misc cleanup
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
CommitLineData
51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
4b189f98 28#include <TMatrixDSym.h>
d46683db 29#include <TPolyMarker3D.h>
30#include <TVector3.h>
31
51ad6848 32#include "AliExternalTrackParam.h"
d46683db 33#include "AliMathBase.h"
58e536c5 34#include "AliVVertex.h"
6c94f330 35#include "AliLog.h"
51ad6848 36
37ClassImp(AliExternalTrackParam)
38
ed5f2849 39Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
40
51ad6848 41//_____________________________________________________________________________
90e48c0c 42AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 43 AliVTrack(),
90e48c0c 44 fX(0),
c9ec41e8 45 fAlpha(0)
51ad6848 46{
90e48c0c 47 //
48 // default constructor
49 //
c9ec41e8 50 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
51 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 52}
53
6c94f330 54//_____________________________________________________________________________
55AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 56 AliVTrack(track),
6c94f330 57 fX(track.fX),
58 fAlpha(track.fAlpha)
59{
60 //
61 // copy constructor
62 //
63 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
64 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
65}
66
def9660e 67//_____________________________________________________________________________
68AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
69{
70 //
71 // assignment operator
72 //
73
74 if (this!=&trkPar) {
4f6e22bd 75 AliVTrack::operator=(trkPar);
def9660e 76 fX = trkPar.fX;
77 fAlpha = trkPar.fAlpha;
78
79 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
80 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
81 }
82
83 return *this;
84}
85
51ad6848 86//_____________________________________________________________________________
87AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
88 const Double_t param[5],
90e48c0c 89 const Double_t covar[15]) :
4f6e22bd 90 AliVTrack(),
90e48c0c 91 fX(x),
c9ec41e8 92 fAlpha(alpha)
51ad6848 93{
90e48c0c 94 //
95 // create external track parameters from given arguments
96 //
c9ec41e8 97 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
98 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 99}
100
4f6e22bd 101//_____________________________________________________________________________
102AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
103 AliVTrack(),
104 fX(0.),
105 fAlpha(0.)
106{
107 //
610e3088 108 // Constructor from virtual track,
109 // This is not a copy contructor !
4f6e22bd 110 //
610e3088 111
112 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
113 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
114 AliWarning("Calling the default constructor...");
115 AliExternalTrackParam();
116 return;
117 }
118
892be05f 119 Double_t xyz[3],pxpypz[3],cv[21];
120 vTrack->GetXYZ(xyz);
121 pxpypz[0]=vTrack->Px();
122 pxpypz[1]=vTrack->Py();
123 pxpypz[2]=vTrack->Pz();
4f6e22bd 124 vTrack->GetCovarianceXYZPxPyPz(cv);
125 Short_t sign = (Short_t)vTrack->Charge();
126
127 Set(xyz,pxpypz,cv,sign);
128}
129
90e48c0c 130//_____________________________________________________________________________
da4e3deb 131AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
132 Double_t cv[21],Short_t sign) :
4f6e22bd 133 AliVTrack(),
da4e3deb 134 fX(0.),
135 fAlpha(0.)
4f6e22bd 136{
137 //
138 // constructor from the global parameters
139 //
140
141 Set(xyz,pxpypz,cv,sign);
142}
143
144//_____________________________________________________________________________
145void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
146 Double_t cv[21],Short_t sign)
da4e3deb 147{
148 //
149 // create external track parameters from the global parameters
150 // x,y,z,px,py,pz and their 6x6 covariance matrix
151 // A.Dainese 10.10.08
152
153 // Calculate alpha: the rotation angle of the corresponding local system
154 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
155
156 // Get the vertex of origin and the momentum
157 TVector3 ver(xyz[0],xyz[1],xyz[2]);
158 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
159
160 // Rotate to the local coordinate system
161 ver.RotateZ(-fAlpha);
162 mom.RotateZ(-fAlpha);
163
164 // x of the reference plane
165 fX = ver.X();
166
167 Double_t charge = (Double_t)sign;
168
169 fP[0] = ver.Y();
170 fP[1] = ver.Z();
171 fP[2] = TMath::Sin(mom.Phi());
172 fP[3] = mom.Pz()/mom.Pt();
173 fP[4] = TMath::Sign(1/mom.Pt(),charge);
174
175 // Covariance matrix (formulas to be simplified)
176
177 Double_t pt=1./TMath::Abs(fP[4]);
178 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
179 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
180
181 Double_t m00=-sn;// m10=cs;
182 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
183 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
184 Double_t m35=pt, m45=-pt*pt*fP[3];
185
186 m43*=GetSign();
187 m44*=GetSign();
188 m45*=GetSign();
189
190 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
191 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
192 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
193 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
194 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
195 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
196 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
197
198 fC[0 ] = cv[0 ]+cv[2 ];
199 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
200 fC[2 ] = cv[5 ];
201 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
202 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
203 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
204 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
205 fC[11] = (cv[8]-fC[4]*m23)/m43;
206 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
207 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
208 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
209 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
210 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
211 Double_t b2=m23*m35;
212 Double_t b3=m43*m35;
213 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
214 Double_t b5=m24*m35;
215 Double_t b6=m44*m35;
216 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
217 fC[13] = b1/b3-b2*fC[8]/b3;
218 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 219
220 return;
da4e3deb 221}
222
51ad6848 223//_____________________________________________________________________________
c9ec41e8 224void AliExternalTrackParam::Reset() {
1530f89c 225 //
226 // Resets all the parameters to 0
227 //
c9ec41e8 228 fX=fAlpha=0.;
229 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
230 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 231}
232
3775b0ca 233//_____________________________________________________________________________
234void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
235 //
236 // Add "something" to the track covarince matrix.
237 // May be needed to account for unknown mis-calibration/mis-alignment
238 //
239 fC[0] +=c[0];
240 fC[1] +=c[1]; fC[2] +=c[2];
241 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
242 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
243 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
244}
245
246
c9ec41e8 247Double_t AliExternalTrackParam::GetP() const {
248 //---------------------------------------------------------------------
249 // This function returns the track momentum
250 // Results for (nearly) straight tracks are meaningless !
251 //---------------------------------------------------------------------
06fb4a2f 252 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 253 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 254}
255
1d99986f 256Double_t AliExternalTrackParam::Get1P() const {
257 //---------------------------------------------------------------------
258 // This function returns the 1/(track momentum)
259 //---------------------------------------------------------------------
260 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
261}
262
c9ec41e8 263//_______________________________________________________________________
c7bafca9 264Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 265 //------------------------------------------------------------------
266 // This function calculates the transverse impact parameter
267 // with respect to a point with global coordinates (x,y)
268 // in the magnetic field "b" (kG)
269 //------------------------------------------------------------------
5773defd 270 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 271 Double_t rp4=GetC(b);
c9ec41e8 272
273 Double_t xt=fX, yt=fP[0];
274
275 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
276 Double_t a = x*cs + y*sn;
277 y = -x*sn + y*cs; x=a;
278 xt-=x; yt-=y;
279
280 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
281 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 282 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
283}
284
285//_______________________________________________________________________
286void AliExternalTrackParam::
287GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
288 //------------------------------------------------------------------
289 // This function calculates the transverse and longitudinal impact parameters
290 // with respect to a point with global coordinates (x,y)
291 // in the magnetic field "b" (kG)
292 //------------------------------------------------------------------
293 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
294 Double_t xt=fX, yt=fP[0];
295 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
296 Double_t a = x*cs + y*sn;
297 y = -x*sn + y*cs; x=a;
298 xt-=x; yt-=y;
299
300 Double_t rp4=GetC(b);
301 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
302 dz[0] = -(xt*f1 - yt*r1);
303 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
304 return;
305 }
306
307 sn=rp4*xt - f1; cs=rp4*yt + r1;
308 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
309 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
310 dz[0] = -a/(1 + rr);
311 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
312 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 313}
314
49d13e89 315//_______________________________________________________________________
316Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
317 //------------------------------------------------------------------
318 // This function calculates the transverse impact parameter
319 // with respect to a point with global coordinates (xv,yv)
320 // neglecting the track curvature.
321 //------------------------------------------------------------------
322 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
323 Double_t x= xv*cs + yv*sn;
324 Double_t y=-xv*sn + yv*cs;
325
326 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
327
1530f89c 328 return -d;
49d13e89 329}
330
116b445b 331Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 332(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
333 Double_t (*Bethe)(Double_t)) {
116b445b 334 //------------------------------------------------------------------
335 // This function corrects the track parameters for the crossed material.
336 // "xOverX0" - X/X0, the thickness in units of the radiation length.
337 // "xTimesRho" - is the product length*density (g/cm^2).
338 // "mass" - the mass of this particle (GeV/c^2).
339 //------------------------------------------------------------------
340 Double_t &fP2=fP[2];
341 Double_t &fP3=fP[3];
342 Double_t &fP4=fP[4];
343
344 Double_t &fC22=fC[5];
345 Double_t &fC33=fC[9];
346 Double_t &fC43=fC[13];
347 Double_t &fC44=fC[14];
348
7dded1d5 349 //Apply angle correction, if requested
350 if(anglecorr) {
351 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
352 xOverX0 *=angle;
353 xTimesRho *=angle;
354 }
355
116b445b 356 Double_t p=GetP();
357 Double_t p2=p*p;
358 Double_t beta2=p2/(p2 + mass*mass);
116b445b 359
360 //Multiple scattering******************
361 if (xOverX0 != 0) {
362 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
9a53dcc6 363 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
116b445b 364 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
365 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
366 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
367 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
368 fC44 += theta2*fP3*fP4*fP3*fP4;
369 }
370
371 //Energy losses************************
372 if ((xTimesRho != 0.) && (beta2 < 1.)) {
d46683db 373 Double_t dE=Bethe(p/mass)*xTimesRho;
116b445b 374 Double_t e=TMath::Sqrt(p2 + mass*mass);
375 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
376 fP4*=(1.- e/p2*dE);
4b2fa3ce 377 if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c
378
116b445b 379
380 // Approximate energy loss fluctuation (M.Ivanov)
381 const Double_t knst=0.07; // To be tuned.
382 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
383 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
384
385 }
386
387 return kTRUE;
388}
389
390
ee5dba5e 391Bool_t AliExternalTrackParam::CorrectForMaterial
392(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 393 //------------------------------------------------------------------
116b445b 394 // Deprecated function !
395 // Better use CorrectForMeanMaterial instead of it.
396 //
c7bafca9 397 // This function corrects the track parameters for the crossed material
398 // "d" - the thickness (fraction of the radiation length)
399 // "x0" - the radiation length (g/cm^2)
400 // "mass" - the mass of this particle (GeV/c^2)
401 //------------------------------------------------------------------
402 Double_t &fP2=fP[2];
403 Double_t &fP3=fP[3];
404 Double_t &fP4=fP[4];
405
406 Double_t &fC22=fC[5];
407 Double_t &fC33=fC[9];
408 Double_t &fC43=fC[13];
409 Double_t &fC44=fC[14];
410
7b5ef2e6 411 Double_t p=GetP();
412 Double_t p2=p*p;
c7bafca9 413 Double_t beta2=p2/(p2 + mass*mass);
414 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
415
416 //Multiple scattering******************
417 if (d!=0) {
418 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
9a53dcc6 419 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
c7bafca9 420 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
421 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
422 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
423 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
424 fC44 += theta2*fP3*fP4*fP3*fP4;
425 }
426
427 //Energy losses************************
8fc1985d 428 if (x0!=0. && beta2<1) {
c7bafca9 429 d*=x0;
d46683db 430 Double_t dE=Bethe(p/mass)*d;
ee5dba5e 431 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 432 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 433 fP4*=(1.- e/p2*dE);
434
435 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 436 const Double_t knst=0.07; // To be tuned.
437 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 438 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
439
c7bafca9 440 }
441
442 return kTRUE;
443}
444
d46683db 445Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 446 //------------------------------------------------------------------
d46683db 447 // This is an approximation of the Bethe-Bloch formula,
448 // reasonable for solid materials.
449 // All the parameters are, in fact, for Si.
450 // The returned value is in [GeV]
ee5dba5e 451 //------------------------------------------------------------------
a821848c 452
d46683db 453 return AliMathBase::BetheBlochGeant(bg);
454}
ee5dba5e 455
d46683db 456Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
457 //------------------------------------------------------------------
458 // This is an approximation of the Bethe-Bloch formula,
459 // reasonable for gas materials.
460 // All the parameters are, in fact, for Ne.
461 // The returned value is in [GeV]
462 //------------------------------------------------------------------
463
464 const Double_t rho = 0.9e-3;
465 const Double_t x0 = 2.;
466 const Double_t x1 = 4.;
467 const Double_t mI = 140.e-9;
468 const Double_t mZA = 0.49555;
469
470 return AliMathBase::BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 471}
472
49d13e89 473Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
474 //------------------------------------------------------------------
475 // Transform this track to the local coord. system rotated
476 // by angle "alpha" (rad) with respect to the global coord. system.
477 //------------------------------------------------------------------
dfcef74c 478 if (TMath::Abs(fP[2]) >= kAlmost1) {
479 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
480 return kFALSE;
481 }
482
49d13e89 483 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
484 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
485
486 Double_t &fP0=fP[0];
487 Double_t &fP2=fP[2];
488 Double_t &fC00=fC[0];
489 Double_t &fC10=fC[1];
490 Double_t &fC20=fC[3];
491 Double_t &fC21=fC[4];
492 Double_t &fC22=fC[5];
493 Double_t &fC30=fC[6];
494 Double_t &fC32=fC[8];
495 Double_t &fC40=fC[10];
496 Double_t &fC42=fC[12];
497
498 Double_t x=fX;
499 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
500 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
501
dfcef74c 502 Double_t tmp=sf*ca - cf*sa;
503 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
504
49d13e89 505 fAlpha = alpha;
506 fX = x*ca + fP0*sa;
507 fP0= -x*sa + fP0*ca;
dfcef74c 508 fP2= tmp;
49d13e89 509
06fb4a2f 510 if (TMath::Abs(cf)<kAlmost0) {
511 AliError(Form("Too small cosine value %f",cf));
512 cf = kAlmost0;
513 }
514
49d13e89 515 Double_t rr=(ca+sf/cf*sa);
516
517 fC00 *= (ca*ca);
518 fC10 *= ca;
519 fC20 *= ca*rr;
520 fC21 *= rr;
521 fC22 *= rr*rr;
522 fC30 *= ca;
523 fC32 *= rr;
524 fC40 *= ca;
525 fC42 *= rr;
526
527 return kTRUE;
528}
529
530Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
531 //----------------------------------------------------------------
532 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
533 //----------------------------------------------------------------
49d13e89 534 Double_t dx=xk-fX;
e421f556 535 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 536
1530f89c 537 Double_t crv=GetC(b);
5773defd 538 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
539
49d13e89 540 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 541 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 542 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
543
544 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
545 Double_t
546 &fC00=fC[0],
547 &fC10=fC[1], &fC11=fC[2],
548 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
549 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
550 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
551
552 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
553
554 fX=xk;
555 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 556 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 557 fP2 += dx*crv;
558
559 //f = F - 1
560
561 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
562 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
563 Double_t f12= dx*fP3*f1/(r1*r1*r1);
564 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
565 Double_t f13= dx/r1;
566 Double_t f24= dx; f24*=cc;
567
568 //b = C*ft
569 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
570 Double_t b02=f24*fC40;
571 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
572 Double_t b12=f24*fC41;
573 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
574 Double_t b22=f24*fC42;
575 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
576 Double_t b42=f24*fC44;
577 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
578 Double_t b32=f24*fC43;
579
580 //a = f*b = f*C*ft
581 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
582 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
583 Double_t a22=f24*b42;
584
585 //F*C*Ft = C + (b + bt + a)
586 fC00 += b00 + b00 + a00;
587 fC10 += b10 + b01 + a01;
588 fC20 += b20 + b02 + a02;
589 fC30 += b30;
590 fC40 += b40;
591 fC11 += b11 + b11 + a11;
592 fC21 += b21 + b12 + a12;
593 fC31 += b31;
594 fC41 += b41;
595 fC22 += b22 + b22 + a22;
596 fC32 += b32;
597 fC42 += b42;
598
599 return kTRUE;
600}
601
052daaff 602void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
603Double_t p[3], Double_t bz) const {
604 //+++++++++++++++++++++++++++++++++++++++++
605 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
606 // Extrapolate track along simple helix in magnetic field
607 // Arguments: len -distance alogn helix, [cm]
608 // bz - mag field, [kGaus]
609 // Returns: x and p contain extrapolated positon and momentum
610 // The momentum returned for straight-line tracks is meaningless !
611 //+++++++++++++++++++++++++++++++++++++++++
612 GetXYZ(x);
613
def9660e 614 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 615 Double_t unit[3]; GetDirection(unit);
616 x[0]+=unit[0]*len;
617 x[1]+=unit[1]*len;
618 x[2]+=unit[2]*len;
619
620 p[0]=unit[0]/kAlmost0;
621 p[1]=unit[1]/kAlmost0;
622 p[2]=unit[2]/kAlmost0;
623 } else {
624 GetPxPyPz(p);
625 Double_t pp=GetP();
626 Double_t a = -kB2C*bz*GetSign();
627 Double_t rho = a/pp;
628 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
629 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
630 x[2] += p[2]*len/pp;
631
632 Double_t p0=p[0];
633 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
634 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
635 }
636}
637
638Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
639Double_t bz) const {
640 //+++++++++++++++++++++++++++++++++++++++++
641 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
642 // Finds point of intersection (if exists) of the helix with the plane.
643 // Stores result in fX and fP.
644 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
645 // and vector, normal to the plane
646 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
647 //+++++++++++++++++++++++++++++++++++++++++
648 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
649
650 //estimates initial helix length up to plane
651 Double_t s=
652 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
653 Double_t dist=99999,distPrev=dist;
654 Double_t x[3],p[3];
655 while(TMath::Abs(dist)>0.00001){
656 //calculates helix at the distance s from x0 ALONG the helix
657 Propagate(s,x,p,bz);
658
659 //distance between current helix position and plane
660 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
661
662 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
663 distPrev=dist;
664 s-=dist;
665 }
666 //on exit pnt is intersection point,norm is track vector at that point,
667 //all in MARS
668 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
669 return kTRUE;
670}
671
49d13e89 672Double_t
673AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
674 //----------------------------------------------------------------
675 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
676 //----------------------------------------------------------------
677 Double_t sdd = fC[0] + cov[0];
678 Double_t sdz = fC[1] + cov[1];
679 Double_t szz = fC[2] + cov[2];
680 Double_t det = sdd*szz - sdz*sdz;
681
682 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
683
684 Double_t d = fP[0] - p[0];
685 Double_t z = fP[1] - p[1];
686
687 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
688}
689
4b189f98 690Double_t AliExternalTrackParam::
691GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
692 //----------------------------------------------------------------
693 // Estimate the chi2 of the 3D space point "p" and
1e023a36 694 // the full covariance matrix "covyz" and "covxyz"
4b189f98 695 //
696 // Cov(x,x) ... : covxyz[0]
697 // Cov(y,x) ... : covxyz[1] covyz[0]
698 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
699 //----------------------------------------------------------------
700
701 Double_t res[3] = {
702 GetX() - p[0],
703 GetY() - p[1],
704 GetZ() - p[2]
705 };
706
707 Double_t f=GetSnp();
708 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
709 Double_t r=TMath::Sqrt(1.- f*f);
710 Double_t a=f/r, b=GetTgl()/r;
711
712 Double_t s2=333.*333.; //something reasonably big (cm^2)
713
714 TMatrixDSym v(3);
715 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
716 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
717 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
718
719 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
720 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
721 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
722
723 v.Invert();
724 if (!v.IsValid()) return kVeryBig;
725
726 Double_t chi2=0.;
727 for (Int_t i = 0; i < 3; i++)
728 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
729
730 return chi2;
731
732
733}
734
1e023a36 735Bool_t AliExternalTrackParam::
736PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
737 //----------------------------------------------------------------
738 // Propagate this track to the plane
739 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
740 // belongs to.
741 // The magnetic field is "bz" (kG)
742 //
743 // The track curvature and the change of the covariance matrix
744 // of the track parameters are negleted !
745 // (So the "step" should be small compared with 1/curvature)
746 //----------------------------------------------------------------
747
748 Double_t f=GetSnp();
749 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
750 Double_t r=TMath::Sqrt(1.- f*f);
751 Double_t a=f/r, b=GetTgl()/r;
752
753 Double_t s2=333.*333.; //something reasonably big (cm^2)
754
755 TMatrixDSym tV(3);
756 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
757 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
758 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
759
760 TMatrixDSym pV(3);
761 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
762 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
763 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
764
765 TMatrixDSym tpV(tV);
766 tpV+=pV;
767 tpV.Invert();
768 if (!tpV.IsValid()) return kFALSE;
769
770 TMatrixDSym pW(3),tW(3);
771 for (Int_t i=0; i<3; i++)
772 for (Int_t j=0; j<3; j++) {
773 pW(i,j)=tW(i,j)=0.;
774 for (Int_t k=0; k<3; k++) {
775 pW(i,j) += tV(i,k)*tpV(k,j);
776 tW(i,j) += pV(i,k)*tpV(k,j);
777 }
778 }
779
780 Double_t t[3] = {GetX(), GetY(), GetZ()};
781
782 Double_t x=0.;
783 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
784 Double_t crv=GetC(bz);
785 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
786 f += crv*(x-fX);
787 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
788 fX=x;
789
790 fP[0]=0.;
791 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
792 fP[1]=0.;
793 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
794
795 return kTRUE;
796}
797
e23a38cb 798Double_t *AliExternalTrackParam::GetResiduals(
799Double_t *p,Double_t *cov,Bool_t updated) const {
800 //------------------------------------------------------------------
801 // Returns the track residuals with the space point "p" having
802 // the covariance matrix "cov".
803 // If "updated" is kTRUE, the track parameters expected to be updated,
804 // otherwise they must be predicted.
805 //------------------------------------------------------------------
806 static Double_t res[2];
807
808 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
809 if (updated) {
810 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
811 } else {
812 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
813 }
814 Double_t det=r00*r11 - r01*r01;
815
816 if (TMath::Abs(det) < kAlmost0) return 0;
817
818 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 819
820 if (r00 < 0.) return 0;
821 if (r11 < 0.) return 0;
822
e23a38cb 823 Double_t dy = fP[0] - p[0];
824 Double_t dz = fP[1] - p[1];
825
826 res[0]=dy*TMath::Sqrt(r00);
827 res[1]=dz*TMath::Sqrt(r11);
828
829 return res;
830}
831
49d13e89 832Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
833 //------------------------------------------------------------------
834 // Update the track parameters with the space point "p" having
835 // the covariance matrix "cov"
836 //------------------------------------------------------------------
837 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
838 Double_t
839 &fC00=fC[0],
840 &fC10=fC[1], &fC11=fC[2],
841 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
842 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
843 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
844
845 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
846 r00+=fC00; r01+=fC10; r11+=fC11;
847 Double_t det=r00*r11 - r01*r01;
848
849 if (TMath::Abs(det) < kAlmost0) return kFALSE;
850
851
852 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
853
854 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
855 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
856 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
857 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
858 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
859
860 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
861 Double_t sf=fP2 + k20*dy + k21*dz;
862 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
863
864 fP0 += k00*dy + k01*dz;
865 fP1 += k10*dy + k11*dz;
866 fP2 = sf;
867 fP3 += k30*dy + k31*dz;
868 fP4 += k40*dy + k41*dz;
869
870 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
871 Double_t c12=fC21, c13=fC31, c14=fC41;
872
873 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
874 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
875 fC40-=k00*c04+k01*c14;
876
877 fC11-=k10*c01+k11*fC11;
878 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
879 fC41-=k10*c04+k11*c14;
880
881 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
882 fC42-=k20*c04+k21*c14;
883
884 fC33-=k30*c03+k31*c13;
885 fC43-=k30*c04+k31*c14;
886
887 fC44-=k40*c04+k41*c14;
888
889 return kTRUE;
890}
891
c7bafca9 892void
893AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
894 //--------------------------------------------------------------------
895 // External track parameters -> helix parameters
896 // "b" - magnetic field (kG)
897 //--------------------------------------------------------------------
898 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
899
1530f89c 900 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 901
902 hlx[5]=fX*cs - hlx[0]*sn; // x0
903 hlx[0]=fX*sn + hlx[0]*cs; // y0
904//hlx[1]= // z0
905 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
906//hlx[3]= // tgl
1530f89c 907 hlx[4]=GetC(b); // C
c7bafca9 908}
909
910
911static void Evaluate(const Double_t *h, Double_t t,
912 Double_t r[3], //radius vector
913 Double_t g[3], //first defivatives
914 Double_t gg[3]) //second derivatives
915{
916 //--------------------------------------------------------------------
917 // Calculate position of a point on a track and some derivatives
918 //--------------------------------------------------------------------
919 Double_t phase=h[4]*t+h[2];
920 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
921
922 r[0] = h[5] + (sn - h[6])/h[4];
923 r[1] = h[0] - (cs - h[7])/h[4];
924 r[2] = h[1] + h[3]*t;
925
926 g[0] = cs; g[1]=sn; g[2]=h[3];
927
928 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
929}
930
931Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
932Double_t b, Double_t &xthis, Double_t &xp) const {
933 //------------------------------------------------------------
934 // Returns the (weighed !) distance of closest approach between
935 // this track and the track "p".
936 // Other returned values:
937 // xthis, xt - coordinates of tracks' reference planes at the DCA
938 //-----------------------------------------------------------
939 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
940 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
941 Double_t dx2=dy2;
942
c7bafca9 943 Double_t p1[8]; GetHelixParameters(p1,b);
944 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
945 Double_t p2[8]; p->GetHelixParameters(p2,b);
946 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
947
948
949 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
950 Evaluate(p1,t1,r1,g1,gg1);
951 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
952 Evaluate(p2,t2,r2,g2,gg2);
953
954 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
955 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
956
957 Int_t max=27;
958 while (max--) {
959 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
960 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
961 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
962 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
963 (g1[2]*g1[2] - dz*gg1[2])/dz2;
964 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
965 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
966 (g2[2]*g2[2] + dz*gg2[2])/dz2;
967 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
968
969 Double_t det=h11*h22-h12*h12;
970
971 Double_t dt1,dt2;
972 if (TMath::Abs(det)<1.e-33) {
973 //(quasi)singular Hessian
974 dt1=-gt1; dt2=-gt2;
975 } else {
976 dt1=-(gt1*h22 - gt2*h12)/det;
977 dt2=-(h11*gt2 - h12*gt1)/det;
978 }
979
980 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
981
982 //check delta(phase1) ?
983 //check delta(phase2) ?
984
985 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
986 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
987 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 988 AliDebug(1," stopped at not a stationary point !");
c7bafca9 989 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
990 if (lmb < 0.)
358f16ae 991 AliDebug(1," stopped at not a minimum !");
c7bafca9 992 break;
993 }
994
995 Double_t dd=dm;
996 for (Int_t div=1 ; ; div*=2) {
997 Evaluate(p1,t1+dt1,r1,g1,gg1);
998 Evaluate(p2,t2+dt2,r2,g2,gg2);
999 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1000 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1001 if (dd<dm) break;
1002 dt1*=0.5; dt2*=0.5;
1003 if (div>512) {
358f16ae 1004 AliDebug(1," overshoot !"); break;
c7bafca9 1005 }
1006 }
1007 dm=dd;
1008
1009 t1+=dt1;
1010 t2+=dt2;
1011
1012 }
1013
358f16ae 1014 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1015
1016 Double_t cs=TMath::Cos(GetAlpha());
1017 Double_t sn=TMath::Sin(GetAlpha());
1018 xthis=r1[0]*cs + r1[1]*sn;
1019
1020 cs=TMath::Cos(p->GetAlpha());
1021 sn=TMath::Sin(p->GetAlpha());
1022 xp=r2[0]*cs + r2[1]*sn;
1023
1024 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1025}
1026
1027Double_t AliExternalTrackParam::
1028PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1029 //--------------------------------------------------------------
1030 // Propagates this track and the argument track to the position of the
1031 // distance of closest approach.
1032 // Returns the (weighed !) distance of closest approach.
1033 //--------------------------------------------------------------
1034 Double_t xthis,xp;
1035 Double_t dca=GetDCA(p,b,xthis,xp);
1036
1037 if (!PropagateTo(xthis,b)) {
1038 //AliWarning(" propagation failed !");
1039 return 1e+33;
1040 }
1041
1042 if (!p->PropagateTo(xp,b)) {
1043 //AliWarning(" propagation failed !";
1044 return 1e+33;
1045 }
1046
1047 return dca;
1048}
1049
1050
58e536c5 1051Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1052Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1053 //
e99a34df 1054 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1055 // if the (rough) transverse impact parameter is not bigger then "maxd".
1056 // Magnetic field is "b" (kG).
1057 //
1058 // a) The track gets extapolated to the DCA to the vertex.
1059 // b) The impact parameters and their covariance matrix are calculated.
1060 //
1061 // In the case of success, the returned value is kTRUE
1062 // (otherwise, it's kFALSE)
1063 //
1064 Double_t alpha=GetAlpha();
1065 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1066 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1067 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1068 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1069 x-=xv; y-=yv;
1070
1071 //Estimate the impact parameter neglecting the track curvature
1072 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
1073 if (d > maxd) return kFALSE;
1074
1075 //Propagate to the DCA
e99a34df 1076 Double_t crv=kB2C*b*GetParameter()[4];
1077 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1078
f76701bf 1079 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
1080 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 1081 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1082 else cs=1.;
f76701bf 1083
1084 x = xv*cs + yv*sn;
1085 yv=-xv*sn + yv*cs; xv=x;
1086
1087 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1088
1089 if (dz==0) return kTRUE;
1090 dz[0] = GetParameter()[0] - yv;
1091 dz[1] = GetParameter()[1] - zv;
1092
1093 if (covar==0) return kTRUE;
58e536c5 1094 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1095
1096 //***** Improvements by A.Dainese
1097 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1098 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1099 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1100 covar[1] = GetCovariance()[1]; // between (x,y) and z
1101 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1102 //*****
1103
29fbcc93 1104 return kTRUE;
f76701bf 1105}
1106
1107
b1149664 1108void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1109 //----------------------------------------------------------------
1110 // This function returns a unit vector along the track direction
1111 // in the global coordinate system.
1112 //----------------------------------------------------------------
1113 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1114 Double_t snp=fP[2];
92934324 1115 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 1116 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1117 d[0]=(csp*cs - snp*sn)/norm;
1118 d[1]=(snp*cs + csp*sn)/norm;
1119 d[2]=fP[3]/norm;
1120}
1121
c683ddc2 1122Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1123 //---------------------------------------------------------------------
1124 // This function returns the global track momentum components
1125 // Results for (nearly) straight tracks are meaningless !
1126 //---------------------------------------------------------------------
1127 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1128 return Local2GlobalMomentum(p,fAlpha);
1129}
a5e407e9 1130
def9660e 1131Double_t AliExternalTrackParam::Px() const {
957fb479 1132 //---------------------------------------------------------------------
1133 // Returns x-component of momentum
1134 // Result for (nearly) straight tracks is meaningless !
1135 //---------------------------------------------------------------------
def9660e 1136
957fb479 1137 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1138 GetPxPyPz(p);
1139
1140 return p[0];
1141}
1142
1143Double_t AliExternalTrackParam::Py() const {
957fb479 1144 //---------------------------------------------------------------------
1145 // Returns y-component of momentum
1146 // Result for (nearly) straight tracks is meaningless !
1147 //---------------------------------------------------------------------
def9660e 1148
957fb479 1149 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1150 GetPxPyPz(p);
1151
1152 return p[1];
1153}
1154
1155Double_t AliExternalTrackParam::Pz() const {
957fb479 1156 //---------------------------------------------------------------------
1157 // Returns z-component of momentum
1158 // Result for (nearly) straight tracks is meaningless !
1159 //---------------------------------------------------------------------
def9660e 1160
957fb479 1161 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1162 GetPxPyPz(p);
1163
1164 return p[2];
1165}
1166
c683ddc2 1167Double_t AliExternalTrackParam::Xv() const {
1168 //---------------------------------------------------------------------
1169 // Returns x-component of first track point
1170 //---------------------------------------------------------------------
1171
1172 Double_t r[3]={0.,0.,0.};
1173 GetXYZ(r);
1174
1175 return r[0];
1176}
1177
1178Double_t AliExternalTrackParam::Yv() const {
1179 //---------------------------------------------------------------------
1180 // Returns y-component of first track point
1181 //---------------------------------------------------------------------
1182
1183 Double_t r[3]={0.,0.,0.};
1184 GetXYZ(r);
1185
1186 return r[1];
1187}
1188
1189Double_t AliExternalTrackParam::Zv() const {
1190 //---------------------------------------------------------------------
1191 // Returns z-component of first track point
1192 //---------------------------------------------------------------------
1193
1194 Double_t r[3]={0.,0.,0.};
1195 GetXYZ(r);
1196
1197 return r[2];
1198}
1199
def9660e 1200Double_t AliExternalTrackParam::Theta() const {
1201 // return theta angle of momentum
1202
7cdd0c20 1203 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1204}
1205
1206Double_t AliExternalTrackParam::Phi() const {
957fb479 1207 //---------------------------------------------------------------------
1208 // Returns the azimuthal angle of momentum
1209 // 0 <= phi < 2*pi
1210 //---------------------------------------------------------------------
def9660e 1211
957fb479 1212 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1213 if (phi<0.) phi+=2.*TMath::Pi();
1214 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1215
1216 return phi;
def9660e 1217}
1218
1219Double_t AliExternalTrackParam::M() const {
1220 // return particle mass
1221
1222 // No mass information available so far.
1223 // Redifine in derived class!
1224
1225 return -999.;
1226}
1227
1228Double_t AliExternalTrackParam::E() const {
1229 // return particle energy
1230
1231 // No PID information available so far.
1232 // Redifine in derived class!
1233
1234 return -999.;
1235}
1236
1237Double_t AliExternalTrackParam::Eta() const {
1238 // return pseudorapidity
1239
1240 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1241}
1242
1243Double_t AliExternalTrackParam::Y() const {
1244 // return rapidity
1245
1246 // No PID information available so far.
1247 // Redifine in derived class!
1248
1249 return -999.;
1250}
1251
c9ec41e8 1252Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1253 //---------------------------------------------------------------------
1254 // This function returns the global track position
1255 //---------------------------------------------------------------------
1256 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1257 return Local2GlobalPosition(r,fAlpha);
51ad6848 1258}
1259
c9ec41e8 1260Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1261 //---------------------------------------------------------------------
1262 // This function returns the global covariance matrix of the track params
1263 //
1264 // Cov(x,x) ... : cv[0]
1265 // Cov(y,x) ... : cv[1] cv[2]
1266 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1267 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1268 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1269 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1270 //
c9ec41e8 1271 // Results for (nearly) straight tracks are meaningless !
1272 //---------------------------------------------------------------------
e421f556 1273 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1274 for (Int_t i=0; i<21; i++) cv[i]=0.;
1275 return kFALSE;
a5e407e9 1276 }
49d13e89 1277 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1278 for (Int_t i=0; i<21; i++) cv[i]=0.;
1279 return kFALSE;
1280 }
1281 Double_t pt=1./TMath::Abs(fP[4]);
1282 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1283 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1284
1285 Double_t m00=-sn, m10=cs;
1286 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1287 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1288 Double_t m35=pt, m45=-pt*pt*fP[3];
1289
854d5d49 1290 m43*=GetSign();
1291 m44*=GetSign();
1292 m45*=GetSign();
1293
c9ec41e8 1294 cv[0 ] = fC[0]*m00*m00;
1295 cv[1 ] = fC[0]*m00*m10;
1296 cv[2 ] = fC[0]*m10*m10;
1297 cv[3 ] = fC[1]*m00;
1298 cv[4 ] = fC[1]*m10;
1299 cv[5 ] = fC[2];
1300 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1301 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1302 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1303 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1304 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1305 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1306 cv[12] = fC[4]*m24 + fC[11]*m44;
1307 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1308 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1309 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1310 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1311 cv[17] = fC[7]*m35 + fC[11]*m45;
1312 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1313 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1314 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1315
c9ec41e8 1316 return kTRUE;
51ad6848 1317}
1318
51ad6848 1319
c9ec41e8 1320Bool_t
1321AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1322 //---------------------------------------------------------------------
1323 // This function returns the global track momentum extrapolated to
1324 // the radial position "x" (cm) in the magnetic field "b" (kG)
1325 //---------------------------------------------------------------------
c9ec41e8 1326 p[0]=fP[4];
1530f89c 1327 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1328 p[2]=fP[3];
1329 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1330}
1331
7cf7bb6c 1332Bool_t
1333AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1334 //---------------------------------------------------------------------
1335 // This function returns the local Y-coordinate of the intersection
1336 // point between this track and the reference plane "x" (cm).
1337 // Magnetic field "b" (kG)
1338 //---------------------------------------------------------------------
1339 Double_t dx=x-fX;
1340 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1341
1530f89c 1342 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1343
1344 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1345 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1346
1347 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1348 y = fP[0] + dx*(f1+f2)/(r1+r2);
1349 return kTRUE;
1350}
1351
6c94f330 1352Bool_t
1353AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1354 //---------------------------------------------------------------------
1355 // This function returns the local Z-coordinate of the intersection
1356 // point between this track and the reference plane "x" (cm).
1357 // Magnetic field "b" (kG)
1358 //---------------------------------------------------------------------
1359 Double_t dx=x-fX;
1360 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1361
1362 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1363
1364 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1365 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1366
1367 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1368 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1369 return kTRUE;
1370}
1371
c9ec41e8 1372Bool_t
1373AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1374 //---------------------------------------------------------------------
1375 // This function returns the global track position extrapolated to
1376 // the radial position "x" (cm) in the magnetic field "b" (kG)
1377 //---------------------------------------------------------------------
c9ec41e8 1378 Double_t dx=x-fX;
e421f556 1379 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1380
1530f89c 1381 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1382
e421f556 1383 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1384 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1385
1386 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1387 r[0] = x;
1388 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1389 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1390
c9ec41e8 1391 return Local2GlobalPosition(r,fAlpha);
51ad6848 1392}
1393
51ad6848 1394//_____________________________________________________________________________
1395void AliExternalTrackParam::Print(Option_t* /*option*/) const
1396{
1397// print the parameters and the covariance matrix
1398
1399 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1400 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1401 fP[0], fP[1], fP[2], fP[3], fP[4]);
1402 printf(" covariance: %12g\n", fC[0]);
1403 printf(" %12g %12g\n", fC[1], fC[2]);
1404 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1405 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1406 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1407 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1408 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1409}
5b77d93c 1410
c194ba83 1411Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1412 //
1413 // Get sinus at given x
1414 //
1530f89c 1415 Double_t crv=GetC(b);
c194ba83 1416 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1417 Double_t dx = x-fX;
1418 Double_t res = fP[2]+dx*crv;
1419 return res;
1420}
bf00ebb8 1421
1422Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1423 //------------------------------------------------------------------------
1424 // Get the distance between two tracks at the local position x
1425 // working in the local frame of this track.
1426 // Origin : Marian.Ivanov@cern.ch
1427 //-----------------------------------------------------------------------
1428 Double_t xyz[3];
1429 Double_t xyz2[3];
1430 xyz[0]=x;
1431 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1432 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1433 //
1434 //
1435 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1436 xyz2[0]=x;
1437 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1438 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1439 }else{
1440 //
1441 Double_t xyz1[3];
1442 Double_t dfi = param2->GetAlpha()-GetAlpha();
1443 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1444 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1445 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1446 //
1447 xyz1[0]=xyz2[0];
1448 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1449 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1450 //
1451 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1452 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1453 xyz2[2] = xyz1[2];
1454 }
1455 dist[0] = xyz[0]-xyz2[0];
1456 dist[1] = xyz[1]-xyz2[1];
1457 dist[2] = xyz[2]-xyz2[2];
1458
1459 return kTRUE;
1460}
0c19adf7 1461
1462
1463//
1464// Draw functionality.
1465// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1466//
1467
1468void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1469 //
1470 // Draw track line
1471 //
1472 if (minR>maxR) return ;
1473 if (stepR<=0) return ;
1474 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1475 if (npoints<1) return;
1476 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1477 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1478 polymarker->Draw();
1479}
1480
1481//
1482void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1483 //
1484 // Fill points in the polymarker
1485 //
1486 Int_t counter=0;
1487 for (Double_t r=minR; r<maxR; r+=stepR){
1488 Double_t point[3];
1489 GetXYZAt(r,magF,point);
1490 pol->SetPoint(counter,point[0],point[1], point[2]);
1491 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1492 counter++;
1493 }
1494}
0e8460af 1495
1496Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1497 //
1498 Int_t min = TMath::Min(i,j);
1499 Int_t max = TMath::Max(i,j);
1500
1501 return min+(max+1)*max/2;
1502}