
641 if (!tpV.IsValid()) return kFALSE;
642
643 TMatrixDSym pW(3),tW(3);
644 for (Int_t i=0; i<3; i++)
645 for (Int_t j=0; j<3; j++) {
646 pW(i,j)=tW(i,j)=0.;
647 for (Int_t k=0; k<3; k++) {
648 pW(i,j) += tV(i,k)*tpV(k,j);
649 tW(i,j) += pV(i,k)*tpV(k,j);
650 }
651 }
652
653 Double_t t[3] = {GetX(), GetY(), GetZ()};
654
655 Double_t x=0.;
656 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
657 Double_t crv=GetC(bz);
658 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
659 f += crv*(x-fX);
660 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
661 fX=x;
662
663 fP[0]=0.;
664 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
665 fP[1]=0.;
666 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
667
668 return kTRUE;
669}
670
e23a38cb 671Double_t *AliExternalTrackParam::GetResiduals(
672Double_t *p,Double_t *cov,Bool_t updated) const {
673 //------------------------------------------------------------------
674 // Returns the track residuals with the space point "p" having
675 // the covariance matrix "cov".
676 // If "updated" is kTRUE, the track parameters expected to be updated,
677 // otherwise they must be predicted.
678 //------------------------------------------------------------------
679 static Double_t res[2];
680
681 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
682 if (updated) {
683 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
684 } else {
685 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
686 }
687 Double_t det=r00*r11 - r01*r01;
688
689 if (TMath::Abs(det) < kAlmost0) return 0;
690
691 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 692
693 if (r00 < 0.) return 0;
694 if (r11 < 0.) return 0;
695
e23a38cb 696 Double_t dy = fP[0] - p[0];
697 Double_t dz = fP[1] - p[1];
698
699 res[0]=dy*TMath::Sqrt(r00);
700 res[1]=dz*TMath::Sqrt(r11);
701
702 return res;
703}
704
49d13e89 705Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
706 //------------------------------------------------------------------
707 // Update the track parameters with the space point "p" having
708 // the covariance matrix "cov"
709 //------------------------------------------------------------------
710 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
711 Double_t
712 &fC00=fC[0],
713 &fC10=fC[1], &fC11=fC[2],
714 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
715 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
716 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
717
718 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
719 r00+=fC00; r01+=fC10; r11+=fC11;
720 Double_t det=r00*r11 - r01*r01;
721
722 if (TMath::Abs(det) < kAlmost0) return kFALSE;
723
724
725 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
726
727 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
728 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
729 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
730 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
731 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
732
733 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
734 Double_t sf=fP2 + k20*dy + k21*dz;
735 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
736
737 fP0 += k00*dy + k01*dz;
738 fP1 += k10*dy + k11*dz;
739 fP2 = sf;
740 fP3 += k30*dy + k31*dz;
741 fP4 += k40*dy + k41*dz;
742
743 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
744 Double_t c12=fC21, c13=fC31, c14=fC41;
745
746 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
747 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
748 fC40-=k00*c04+k01*c14;
749
750 fC11-=k10*c01+k11*fC11;
751 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
752 fC41-=k10*c04+k11*c14;
753
754 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
755 fC42-=k20*c04+k21*c14;
756
757 fC33-=k30*c03+k31*c13;
758 fC43-=k30*c04+k31*c14;
759
760 fC44-=k40*c04+k41*c14;
761
762 return kTRUE;
763}
764
c7bafca9 765void
766AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
767 //--------------------------------------------------------------------
768 // External track parameters -> helix parameters
769 // "b" - magnetic field (kG)
770 //--------------------------------------------------------------------
771 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
772
1530f89c 773 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 774
775 hlx[5]=fX*cs - hlx[0]*sn; // x0
776 hlx[0]=fX*sn + hlx[0]*cs; // y0
777//hlx[1]= // z0
778 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
779//hlx[3]= // tgl
1530f89c 780 hlx[4]=GetC(b); // C
c7bafca9 781}
782
783
784static void Evaluate(const Double_t *h, Double_t t,
785 Double_t r[3], //radius vector
786 Double_t g[3], //first defivatives
787 Double_t gg[3]) //second derivatives
788{
789 //--------------------------------------------------------------------
790 // Calculate position of a point on a track and some derivatives
791 //--------------------------------------------------------------------
792 Double_t phase=h[4]*t+h[2];
793 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
794
795 r[0] = h[5] + (sn - h[6])/h[4];
796 r[1] = h[0] - (cs - h[7])/h[4];
797 r[2] = h[1] + h[3]*t;
798
799 g[0] = cs; g[1]=sn; g[2]=h[3];
800
801 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
802}
803
804Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
805Double_t b, Double_t &xthis, Double_t &xp) const {
806 //------------------------------------------------------------
807 // Returns the (weighed !) distance of closest approach between
808 // this track and the track "p".
809 // Other returned values:
810 // xthis, xt - coordinates of tracks' reference planes at the DCA
811 //-----------------------------------------------------------
812 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
813 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
814 Double_t dx2=dy2;
815
816 //dx2=dy2=dz2=1.;
817
818 Double_t p1[8]; GetHelixParameters(p1,b);
819 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
820 Double_t p2[8]; p->GetHelixParameters(p2,b);
821 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
822
823
824 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
825 Evaluate(p1,t1,r1,g1,gg1);
826 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
827 Evaluate(p2,t2,r2,g2,gg2);
828
829 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
830 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
831
832 Int_t max=27;
833 while (max--) {
834 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
835 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
836 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
837 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
838 (g1[2]*g1[2] - dz*gg1[2])/dz2;
839 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
840 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
841 (g2[2]*g2[2] + dz*gg2[2])/dz2;
842 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
843
844 Double_t det=h11*h22-h12*h12;
845
846 Double_t dt1,dt2;
847 if (TMath::Abs(det)<1.e-33) {
848 //(quasi)singular Hessian
849 dt1=-gt1; dt2=-gt2;
850 } else {
851 dt1=-(gt1*h22 - gt2*h12)/det;
852 dt2=-(h11*gt2 - h12*gt1)/det;
853 }
854
855 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
856
857 //check delta(phase1) ?
858 //check delta(phase2) ?
859
860 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
861 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
862 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 863 AliDebug(1," stopped at not a stationary point !");
c7bafca9 864 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
865 if (lmb < 0.)
358f16ae 866 AliDebug(1," stopped at not a minimum !");
c7bafca9 867 break;
868 }
869
870 Double_t dd=dm;
871 for (Int_t div=1 ; ; div*=2) {
872 Evaluate(p1,t1+dt1,r1,g1,gg1);
873 Evaluate(p2,t2+dt2,r2,g2,gg2);
874 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
875 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
876 if (dd<dm) break;
877 dt1*=0.5; dt2*=0.5;
878 if (div>512) {
358f16ae 879 AliDebug(1," overshoot !"); break;
c7bafca9 880 }
881 }
882 dm=dd;
883
884 t1+=dt1;
885 t2+=dt2;
886
887 }
888
358f16ae 889 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 890
891 Double_t cs=TMath::Cos(GetAlpha());
892 Double_t sn=TMath::Sin(GetAlpha());
893 xthis=r1[0]*cs + r1[1]*sn;
894
895 cs=TMath::Cos(p->GetAlpha());
896 sn=TMath::Sin(p->GetAlpha());
897 xp=r2[0]*cs + r2[1]*sn;
898
899 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
900}
901
902Double_t AliExternalTrackParam::
903PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
904 //--------------------------------------------------------------
905 // Propagates this track and the argument track to the position of the
906 // distance of closest approach.
907 // Returns the (weighed !) distance of closest approach.
908 //--------------------------------------------------------------
909 Double_t xthis,xp;
910 Double_t dca=GetDCA(p,b,xthis,xp);
911
912 if (!PropagateTo(xthis,b)) {
913 //AliWarning(" propagation failed !");
914 return 1e+33;
915 }
916
917 if (!p->PropagateTo(xp,b)) {
918 //AliWarning(" propagation failed !";
919 return 1e+33;
920 }
921
922 return dca;
923}
924
925
e99a34df 926Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx,
927Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 928 //
e99a34df 929 // Propagate this track to the DCA to vertex "vtx",
f76701bf 930 // if the (rough) transverse impact parameter is not bigger then "maxd".
931 // Magnetic field is "b" (kG).
932 //
933 // a) The track gets extapolated to the DCA to the vertex.
934 // b) The impact parameters and their covariance matrix are calculated.
935 //
936 // In the case of success, the returned value is kTRUE
937 // (otherwise, it's kFALSE)
938 //
939 Double_t alpha=GetAlpha();
940 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
941 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
942 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
e99a34df 943 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs, zv=vtx->GetZv();
f76701bf 944 x-=xv; y-=yv;
945
946 //Estimate the impact parameter neglecting the track curvature
947 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
948 if (d > maxd) return kFALSE;
949
950 //Propagate to the DCA
e99a34df 951 Double_t crv=kB2C*b*GetParameter()[4];
952 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
953
f76701bf 954 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
955 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 956 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
957 else cs=1.;
f76701bf 958
959 x = xv*cs + yv*sn;
960 yv=-xv*sn + yv*cs; xv=x;
961
962 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 963
964 if (dz==0) return kTRUE;
965 dz[0] = GetParameter()[0] - yv;
966 dz[1] = GetParameter()[1] - zv;
967
968 if (covar==0) return kTRUE;
969 Double_t cov[6]; vtx->GetCovMatrix(cov);
970
971 //***** Improvements by A.Dainese
972 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
973 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
974 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
975 covar[1] = GetCovariance()[1]; // between (x,y) and z
976 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
977 //*****
978
29fbcc93 979 return kTRUE;
f76701bf 980}
981
982
b1149664 983void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
984 //----------------------------------------------------------------
985 // This function returns a unit vector along the track direction
986 // in the global coordinate system.
987 //----------------------------------------------------------------
988 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
989 Double_t snp=fP[2];
92934324 990 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 991 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
992 d[0]=(csp*cs - snp*sn)/norm;
993 d[1]=(snp*cs + csp*sn)/norm;
994 d[2]=fP[3]/norm;
995}
996
c683ddc2 997Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 998 //---------------------------------------------------------------------
999 // This function returns the global track momentum components
1000 // Results for (nearly) straight tracks are meaningless !
1001 //---------------------------------------------------------------------
1002 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1003 return Local2GlobalMomentum(p,fAlpha);
1004}
a5e407e9 1005
def9660e 1006Double_t AliExternalTrackParam::Px() const {
957fb479 1007 //---------------------------------------------------------------------
1008 // Returns x-component of momentum
1009 // Result for (nearly) straight tracks is meaningless !
1010 //---------------------------------------------------------------------
def9660e 1011
957fb479 1012 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1013 GetPxPyPz(p);
1014
1015 return p[0];
1016}
1017
1018Double_t AliExternalTrackParam::Py() const {
957fb479 1019 //---------------------------------------------------------------------
1020 // Returns y-component of momentum
1021 // Result for (nearly) straight tracks is meaningless !
1022 //---------------------------------------------------------------------
def9660e 1023
957fb479 1024 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1025 GetPxPyPz(p);
1026
1027 return p[1];
1028}
1029
1030Double_t AliExternalTrackParam::Pz() const {
957fb479 1031 //---------------------------------------------------------------------
1032 // Returns z-component of momentum
1033 // Result for (nearly) straight tracks is meaningless !
1034 //---------------------------------------------------------------------
def9660e 1035
957fb479 1036 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1037 GetPxPyPz(p);
1038
1039 return p[2];
1040}
1041
c683ddc2 1042Double_t AliExternalTrackParam::Xv() const {
1043 //---------------------------------------------------------------------
1044 // Returns x-component of first track point
1045 //---------------------------------------------------------------------
1046
1047 Double_t r[3]={0.,0.,0.};
1048 GetXYZ(r);
1049
1050 return r[0];
1051}
1052
1053Double_t AliExternalTrackParam::Yv() const {
1054 //---------------------------------------------------------------------
1055 // Returns y-component of first track point
1056 //---------------------------------------------------------------------
1057
1058 Double_t r[3]={0.,0.,0.};
1059 GetXYZ(r);
1060
1061 return r[1];
1062}
1063
1064Double_t AliExternalTrackParam::Zv() const {
1065 //---------------------------------------------------------------------
1066 // Returns z-component of first track point
1067 //---------------------------------------------------------------------
1068
1069 Double_t r[3]={0.,0.,0.};
1070 GetXYZ(r);
1071
1072 return r[2];
1073}
1074
def9660e 1075Double_t AliExternalTrackParam::Theta() const {
1076 // return theta angle of momentum
1077
7cdd0c20 1078 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1079}
1080
1081Double_t AliExternalTrackParam::Phi() const {
957fb479 1082 //---------------------------------------------------------------------
1083 // Returns the azimuthal angle of momentum
1084 // 0 <= phi < 2*pi
1085 //---------------------------------------------------------------------
def9660e 1086
957fb479 1087 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1088 if (phi<0.) phi+=2.*TMath::Pi();
1089 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1090
1091 return phi;
def9660e 1092}
1093
1094Double_t AliExternalTrackParam::M() const {
1095 // return particle mass
1096
1097 // No mass information available so far.
1098 // Redifine in derived class!
1099
1100 return -999.;
1101}
1102
1103Double_t AliExternalTrackParam::E() const {
1104 // return particle energy
1105
1106 // No PID information available so far.
1107 // Redifine in derived class!
1108
1109 return -999.;
1110}
1111
1112Double_t AliExternalTrackParam::Eta() const {
1113 // return pseudorapidity
1114
1115 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1116}
1117
1118Double_t AliExternalTrackParam::Y() const {
1119 // return rapidity
1120
1121 // No PID information available so far.
1122 // Redifine in derived class!
1123
1124 return -999.;
1125}
1126
c9ec41e8 1127Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1128 //---------------------------------------------------------------------
1129 // This function returns the global track position
1130 //---------------------------------------------------------------------
1131 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1132 return Local2GlobalPosition(r,fAlpha);
51ad6848 1133}
1134
c9ec41e8 1135Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1136 //---------------------------------------------------------------------
1137 // This function returns the global covariance matrix of the track params
1138 //
1139 // Cov(x,x) ... : cv[0]
1140 // Cov(y,x) ... : cv[1] cv[2]
1141 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1142 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1143 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1144 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1145 //
c9ec41e8 1146 // Results for (nearly) straight tracks are meaningless !
1147 //---------------------------------------------------------------------
e421f556 1148 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1149 for (Int_t i=0; i<21; i++) cv[i]=0.;
1150 return kFALSE;
a5e407e9 1151 }
49d13e89 1152 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1153 for (Int_t i=0; i<21; i++) cv[i]=0.;
1154 return kFALSE;
1155 }
1156 Double_t pt=1./TMath::Abs(fP[4]);
1157 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1158 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1159
1160 Double_t m00=-sn, m10=cs;
1161 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1162 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1163 Double_t m35=pt, m45=-pt*pt*fP[3];
1164
854d5d49 1165 m43*=GetSign();
1166 m44*=GetSign();
1167 m45*=GetSign();
1168
c9ec41e8 1169 cv[0 ] = fC[0]*m00*m00;
1170 cv[1 ] = fC[0]*m00*m10;
1171 cv[2 ] = fC[0]*m10*m10;
1172 cv[3 ] = fC[1]*m00;
1173 cv[4 ] = fC[1]*m10;
1174 cv[5 ] = fC[2];
1175 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1176 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1177 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1178 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1179 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1180 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1181 cv[12] = fC[4]*m24 + fC[11]*m44;
1182 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1183 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1184 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1185 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1186 cv[17] = fC[7]*m35 + fC[11]*m45;
1187 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1188 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1189 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1190
c9ec41e8 1191 return kTRUE;
51ad6848 1192}
1193
51ad6848 1194
c9ec41e8 1195Bool_t
1196AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1197 //---------------------------------------------------------------------
1198 // This function returns the global track momentum extrapolated to
1199 // the radial position "x" (cm) in the magnetic field "b" (kG)
1200 //---------------------------------------------------------------------
c9ec41e8 1201 p[0]=fP[4];
1530f89c 1202 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1203 p[2]=fP[3];
1204 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1205}
1206
7cf7bb6c 1207Bool_t
1208AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1209 //---------------------------------------------------------------------
1210 // This function returns the local Y-coordinate of the intersection
1211 // point between this track and the reference plane "x" (cm).
1212 // Magnetic field "b" (kG)
1213 //---------------------------------------------------------------------
1214 Double_t dx=x-fX;
1215 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1216
1530f89c 1217 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1218
1219 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1220 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1221
1222 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1223 y = fP[0] + dx*(f1+f2)/(r1+r2);
1224 return kTRUE;
1225}
1226
6c94f330 1227Bool_t
1228AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1229 //---------------------------------------------------------------------
1230 // This function returns the local Z-coordinate of the intersection
1231 // point between this track and the reference plane "x" (cm).
1232 // Magnetic field "b" (kG)
1233 //---------------------------------------------------------------------
1234 Double_t dx=x-fX;
1235 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1236
1237 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1238
1239 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1240 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1241
1242 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1243 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1244 return kTRUE;
1245}
1246
c9ec41e8 1247Bool_t
1248AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1249 //---------------------------------------------------------------------
1250 // This function returns the global track position extrapolated to
1251 // the radial position "x" (cm) in the magnetic field "b" (kG)
1252 //---------------------------------------------------------------------
c9ec41e8 1253 Double_t dx=x-fX;
e421f556 1254 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1255
1530f89c 1256 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1257
e421f556 1258 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1259 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1260
1261 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1262 r[0] = x;
1263 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 1264 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 1265 return Local2GlobalPosition(r,fAlpha);
51ad6848 1266}
1267
51ad6848 1268//_____________________________________________________________________________
1269void AliExternalTrackParam::Print(Option_t* /*option*/) const
1270{
1271// print the parameters and the covariance matrix
1272
1273 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1274 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1275 fP[0], fP[1], fP[2], fP[3], fP[4]);
1276 printf(" covariance: %12g\n", fC[0]);
1277 printf(" %12g %12g\n", fC[1], fC[2]);
1278 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1279 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1280 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1281 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1282 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1283}
5b77d93c 1284
c194ba83 1285Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1286 //
1287 // Get sinus at given x
1288 //
1530f89c 1289 Double_t crv=GetC(b);
c194ba83 1290 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1291 Double_t dx = x-fX;
1292 Double_t res = fP[2]+dx*crv;
1293 return res;
1294}
bf00ebb8 1295
1296Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1297 //------------------------------------------------------------------------
1298 // Get the distance between two tracks at the local position x
1299 // working in the local frame of this track.
1300 // Origin : Marian.Ivanov@cern.ch
1301 //-----------------------------------------------------------------------
1302 Double_t xyz[3];
1303 Double_t xyz2[3];
1304 xyz[0]=x;
1305 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1306 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1307 //
1308 //
1309 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1310 xyz2[0]=x;
1311 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1312 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1313 }else{
1314 //
1315 Double_t xyz1[3];
1316 Double_t dfi = param2->GetAlpha()-GetAlpha();
1317 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1318 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1319 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1320 //
1321 xyz1[0]=xyz2[0];
1322 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1323 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1324 //
1325 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1326 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1327 xyz2[2] = xyz1[2];
1328 }
1329 dist[0] = xyz[0]-xyz2[0];
1330 dist[1] = xyz[1]-xyz2[1];
1331 dist[2] = xyz[2]-xyz2[2];
1332
1333 return kTRUE;
1334}
0c19adf7 1335
1336
1337//
1338// Draw functionality.
1339// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1340//
1341
1342void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1343 //
1344 // Draw track line
1345 //
1346 if (minR>maxR) return ;
1347 if (stepR<=0) return ;
1348 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1349 if (npoints<1) return;
1350 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1351 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1352 polymarker->Draw();
1353}
1354
1355//
1356void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1357 //
1358 // Fill points in the polymarker
1359 //
1360 Int_t counter=0;
1361 for (Double_t r=minR; r<maxR; r+=stepR){
1362 Double_t point[3];
1363 GetXYZAt(r,magF,point);
1364 pol->SetPoint(counter,point[0],point[1], point[2]);
1365 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1366 counter++;
1367 }
1368}