Added V0A23 (V0 rings 2-3), V0C01 (V0 rings 0-1) and V0S = V0A23+V0C01
[u/mrichter/AliRoot.git] / STEER / STEERBase / AliExternalTrackParam.cxx
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51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
86be8934 28#include <cassert>
29
30#include <TVectorD.h>
4b189f98 31#include <TMatrixDSym.h>
d46683db 32#include <TPolyMarker3D.h>
33#include <TVector3.h>
cfdb62d4 34#include <TMatrixD.h>
d46683db 35
51ad6848 36#include "AliExternalTrackParam.h"
58e536c5 37#include "AliVVertex.h"
6c94f330 38#include "AliLog.h"
51ad6848 39
40ClassImp(AliExternalTrackParam)
41
ed5f2849 42Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
f2cef1b5 43Bool_t AliExternalTrackParam::fgUseLogTermMS = kFALSE;;
51ad6848 44//_____________________________________________________________________________
90e48c0c 45AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 46 AliVTrack(),
90e48c0c 47 fX(0),
c9ec41e8 48 fAlpha(0)
51ad6848 49{
90e48c0c 50 //
51 // default constructor
52 //
c9ec41e8 53 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
54 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 55}
56
57//_____________________________________________________________________________
6c94f330 58AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 59 AliVTrack(track),
6c94f330 60 fX(track.fX),
61 fAlpha(track.fAlpha)
62{
63 //
64 // copy constructor
65 //
66 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
67 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
86be8934 68 CheckCovariance();
6c94f330 69}
70
71//_____________________________________________________________________________
def9660e 72AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
73{
74 //
75 // assignment operator
76 //
77
78 if (this!=&trkPar) {
4f6e22bd 79 AliVTrack::operator=(trkPar);
def9660e 80 fX = trkPar.fX;
81 fAlpha = trkPar.fAlpha;
82
83 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
84 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
86be8934 85 CheckCovariance();
def9660e 86 }
87
88 return *this;
89}
90
91//_____________________________________________________________________________
51ad6848 92AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
93 const Double_t param[5],
90e48c0c 94 const Double_t covar[15]) :
4f6e22bd 95 AliVTrack(),
90e48c0c 96 fX(x),
c9ec41e8 97 fAlpha(alpha)
51ad6848 98{
90e48c0c 99 //
100 // create external track parameters from given arguments
101 //
c9ec41e8 102 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
103 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
86be8934 104 CheckCovariance();
51ad6848 105}
106
90e48c0c 107//_____________________________________________________________________________
4ec1ca0f 108void AliExternalTrackParam::CopyFromVTrack(const AliVTrack *vTrack)
109{
110 //
111 // Recreate TrackParams from VTrack
112 // This is not a copy contructor !
113 //
114 if (!vTrack) {
115 AliError("Source VTrack is NULL");
116 return;
117 }
118 if (this==vTrack) {
119 AliError("Copy of itself is requested");
120 return;
121 }
122 //
123 if (vTrack->InheritsFrom(AliExternalTrackParam::Class())) {
124 AliDebug(1,"Source itself is AliExternalTrackParam, using assignment operator");
125 *this = *(AliExternalTrackParam*)vTrack;
126 return;
127 }
128 //
129 AliVTrack::operator=( *vTrack );
130 //
131 Double_t xyz[3],pxpypz[3],cv[21];
132 vTrack->GetXYZ(xyz);
133 pxpypz[0]=vTrack->Px();
134 pxpypz[1]=vTrack->Py();
135 pxpypz[2]=vTrack->Pz();
136 vTrack->GetCovarianceXYZPxPyPz(cv);
137 Short_t sign = (Short_t)vTrack->Charge();
138 Set(xyz,pxpypz,cv,sign);
139}
140
141//_____________________________________________________________________________
4f6e22bd 142AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
143 AliVTrack(),
144 fX(0.),
145 fAlpha(0.)
146{
147 //
610e3088 148 // Constructor from virtual track,
149 // This is not a copy contructor !
4f6e22bd 150 //
610e3088 151
152 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
153 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
154 AliWarning("Calling the default constructor...");
155 AliExternalTrackParam();
156 return;
157 }
158
892be05f 159 Double_t xyz[3],pxpypz[3],cv[21];
160 vTrack->GetXYZ(xyz);
161 pxpypz[0]=vTrack->Px();
162 pxpypz[1]=vTrack->Py();
163 pxpypz[2]=vTrack->Pz();
4f6e22bd 164 vTrack->GetCovarianceXYZPxPyPz(cv);
165 Short_t sign = (Short_t)vTrack->Charge();
166
167 Set(xyz,pxpypz,cv,sign);
168}
169
170//_____________________________________________________________________________
da4e3deb 171AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
172 Double_t cv[21],Short_t sign) :
4f6e22bd 173 AliVTrack(),
da4e3deb 174 fX(0.),
175 fAlpha(0.)
176{
177 //
4f6e22bd 178 // constructor from the global parameters
179 //
180
181 Set(xyz,pxpypz,cv,sign);
182}
183
d14ea120 184/*
4f6e22bd 185//_____________________________________________________________________________
186void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
187 Double_t cv[21],Short_t sign)
188{
189 //
da4e3deb 190 // create external track parameters from the global parameters
191 // x,y,z,px,py,pz and their 6x6 covariance matrix
192 // A.Dainese 10.10.08
193
aff56ff7 194 // Calculate alpha: the rotation angle of the corresponding local system.
195 //
196 // For global radial position inside the beam pipe, alpha is the
197 // azimuthal angle of the momentum projected on (x,y).
198 //
c99948ce 199 // For global radial position outside the ITS, alpha is the
aff56ff7 200 // azimuthal angle of the centre of the TPC sector in which the point
201 // xyz lies
202 //
4349f5a4 203 const double kSafe = 1e-5;
aff56ff7 204 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
c99948ce 205 Double_t radMax = 45.; // approximately ITS outer radius
4349f5a4 206 if (radPos2 < radMax*radMax) { // inside the ITS
aff56ff7 207 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
c99948ce 208 } else { // outside the ITS
aff56ff7 209 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
210 fAlpha =
211 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
212 }
4349f5a4 213 //
214 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
215 // protection: avoid alpha being too close to 0 or +-pi/2
5123be3b 216 if (TMath::Abs(sn)<2*kSafe) {
217 if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
218 else fAlpha += fAlpha>-TMath::Pi()/2. ? -2*kSafe : 2*kSafe;
4349f5a4 219 cs=TMath::Cos(fAlpha);
220 sn=TMath::Sin(fAlpha);
221 }
5123be3b 222 else if (TMath::Abs(cs)<2*kSafe) {
223 if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
224 else fAlpha += fAlpha>-TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
4349f5a4 225 cs=TMath::Cos(fAlpha);
8defb4a0 226 sn=TMath::Sin(fAlpha);
4349f5a4 227 }
da4e3deb 228 // Get the vertex of origin and the momentum
229 TVector3 ver(xyz[0],xyz[1],xyz[2]);
230 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
4349f5a4 231 //
232 // avoid momenta along axis
233 if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]);
234 if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]);
da4e3deb 235
236 // Rotate to the local coordinate system
237 ver.RotateZ(-fAlpha);
238 mom.RotateZ(-fAlpha);
239
d14ea120 240 //
da4e3deb 241 // x of the reference plane
242 fX = ver.X();
243
244 Double_t charge = (Double_t)sign;
245
246 fP[0] = ver.Y();
247 fP[1] = ver.Z();
248 fP[2] = TMath::Sin(mom.Phi());
249 fP[3] = mom.Pz()/mom.Pt();
250 fP[4] = TMath::Sign(1/mom.Pt(),charge);
d14ea120 251 //
252 if (TMath::Abs( 1-fP[2]) < 3*kSafe) fP[2] = 1.- 3*kSafe; //Protection
253 else if (TMath::Abs(-1-fP[2]) < 3*kSafe) fP[2] =-1.+ 3*kSafe; //Protection
254 //
da4e3deb 255 // Covariance matrix (formulas to be simplified)
da4e3deb 256 Double_t pt=1./TMath::Abs(fP[4]);
d14ea120 257 // avoid alpha+phi being to close to +-pi/2 in the cov.matrix evaluation
258 double fp2 = fP[2];
259 Double_t r=TMath::Sqrt((1.-fp2)*(1.+fp2));
260 //
da4e3deb 261 Double_t m00=-sn;// m10=cs;
d14ea120 262 Double_t m23=-pt*(sn + fp2*cs/r), m43=-pt*pt*(r*cs - fp2*sn);
263 Double_t m24= pt*(cs - fp2*sn/r), m44=-pt*pt*(r*sn + fp2*cs);
da4e3deb 264 Double_t m35=pt, m45=-pt*pt*fP[3];
265
266 m43*=GetSign();
267 m44*=GetSign();
268 m45*=GetSign();
269
270 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
271 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
272 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
273 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
d14ea120 274 Double_t a4=cv[14]+2.*cv[9]; //cv[14]-2.*cv[9]*m24*m44/m23/m43;
da4e3deb 275 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
276 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
277
278 fC[0 ] = cv[0 ]+cv[2 ];
279 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
280 fC[2 ] = cv[5 ];
5123be3b 281 fC[3 ] = (cv[10]*m43-cv[6]*m44)/(m24*m43-m23*m44)/m00;
da4e3deb 282 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
283 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
5123be3b 284 fC[4 ] = (cv[12]*m43-cv[8]*m44)/(m24*m43-m23*m44);
da4e3deb 285 fC[11] = (cv[8]-fC[4]*m23)/m43;
286 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
5123be3b 287 fC[5 ] = TMath::Abs((a4*a3-a6*a1)/(a5*a3-a6*a2));
288 fC[14] = TMath::Abs((a1-a2*fC[5])/a3);
da4e3deb 289 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
290 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
291 Double_t b2=m23*m35;
292 Double_t b3=m43*m35;
293 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
294 Double_t b5=m24*m35;
295 Double_t b6=m44*m35;
296 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
297 fC[13] = b1/b3-b2*fC[8]/b3;
298 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 299
86be8934 300 CheckCovariance();
301
4f6e22bd 302 return;
da4e3deb 303}
d14ea120 304*/
305
306//_____________________________________________________________________________
307void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
308 Double_t cv[21],Short_t sign)
309{
310 //
311 // create external track parameters from the global parameters
312 // x,y,z,px,py,pz and their 6x6 covariance matrix
313 // A.Dainese 10.10.08
314
315 // Calculate alpha: the rotation angle of the corresponding local system.
316 //
317 // For global radial position inside the beam pipe, alpha is the
318 // azimuthal angle of the momentum projected on (x,y).
319 //
320 // For global radial position outside the ITS, alpha is the
321 // azimuthal angle of the centre of the TPC sector in which the point
322 // xyz lies
323 //
324 const double kSafe = 1e-5;
325 Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
326 Double_t radMax = 45.; // approximately ITS outer radius
327 if (radPos2 < radMax*radMax) { // inside the ITS
328 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
329 } else { // outside the ITS
330 Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
331 fAlpha =
332 TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
333 }
334 //
335 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
336 // protection: avoid alpha being too close to 0 or +-pi/2
337 if (TMath::Abs(sn)<2*kSafe) {
338 if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
339 else fAlpha += fAlpha>-TMath::Pi()/2. ? -2*kSafe : 2*kSafe;
340 cs=TMath::Cos(fAlpha);
341 sn=TMath::Sin(fAlpha);
342 }
343 else if (TMath::Abs(cs)<2*kSafe) {
344 if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
345 else fAlpha += fAlpha>-TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
346 cs=TMath::Cos(fAlpha);
347 sn=TMath::Sin(fAlpha);
348 }
349 // Get the vertex of origin and the momentum
350 TVector3 ver(xyz[0],xyz[1],xyz[2]);
351 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
352 //
353 // Rotate to the local coordinate system
354 ver.RotateZ(-fAlpha);
355 mom.RotateZ(-fAlpha);
356
357 //
358 // x of the reference plane
359 fX = ver.X();
360
361 Double_t charge = (Double_t)sign;
362
363 fP[0] = ver.Y();
364 fP[1] = ver.Z();
365 fP[2] = TMath::Sin(mom.Phi());
366 fP[3] = mom.Pz()/mom.Pt();
367 fP[4] = TMath::Sign(1/mom.Pt(),charge);
368 //
369 if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection
370 else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection
371 //
372 // Covariance matrix (formulas to be simplified)
373 Double_t pt=1./TMath::Abs(fP[4]);
374 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
375 //
376 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
377 //
378 Int_t special = 0;
379 double sgcheck = r*sn + fP[2]*cs;
380 if (TMath::Abs(sgcheck)>=1-kSafe) { // special case: lab phi is +-pi/2
381 special = 1;
382 sgcheck = TMath::Sign(1.0,sgcheck);
383 }
384 else if (TMath::Abs(sgcheck)<kSafe) {
385 sgcheck = TMath::Sign(1.0,cs);
386 special = 2; // special case: lab phi is 0
387 }
388 //
389 fC[0 ] = cv[0 ]+cv[2 ];
390 fC[1 ] = TMath::Sign(cv34,-cv[3 ]*sn);
391 fC[2 ] = cv[5 ];
392 //
393 if (special==1) {
394 double pti = 1./pt;
395 double pti2 = pti*pti;
396 int q = GetSign();
397 fC[3 ] = cv[6]*pti;
398 fC[4 ] = -sgcheck*cv[8]*r*pti;
399 fC[5 ] = TMath::Abs(cv[9]*r*r*pti2);
400 fC[6 ] = (cv[10]*fP[3]-sgcheck*cv[15])*pti/r;
401 fC[7 ] = (cv[17]-sgcheck*cv[12]*fP[3])*pti;
402 fC[8 ] = (-sgcheck*cv[18]+cv[13]*fP[3])*r*pti2;
403 fC[9 ] = TMath::Abs( cv[20]-2*sgcheck*cv[19]*fP[3]+cv[14]*fP[3]*fP[3])*pti2;
404 fC[10] = cv[10]*pti2/r*q;
405 fC[11] = -sgcheck*cv[12]*pti2*q;
406 fC[12] = cv[13]*r*pti*pti2*q;
407 fC[13] = (-sgcheck*cv[19]+cv[14]*fP[3])*r*pti2*pti;
408 fC[14] = TMath::Abs(cv[14]*pti2*pti2);
409 } else if (special==2) {
410 double pti = 1./pt;
411 double pti2 = pti*pti;
412 int q = GetSign();
413 fC[3 ] = -cv[10]*pti*cs/sn;
414 fC[4 ] = cv[12]*cs*pti;
415 fC[5 ] = TMath::Abs(cv[14]*cs*cs*pti2);
416 fC[6 ] = (sgcheck*cv[6]*fP[3]-cv[15])*pti/sn;
417 fC[7 ] = (cv[17]-sgcheck*cv[8]*fP[3])*pti;
418 fC[8 ] = (cv[19]-sgcheck*cv[13]*fP[3])*cs*pti2;
419 fC[9 ] = TMath::Abs( cv[20]-2*sgcheck*cv[18]*fP[3]+cv[9]*fP[3]*fP[3])*pti2;
420 fC[10] = sgcheck*cv[6]*pti2/sn*q;
421 fC[11] = -sgcheck*cv[8]*pti2*q;
422 fC[12] = -sgcheck*cv[13]*cs*pti*pti2*q;
423 fC[13] = (-sgcheck*cv[18]+cv[9]*fP[3])*pti2*pti*q;
424 fC[14] = TMath::Abs(cv[9]*pti2*pti2);
425 }
426 else {
427 Double_t m00=-sn;// m10=cs;
428 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
429 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
430 Double_t m35=pt, m45=-pt*pt*fP[3];
431 //
432 m43*=GetSign();
433 m44*=GetSign();
434 m45*=GetSign();
435 //
436 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
437 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
438 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
439 Double_t a4=cv[14]+2.*cv[9]; //cv[14]-2.*cv[9]*m24*m44/m23/m43;
440 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
441 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
442 //
443 fC[3 ] = (cv[10]*m43-cv[6]*m44)/(m24*m43-m23*m44)/m00;
444 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
445 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
446 fC[4 ] = (cv[12]*m43-cv[8]*m44)/(m24*m43-m23*m44);
447 fC[11] = (cv[8]-fC[4]*m23)/m43;
448 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
449 fC[5 ] = TMath::Abs((a4*a3-a6*a1)/(a5*a3-a6*a2));
450 fC[14] = TMath::Abs((a1-a2*fC[5])/a3);
451 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
452 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
453 Double_t b2=m23*m35;
454 Double_t b3=m43*m35;
455 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
456 Double_t b5=m24*m35;
457 Double_t b6=m44*m35;
458 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
459 fC[13] = b1/b3-b2*fC[8]/b3;
460 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
461 }
462 CheckCovariance();
463
464 return;
465}
da4e3deb 466
467//_____________________________________________________________________________
c9ec41e8 468void AliExternalTrackParam::Reset() {
1530f89c 469 //
470 // Resets all the parameters to 0
471 //
c9ec41e8 472 fX=fAlpha=0.;
473 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
474 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 475}
476
3775b0ca 477//_____________________________________________________________________________
478void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
479 //
480 // Add "something" to the track covarince matrix.
481 // May be needed to account for unknown mis-calibration/mis-alignment
482 //
483 fC[0] +=c[0];
484 fC[1] +=c[1]; fC[2] +=c[2];
485 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
486 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
487 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
86be8934 488 CheckCovariance();
3775b0ca 489}
490
491
c9ec41e8 492Double_t AliExternalTrackParam::GetP() const {
493 //---------------------------------------------------------------------
494 // This function returns the track momentum
495 // Results for (nearly) straight tracks are meaningless !
496 //---------------------------------------------------------------------
06fb4a2f 497 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 498 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 499}
500
1d99986f 501Double_t AliExternalTrackParam::Get1P() const {
502 //---------------------------------------------------------------------
503 // This function returns the 1/(track momentum)
504 //---------------------------------------------------------------------
505 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
506}
507
c9ec41e8 508//_______________________________________________________________________
c7bafca9 509Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 510 //------------------------------------------------------------------
511 // This function calculates the transverse impact parameter
512 // with respect to a point with global coordinates (x,y)
513 // in the magnetic field "b" (kG)
514 //------------------------------------------------------------------
5773defd 515 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 516 Double_t rp4=GetC(b);
c9ec41e8 517
518 Double_t xt=fX, yt=fP[0];
519
520 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
521 Double_t a = x*cs + y*sn;
522 y = -x*sn + y*cs; x=a;
523 xt-=x; yt-=y;
524
bfd20868 525 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2]));
526 a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
1530f89c 527 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
528}
529
530//_______________________________________________________________________
531void AliExternalTrackParam::
532GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
533 //------------------------------------------------------------------
534 // This function calculates the transverse and longitudinal impact parameters
535 // with respect to a point with global coordinates (x,y)
536 // in the magnetic field "b" (kG)
537 //------------------------------------------------------------------
bfd20868 538 Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1));
1530f89c 539 Double_t xt=fX, yt=fP[0];
540 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
541 Double_t a = x*cs + y*sn;
542 y = -x*sn + y*cs; x=a;
543 xt-=x; yt-=y;
544
545 Double_t rp4=GetC(b);
546 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
547 dz[0] = -(xt*f1 - yt*r1);
548 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
549 return;
550 }
551
552 sn=rp4*xt - f1; cs=rp4*yt + r1;
553 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
554 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
555 dz[0] = -a/(1 + rr);
bfd20868 556 Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2));
1530f89c 557 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 558}
559
49d13e89 560//_______________________________________________________________________
561Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
562 //------------------------------------------------------------------
563 // This function calculates the transverse impact parameter
564 // with respect to a point with global coordinates (xv,yv)
565 // neglecting the track curvature.
566 //------------------------------------------------------------------
567 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
568 Double_t x= xv*cs + yv*sn;
569 Double_t y=-xv*sn + yv*cs;
570
bfd20868 571 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
49d13e89 572
1530f89c 573 return -d;
49d13e89 574}
575
b8e07ed6 576Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx
577(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
578 Double_t dEdx,
579 Bool_t anglecorr) {
116b445b 580 //------------------------------------------------------------------
581 // This function corrects the track parameters for the crossed material.
582 // "xOverX0" - X/X0, the thickness in units of the radiation length.
2b99ff83 583 // "xTimesRho" - is the product length*density (g/cm^2).
584 // It should be passed as negative when propagating tracks
585 // from the intreaction point to the outside of the central barrel.
1d26da6d 586 // "mass" - the mass of this particle (GeV/c^2). Negative mass means charge=2 particle
b8e07ed6 587 // "dEdx" - mean enery loss (GeV/(g/cm^2)
588 // "anglecorr" - switch for the angular correction
116b445b 589 //------------------------------------------------------------------
590 Double_t &fP2=fP[2];
591 Double_t &fP3=fP[3];
592 Double_t &fP4=fP[4];
593
594 Double_t &fC22=fC[5];
595 Double_t &fC33=fC[9];
596 Double_t &fC43=fC[13];
597 Double_t &fC44=fC[14];
598
7dded1d5 599 //Apply angle correction, if requested
600 if(anglecorr) {
bfd20868 601 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
7dded1d5 602 xOverX0 *=angle;
603 xTimesRho *=angle;
604 }
605
116b445b 606 Double_t p=GetP();
1d26da6d 607 if (mass<0) p += p; // q=2 particle
116b445b 608 Double_t p2=p*p;
609 Double_t beta2=p2/(p2 + mass*mass);
116b445b 610
9f2bec63 611 //Calculating the multiple scattering corrections******************
612 Double_t cC22 = 0.;
613 Double_t cC33 = 0.;
614 Double_t cC43 = 0.;
615 Double_t cC44 = 0.;
116b445b 616 if (xOverX0 != 0) {
f2cef1b5 617 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
618 Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0);
619 if (GetUseLogTermMS()) {
620 double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0));
621 if (lt>0) theta2 *= lt*lt;
622 }
1d26da6d 623 if (mass<0) theta2 *= 4; // q=2 particle
f2cef1b5 624 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
625 cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3);
626 cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
627 cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
628 cC44 = theta2*fP3*fP4*fP3*fP4;
116b445b 629 }
630
9f2bec63 631 //Calculating the energy loss corrections************************
632 Double_t cP4=1.;
116b445b 633 if ((xTimesRho != 0.) && (beta2 < 1.)) {
b8e07ed6 634 Double_t dE=dEdx*xTimesRho;
116b445b 635 Double_t e=TMath::Sqrt(p2 + mass*mass);
636 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
76ece3d8 637 if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE;
c9038cae 638 cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben !
9f2bec63 639 if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
4b2fa3ce 640
116b445b 641
642 // Approximate energy loss fluctuation (M.Ivanov)
643 const Double_t knst=0.07; // To be tuned.
644 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
9f2bec63 645 cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
116b445b 646
647 }
648
9f2bec63 649 //Applying the corrections*****************************
650 fC22 += cC22;
651 fC33 += cC33;
652 fC43 += cC43;
653 fC44 += cC44;
654 fP4 *= cP4;
655
86be8934 656 CheckCovariance();
657
116b445b 658 return kTRUE;
659}
660
b8e07ed6 661Bool_t AliExternalTrackParam::CorrectForMeanMaterial
662(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
663 Bool_t anglecorr,
664 Double_t (*Bethe)(Double_t)) {
665 //------------------------------------------------------------------
666 // This function corrects the track parameters for the crossed material.
667 // "xOverX0" - X/X0, the thickness in units of the radiation length.
668 // "xTimesRho" - is the product length*density (g/cm^2).
2b99ff83 669 // It should be passed as negative when propagating tracks
670 // from the intreaction point to the outside of the central barrel.
1d26da6d 671 // "mass" - the mass of this particle (GeV/c^2). mass<0 means charge=2
b8e07ed6 672 // "anglecorr" - switch for the angular correction
673 // "Bethe" - function calculating the energy loss (GeV/(g/cm^2))
674 //------------------------------------------------------------------
37486ceb 675
b8e07ed6 676 Double_t bg=GetP()/mass;
1d26da6d 677 if (mass<0) {
678 if (mass<-990) {
d4da4017 679 AliDebug(2,Form("Mass %f corresponds to unknown PID particle",mass));
1d26da6d 680 return kFALSE;
681 }
682 bg = -2*bg;
937a4c16 683 }
b8e07ed6 684 Double_t dEdx=Bethe(bg);
1d26da6d 685 if (mass<0) dEdx *= 4;
b8e07ed6 686
687 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
688}
689
690Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA
691(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
692 Double_t zOverA,
693 Double_t density,
694 Double_t exEnergy,
695 Double_t jp1,
696 Double_t jp2,
697 Bool_t anglecorr) {
698 //------------------------------------------------------------------
699 // This function corrects the track parameters for the crossed material
700 // using the full Geant-like Bethe-Bloch formula parameterization
701 // "xOverX0" - X/X0, the thickness in units of the radiation length.
702 // "xTimesRho" - is the product length*density (g/cm^2).
2b99ff83 703 // It should be passed as negative when propagating tracks
704 // from the intreaction point to the outside of the central barrel.
1d26da6d 705 // "mass" - the mass of this particle (GeV/c^2). mass<0 means charge=2 particle
b8e07ed6 706 // "density" - mean density (g/cm^3)
707 // "zOverA" - mean Z/A
708 // "exEnergy" - mean exitation energy (GeV)
709 // "jp1" - density effect first junction point
710 // "jp2" - density effect second junction point
711 // "anglecorr" - switch for the angular correction
712 //
713 // The default values of the parameters are for silicon
714 //
715 //------------------------------------------------------------------
716
717 Double_t bg=GetP()/mass;
1d26da6d 718 if (mass<0) {
719 if (mass<-990) {
86a725e3 720 AliDebug(2,Form("Mass %f corresponds to unknown PID particle",mass));
1d26da6d 721 return kFALSE;
722 }
723 bg = -2*bg;
724 }
b8e07ed6 725 Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA);
726
1d26da6d 727 if (mass<0) dEdx *= 4;
b8e07ed6 728 return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
729}
730
731
116b445b 732
ee5dba5e 733Bool_t AliExternalTrackParam::CorrectForMaterial
734(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 735 //------------------------------------------------------------------
116b445b 736 // Deprecated function !
737 // Better use CorrectForMeanMaterial instead of it.
738 //
c7bafca9 739 // This function corrects the track parameters for the crossed material
740 // "d" - the thickness (fraction of the radiation length)
2b99ff83 741 // It should be passed as negative when propagating tracks
742 // from the intreaction point to the outside of the central barrel.
c7bafca9 743 // "x0" - the radiation length (g/cm^2)
744 // "mass" - the mass of this particle (GeV/c^2)
745 //------------------------------------------------------------------
c7bafca9 746
b8e07ed6 747 return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe);
c7bafca9 748
c7bafca9 749}
750
9c56b409 751Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
752 Double_t kp1,
753 Double_t kp2,
754 Double_t kp3,
755 Double_t kp4,
756 Double_t kp5) {
757 //
758 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
759 // It is normalized to 1 at the minimum.
760 //
761 // bg - beta*gamma
762 //
763 // The default values for the kp* parameters are for ALICE TPC.
764 // The returned value is in MIP units
765 //
766
767 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
768
769 Double_t aa = TMath::Power(beta,kp4);
770 Double_t bb = TMath::Power(1./bg,kp5);
771
772 bb=TMath::Log(kp3+bb);
773
774 return (kp2-aa-bb)*kp1/aa;
775}
776
777Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
778 Double_t kp0,
779 Double_t kp1,
780 Double_t kp2,
781 Double_t kp3,
782 Double_t kp4) {
783 //
784 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
785 //
786 // bg - beta*gamma
787 // kp0 - density [g/cm^3]
788 // kp1 - density effect first junction point
789 // kp2 - density effect second junction point
790 // kp3 - mean excitation energy [GeV]
791 // kp4 - mean Z/A
792 //
793 // The default values for the kp* parameters are for silicon.
794 // The returned value is in [GeV/(g/cm^2)].
795 //
796
797 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
798 const Double_t me = 0.511e-3; // [GeV/c^2]
799 const Double_t rho = kp0;
800 const Double_t x0 = kp1*2.303;
801 const Double_t x1 = kp2*2.303;
802 const Double_t mI = kp3;
803 const Double_t mZA = kp4;
804 const Double_t bg2 = bg*bg;
805 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
806
807 //*** Density effect
808 Double_t d2=0.;
809 const Double_t x=TMath::Log(bg);
810 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
811 if (x > x1) {
812 d2 = lhwI + x - 0.5;
813 } else if (x > x0) {
814 const Double_t r=(x1-x)/(x1-x0);
815 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
816 }
817
818 return mK*mZA*(1+bg2)/bg2*
819 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
820}
821
d46683db 822Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 823 //------------------------------------------------------------------
d46683db 824 // This is an approximation of the Bethe-Bloch formula,
825 // reasonable for solid materials.
826 // All the parameters are, in fact, for Si.
9b655cba 827 // The returned value is in [GeV/(g/cm^2)]
ee5dba5e 828 //------------------------------------------------------------------
a821848c 829
9c56b409 830 return BetheBlochGeant(bg);
d46683db 831}
ee5dba5e 832
d46683db 833Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
834 //------------------------------------------------------------------
835 // This is an approximation of the Bethe-Bloch formula,
836 // reasonable for gas materials.
837 // All the parameters are, in fact, for Ne.
9b655cba 838 // The returned value is in [GeV/(g/cm^2)]
d46683db 839 //------------------------------------------------------------------
840
841 const Double_t rho = 0.9e-3;
842 const Double_t x0 = 2.;
843 const Double_t x1 = 4.;
844 const Double_t mI = 140.e-9;
845 const Double_t mZA = 0.49555;
846
9c56b409 847 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 848}
849
49d13e89 850Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
851 //------------------------------------------------------------------
852 // Transform this track to the local coord. system rotated
853 // by angle "alpha" (rad) with respect to the global coord. system.
854 //------------------------------------------------------------------
dfcef74c 855 if (TMath::Abs(fP[2]) >= kAlmost1) {
856 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
857 return kFALSE;
858 }
859
49d13e89 860 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
861 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
862
863 Double_t &fP0=fP[0];
864 Double_t &fP2=fP[2];
865 Double_t &fC00=fC[0];
866 Double_t &fC10=fC[1];
867 Double_t &fC20=fC[3];
868 Double_t &fC21=fC[4];
869 Double_t &fC22=fC[5];
870 Double_t &fC30=fC[6];
871 Double_t &fC32=fC[8];
872 Double_t &fC40=fC[10];
873 Double_t &fC42=fC[12];
874
875 Double_t x=fX;
876 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
bfd20868 877 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
07dfd570 878 // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle
879 // direction in local frame is along the X axis
880 if ((cf*ca+sf*sa)<0) {
1450dc8a 881 AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa));
07dfd570 882 return kFALSE;
883 }
884 //
dfcef74c 885 Double_t tmp=sf*ca - cf*sa;
6e50abb1 886
7248cf51 887 if (TMath::Abs(tmp) >= kAlmost1) {
888 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
889 AliWarning(Form("Rotation failed ! %.10e",tmp));
0b69bbb2 890 return kFALSE;
891 }
49d13e89 892 fAlpha = alpha;
893 fX = x*ca + fP0*sa;
894 fP0= -x*sa + fP0*ca;
dfcef74c 895 fP2= tmp;
49d13e89 896
06fb4a2f 897 if (TMath::Abs(cf)<kAlmost0) {
898 AliError(Form("Too small cosine value %f",cf));
899 cf = kAlmost0;
900 }
901
49d13e89 902 Double_t rr=(ca+sf/cf*sa);
903
904 fC00 *= (ca*ca);
905 fC10 *= ca;
906 fC20 *= ca*rr;
907 fC21 *= rr;
908 fC22 *= rr*rr;
909 fC30 *= ca;
910 fC32 *= rr;
911 fC40 *= ca;
912 fC42 *= rr;
913
86be8934 914 CheckCovariance();
915
49d13e89 916 return kTRUE;
917}
918
a251382e 919//______________________________________________________
920Bool_t AliExternalTrackParam::RotateParamOnly(Double_t alpha)
921{
922 // rotate to new frame, ignore covariance
923 if (TMath::Abs(fP[2]) >= kAlmost1) {
924 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
925 return kFALSE;
926 }
927 //
928 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
929 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
930 //
931 Double_t &fP0=fP[0];
932 Double_t &fP2=fP[2];
933 //
934 Double_t x=fX;
935 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
936 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
937 // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle
938 // direction in local frame is along the X axis
939 if ((cf*ca+sf*sa)<0) {
940 AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa));
941 return kFALSE;
942 }
943 //
944 Double_t tmp=sf*ca - cf*sa;
945
946 if (TMath::Abs(tmp) >= kAlmost1) {
947 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
948 AliWarning(Form("Rotation failed ! %.10e",tmp));
949 return kFALSE;
950 }
951 fAlpha = alpha;
952 fX = x*ca + fP0*sa;
953 fP0= -x*sa + fP0*ca;
954 fP2= tmp;
955 return kTRUE;
956}
957
2d2fd909 958Bool_t AliExternalTrackParam::Invert() {
959 //------------------------------------------------------------------
960 // Transform this track to the local coord. system rotated by 180 deg.
961 //------------------------------------------------------------------
962 fX = -fX;
963 fAlpha += TMath::Pi();
964 while (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
965 while (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
966 //
967 fP[0] = -fP[0];
6e50abb1 968 //fP[2] = -fP[2];
2d2fd909 969 fP[3] = -fP[3];
970 fP[4] = -fP[4];
971 //
6e50abb1 972 fC[1] = -fC[1]; // since the fP1 and fP2 are not inverted, their covariances with others change sign
973 fC[3] = -fC[3];
2d2fd909 974 fC[7] = -fC[7];
6e50abb1 975 fC[8] = -fC[8];
2d2fd909 976 fC[11] = -fC[11];
6e50abb1 977 fC[12] = -fC[12];
2d2fd909 978 //
979 return kTRUE;
980}
981
49d13e89 982Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
983 //----------------------------------------------------------------
984 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
985 //----------------------------------------------------------------
49d13e89 986 Double_t dx=xk-fX;
e421f556 987 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 988
1530f89c 989 Double_t crv=GetC(b);
5773defd 990 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
991
2de63fc5 992 Double_t x2r = crv*dx;
993 Double_t f1=fP[2], f2=f1 + x2r;
bbefa4c4 994 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 995 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
4349f5a4 996 if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
49d13e89 997
998 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
999 Double_t
1000 &fC00=fC[0],
1001 &fC10=fC[1], &fC11=fC[2],
1002 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1003 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1004 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1005
bfd20868 1006 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
4349f5a4 1007 if (TMath::Abs(r1)<kAlmost0) return kFALSE;
1008 if (TMath::Abs(r2)<kAlmost0) return kFALSE;
49d13e89 1009
1010 fX=xk;
2de63fc5 1011 double dy2dx = (f1+f2)/(r1+r2);
1012 fP0 += dx*dy2dx;
0effb2c3 1013 fP2 += x2r;
1014 if (TMath::Abs(x2r)<0.05) fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov !
2de63fc5 1015 else {
1016 // for small dx/R the linear apporximation of the arc by the segment is OK,
1017 // but at large dx/R the error is very large and leads to incorrect Z propagation
1018 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
1019 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
0effb2c3 1020 // double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
1021 // double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
1022 // fP1 += rot/crv*fP3;
1023 //
1024 fP1 += fP3/crv*TMath::ASin(r1*f2 - r2*f1); // more economic version from Yura.
2de63fc5 1025 }
49d13e89 1026
1027 //f = F - 1
e804766b 1028 /*
49d13e89 1029 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
1030 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
1031 Double_t f12= dx*fP3*f1/(r1*r1*r1);
1032 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
1033 Double_t f13= dx/r1;
1034 Double_t f24= dx; f24*=cc;
e804766b 1035 */
1036 Double_t rinv = 1./r1;
1037 Double_t r3inv = rinv*rinv*rinv;
1038 Double_t f24= x2r/fP4;
1039 Double_t f02= dx*r3inv;
1040 Double_t f04=0.5*f24*f02;
1041 Double_t f12= f02*fP3*f1;
1042 Double_t f14=0.5*f24*f02*fP3*f1;
1043 Double_t f13= dx*rinv;
1044
49d13e89 1045 //b = C*ft
1046 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
1047 Double_t b02=f24*fC40;
1048 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
1049 Double_t b12=f24*fC41;
1050 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
1051 Double_t b22=f24*fC42;
1052 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
1053 Double_t b42=f24*fC44;
1054 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
1055 Double_t b32=f24*fC43;
1056
1057 //a = f*b = f*C*ft
1058 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
1059 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
1060 Double_t a22=f24*b42;
1061
1062 //F*C*Ft = C + (b + bt + a)
1063 fC00 += b00 + b00 + a00;
1064 fC10 += b10 + b01 + a01;
1065 fC20 += b20 + b02 + a02;
1066 fC30 += b30;
1067 fC40 += b40;
1068 fC11 += b11 + b11 + a11;
1069 fC21 += b21 + b12 + a12;
1070 fC31 += b31;
1071 fC41 += b41;
1072 fC22 += b22 + b22 + a22;
1073 fC32 += b32;
1074 fC42 += b42;
1075
86be8934 1076 CheckCovariance();
1077
49d13e89 1078 return kTRUE;
1079}
1080
599b440e 1081Bool_t AliExternalTrackParam::PropagateParamOnlyTo(Double_t xk, Double_t b) {
1082 //----------------------------------------------------------------
1083 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
1084 // Only parameters are propagated, not the matrix. To be used for small
1085 // distances only (<mm, i.e. misalignment)
1086 //----------------------------------------------------------------
1087 Double_t dx=xk-fX;
1088 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
1089
1090 Double_t crv=GetC(b);
1091 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1092
1093 Double_t x2r = crv*dx;
1094 Double_t f1=fP[2], f2=f1 + x2r;
1095 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1096 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1097 if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
1098
1099 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
1100 if (TMath::Abs(r1)<kAlmost0) return kFALSE;
1101 if (TMath::Abs(r2)<kAlmost0) return kFALSE;
1102
1103 fX=xk;
1104 double dy2dx = (f1+f2)/(r1+r2);
1105 fP[0] += dx*dy2dx;
1106 fP[1] += dx*(r2 + f2*dy2dx)*fP[3]; // Many thanks to P.Hristov !
1107 fP[2] += x2r;
1108
1109 return kTRUE;
1110}
1111
9f2bec63 1112Bool_t
1113AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
1114 //------------------------------------------------------------------
1115 // Transform this track to the local coord. system rotated
1116 // by angle "alpha" (rad) with respect to the global coord. system,
1117 // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
1118 //------------------------------------------------------------------
1119
1120 //Save the parameters
1121 Double_t as=fAlpha;
1122 Double_t xs=fX;
1123 Double_t ps[5], cs[15];
1124 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
1125 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
1126
1127 if (Rotate(alpha))
1128 if (PropagateTo(x,b)) return kTRUE;
1129
1130 //Restore the parameters, if the operation failed
1131 fAlpha=as;
1132 fX=xs;
1133 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
1134 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
1135 return kFALSE;
1136}
1137
266a0f9b 1138Bool_t AliExternalTrackParam::PropagateBxByBz
1139(Double_t alpha, Double_t x, Double_t b[3]) {
1140 //------------------------------------------------------------------
1141 // Transform this track to the local coord. system rotated
1142 // by angle "alpha" (rad) with respect to the global coord. system,
1143 // and propagate this track to the plane X=xk (cm),
1144 // taking into account all three components of the B field, "b[3]" (kG)
1145 //------------------------------------------------------------------
1146
1147 //Save the parameters
1148 Double_t as=fAlpha;
1149 Double_t xs=fX;
1150 Double_t ps[5], cs[15];
1151 for (Int_t i=0; i<5; i++) ps[i]=fP[i];
1152 for (Int_t i=0; i<15; i++) cs[i]=fC[i];
1153
1154 if (Rotate(alpha))
1155 if (PropagateToBxByBz(x,b)) return kTRUE;
1156
1157 //Restore the parameters, if the operation failed
1158 fAlpha=as;
1159 fX=xs;
1160 for (Int_t i=0; i<5; i++) fP[i]=ps[i];
1161 for (Int_t i=0; i<15; i++) fC[i]=cs[i];
1162 return kFALSE;
1163}
1164
9f2bec63 1165
052daaff 1166void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
1167Double_t p[3], Double_t bz) const {
1168 //+++++++++++++++++++++++++++++++++++++++++
1169 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
1170 // Extrapolate track along simple helix in magnetic field
1171 // Arguments: len -distance alogn helix, [cm]
1172 // bz - mag field, [kGaus]
1173 // Returns: x and p contain extrapolated positon and momentum
1174 // The momentum returned for straight-line tracks is meaningless !
1175 //+++++++++++++++++++++++++++++++++++++++++
1176 GetXYZ(x);
1177
2258e165 1178 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 1179 Double_t unit[3]; GetDirection(unit);
1180 x[0]+=unit[0]*len;
1181 x[1]+=unit[1]*len;
1182 x[2]+=unit[2]*len;
1183
1184 p[0]=unit[0]/kAlmost0;
1185 p[1]=unit[1]/kAlmost0;
1186 p[2]=unit[2]/kAlmost0;
1187 } else {
1188 GetPxPyPz(p);
1189 Double_t pp=GetP();
1190 Double_t a = -kB2C*bz*GetSign();
1191 Double_t rho = a/pp;
1192 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
1193 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
1194 x[2] += p[2]*len/pp;
1195
1196 Double_t p0=p[0];
1197 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
1198 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
1199 }
1200}
1201
1202Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
1203Double_t bz) const {
1204 //+++++++++++++++++++++++++++++++++++++++++
1205 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
1206 // Finds point of intersection (if exists) of the helix with the plane.
1207 // Stores result in fX and fP.
1208 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
1209 // and vector, normal to the plane
1210 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
1211 //+++++++++++++++++++++++++++++++++++++++++
1212 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
1213
1214 //estimates initial helix length up to plane
1215 Double_t s=
1216 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
1217 Double_t dist=99999,distPrev=dist;
1218 Double_t x[3],p[3];
1219 while(TMath::Abs(dist)>0.00001){
1220 //calculates helix at the distance s from x0 ALONG the helix
1221 Propagate(s,x,p,bz);
1222
1223 //distance between current helix position and plane
1224 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
1225
1226 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
1227 distPrev=dist;
1228 s-=dist;
1229 }
1230 //on exit pnt is intersection point,norm is track vector at that point,
1231 //all in MARS
1232 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
1233 return kTRUE;
1234}
1235
49d13e89 1236Double_t
6b1e75b2 1237AliExternalTrackParam::GetPredictedChi2(const Double_t p[2],const Double_t cov[3]) const {
49d13e89 1238 //----------------------------------------------------------------
1239 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
1240 //----------------------------------------------------------------
1241 Double_t sdd = fC[0] + cov[0];
1242 Double_t sdz = fC[1] + cov[1];
1243 Double_t szz = fC[2] + cov[2];
1244 Double_t det = sdd*szz - sdz*sdz;
1245
1246 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
1247
1248 Double_t d = fP[0] - p[0];
1249 Double_t z = fP[1] - p[1];
1250
1251 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
1252}
1253
4b189f98 1254Double_t AliExternalTrackParam::
6b1e75b2 1255GetPredictedChi2(const Double_t p[3],const Double_t covyz[3],const Double_t covxyz[3]) const {
4b189f98 1256 //----------------------------------------------------------------
1257 // Estimate the chi2 of the 3D space point "p" and
1e023a36 1258 // the full covariance matrix "covyz" and "covxyz"
4b189f98 1259 //
1260 // Cov(x,x) ... : covxyz[0]
1261 // Cov(y,x) ... : covxyz[1] covyz[0]
1262 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
1263 //----------------------------------------------------------------
1264
1265 Double_t res[3] = {
1266 GetX() - p[0],
1267 GetY() - p[1],
1268 GetZ() - p[2]
1269 };
1270
1271 Double_t f=GetSnp();
1272 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
bfd20868 1273 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
4b189f98 1274 Double_t a=f/r, b=GetTgl()/r;
1275
1276 Double_t s2=333.*333.; //something reasonably big (cm^2)
1277
1278 TMatrixDSym v(3);
1279 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
1280 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
1281 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
1282
1283 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
1284 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
1285 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
1286
1287 v.Invert();
1288 if (!v.IsValid()) return kVeryBig;
1289
1290 Double_t chi2=0.;
1291 for (Int_t i = 0; i < 3; i++)
1292 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
1293
1294 return chi2;
acdfbc78 1295}
1296
1297Double_t AliExternalTrackParam::
1298GetPredictedChi2(const AliExternalTrackParam *t) const {
1299 //----------------------------------------------------------------
1300 // Estimate the chi2 (5 dof) of this track with respect to the track
1301 // given by the argument.
1302 // The two tracks must be in the same reference system
1303 // and estimated at the same reference plane.
1304 //----------------------------------------------------------------
1305
95972410 1306 if (TMath::Abs(t->GetAlpha()-GetAlpha()) > FLT_EPSILON) {
acdfbc78 1307 AliError("The reference systems of the tracks differ !");
1308 return kVeryBig;
1309 }
8a3b848d 1310 if (TMath::Abs(t->GetX()-GetX()) > FLT_EPSILON) {
acdfbc78 1311 AliError("The reference of the tracks planes differ !");
1312 return kVeryBig;
1313 }
1314
1315 TMatrixDSym c(5);
1316 c(0,0)=GetSigmaY2();
1317 c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
1318 c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
1319 c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
1320 c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
1321
1322 c(0,0)+=t->GetSigmaY2();
1323 c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
1324 c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
1325 c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
1326 c(4,0)+=t->GetSigma1PtY();c(4,1)+=t->GetSigma1PtZ();c(4,2)+=t->GetSigma1PtSnp();c(4,3)+=t->GetSigma1PtTgl();c(4,4)+=t->GetSigma1Pt2();
1327 c(0,1)=c(1,0);
1328 c(0,2)=c(2,0); c(1,2)=c(2,1);
1329 c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
1330 c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
1331
1332 c.Invert();
1333 if (!c.IsValid()) return kVeryBig;
1334
1335
1336 Double_t res[5] = {
1337 GetY() - t->GetY(),
1338 GetZ() - t->GetZ(),
1339 GetSnp() - t->GetSnp(),
1340 GetTgl() - t->GetTgl(),
1341 GetSigned1Pt() - t->GetSigned1Pt()
1342 };
4b189f98 1343
acdfbc78 1344 Double_t chi2=0.;
1345 for (Int_t i = 0; i < 5; i++)
1346 for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
4b189f98 1347
acdfbc78 1348 return chi2;
4b189f98 1349}
1350
1e023a36 1351Bool_t AliExternalTrackParam::
1352PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
1353 //----------------------------------------------------------------
1354 // Propagate this track to the plane
1355 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
1356 // belongs to.
1357 // The magnetic field is "bz" (kG)
1358 //
1359 // The track curvature and the change of the covariance matrix
1360 // of the track parameters are negleted !
1361 // (So the "step" should be small compared with 1/curvature)
1362 //----------------------------------------------------------------
1363
1364 Double_t f=GetSnp();
1365 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
bfd20868 1366 Double_t r=TMath::Sqrt((1.-f)*(1.+f));
1e023a36 1367 Double_t a=f/r, b=GetTgl()/r;
1368
1369 Double_t s2=333.*333.; //something reasonably big (cm^2)
1370
1371 TMatrixDSym tV(3);
1372 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
1373 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
1374 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
1375
1376 TMatrixDSym pV(3);
1377 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
1378 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
1379 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
1380
1381 TMatrixDSym tpV(tV);
1382 tpV+=pV;
1383 tpV.Invert();
1384 if (!tpV.IsValid()) return kFALSE;
1385
1386 TMatrixDSym pW(3),tW(3);
1387 for (Int_t i=0; i<3; i++)
1388 for (Int_t j=0; j<3; j++) {
1389 pW(i,j)=tW(i,j)=0.;
1390 for (Int_t k=0; k<3; k++) {
1391 pW(i,j) += tV(i,k)*tpV(k,j);
1392 tW(i,j) += pV(i,k)*tpV(k,j);
1393 }
1394 }
1395
1396 Double_t t[3] = {GetX(), GetY(), GetZ()};
1397
1398 Double_t x=0.;
1399 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
1400 Double_t crv=GetC(bz);
1401 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1402 f += crv*(x-fX);
1403 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
1404 fX=x;
1405
1406 fP[0]=0.;
1407 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
1408 fP[1]=0.;
1409 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
1410
1411 return kTRUE;
1412}
1413
e23a38cb 1414Double_t *AliExternalTrackParam::GetResiduals(
1415Double_t *p,Double_t *cov,Bool_t updated) const {
1416 //------------------------------------------------------------------
1417 // Returns the track residuals with the space point "p" having
1418 // the covariance matrix "cov".
1419 // If "updated" is kTRUE, the track parameters expected to be updated,
1420 // otherwise they must be predicted.
1421 //------------------------------------------------------------------
1422 static Double_t res[2];
1423
1424 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1425 if (updated) {
1426 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
1427 } else {
1428 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
1429 }
1430 Double_t det=r00*r11 - r01*r01;
1431
1432 if (TMath::Abs(det) < kAlmost0) return 0;
1433
1434 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 1435
1436 if (r00 < 0.) return 0;
1437 if (r11 < 0.) return 0;
1438
e23a38cb 1439 Double_t dy = fP[0] - p[0];
1440 Double_t dz = fP[1] - p[1];
1441
1442 res[0]=dy*TMath::Sqrt(r00);
1443 res[1]=dz*TMath::Sqrt(r11);
1444
1445 return res;
1446}
1447
6b1e75b2 1448Bool_t AliExternalTrackParam::Update(const Double_t p[2], const Double_t cov[3]) {
49d13e89 1449 //------------------------------------------------------------------
1450 // Update the track parameters with the space point "p" having
1451 // the covariance matrix "cov"
1452 //------------------------------------------------------------------
1453 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
1454 Double_t
1455 &fC00=fC[0],
1456 &fC10=fC[1], &fC11=fC[2],
1457 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
1458 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
1459 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
1460
1461 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
1462 r00+=fC00; r01+=fC10; r11+=fC11;
1463 Double_t det=r00*r11 - r01*r01;
1464
1465 if (TMath::Abs(det) < kAlmost0) return kFALSE;
1466
1467
1468 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
1469
1470 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
1471 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
1472 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
1473 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
1474 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
1475
1476 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
1477 Double_t sf=fP2 + k20*dy + k21*dz;
1478 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
1479
1480 fP0 += k00*dy + k01*dz;
1481 fP1 += k10*dy + k11*dz;
1482 fP2 = sf;
1483 fP3 += k30*dy + k31*dz;
1484 fP4 += k40*dy + k41*dz;
1485
1486 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
1487 Double_t c12=fC21, c13=fC31, c14=fC41;
1488
1489 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
1490 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
1491 fC40-=k00*c04+k01*c14;
1492
1493 fC11-=k10*c01+k11*fC11;
1494 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
1495 fC41-=k10*c04+k11*c14;
1496
1497 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
1498 fC42-=k20*c04+k21*c14;
1499
1500 fC33-=k30*c03+k31*c13;
1501 fC43-=k30*c04+k31*c14;
599b440e 1502
49d13e89 1503 fC44-=k40*c04+k41*c14;
1504
86be8934 1505 CheckCovariance();
1506
49d13e89 1507 return kTRUE;
1508}
1509
c7bafca9 1510void
1511AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
1512 //--------------------------------------------------------------------
1513 // External track parameters -> helix parameters
1514 // "b" - magnetic field (kG)
1515 //--------------------------------------------------------------------
1516 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1517
1530f89c 1518 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 1519
1520 hlx[5]=fX*cs - hlx[0]*sn; // x0
1521 hlx[0]=fX*sn + hlx[0]*cs; // y0
1522//hlx[1]= // z0
1523 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
1524//hlx[3]= // tgl
1530f89c 1525 hlx[4]=GetC(b); // C
c7bafca9 1526}
1527
1528
1529static void Evaluate(const Double_t *h, Double_t t,
1530 Double_t r[3], //radius vector
1531 Double_t g[3], //first defivatives
1532 Double_t gg[3]) //second derivatives
1533{
1534 //--------------------------------------------------------------------
1535 // Calculate position of a point on a track and some derivatives
1536 //--------------------------------------------------------------------
1537 Double_t phase=h[4]*t+h[2];
1538 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
1539
ba4550c4 1540 r[0] = h[5];
1541 r[1] = h[0];
1542 if (TMath::Abs(h[4])>kAlmost0) {
1543 r[0] += (sn - h[6])/h[4];
1544 r[1] -= (cs - h[7])/h[4];
1545 }
c7bafca9 1546 r[2] = h[1] + h[3]*t;
1547
1548 g[0] = cs; g[1]=sn; g[2]=h[3];
1549
1550 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
1551}
1552
1553Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1554Double_t b, Double_t &xthis, Double_t &xp) const {
1555 //------------------------------------------------------------
1556 // Returns the (weighed !) distance of closest approach between
1557 // this track and the track "p".
1558 // Other returned values:
1559 // xthis, xt - coordinates of tracks' reference planes at the DCA
1560 //-----------------------------------------------------------
1561 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1562 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1563 Double_t dx2=dy2;
1564
c7bafca9 1565 Double_t p1[8]; GetHelixParameters(p1,b);
1566 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1567 Double_t p2[8]; p->GetHelixParameters(p2,b);
1568 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1569
1570
1571 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1572 Evaluate(p1,t1,r1,g1,gg1);
1573 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1574 Evaluate(p2,t2,r2,g2,gg2);
1575
1576 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1577 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1578
1579 Int_t max=27;
1580 while (max--) {
1581 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1582 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1583 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1584 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1585 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1586 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1587 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1588 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1589 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1590
1591 Double_t det=h11*h22-h12*h12;
1592
1593 Double_t dt1,dt2;
1594 if (TMath::Abs(det)<1.e-33) {
1595 //(quasi)singular Hessian
1596 dt1=-gt1; dt2=-gt2;
1597 } else {
1598 dt1=-(gt1*h22 - gt2*h12)/det;
1599 dt2=-(h11*gt2 - h12*gt1)/det;
1600 }
1601
1602 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1603
1604 //check delta(phase1) ?
1605 //check delta(phase2) ?
1606
1607 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1608 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1609 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1610 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1611 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1612 if (lmb < 0.)
358f16ae 1613 AliDebug(1," stopped at not a minimum !");
c7bafca9 1614 break;
1615 }
1616
1617 Double_t dd=dm;
1618 for (Int_t div=1 ; ; div*=2) {
1619 Evaluate(p1,t1+dt1,r1,g1,gg1);
1620 Evaluate(p2,t2+dt2,r2,g2,gg2);
1621 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1622 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1623 if (dd<dm) break;
1624 dt1*=0.5; dt2*=0.5;
1625 if (div>512) {
358f16ae 1626 AliDebug(1," overshoot !"); break;
c7bafca9 1627 }
1628 }
1629 dm=dd;
1630
1631 t1+=dt1;
1632 t2+=dt2;
1633
1634 }
1635
358f16ae 1636 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1637
1638 Double_t cs=TMath::Cos(GetAlpha());
1639 Double_t sn=TMath::Sin(GetAlpha());
1640 xthis=r1[0]*cs + r1[1]*sn;
1641
1642 cs=TMath::Cos(p->GetAlpha());
1643 sn=TMath::Sin(p->GetAlpha());
1644 xp=r2[0]*cs + r2[1]*sn;
1645
1646 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1647}
1648
1649Double_t AliExternalTrackParam::
1650PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1651 //--------------------------------------------------------------
1652 // Propagates this track and the argument track to the position of the
1653 // distance of closest approach.
1654 // Returns the (weighed !) distance of closest approach.
1655 //--------------------------------------------------------------
1656 Double_t xthis,xp;
1657 Double_t dca=GetDCA(p,b,xthis,xp);
1658
1659 if (!PropagateTo(xthis,b)) {
1660 //AliWarning(" propagation failed !");
1661 return 1e+33;
1662 }
1663
1664 if (!p->PropagateTo(xp,b)) {
1665 //AliWarning(" propagation failed !";
1666 return 1e+33;
1667 }
1668
1669 return dca;
1670}
1671
1672
58e536c5 1673Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1674Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1675 //
e99a34df 1676 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1677 // if the (rough) transverse impact parameter is not bigger then "maxd".
1678 // Magnetic field is "b" (kG).
1679 //
1680 // a) The track gets extapolated to the DCA to the vertex.
1681 // b) The impact parameters and their covariance matrix are calculated.
1682 //
1683 // In the case of success, the returned value is kTRUE
1684 // (otherwise, it's kFALSE)
1685 //
1686 Double_t alpha=GetAlpha();
1687 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1688 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1689 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1690 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1691 x-=xv; y-=yv;
1692
1693 //Estimate the impact parameter neglecting the track curvature
bfd20868 1694 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
f76701bf 1695 if (d > maxd) return kFALSE;
1696
1697 //Propagate to the DCA
2258e165 1698 Double_t crv=GetC(b);
e99a34df 1699 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1700
bfd20868 1701 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1702 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
e99a34df 1703 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1704 else cs=1.;
f76701bf 1705
1706 x = xv*cs + yv*sn;
1707 yv=-xv*sn + yv*cs; xv=x;
1708
1709 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
266a0f9b 1710
1711 if (dz==0) return kTRUE;
1712 dz[0] = GetParameter()[0] - yv;
1713 dz[1] = GetParameter()[1] - zv;
1714
1715 if (covar==0) return kTRUE;
1716 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
1717
1718 //***** Improvements by A.Dainese
1719 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1720 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1721 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1722 covar[1] = GetCovariance()[1]; // between (x,y) and z
1723 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1724 //*****
1725
1726 return kTRUE;
1727}
1728
1729Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
1730Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
1731 //
1732 // Propagate this track to the DCA to vertex "vtx",
1733 // if the (rough) transverse impact parameter is not bigger then "maxd".
1734 //
1735 // This function takes into account all three components of the magnetic
1736 // field given by the b[3] arument (kG)
1737 //
1738 // a) The track gets extapolated to the DCA to the vertex.
1739 // b) The impact parameters and their covariance matrix are calculated.
1740 //
1741 // In the case of success, the returned value is kTRUE
1742 // (otherwise, it's kFALSE)
1743 //
1744 Double_t alpha=GetAlpha();
1745 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1746 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
1747 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1748 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
1749 x-=xv; y-=yv;
1750
1751 //Estimate the impact parameter neglecting the track curvature
bfd20868 1752 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
266a0f9b 1753 if (d > maxd) return kFALSE;
1754
1755 //Propagate to the DCA
8567bf39 1756 Double_t crv=GetC(b[2]);
1757 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
266a0f9b 1758
bfd20868 1759 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
1760 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
266a0f9b 1761 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1762 else cs=1.;
1763
1764 x = xv*cs + yv*sn;
1765 yv=-xv*sn + yv*cs; xv=x;
1766
1767 if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1768
1769 if (dz==0) return kTRUE;
1770 dz[0] = GetParameter()[0] - yv;
1771 dz[1] = GetParameter()[1] - zv;
1772
1773 if (covar==0) return kTRUE;
58e536c5 1774 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1775
1776 //***** Improvements by A.Dainese
1777 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1778 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1779 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1780 covar[1] = GetCovariance()[1]; // between (x,y) and z
1781 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1782 //*****
1783
29fbcc93 1784 return kTRUE;
f76701bf 1785}
1786
b1149664 1787void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1788 //----------------------------------------------------------------
1789 // This function returns a unit vector along the track direction
1790 // in the global coordinate system.
1791 //----------------------------------------------------------------
1792 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1793 Double_t snp=fP[2];
bfd20868 1794 Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp));
b1149664 1795 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1796 d[0]=(csp*cs - snp*sn)/norm;
1797 d[1]=(snp*cs + csp*sn)/norm;
1798 d[2]=fP[3]/norm;
1799}
1800
c683ddc2 1801Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1802 //---------------------------------------------------------------------
1803 // This function returns the global track momentum components
1804 // Results for (nearly) straight tracks are meaningless !
1805 //---------------------------------------------------------------------
1806 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1807 return Local2GlobalMomentum(p,fAlpha);
1808}
a5e407e9 1809
def9660e 1810Double_t AliExternalTrackParam::Px() const {
957fb479 1811 //---------------------------------------------------------------------
1812 // Returns x-component of momentum
1813 // Result for (nearly) straight tracks is meaningless !
1814 //---------------------------------------------------------------------
def9660e 1815
957fb479 1816 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1817 GetPxPyPz(p);
1818
1819 return p[0];
1820}
1821
1822Double_t AliExternalTrackParam::Py() const {
957fb479 1823 //---------------------------------------------------------------------
1824 // Returns y-component of momentum
1825 // Result for (nearly) straight tracks is meaningless !
1826 //---------------------------------------------------------------------
def9660e 1827
957fb479 1828 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1829 GetPxPyPz(p);
1830
1831 return p[1];
1832}
1833
c683ddc2 1834Double_t AliExternalTrackParam::Xv() const {
1835 //---------------------------------------------------------------------
1836 // Returns x-component of first track point
1837 //---------------------------------------------------------------------
1838
1839 Double_t r[3]={0.,0.,0.};
1840 GetXYZ(r);
1841
1842 return r[0];
1843}
1844
1845Double_t AliExternalTrackParam::Yv() const {
1846 //---------------------------------------------------------------------
1847 // Returns y-component of first track point
1848 //---------------------------------------------------------------------
1849
1850 Double_t r[3]={0.,0.,0.};
1851 GetXYZ(r);
1852
1853 return r[1];
1854}
1855
def9660e 1856Double_t AliExternalTrackParam::Theta() const {
1857 // return theta angle of momentum
1858
7cdd0c20 1859 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1860}
1861
1862Double_t AliExternalTrackParam::Phi() const {
957fb479 1863 //---------------------------------------------------------------------
1864 // Returns the azimuthal angle of momentum
1865 // 0 <= phi < 2*pi
1866 //---------------------------------------------------------------------
def9660e 1867
957fb479 1868 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1869 if (phi<0.) phi+=2.*TMath::Pi();
1870 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1871
1872 return phi;
def9660e 1873}
1874
1875Double_t AliExternalTrackParam::M() const {
1876 // return particle mass
1877
1878 // No mass information available so far.
1879 // Redifine in derived class!
1880
1881 return -999.;
1882}
1883
1884Double_t AliExternalTrackParam::E() const {
1885 // return particle energy
1886
1887 // No PID information available so far.
1888 // Redifine in derived class!
1889
1890 return -999.;
1891}
1892
1893Double_t AliExternalTrackParam::Eta() const {
1894 // return pseudorapidity
1895
1896 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1897}
1898
1899Double_t AliExternalTrackParam::Y() const {
1900 // return rapidity
1901
1902 // No PID information available so far.
1903 // Redifine in derived class!
1904
1905 return -999.;
1906}
1907
c9ec41e8 1908Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1909 //---------------------------------------------------------------------
1910 // This function returns the global track position
1911 //---------------------------------------------------------------------
1912 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1913 return Local2GlobalPosition(r,fAlpha);
51ad6848 1914}
1915
c9ec41e8 1916Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1917 //---------------------------------------------------------------------
1918 // This function returns the global covariance matrix of the track params
1919 //
1920 // Cov(x,x) ... : cv[0]
1921 // Cov(y,x) ... : cv[1] cv[2]
1922 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1923 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1924 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1925 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1926 //
c9ec41e8 1927 // Results for (nearly) straight tracks are meaningless !
1928 //---------------------------------------------------------------------
e421f556 1929 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1930 for (Int_t i=0; i<21; i++) cv[i]=0.;
1931 return kFALSE;
a5e407e9 1932 }
49d13e89 1933 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1934 for (Int_t i=0; i<21; i++) cv[i]=0.;
1935 return kFALSE;
1936 }
1937 Double_t pt=1./TMath::Abs(fP[4]);
1938 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1939 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1940
1941 Double_t m00=-sn, m10=cs;
1942 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1943 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1944 Double_t m35=pt, m45=-pt*pt*fP[3];
1945
854d5d49 1946 m43*=GetSign();
1947 m44*=GetSign();
1948 m45*=GetSign();
1949
c9ec41e8 1950 cv[0 ] = fC[0]*m00*m00;
1951 cv[1 ] = fC[0]*m00*m10;
1952 cv[2 ] = fC[0]*m10*m10;
1953 cv[3 ] = fC[1]*m00;
1954 cv[4 ] = fC[1]*m10;
1955 cv[5 ] = fC[2];
1956 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1957 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1958 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1959 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1960 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1961 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1962 cv[12] = fC[4]*m24 + fC[11]*m44;
1963 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1964 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1965 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1966 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1967 cv[17] = fC[7]*m35 + fC[11]*m45;
1968 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1969 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1970 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1971
c9ec41e8 1972 return kTRUE;
51ad6848 1973}
1974
51ad6848 1975
c9ec41e8 1976Bool_t
1977AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1978 //---------------------------------------------------------------------
1979 // This function returns the global track momentum extrapolated to
1980 // the radial position "x" (cm) in the magnetic field "b" (kG)
1981 //---------------------------------------------------------------------
c9ec41e8 1982 p[0]=fP[4];
1530f89c 1983 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1984 p[2]=fP[3];
1985 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1986}
1987
c9ec41e8 1988Bool_t
7cf7bb6c 1989AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1990 //---------------------------------------------------------------------
1991 // This function returns the local Y-coordinate of the intersection
1992 // point between this track and the reference plane "x" (cm).
1993 // Magnetic field "b" (kG)
1994 //---------------------------------------------------------------------
1995 Double_t dx=x-fX;
1996 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1997
1530f89c 1998 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1999
2000 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
2001 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
2002
60e55aee 2003 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
7cf7bb6c 2004 y = fP[0] + dx*(f1+f2)/(r1+r2);
2005 return kTRUE;
2006}
2007
2008Bool_t
6c94f330 2009AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
2010 //---------------------------------------------------------------------
2011 // This function returns the local Z-coordinate of the intersection
2012 // point between this track and the reference plane "x" (cm).
2013 // Magnetic field "b" (kG)
2014 //---------------------------------------------------------------------
2015 Double_t dx=x-fX;
2016 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
2017
71cec41f 2018 Double_t crv=GetC(b);
2019 Double_t x2r = crv*dx;
2020 Double_t f1=fP[2], f2=f1 + x2r;
6c94f330 2021
2022 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
2023 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
2024
60e55aee 2025 Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
71cec41f 2026 double dy2dx = (f1+f2)/(r1+r2);
2027 if (TMath::Abs(x2r)<0.05) {
2028 z = fP[1] + dx*(r2 + f2*dy2dx)*fP[3]; // Many thanks to P.Hristov !
2029 }
2030 else {
2031 // for small dx/R the linear apporximation of the arc by the segment is OK,
2032 // but at large dx/R the error is very large and leads to incorrect Z propagation
2033 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
2034 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
2035 // Similarly, the rotation angle in linear in dx only for dx<<R
2036 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
2037 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
2038 z = fP[1] + rot/crv*fP[3];
2039 }
6c94f330 2040 return kTRUE;
2041}
2042
2043Bool_t
c9ec41e8 2044AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
2045 //---------------------------------------------------------------------
2046 // This function returns the global track position extrapolated to
2047 // the radial position "x" (cm) in the magnetic field "b" (kG)
2048 //---------------------------------------------------------------------
c9ec41e8 2049 Double_t dx=x-fX;
e421f556 2050 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
2051
71cec41f 2052 Double_t crv=GetC(b);
2053 Double_t x2r = crv*dx;
2054 Double_t f1=fP[2], f2=f1 + dx*crv;
c9ec41e8 2055
e421f556 2056 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 2057 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 2058
60e55aee 2059 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
71cec41f 2060 double dy2dx = (f1+f2)/(r1+r2);
c9ec41e8 2061 r[0] = x;
71cec41f 2062 r[1] = fP[0] + dx*dy2dx;
2063 if (TMath::Abs(x2r)<0.05) {
2064 r[2] = fP[1] + dx*(r2 + f2*dy2dx)*fP[3];//Thanks to Andrea & Peter
2065 }
2066 else {
2067 // for small dx/R the linear apporximation of the arc by the segment is OK,
2068 // but at large dx/R the error is very large and leads to incorrect Z propagation
2069 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
2070 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
2071 // Similarly, the rotation angle in linear in dx only for dx<<R
2072 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
2073 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
2074 r[2] = fP[1] + rot/crv*fP[3];
2075 }
f90a11c9 2076
c9ec41e8 2077 return Local2GlobalPosition(r,fAlpha);
51ad6848 2078}
2079
edc97986 2080//_____________________________________________________________________________
51ad6848 2081void AliExternalTrackParam::Print(Option_t* /*option*/) const
2082{
2083// print the parameters and the covariance matrix
2084
2085 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
2086 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 2087 fP[0], fP[1], fP[2], fP[3], fP[4]);
2088 printf(" covariance: %12g\n", fC[0]);
2089 printf(" %12g %12g\n", fC[1], fC[2]);
2090 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 2091 printf(" %12g %12g %12g %12g\n",
c9ec41e8 2092 fC[6], fC[7], fC[8], fC[9]);
51ad6848 2093 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 2094 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 2095}
5b77d93c 2096
c194ba83 2097Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
2098 //
2099 // Get sinus at given x
2100 //
1530f89c 2101 Double_t crv=GetC(b);
c194ba83 2102 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
2103 Double_t dx = x-fX;
2104 Double_t res = fP[2]+dx*crv;
2105 return res;
2106}
bf00ebb8 2107
2108Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
2109 //------------------------------------------------------------------------
2110 // Get the distance between two tracks at the local position x
2111 // working in the local frame of this track.
2112 // Origin : Marian.Ivanov@cern.ch
2113 //-----------------------------------------------------------------------
2114 Double_t xyz[3];
2115 Double_t xyz2[3];
2116 xyz[0]=x;
2117 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
2118 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
2119 //
2120 //
2121 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
2122 xyz2[0]=x;
2123 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
2124 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
2125 }else{
2126 //
2127 Double_t xyz1[3];
2128 Double_t dfi = param2->GetAlpha()-GetAlpha();
2129 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
2130 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
2131 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
2132 //
2133 xyz1[0]=xyz2[0];
2134 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
2135 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
2136 //
2137 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
2138 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
2139 xyz2[2] = xyz1[2];
2140 }
2141 dist[0] = xyz[0]-xyz2[0];
2142 dist[1] = xyz[1]-xyz2[1];
2143 dist[2] = xyz[2]-xyz2[2];
2144
2145 return kTRUE;
2146}
0c19adf7 2147
2148
2149//
2150// Draw functionality.
2151// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
2152//
2153
2154void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
2155 //
2156 // Draw track line
2157 //
2158 if (minR>maxR) return ;
2159 if (stepR<=0) return ;
2160 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
2161 if (npoints<1) return;
2162 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
2163 FillPolymarker(polymarker, magf,minR,maxR,stepR);
2164 polymarker->Draw();
2165}
2166
2167//
2168void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
2169 //
2170 // Fill points in the polymarker
2171 //
2172 Int_t counter=0;
2173 for (Double_t r=minR; r<maxR; r+=stepR){
2174 Double_t point[3];
2175 GetXYZAt(r,magF,point);
2176 pol->SetPoint(counter,point[0],point[1], point[2]);
047640da 2177 // printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
0c19adf7 2178 counter++;
2179 }
2180}
0e8460af 2181
2182Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
2183 //
2184 Int_t min = TMath::Min(i,j);
2185 Int_t max = TMath::Max(i,j);
2186
2187 return min+(max+1)*max/2;
2188}
8b6e3369 2189
2190
2191void AliExternalTrackParam::g3helx3(Double_t qfield,
2192 Double_t step,
2193 Double_t vect[7]) {
2194/******************************************************************
2195 * *
2196 * GEANT3 tracking routine in a constant field oriented *
2197 * along axis 3 *
2198 * Tracking is performed with a conventional *
2199 * helix step method *
2200 * *
2201 * Authors R.Brun, M.Hansroul ********* *
2202 * Rewritten V.Perevoztchikov *
2203 * *
2204 * Rewritten in C++ by I.Belikov *
2205 * *
2206 * qfield (kG) - particle charge times magnetic field *
2207 * step (cm) - step length along the helix *
2208 * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
2209 * *
2210 ******************************************************************/
2211 const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
bfd20868 2212 const Double_t kOvSqSix=TMath::Sqrt(1./6.);
8b6e3369 2213
2214 Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
2215
2216 Double_t rho = qfield*kB2C/vect[ipp];
2217 Double_t tet = rho*step;
2218
2219 Double_t tsint, sintt, sint, cos1t;
2de63fc5 2220 if (TMath::Abs(tet) > 0.03) {
8b6e3369 2221 sint = TMath::Sin(tet);
2222 sintt = sint/tet;
2223 tsint = (tet - sint)/tet;
2224 Double_t t=TMath::Sin(0.5*tet);
2225 cos1t = 2*t*t/tet;
2226 } else {
2227 tsint = tet*tet/6.;
bfd20868 2228 sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint;
8b6e3369 2229 sint = tet*sintt;
2230 cos1t = 0.5*tet;
2231 }
2232
2233 Double_t f1 = step*sintt;
2234 Double_t f2 = step*cos1t;
2235 Double_t f3 = step*tsint*cosz;
2236 Double_t f4 = -tet*cos1t;
2237 Double_t f5 = sint;
2238
2239 vect[ix] += f1*cosx - f2*cosy;
2240 vect[iy] += f1*cosy + f2*cosx;
2241 vect[iz] += f1*cosz + f3;
2242
2243 vect[ipx] += f4*cosx - f5*cosy;
2244 vect[ipy] += f4*cosy + f5*cosx;
2245
2246}
2247
2248Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
2249 //----------------------------------------------------------------
2250 // Extrapolate this track to the plane X=xk in the field b[].
2251 //
2252 // X [cm] is in the "tracking coordinate system" of this track.
2253 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
2254 //----------------------------------------------------------------
2255
2256 Double_t dx=xk-fX;
2257 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
7e1b73dd 2258 if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
ef3508c5 2259 // Do not propagate tracks outside the ALICE detector
2260 if (TMath::Abs(dx)>1e5 ||
2261 TMath::Abs(GetY())>1e5 ||
2262 TMath::Abs(GetZ())>1e5) {
2263 AliWarning(Form("Anomalous track, target X:%f",xk));
2264 Print();
2265 return kFALSE;
2266 }
8b6e3369 2267
2268 Double_t crv=GetC(b[2]);
2269 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
2270
2de63fc5 2271 Double_t x2r = crv*dx;
2272 Double_t f1=fP[2], f2=f1 + x2r;
8b6e3369 2273 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
2274 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
2275
2276
2277 // Estimate the covariance matrix
2278 Double_t &fP3=fP[3], &fP4=fP[4];
2279 Double_t
2280 &fC00=fC[0],
2281 &fC10=fC[1], &fC11=fC[2],
2282 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
2283 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
2284 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
2285
bfd20868 2286 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
8b6e3369 2287
2288 //f = F - 1
e804766b 2289 /*
8b6e3369 2290 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
2291 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
2292 Double_t f12= dx*fP3*f1/(r1*r1*r1);
2293 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
2294 Double_t f13= dx/r1;
2295 Double_t f24= dx; f24*=cc;
e804766b 2296 */
2297 Double_t rinv = 1./r1;
2298 Double_t r3inv = rinv*rinv*rinv;
2299 Double_t f24= x2r/fP4;
2300 Double_t f02= dx*r3inv;
2301 Double_t f04=0.5*f24*f02;
2302 Double_t f12= f02*fP3*f1;
2303 Double_t f14=0.5*f24*f02*fP3*f1;
2304 Double_t f13= dx*rinv;
2305
8b6e3369 2306 //b = C*ft
2307 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
2308 Double_t b02=f24*fC40;
2309 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
2310 Double_t b12=f24*fC41;
2311 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
2312 Double_t b22=f24*fC42;
2313 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
2314 Double_t b42=f24*fC44;
2315 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
2316 Double_t b32=f24*fC43;
2317
2318 //a = f*b = f*C*ft
2319 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
2320 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
2321 Double_t a22=f24*b42;
2322
2323 //F*C*Ft = C + (b + bt + a)
2324 fC00 += b00 + b00 + a00;
2325 fC10 += b10 + b01 + a01;
2326 fC20 += b20 + b02 + a02;
2327 fC30 += b30;
2328 fC40 += b40;
2329 fC11 += b11 + b11 + a11;
2330 fC21 += b21 + b12 + a12;
2331 fC31 += b31;
2332 fC41 += b41;
2333 fC22 += b22 + b22 + a22;
2334 fC32 += b32;
2335 fC42 += b42;
2336
86be8934 2337 CheckCovariance();
8b6e3369 2338
2339 // Appoximate step length
2de63fc5 2340 double dy2dx = (f1+f2)/(r1+r2);
2341 Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord
2342 : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc
8b6e3369 2343 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
2344
8b6e3369 2345 // Get the track's (x,y,z) and (px,py,pz) in the Global System
2346 Double_t r[3]; GetXYZ(r);
2347 Double_t p[3]; GetPxPyPz(p);
2348 Double_t pp=GetP();
2349 p[0] /= pp;
2350 p[1] /= pp;
2351 p[2] /= pp;
2352
2353
2354 // Rotate to the system where Bx=By=0.
2355 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
2356 Double_t cosphi=1., sinphi=0.;
2357 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
2358 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
2359 Double_t costet=1., sintet=0.;
2360 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
2361 Double_t vect[7];
2362
2363 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
2364 vect[1] = -sinphi*r[0] + cosphi*r[1];
2365 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
2366
2367 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
2368 vect[4] = -sinphi*p[0] + cosphi*p[1];
2369 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
2370
2371 vect[6] = pp;
2372
2373
2374 // Do the helix step
2375 g3helx3(GetSign()*bb,step,vect);
2376
2377
2378 // Rotate back to the Global System
2379 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
2380 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
2381 r[2] = -sintet*vect[0] + costet*vect[2];
2382
2383 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
2384 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
2385 p[2] = -sintet*vect[3] + costet*vect[5];
2386
2387
2388 // Rotate back to the Tracking System
2389 Double_t cosalp = TMath::Cos(fAlpha);
2390 Double_t sinalp =-TMath::Sin(fAlpha);
2391
2392 Double_t
2393 t = cosalp*r[0] - sinalp*r[1];
2394 r[1] = sinalp*r[0] + cosalp*r[1];
2395 r[0] = t;
2396
2397 t = cosalp*p[0] - sinalp*p[1];
2398 p[1] = sinalp*p[0] + cosalp*p[1];
2399 p[0] = t;
2400
2401
2402 // Do the final correcting step to the target plane (linear approximation)
2403 Double_t x=r[0], y=r[1], z=r[2];
2404 if (TMath::Abs(dx) > kAlmost0) {
2405 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
2406 dx = xk - r[0];
2407 x += dx;
2408 y += p[1]/p[0]*dx;
2409 z += p[2]/p[0]*dx;
2410 }
2411
2412
2413 // Calculate the track parameters
2414 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
2415 fX = x;
2416 fP[0] = y;
2417 fP[1] = z;
2418 fP[2] = p[1]/t;
2419 fP[3] = p[2]/t;
2420 fP[4] = GetSign()/(t*pp);
2421
2422 return kTRUE;
2423}
2424
e0302afb 2425Bool_t AliExternalTrackParam::PropagateParamOnlyBxByBzTo(Double_t xk, const Double_t b[3]) {
2426 //----------------------------------------------------------------
2427 // Extrapolate this track params (w/o cov matrix) to the plane X=xk in the field b[].
2428 //
2429 // X [cm] is in the "tracking coordinate system" of this track.
2430 // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
2431 //----------------------------------------------------------------
2432
2433 Double_t dx=xk-fX;
2434 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
2435 if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
2436 // Do not propagate tracks outside the ALICE detector
2437 if (TMath::Abs(dx)>1e5 ||
2438 TMath::Abs(GetY())>1e5 ||
2439 TMath::Abs(GetZ())>1e5) {
2440 AliWarning(Form("Anomalous track, target X:%f",xk));
2441 Print();
2442 return kFALSE;
2443 }
2444
2445 Double_t crv=GetC(b[2]);
2446 if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
2447
2448 Double_t x2r = crv*dx;
2449 Double_t f1=fP[2], f2=f1 + x2r;
2450 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
2451 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
2452 //
2453 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
2454 //
2455 // Appoximate step length
2456 double dy2dx = (f1+f2)/(r1+r2);
2457 Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord
2458 : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc
2459 step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
2460
2461 // Get the track's (x,y,z) and (px,py,pz) in the Global System
2462 Double_t r[3]; GetXYZ(r);
2463 Double_t p[3]; GetPxPyPz(p);
2464 Double_t pp=GetP();
2465 p[0] /= pp;
2466 p[1] /= pp;
2467 p[2] /= pp;
2468
2469 // Rotate to the system where Bx=By=0.
2470 Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
2471 Double_t cosphi=1., sinphi=0.;
2472 if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
2473 Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
2474 Double_t costet=1., sintet=0.;
2475 if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
2476 Double_t vect[7];
2477
2478 vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
2479 vect[1] = -sinphi*r[0] + cosphi*r[1];
2480 vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
2481
2482 vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
2483 vect[4] = -sinphi*p[0] + cosphi*p[1];
2484 vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
2485
2486 vect[6] = pp;
2487
2488 // Do the helix step
2489 g3helx3(GetSign()*bb,step,vect);
2490
2491 // Rotate back to the Global System
2492 r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
2493 r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
2494 r[2] = -sintet*vect[0] + costet*vect[2];
2495
2496 p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
2497 p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
2498 p[2] = -sintet*vect[3] + costet*vect[5];
2499
2500 // Rotate back to the Tracking System
2501 Double_t cosalp = TMath::Cos(fAlpha);
2502 Double_t sinalp =-TMath::Sin(fAlpha);
2503
2504 Double_t
2505 t = cosalp*r[0] - sinalp*r[1];
2506 r[1] = sinalp*r[0] + cosalp*r[1];
2507 r[0] = t;
2508
2509 t = cosalp*p[0] - sinalp*p[1];
2510 p[1] = sinalp*p[0] + cosalp*p[1];
2511 p[0] = t;
2512
2513 // Do the final correcting step to the target plane (linear approximation)
2514 Double_t x=r[0], y=r[1], z=r[2];
2515 if (TMath::Abs(dx) > kAlmost0) {
2516 if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
2517 dx = xk - r[0];
2518 x += dx;
2519 y += p[1]/p[0]*dx;
2520 z += p[2]/p[0]*dx;
2521 }
2522
2523
2524 // Calculate the track parameters
2525 t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
2526 fX = x;
2527 fP[0] = y;
2528 fP[1] = z;
2529 fP[2] = p[1]/t;
2530 fP[3] = p[2]/t;
2531 fP[4] = GetSign()/(t*pp);
2532
2533 return kTRUE;
2534}
2535
2536
cfdb62d4 2537Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
2538 //
2539 //Translation: in the event mixing, the tracks can be shifted
2540 //of the difference among primary vertices (vTrasl) and
2541 //the covariance matrix is changed accordingly
2542 //(covV = covariance of the primary vertex).
2543 //Origin: "Romita, Rossella" <R.Romita@gsi.de>
2544 //
2545 TVector3 translation;
2546 // vTrasl coordinates in the local system
2547 translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
2548 translation.RotateZ(-fAlpha);
2549 translation.GetXYZ(vTrasl);
2550
2551 //compute the new x,y,z of the track
5a87bb3d 2552 Double_t newX=fX-vTrasl[0];
2553 Double_t newY=fP[0]-vTrasl[1];
2554 Double_t newZ=fP[1]-vTrasl[2];
cfdb62d4 2555
2556 //define the new parameters
5a87bb3d 2557 Double_t newParam[5];
2558 newParam[0]=newY;
2559 newParam[1]=newZ;
2560 newParam[2]=fP[2];
2561 newParam[3]=fP[3];
2562 newParam[4]=fP[4];
cfdb62d4 2563
2564 // recompute the covariance matrix:
2565 // 1. covV in the local system
2566 Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
2567 TMatrixD qQi(3,3);
2568 qQi(0,0) = cosRot;
2569 qQi(0,1) = sinRot;
2570 qQi(0,2) = 0.;
2571 qQi(1,0) = -sinRot;
2572 qQi(1,1) = cosRot;
2573 qQi(1,2) = 0.;
2574 qQi(2,0) = 0.;
2575 qQi(2,1) = 0.;
2576 qQi(2,2) = 1.;
2577 TMatrixD uUi(3,3);
2578 uUi(0,0) = covV[0];
2579 uUi(0,0) = covV[0];
2580 uUi(1,0) = covV[1];
2581 uUi(0,1) = covV[1];
2582 uUi(2,0) = covV[3];
2583 uUi(0,2) = covV[3];
2584 uUi(1,1) = covV[2];
2585 uUi(2,2) = covV[5];
2586 uUi(1,2) = covV[4];
2587 if(uUi.Determinant() <= 0.) {return kFALSE;}
2588 TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
2589 TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
2590
2591 //2. compute the new covariance matrix of the track
2592 Double_t sigmaXX=m(0,0);
2593 Double_t sigmaXZ=m(2,0);
2594 Double_t sigmaXY=m(1,0);
2595 Double_t sigmaYY=GetSigmaY2()+m(1,1);
2596 Double_t sigmaYZ=fC[1]+m(1,2);
2597 Double_t sigmaZZ=fC[2]+m(2,2);
2598 Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
2599 Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
2600 Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
2601
2602 Double_t newCov[15];
2603 newCov[0]=covarianceYY;
2604 newCov[1]=covarianceYZ;
2605 newCov[2]=covarianceZZ;
2606 for(Int_t i=3;i<15;i++){
2607 newCov[i]=fC[i];
2608 }
2609
2610 // set the new parameters
2611
5a87bb3d 2612 Set(newX,fAlpha,newParam,newCov);
cfdb62d4 2613
2614 return kTRUE;
2615 }
86be8934 2616
2617void AliExternalTrackParam::CheckCovariance() {
2618
2619 // This function forces the diagonal elements of the covariance matrix to be positive.
2620 // In case the diagonal element is bigger than the maximal allowed value, it is set to
2621 // the limit and the off-diagonal elements that correspond to it are set to zero.
2622
32e55f82 2623 fC[0] = TMath::Abs(fC[0]);
2624 if (fC[0]>kC0max) {
2625 double scl = TMath::Sqrt(kC0max/fC[0]);
2626 fC[0] = kC0max;
2627 fC[1] *= scl;
2628 fC[3] *= scl;
2629 fC[6] *= scl;
2630 fC[10] *= scl;
2631 }
2632 fC[2] = TMath::Abs(fC[2]);
2633 if (fC[2]>kC2max) {
2634 double scl = TMath::Sqrt(kC2max/fC[2]);
2635 fC[2] = kC2max;
2636 fC[1] *= scl;
2637 fC[4] *= scl;
2638 fC[7] *= scl;
2639 fC[11] *= scl;
2640 }
2641 fC[5] = TMath::Abs(fC[5]);
2642 if (fC[5]>kC5max) {
2643 double scl = TMath::Sqrt(kC5max/fC[5]);
2644 fC[5] = kC5max;
2645 fC[3] *= scl;
2646 fC[4] *= scl;
2647 fC[8] *= scl;
2648 fC[12] *= scl;
2649 }
2650 fC[9] = TMath::Abs(fC[9]);
2651 if (fC[9]>kC9max) {
2652 double scl = TMath::Sqrt(kC9max/fC[9]);
2653 fC[9] = kC9max;
2654 fC[6] *= scl;
2655 fC[7] *= scl;
2656 fC[8] *= scl;
2657 fC[13] *= scl;
2658 }
2659 fC[14] = TMath::Abs(fC[14]);
2660 if (fC[14]>kC14max) {
2661 double scl = TMath::Sqrt(kC14max/fC[14]);
2662 fC[14] = kC14max;
2663 fC[10] *= scl;
2664 fC[11] *= scl;
2665 fC[12] *= scl;
2666 fC[13] *= scl;
2667 }
2668
86be8934 2669 // The part below is used for tests and normally is commented out
2670// TMatrixDSym m(5);
2671// TVectorD eig(5);
2672
2673// m(0,0)=fC[0];
2674// m(1,0)=fC[1]; m(1,1)=fC[2];
2675// m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5];
2676// m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9];
2677// m(4,0)=fC[10]; m(4,1)=fC[11]; m(4,2)=fC[12]; m(4,3)=fC[13]; m(4,4)=fC[14];
2678
2679// m(0,1)=m(1,0);
2680// m(0,2)=m(2,0); m(1,2)=m(2,1);
2681// m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2);
2682// m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3);
2683// m.EigenVectors(eig);
2684
2685// // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0);
2686// if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) {
2687// AliWarning("Negative eigenvalues of the covariance matrix!");
2688// this->Print();
2689// eig.Print();
2690// }
2691}
4c3dc2a0 2692
2693Bool_t AliExternalTrackParam::ConstrainToVertex(const AliVVertex* vtx, Double_t b[3])
2694{
2695 // Constrain TPC inner params constrained
2696 //
2697 if (!vtx)
2698 return kFALSE;
2699
2700 Double_t dz[2], cov[3];
2701 if (!PropagateToDCABxByBz(vtx, b, 3, dz, cov))
2702 return kFALSE;
2703
2704 Double_t covar[6];
2705 vtx->GetCovarianceMatrix(covar);
2706
2707 Double_t p[2]= { fP[0] - dz[0], fP[1] - dz[1] };
2708 Double_t c[3]= { covar[2], 0., covar[5] };
2709
2710 Double_t chi2C = GetPredictedChi2(p,c);
2711 if (chi2C>kVeryBig)
2712 return kFALSE;
2713
2714 if (!Update(p,c))
2715 return kFALSE;
2716
2717 return kTRUE;
2718}
70580f26 2719
2720//___________________________________________________________________________________________
2721Bool_t AliExternalTrackParam::GetXatLabR(Double_t r,Double_t &x, Double_t bz, Int_t dir) const
2722{
2723 // Get local X of the track position estimated at the radius lab radius r.
2724 // The track curvature is accounted exactly
2725 //
2726 // The flag "dir" can be used to remove the ambiguity of which intersection to take (out of 2 possible)
2727 // 0 - take the intersection closest to the current track position
2728 // >0 - go along the track (increasing fX)
2729 // <0 - go backward (decreasing fX)
2730 //
2731 const Double_t &fy=fP[0], &sn = fP[2];
45fa8186 2732 const double kEps = 1.e-6;
70580f26 2733 //
2734 double crv = GetC(bz);
45fa8186 2735 if (TMath::Abs(crv)>kAlmost0) { // helix
2736 // get center of the track circle
2737 double tR = 1./crv; // track radius (for the moment signed)
2738 double cs = TMath::Sqrt((1-sn)*(1+sn));
2739 double x0 = fX - sn*tR;
2740 double y0 = fy + cs*tR;
2741 double r0 = TMath::Sqrt(x0*x0+y0*y0);
2742 // printf("Xc:%+e Yc:%+e tR:%e r0:%e\n",x0,y0,tR,r0);
2743 //
2744 if (r0<=kAlmost0) return kFALSE; // the track is concentric to circle
2745 tR = TMath::Abs(tR);
2746 double tR2r0=1.,g=0,tmp=0;
2747 if (TMath::Abs(tR-r0)>kEps) {
2748 tR2r0 = tR/r0;
2749 g = 0.5*(r*r/(r0*tR) - tR2r0 - 1./tR2r0);
2750 tmp = 1.+g*tR2r0;
2751 }
2752 else {
2753 tR2r0 = 1.0;
2754 g = 0.5*r*r/(r0*tR) - 1;
2755 tmp = 0.5*r*r/(r0*r0);
2756 }
2757 double det = (1.-g)*(1.+g);
2758 if (det<0) return kFALSE; // does not reach raduis r
2759 det = TMath::Sqrt(det);
2760 //
2761 // the intersection happens in 2 points: {x0+tR*C,y0+tR*S}
2762 // with C=f*c0+-|s0|*det and S=f*s0-+c0 sign(s0)*det
2763 // where s0 and c0 make direction for the circle center (=x0/r0 and y0/r0)
2764 //
2765 x = x0*tmp;
2766 double y = y0*tmp;
2767 if (TMath::Abs(y0)>kAlmost0) { // when y0==0 the x,y is unique
2768 double dfx = tR2r0*TMath::Abs(y0)*det;
2769 double dfy = tR2r0*x0*TMath::Sign(det,y0);
2770 if (dir==0) { // chose the one which corresponds to smallest step
2771 double delta = (x-fX)*dfx-(y-fy)*dfy; // the choice of + in C will lead to smaller step if delta<0
2772 if (delta<0) x += dfx;
2773 else x -= dfx;
2774 }
2775 else if (dir>0) { // along track direction: x must be > fX
2776 x -= dfx; // try the smallest step (dfx is positive)
2777 double dfeps = fX-x; // handle special case of very small step
0ce0138a 2778 if (dfeps<-kEps) return kTRUE;
2779 if (TMath::Abs(dfeps)<kEps && // are we already in right r?
2780 TMath::Abs(fX*fX+fy*fy - r*r)<kEps) return fX;
35cb72bc 2781 x += dfx+dfx;
2782 if (x-fX>0) return kTRUE;
2783 if (x-fX<-kEps) return kFALSE;
2784 x = fX; // don't move
45fa8186 2785 }
2786 else { // backward: x must be < fX
2787 x += dfx; // try the smallest step (dfx is positive)
2788 double dfeps = x-fX; // handle special case of very small step
0ce0138a 2789 if (dfeps<-kEps) return kTRUE;
2790 if (TMath::Abs(dfeps)<kEps && // are we already in right r?
2791 TMath::Abs(fX*fX+fy*fy - r*r)<kEps) return fX;
35cb72bc 2792 x-=dfx+dfx;
2793 if (x-fX<0) return kTRUE;
2794 if (x-fX>kEps) return kFALSE;
2795 x = fX; // don't move
45fa8186 2796 }
2797 }
2798 else { // special case: track touching the circle just in 1 point
2799 if ( (dir>0&&x<fX) || (dir<0&&x>fX) ) return kFALSE;
2800 }
2801 }
2802 else { // this is a straight track
70580f26 2803 if (TMath::Abs(sn)>=kAlmost1) { // || to Y axis
2804 double det = (r-fX)*(r+fX);
2805 if (det<0) return kFALSE; // does not reach raduis r
2806 x = fX;
2807 if (dir==0) return kTRUE;
2808 det = TMath::Sqrt(det);
2809 if (dir>0) { // along the track direction
2810 if (sn>0) {if (fy>det) return kFALSE;} // track is along Y axis and above the circle
2811 else {if (fy<-det) return kFALSE;} // track is against Y axis amd belo the circle
2812 }
45fa8186 2813 else if(dir>0) { // agains track direction
70580f26 2814 if (sn>0) {if (fy<-det) return kFALSE;} // track is along Y axis
2815 else if (fy>det) return kFALSE; // track is against Y axis
2816 }
2817 }
2818 else if (TMath::Abs(sn)<=kAlmost0) { // || to X axis
2819 double det = (r-fy)*(r+fy);
2820 if (det<0) return kFALSE; // does not reach raduis r
2821 det = TMath::Sqrt(det);
2822 if (!dir) {
2823 x = fX>0 ? det : -det; // choose the solution requiring the smalest step
2824 return kTRUE;
2825 }
2826 else if (dir>0) { // along the track direction
2827 if (fX > det) return kFALSE; // current point is in on the right from the circle
2828 else if (fX <-det) x = -det; // on the left
2829 else x = det; // within the circle
2830 }
2831 else { // against the track direction
2832 if (fX <-det) return kFALSE;
2833 else if (fX > det) x = det;
2834 else x = -det;
2835 }
2836 }
2837 else { // general case of straight line
2838 double cs = TMath::Sqrt((1-sn)*(1+sn));
2839 double xsyc = fX*sn-fy*cs;
2840 double det = (r-xsyc)*(r+xsyc);
2841 if (det<0) return kFALSE; // does not reach raduis r
2842 det = TMath::Sqrt(det);
2843 double xcys = fX*cs+fy*sn;
2844 double t = -xcys;
2845 if (dir==0) t += t>0 ? -det:det; // chose the solution requiring the smalest step
2846 else if (dir>0) { // go in increasing fX direction. ( t+-det > 0)
2847 if (t>=-det) t += -det; // take minimal step giving t>0
2848 else return kFALSE; // both solutions have negative t
2849 }
2850 else { // go in increasing fX direction. (t+-det < 0)
2851 if (t<det) t -= det; // take minimal step giving t<0
2852 else return kFALSE; // both solutions have positive t
2853 }
2854 x = fX + cs*t;
2855 }
2856 }
70580f26 2857 //
2858 return kTRUE;
2859}
7d2e151a 2860//_________________________________________________________
2861Bool_t AliExternalTrackParam::GetXYZatR(Double_t xr,Double_t bz, Double_t *xyz, Double_t* alpSect) const
1445f03c 2862{
7d2e151a 2863 // This method has 3 modes of behaviour
2864 // 1) xyz[3] array is provided but alpSect pointer is 0: calculate the position of track intersection
2865 // with circle of radius xr and fill it in xyz array
2866 // 2) alpSect pointer is provided: find alpha of the sector where the track reaches local coordinate xr
2867 // Note that in this case xr is NOT the radius but the local coordinate.
2868 // If the xyz array is provided, it will be filled by track lab coordinates at local X in this sector
2869 // 3) Neither alpSect nor xyz pointers are provided: just check if the track reaches radius xr
1445f03c 2870 //
1445f03c 2871 //
7d2e151a 2872 double crv = GetC(bz);
2873 if ( (TMath::Abs(bz))<kAlmost0Field ) crv=0.;
2874 const double &fy = fP[0];
2875 const double &fz = fP[1];
2876 const double &sn = fP[2];
2877 const double &tgl = fP[3];
2878 //
2879 // general circle parameterization:
2880 // x = (r0+tR)cos(phi0) - tR cos(t+phi0)
2881 // y = (r0+tR)sin(phi0) - tR sin(t+phi0)
2882 // where qb is the sign of the curvature, tR is the track's signed radius and r0
2883 // is the DCA of helix to origin
2884 //
2885 double tR = 1./crv; // track radius signed
2886 double cs = TMath::Sqrt((1-sn)*(1+sn));
2887 double x0 = fX - sn*tR; // helix center coordinates
2888 double y0 = fy + cs*tR;
2889 double phi0 = TMath::ATan2(y0,x0); // angle of PCA wrt to the origin
2890 if (tR<0) phi0 += TMath::Pi();
2891 if (phi0 > TMath::Pi()) phi0 -= 2.*TMath::Pi();
2892 else if (phi0 <-TMath::Pi()) phi0 += 2.*TMath::Pi();
2893 double cs0 = TMath::Cos(phi0);
2894 double sn0 = TMath::Sin(phi0);
2895 double r0 = x0*cs0 + y0*sn0 - tR; // DCA to origin
2896 double r2R = 1.+r0/tR;
2897 //
2898 //
2899 if (r2R<kAlmost0) return kFALSE; // helix is centered at the origin, no specific intersection with other concetric circle
2900 if (!xyz && !alpSect) return kTRUE;
2901 double xr2R = xr/tR;
2902 double r2Ri = 1./r2R;
2903 // the intersection cos(t) = [1 + (r0/tR+1)^2 - (r0/tR)^2]/[2(1+r0/tR)]
2904 double cosT = 0.5*(r2R + (1-xr2R*xr2R)*r2Ri);
2905 if ( TMath::Abs(cosT)>kAlmost1 ) {
2906 // printf("Does not reach : %f %f\n",r0,tR);
2907 return kFALSE; // track does not reach the radius xr
1445f03c 2908 }
2909 //
7d2e151a 2910 double t = TMath::ACos(cosT);
2911 if (tR<0) t = -t;
2912 // intersection point
2913 double xyzi[3];
2914 xyzi[0] = x0 - tR*TMath::Cos(t+phi0);
2915 xyzi[1] = y0 - tR*TMath::Sin(t+phi0);
2916 if (xyz) { // if postition is requested, then z is needed:
2917 double t0 = TMath::ATan2(cs,-sn) - phi0;
2918 double z0 = fz - t0*tR*tgl;
2919 xyzi[2] = z0 + tR*t*tgl;
1445f03c 2920 }
7d2e151a 2921 else xyzi[2] = 0;
2922 //
2923 Local2GlobalPosition(xyzi,fAlpha);
2924 //
2925 if (xyz) {
2926 xyz[0] = xyzi[0];
2927 xyz[1] = xyzi[1];
2928 xyz[2] = xyzi[2];
1445f03c 2929 }
7d2e151a 2930 //
2931 if (alpSect) {
2932 double &alp = *alpSect;
2933 // determine the sector of crossing
2934 double phiPos = TMath::Pi()+TMath::ATan2(-xyzi[1],-xyzi[0]);
2935 int sect = ((Int_t)(phiPos*TMath::RadToDeg()))/20;
2936 alp = TMath::DegToRad()*(20*sect+10);
2937 double x2r,f1,f2,r1,r2,dx,dy2dx,yloc=0, ylocMax = xr*TMath::Tan(TMath::Pi()/18); // min max Y within sector at given X
2938 //
2939 while(1) {
2940 Double_t ca=TMath::Cos(alp-fAlpha), sa=TMath::Sin(alp-fAlpha);
2941 if ((cs*ca+sn*sa)<0) {
2942 AliDebug(1,Form("Rotation to target sector impossible: local cos(phi) would become %.2f",cs*ca+sn*sa));
2943 return kFALSE;
2944 }
2945 //
2946 f1 = sn*ca - cs*sa;
2947 if (TMath::Abs(f1) >= kAlmost1) {
2948 AliDebug(1,Form("Rotation to target sector impossible: local sin(phi) would become %.2f",f1));
2949 return kFALSE;
2950 }
2951 //
2952 double tmpX = fX*ca + fy*sa;
2953 double tmpY = -fX*sa + fy*ca;
2954 //
2955 // estimate Y at X=xr
2956 dx=xr-tmpX;
2957 x2r = crv*dx;
2958 f2=f1 + x2r;
2959 if (TMath::Abs(f2) >= kAlmost1) {
2960 AliDebug(1,Form("Propagation in target sector failed ! %.10e",f2));
2961 return kFALSE;
2962 }
2963 r1 = TMath::Sqrt((1.-f1)*(1.+f1));
2964 r2 = TMath::Sqrt((1.-f2)*(1.+f2));
2965 dy2dx = (f1+f2)/(r1+r2);
2966 yloc = tmpY + dx*dy2dx;
2967 if (yloc>ylocMax) {alp += 2*TMath::Pi()/18; sect++;}
2968 else if (yloc<-ylocMax) {alp -= 2*TMath::Pi()/18; sect--;}
2969 else break;
2970 if (alp >= TMath::Pi()) alp -= 2*TMath::Pi();
2971 else if (alp < -TMath::Pi()) alp += 2*TMath::Pi();
2972 // if (sect>=18) sect = 0;
2973 // if (sect<=0) sect = 17;
2974 }
2975 //
2976 // if alpha was requested, then recalculate the position at intersection in sector
2977 if (xyz) {
2978 xyz[0] = xr;
2979 xyz[1] = yloc;
2980 if (TMath::Abs(x2r)<0.05) xyz[2] = fz + dx*(r2 + f2*dy2dx)*tgl;
2981 else {
2982 // for small dx/R the linear apporximation of the arc by the segment is OK,
2983 // but at large dx/R the error is very large and leads to incorrect Z propagation
2984 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
2985 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
2986 // Similarly, the rotation angle in linear in dx only for dx<<R
2987 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
2988 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
2989 xyz[2] = fz + rot/crv*tgl;
2990 }
2991 Local2GlobalPosition(xyz,alp);
2992 }
1445f03c 2993 }
7d2e151a 2994 return kTRUE;
2995 //
1445f03c 2996}
b8b98dc2 2997
2998
2999Double_t AliExternalTrackParam::GetParameterAtRadius(Double_t r, Double_t bz, Int_t parType) const
3000{
3001 //
3002 // Get track parameters at the radius of interest.
3003 // Given function is aimed to be used to interactivelly (tree->Draw())
3004 // access track properties at different radii
3005 //
3006 // TO BE USED WITH SPECICAL CARE -
3007 // it is aimed to be used for rough calculation as constant field and
3008 // no correction for material is used
3009 //
3010 // r - radius of interest
3011 // bz - magentic field
3012 // retun values dependens on parType:
3013 // parType = 0 -gx
3014 // parType = 1 -gy
3015 // parType = 2 -gz
3016 //
3017 // parType = 3 -pgx
3018 // parType = 4 -pgy
3019 // parType = 5 -pgz
3020 //
3021 // parType = 6 - r
3022 // parType = 7 - global position phi
3023 // parType = 8 - global direction phi
3024 // parType = 9 - direction phi- positionphi
3025 if (parType<0) {
3026 parType=-1;
3027 return 0;
3028 }
3029 Double_t xyz[3];
3030 Double_t pxyz[3];
3031 Double_t localX=0;
3032 Bool_t res = GetXatLabR(r,localX,bz,1);
3033 if (!res) {
3034 parType=-1;
3035 return 0;
3036 }
3037 //
3038 // position parameters
3039 //
3040 GetXYZAt(localX,bz,xyz);
3041 if (parType<3) {
3042 return xyz[parType];
3043 }
3044
3045 if (parType==6) return TMath::Sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]);
3046 if (parType==7) return TMath::ATan2(xyz[1],xyz[0]);
3047 //
3048 // momenta parameters
3049 //
3050 GetPxPyPzAt(localX,bz,pxyz);
3051 if (parType==8) return TMath::ATan2(pxyz[1],pxyz[0]);
3052 if (parType==9) {
3053 Double_t diff = TMath::ATan2(pxyz[1],pxyz[0])-TMath::ATan2(xyz[1],xyz[0]);
3054 if (diff>TMath::Pi()) diff-=TMath::TwoPi();
3055 if (diff<-TMath::Pi()) diff+=TMath::TwoPi();
3056 return diff;
3057 }
3058 if (parType>=3&&parType<6) {
3059 return pxyz[parType%3];
3060 }
3061 return 0;
3062}