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