The FMD analysis tasks. This is a first version and there is work to do
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
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51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
4b189f98 28#include <TMatrixDSym.h>
51ad6848 29#include "AliExternalTrackParam.h"
58e536c5 30#include "AliVVertex.h"
0c19adf7 31#include "TPolyMarker3D.h"
da4e3deb 32#include "TVector3.h"
6c94f330 33#include "AliLog.h"
51ad6848 34
35ClassImp(AliExternalTrackParam)
36
ed5f2849 37Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
38
51ad6848 39//_____________________________________________________________________________
90e48c0c 40AliExternalTrackParam::AliExternalTrackParam() :
def9660e 41 AliVParticle(),
90e48c0c 42 fX(0),
c9ec41e8 43 fAlpha(0)
51ad6848 44{
90e48c0c 45 //
46 // default constructor
47 //
c9ec41e8 48 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
49 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 50}
51
6c94f330 52//_____________________________________________________________________________
53AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
def9660e 54 AliVParticle(track),
6c94f330 55 fX(track.fX),
56 fAlpha(track.fAlpha)
57{
58 //
59 // copy constructor
60 //
61 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
62 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
63}
64
def9660e 65//_____________________________________________________________________________
66AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
67{
68 //
69 // assignment operator
70 //
71
72 if (this!=&trkPar) {
73 AliVParticle::operator=(trkPar);
74 fX = trkPar.fX;
75 fAlpha = trkPar.fAlpha;
76
77 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
78 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
79 }
80
81 return *this;
82}
83
51ad6848 84//_____________________________________________________________________________
85AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
86 const Double_t param[5],
90e48c0c 87 const Double_t covar[15]) :
def9660e 88 AliVParticle(),
90e48c0c 89 fX(x),
c9ec41e8 90 fAlpha(alpha)
51ad6848 91{
90e48c0c 92 //
93 // create external track parameters from given arguments
94 //
c9ec41e8 95 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
96 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 97}
98
90e48c0c 99//_____________________________________________________________________________
da4e3deb 100AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
101 Double_t cv[21],Short_t sign) :
102 AliVParticle(),
103 fX(0.),
104 fAlpha(0.)
105{
106 //
107 // create external track parameters from the global parameters
108 // x,y,z,px,py,pz and their 6x6 covariance matrix
109 // A.Dainese 10.10.08
110
111 // Calculate alpha: the rotation angle of the corresponding local system
112 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
113
114 // Get the vertex of origin and the momentum
115 TVector3 ver(xyz[0],xyz[1],xyz[2]);
116 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
117
118 // Rotate to the local coordinate system
119 ver.RotateZ(-fAlpha);
120 mom.RotateZ(-fAlpha);
121
122 // x of the reference plane
123 fX = ver.X();
124
125 Double_t charge = (Double_t)sign;
126
127 fP[0] = ver.Y();
128 fP[1] = ver.Z();
129 fP[2] = TMath::Sin(mom.Phi());
130 fP[3] = mom.Pz()/mom.Pt();
131 fP[4] = TMath::Sign(1/mom.Pt(),charge);
132
133 // Covariance matrix (formulas to be simplified)
134
135 Double_t pt=1./TMath::Abs(fP[4]);
136 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
137 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
138
139 Double_t m00=-sn;// m10=cs;
140 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
141 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
142 Double_t m35=pt, m45=-pt*pt*fP[3];
143
144 m43*=GetSign();
145 m44*=GetSign();
146 m45*=GetSign();
147
148 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
149 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
150 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
151 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
152 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
153 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
154 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
155
156 fC[0 ] = cv[0 ]+cv[2 ];
157 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
158 fC[2 ] = cv[5 ];
159 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
160 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
161 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
162 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
163 fC[11] = (cv[8]-fC[4]*m23)/m43;
164 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
165 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
166 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
167 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
168 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
169 Double_t b2=m23*m35;
170 Double_t b3=m43*m35;
171 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
172 Double_t b5=m24*m35;
173 Double_t b6=m44*m35;
174 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
175 fC[13] = b1/b3-b2*fC[8]/b3;
176 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
177}
178
179//_____________________________________________________________________________
6c94f330 180void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
181 const Double_t p[5], const Double_t cov[15]) {
c9ec41e8 182 //
6c94f330 183 // Sets the parameters
c9ec41e8 184 //
6c94f330 185 fX=x;
186 fAlpha=alpha;
187 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
188 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
51ad6848 189}
190
191//_____________________________________________________________________________
c9ec41e8 192void AliExternalTrackParam::Reset() {
1530f89c 193 //
194 // Resets all the parameters to 0
195 //
c9ec41e8 196 fX=fAlpha=0.;
197 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
198 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 199}
200
3775b0ca 201//_____________________________________________________________________________
202void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
203 //
204 // Add "something" to the track covarince matrix.
205 // May be needed to account for unknown mis-calibration/mis-alignment
206 //
207 fC[0] +=c[0];
208 fC[1] +=c[1]; fC[2] +=c[2];
209 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
210 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
211 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
212}
213
214
c9ec41e8 215Double_t AliExternalTrackParam::GetP() const {
216 //---------------------------------------------------------------------
217 // This function returns the track momentum
218 // Results for (nearly) straight tracks are meaningless !
219 //---------------------------------------------------------------------
06fb4a2f 220 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 221 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 222}
223
1d99986f 224Double_t AliExternalTrackParam::Get1P() const {
225 //---------------------------------------------------------------------
226 // This function returns the 1/(track momentum)
227 //---------------------------------------------------------------------
228 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
229}
230
c9ec41e8 231//_______________________________________________________________________
c7bafca9 232Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 233 //------------------------------------------------------------------
234 // This function calculates the transverse impact parameter
235 // with respect to a point with global coordinates (x,y)
236 // in the magnetic field "b" (kG)
237 //------------------------------------------------------------------
5773defd 238 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 239 Double_t rp4=GetC(b);
c9ec41e8 240
241 Double_t xt=fX, yt=fP[0];
242
243 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
244 Double_t a = x*cs + y*sn;
245 y = -x*sn + y*cs; x=a;
246 xt-=x; yt-=y;
247
248 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
249 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 250 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
251}
252
253//_______________________________________________________________________
254void AliExternalTrackParam::
255GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
256 //------------------------------------------------------------------
257 // This function calculates the transverse and longitudinal impact parameters
258 // with respect to a point with global coordinates (x,y)
259 // in the magnetic field "b" (kG)
260 //------------------------------------------------------------------
261 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
262 Double_t xt=fX, yt=fP[0];
263 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
264 Double_t a = x*cs + y*sn;
265 y = -x*sn + y*cs; x=a;
266 xt-=x; yt-=y;
267
268 Double_t rp4=GetC(b);
269 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
270 dz[0] = -(xt*f1 - yt*r1);
271 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
272 return;
273 }
274
275 sn=rp4*xt - f1; cs=rp4*yt + r1;
276 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
277 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
278 dz[0] = -a/(1 + rr);
279 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
280 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 281}
282
49d13e89 283//_______________________________________________________________________
284Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
285 //------------------------------------------------------------------
286 // This function calculates the transverse impact parameter
287 // with respect to a point with global coordinates (xv,yv)
288 // neglecting the track curvature.
289 //------------------------------------------------------------------
290 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
291 Double_t x= xv*cs + yv*sn;
292 Double_t y=-xv*sn + yv*cs;
293
294 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
295
1530f89c 296 return -d;
49d13e89 297}
298
116b445b 299Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 300(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
301 Double_t (*Bethe)(Double_t)) {
116b445b 302 //------------------------------------------------------------------
303 // This function corrects the track parameters for the crossed material.
304 // "xOverX0" - X/X0, the thickness in units of the radiation length.
305 // "xTimesRho" - is the product length*density (g/cm^2).
306 // "mass" - the mass of this particle (GeV/c^2).
307 //------------------------------------------------------------------
308 Double_t &fP2=fP[2];
309 Double_t &fP3=fP[3];
310 Double_t &fP4=fP[4];
311
312 Double_t &fC22=fC[5];
313 Double_t &fC33=fC[9];
314 Double_t &fC43=fC[13];
315 Double_t &fC44=fC[14];
316
7dded1d5 317 //Apply angle correction, if requested
318 if(anglecorr) {
319 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
320 xOverX0 *=angle;
321 xTimesRho *=angle;
322 }
323
116b445b 324 Double_t p=GetP();
325 Double_t p2=p*p;
326 Double_t beta2=p2/(p2 + mass*mass);
116b445b 327
328 //Multiple scattering******************
329 if (xOverX0 != 0) {
330 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
9a53dcc6 331 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
116b445b 332 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
333 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
334 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
335 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
336 fC44 += theta2*fP3*fP4*fP3*fP4;
337 }
338
339 //Energy losses************************
340 if ((xTimesRho != 0.) && (beta2 < 1.)) {
341 Double_t dE=Bethe(beta2)*xTimesRho;
342 Double_t e=TMath::Sqrt(p2 + mass*mass);
343 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
344 fP4*=(1.- e/p2*dE);
4b2fa3ce 345 if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c
346
116b445b 347
348 // Approximate energy loss fluctuation (M.Ivanov)
349 const Double_t knst=0.07; // To be tuned.
350 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
351 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
352
353 }
354
355 return kTRUE;
356}
357
358
ee5dba5e 359Bool_t AliExternalTrackParam::CorrectForMaterial
360(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 361 //------------------------------------------------------------------
116b445b 362 // Deprecated function !
363 // Better use CorrectForMeanMaterial instead of it.
364 //
c7bafca9 365 // This function corrects the track parameters for the crossed material
366 // "d" - the thickness (fraction of the radiation length)
367 // "x0" - the radiation length (g/cm^2)
368 // "mass" - the mass of this particle (GeV/c^2)
369 //------------------------------------------------------------------
370 Double_t &fP2=fP[2];
371 Double_t &fP3=fP[3];
372 Double_t &fP4=fP[4];
373
374 Double_t &fC22=fC[5];
375 Double_t &fC33=fC[9];
376 Double_t &fC43=fC[13];
377 Double_t &fC44=fC[14];
378
7b5ef2e6 379 Double_t p=GetP();
380 Double_t p2=p*p;
c7bafca9 381 Double_t beta2=p2/(p2 + mass*mass);
382 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
383
384 //Multiple scattering******************
385 if (d!=0) {
386 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
9a53dcc6 387 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
c7bafca9 388 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
389 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
390 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
391 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
392 fC44 += theta2*fP3*fP4*fP3*fP4;
393 }
394
395 //Energy losses************************
8fc1985d 396 if (x0!=0. && beta2<1) {
c7bafca9 397 d*=x0;
ee5dba5e 398 Double_t dE=Bethe(beta2)*d;
399 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 400 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 401 fP4*=(1.- e/p2*dE);
402
403 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 404 const Double_t knst=0.07; // To be tuned.
405 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 406 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
407
c7bafca9 408 }
409
410 return kTRUE;
411}
412
ee5dba5e 413Double_t ApproximateBetheBloch(Double_t beta2) {
414 //------------------------------------------------------------------
415 // This is an approximation of the Bethe-Bloch formula with
416 // the density effect taken into account at beta*gamma > 3.5
417 // (the approximation is reasonable only for solid materials)
418 //------------------------------------------------------------------
a821848c 419 if (beta2 >= 1) return kVeryBig;
420
ee5dba5e 421 if (beta2/(1-beta2)>3.5*3.5)
422 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
423
424 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
425}
426
49d13e89 427Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
428 //------------------------------------------------------------------
429 // Transform this track to the local coord. system rotated
430 // by angle "alpha" (rad) with respect to the global coord. system.
431 //------------------------------------------------------------------
dfcef74c 432 if (TMath::Abs(fP[2]) >= kAlmost1) {
433 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
434 return kFALSE;
435 }
436
49d13e89 437 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
438 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
439
440 Double_t &fP0=fP[0];
441 Double_t &fP2=fP[2];
442 Double_t &fC00=fC[0];
443 Double_t &fC10=fC[1];
444 Double_t &fC20=fC[3];
445 Double_t &fC21=fC[4];
446 Double_t &fC22=fC[5];
447 Double_t &fC30=fC[6];
448 Double_t &fC32=fC[8];
449 Double_t &fC40=fC[10];
450 Double_t &fC42=fC[12];
451
452 Double_t x=fX;
453 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
454 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
455
dfcef74c 456 Double_t tmp=sf*ca - cf*sa;
457 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
458
49d13e89 459 fAlpha = alpha;
460 fX = x*ca + fP0*sa;
461 fP0= -x*sa + fP0*ca;
dfcef74c 462 fP2= tmp;
49d13e89 463
06fb4a2f 464 if (TMath::Abs(cf)<kAlmost0) {
465 AliError(Form("Too small cosine value %f",cf));
466 cf = kAlmost0;
467 }
468
49d13e89 469 Double_t rr=(ca+sf/cf*sa);
470
471 fC00 *= (ca*ca);
472 fC10 *= ca;
473 fC20 *= ca*rr;
474 fC21 *= rr;
475 fC22 *= rr*rr;
476 fC30 *= ca;
477 fC32 *= rr;
478 fC40 *= ca;
479 fC42 *= rr;
480
481 return kTRUE;
482}
483
484Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
485 //----------------------------------------------------------------
486 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
487 //----------------------------------------------------------------
49d13e89 488 Double_t dx=xk-fX;
e421f556 489 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 490
1530f89c 491 Double_t crv=GetC(b);
5773defd 492 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
493
49d13e89 494 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 495 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 496 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
497
498 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
499 Double_t
500 &fC00=fC[0],
501 &fC10=fC[1], &fC11=fC[2],
502 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
503 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
504 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
505
506 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
507
508 fX=xk;
509 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 510 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 511 fP2 += dx*crv;
512
513 //f = F - 1
514
515 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
516 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
517 Double_t f12= dx*fP3*f1/(r1*r1*r1);
518 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
519 Double_t f13= dx/r1;
520 Double_t f24= dx; f24*=cc;
521
522 //b = C*ft
523 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
524 Double_t b02=f24*fC40;
525 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
526 Double_t b12=f24*fC41;
527 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
528 Double_t b22=f24*fC42;
529 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
530 Double_t b42=f24*fC44;
531 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
532 Double_t b32=f24*fC43;
533
534 //a = f*b = f*C*ft
535 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
536 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
537 Double_t a22=f24*b42;
538
539 //F*C*Ft = C + (b + bt + a)
540 fC00 += b00 + b00 + a00;
541 fC10 += b10 + b01 + a01;
542 fC20 += b20 + b02 + a02;
543 fC30 += b30;
544 fC40 += b40;
545 fC11 += b11 + b11 + a11;
546 fC21 += b21 + b12 + a12;
547 fC31 += b31;
548 fC41 += b41;
549 fC22 += b22 + b22 + a22;
550 fC32 += b32;
551 fC42 += b42;
552
553 return kTRUE;
554}
555
052daaff 556void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
557Double_t p[3], Double_t bz) const {
558 //+++++++++++++++++++++++++++++++++++++++++
559 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
560 // Extrapolate track along simple helix in magnetic field
561 // Arguments: len -distance alogn helix, [cm]
562 // bz - mag field, [kGaus]
563 // Returns: x and p contain extrapolated positon and momentum
564 // The momentum returned for straight-line tracks is meaningless !
565 //+++++++++++++++++++++++++++++++++++++++++
566 GetXYZ(x);
567
def9660e 568 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 569 Double_t unit[3]; GetDirection(unit);
570 x[0]+=unit[0]*len;
571 x[1]+=unit[1]*len;
572 x[2]+=unit[2]*len;
573
574 p[0]=unit[0]/kAlmost0;
575 p[1]=unit[1]/kAlmost0;
576 p[2]=unit[2]/kAlmost0;
577 } else {
578 GetPxPyPz(p);
579 Double_t pp=GetP();
580 Double_t a = -kB2C*bz*GetSign();
581 Double_t rho = a/pp;
582 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
583 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
584 x[2] += p[2]*len/pp;
585
586 Double_t p0=p[0];
587 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
588 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
589 }
590}
591
592Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
593Double_t bz) const {
594 //+++++++++++++++++++++++++++++++++++++++++
595 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
596 // Finds point of intersection (if exists) of the helix with the plane.
597 // Stores result in fX and fP.
598 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
599 // and vector, normal to the plane
600 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
601 //+++++++++++++++++++++++++++++++++++++++++
602 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
603
604 //estimates initial helix length up to plane
605 Double_t s=
606 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
607 Double_t dist=99999,distPrev=dist;
608 Double_t x[3],p[3];
609 while(TMath::Abs(dist)>0.00001){
610 //calculates helix at the distance s from x0 ALONG the helix
611 Propagate(s,x,p,bz);
612
613 //distance between current helix position and plane
614 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
615
616 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
617 distPrev=dist;
618 s-=dist;
619 }
620 //on exit pnt is intersection point,norm is track vector at that point,
621 //all in MARS
622 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
623 return kTRUE;
624}
625
49d13e89 626Double_t
627AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
628 //----------------------------------------------------------------
629 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
630 //----------------------------------------------------------------
631 Double_t sdd = fC[0] + cov[0];
632 Double_t sdz = fC[1] + cov[1];
633 Double_t szz = fC[2] + cov[2];
634 Double_t det = sdd*szz - sdz*sdz;
635
636 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
637
638 Double_t d = fP[0] - p[0];
639 Double_t z = fP[1] - p[1];
640
641 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
642}
643
4b189f98 644Double_t AliExternalTrackParam::
645GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
646 //----------------------------------------------------------------
647 // Estimate the chi2 of the 3D space point "p" and
1e023a36 648 // the full covariance matrix "covyz" and "covxyz"
4b189f98 649 //
650 // Cov(x,x) ... : covxyz[0]
651 // Cov(y,x) ... : covxyz[1] covyz[0]
652 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
653 //----------------------------------------------------------------
654
655 Double_t res[3] = {
656 GetX() - p[0],
657 GetY() - p[1],
658 GetZ() - p[2]
659 };
660
661 Double_t f=GetSnp();
662 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
663 Double_t r=TMath::Sqrt(1.- f*f);
664 Double_t a=f/r, b=GetTgl()/r;
665
666 Double_t s2=333.*333.; //something reasonably big (cm^2)
667
668 TMatrixDSym v(3);
669 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
670 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
671 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
672
673 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
674 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
675 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
676
677 v.Invert();
678 if (!v.IsValid()) return kVeryBig;
679
680 Double_t chi2=0.;
681 for (Int_t i = 0; i < 3; i++)
682 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
683
684 return chi2;
685
686
687}
688
1e023a36 689Bool_t AliExternalTrackParam::
690PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
691 //----------------------------------------------------------------
692 // Propagate this track to the plane
693 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
694 // belongs to.
695 // The magnetic field is "bz" (kG)
696 //
697 // The track curvature and the change of the covariance matrix
698 // of the track parameters are negleted !
699 // (So the "step" should be small compared with 1/curvature)
700 //----------------------------------------------------------------
701
702 Double_t f=GetSnp();
703 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
704 Double_t r=TMath::Sqrt(1.- f*f);
705 Double_t a=f/r, b=GetTgl()/r;
706
707 Double_t s2=333.*333.; //something reasonably big (cm^2)
708
709 TMatrixDSym tV(3);
710 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
711 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
712 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
713
714 TMatrixDSym pV(3);
715 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
716 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
717 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
718
719 TMatrixDSym tpV(tV);
720 tpV+=pV;
721 tpV.Invert();
722 if (!tpV.IsValid()) return kFALSE;
723
724 TMatrixDSym pW(3),tW(3);
725 for (Int_t i=0; i<3; i++)
726 for (Int_t j=0; j<3; j++) {
727 pW(i,j)=tW(i,j)=0.;
728 for (Int_t k=0; k<3; k++) {
729 pW(i,j) += tV(i,k)*tpV(k,j);
730 tW(i,j) += pV(i,k)*tpV(k,j);
731 }
732 }
733
734 Double_t t[3] = {GetX(), GetY(), GetZ()};
735
736 Double_t x=0.;
737 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
738 Double_t crv=GetC(bz);
739 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
740 f += crv*(x-fX);
741 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
742 fX=x;
743
744 fP[0]=0.;
745 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
746 fP[1]=0.;
747 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
748
749 return kTRUE;
750}
751
e23a38cb 752Double_t *AliExternalTrackParam::GetResiduals(
753Double_t *p,Double_t *cov,Bool_t updated) const {
754 //------------------------------------------------------------------
755 // Returns the track residuals with the space point "p" having
756 // the covariance matrix "cov".
757 // If "updated" is kTRUE, the track parameters expected to be updated,
758 // otherwise they must be predicted.
759 //------------------------------------------------------------------
760 static Double_t res[2];
761
762 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
763 if (updated) {
764 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
765 } else {
766 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
767 }
768 Double_t det=r00*r11 - r01*r01;
769
770 if (TMath::Abs(det) < kAlmost0) return 0;
771
772 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 773
774 if (r00 < 0.) return 0;
775 if (r11 < 0.) return 0;
776
e23a38cb 777 Double_t dy = fP[0] - p[0];
778 Double_t dz = fP[1] - p[1];
779
780 res[0]=dy*TMath::Sqrt(r00);
781 res[1]=dz*TMath::Sqrt(r11);
782
783 return res;
784}
785
49d13e89 786Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
787 //------------------------------------------------------------------
788 // Update the track parameters with the space point "p" having
789 // the covariance matrix "cov"
790 //------------------------------------------------------------------
791 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
792 Double_t
793 &fC00=fC[0],
794 &fC10=fC[1], &fC11=fC[2],
795 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
796 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
797 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
798
799 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
800 r00+=fC00; r01+=fC10; r11+=fC11;
801 Double_t det=r00*r11 - r01*r01;
802
803 if (TMath::Abs(det) < kAlmost0) return kFALSE;
804
805
806 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
807
808 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
809 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
810 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
811 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
812 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
813
814 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
815 Double_t sf=fP2 + k20*dy + k21*dz;
816 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
817
818 fP0 += k00*dy + k01*dz;
819 fP1 += k10*dy + k11*dz;
820 fP2 = sf;
821 fP3 += k30*dy + k31*dz;
822 fP4 += k40*dy + k41*dz;
823
824 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
825 Double_t c12=fC21, c13=fC31, c14=fC41;
826
827 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
828 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
829 fC40-=k00*c04+k01*c14;
830
831 fC11-=k10*c01+k11*fC11;
832 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
833 fC41-=k10*c04+k11*c14;
834
835 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
836 fC42-=k20*c04+k21*c14;
837
838 fC33-=k30*c03+k31*c13;
839 fC43-=k30*c04+k31*c14;
840
841 fC44-=k40*c04+k41*c14;
842
843 return kTRUE;
844}
845
c7bafca9 846void
847AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
848 //--------------------------------------------------------------------
849 // External track parameters -> helix parameters
850 // "b" - magnetic field (kG)
851 //--------------------------------------------------------------------
852 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
853
1530f89c 854 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 855
856 hlx[5]=fX*cs - hlx[0]*sn; // x0
857 hlx[0]=fX*sn + hlx[0]*cs; // y0
858//hlx[1]= // z0
859 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
860//hlx[3]= // tgl
1530f89c 861 hlx[4]=GetC(b); // C
c7bafca9 862}
863
864
865static void Evaluate(const Double_t *h, Double_t t,
866 Double_t r[3], //radius vector
867 Double_t g[3], //first defivatives
868 Double_t gg[3]) //second derivatives
869{
870 //--------------------------------------------------------------------
871 // Calculate position of a point on a track and some derivatives
872 //--------------------------------------------------------------------
873 Double_t phase=h[4]*t+h[2];
874 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
875
876 r[0] = h[5] + (sn - h[6])/h[4];
877 r[1] = h[0] - (cs - h[7])/h[4];
878 r[2] = h[1] + h[3]*t;
879
880 g[0] = cs; g[1]=sn; g[2]=h[3];
881
882 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
883}
884
885Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
886Double_t b, Double_t &xthis, Double_t &xp) const {
887 //------------------------------------------------------------
888 // Returns the (weighed !) distance of closest approach between
889 // this track and the track "p".
890 // Other returned values:
891 // xthis, xt - coordinates of tracks' reference planes at the DCA
892 //-----------------------------------------------------------
893 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
894 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
895 Double_t dx2=dy2;
896
897 //dx2=dy2=dz2=1.;
898
899 Double_t p1[8]; GetHelixParameters(p1,b);
900 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
901 Double_t p2[8]; p->GetHelixParameters(p2,b);
902 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
903
904
905 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
906 Evaluate(p1,t1,r1,g1,gg1);
907 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
908 Evaluate(p2,t2,r2,g2,gg2);
909
910 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
911 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
912
913 Int_t max=27;
914 while (max--) {
915 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
916 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
917 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
918 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
919 (g1[2]*g1[2] - dz*gg1[2])/dz2;
920 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
921 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
922 (g2[2]*g2[2] + dz*gg2[2])/dz2;
923 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
924
925 Double_t det=h11*h22-h12*h12;
926
927 Double_t dt1,dt2;
928 if (TMath::Abs(det)<1.e-33) {
929 //(quasi)singular Hessian
930 dt1=-gt1; dt2=-gt2;
931 } else {
932 dt1=-(gt1*h22 - gt2*h12)/det;
933 dt2=-(h11*gt2 - h12*gt1)/det;
934 }
935
936 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
937
938 //check delta(phase1) ?
939 //check delta(phase2) ?
940
941 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
942 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
943 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 944 AliDebug(1," stopped at not a stationary point !");
c7bafca9 945 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
946 if (lmb < 0.)
358f16ae 947 AliDebug(1," stopped at not a minimum !");
c7bafca9 948 break;
949 }
950
951 Double_t dd=dm;
952 for (Int_t div=1 ; ; div*=2) {
953 Evaluate(p1,t1+dt1,r1,g1,gg1);
954 Evaluate(p2,t2+dt2,r2,g2,gg2);
955 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
956 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
957 if (dd<dm) break;
958 dt1*=0.5; dt2*=0.5;
959 if (div>512) {
358f16ae 960 AliDebug(1," overshoot !"); break;
c7bafca9 961 }
962 }
963 dm=dd;
964
965 t1+=dt1;
966 t2+=dt2;
967
968 }
969
358f16ae 970 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 971
972 Double_t cs=TMath::Cos(GetAlpha());
973 Double_t sn=TMath::Sin(GetAlpha());
974 xthis=r1[0]*cs + r1[1]*sn;
975
976 cs=TMath::Cos(p->GetAlpha());
977 sn=TMath::Sin(p->GetAlpha());
978 xp=r2[0]*cs + r2[1]*sn;
979
980 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
981}
982
983Double_t AliExternalTrackParam::
984PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
985 //--------------------------------------------------------------
986 // Propagates this track and the argument track to the position of the
987 // distance of closest approach.
988 // Returns the (weighed !) distance of closest approach.
989 //--------------------------------------------------------------
990 Double_t xthis,xp;
991 Double_t dca=GetDCA(p,b,xthis,xp);
992
993 if (!PropagateTo(xthis,b)) {
994 //AliWarning(" propagation failed !");
995 return 1e+33;
996 }
997
998 if (!p->PropagateTo(xp,b)) {
999 //AliWarning(" propagation failed !";
1000 return 1e+33;
1001 }
1002
1003 return dca;
1004}
1005
1006
58e536c5 1007Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1008Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1009 //
e99a34df 1010 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1011 // if the (rough) transverse impact parameter is not bigger then "maxd".
1012 // Magnetic field is "b" (kG).
1013 //
1014 // a) The track gets extapolated to the DCA to the vertex.
1015 // b) The impact parameters and their covariance matrix are calculated.
1016 //
1017 // In the case of success, the returned value is kTRUE
1018 // (otherwise, it's kFALSE)
1019 //
1020 Double_t alpha=GetAlpha();
1021 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1022 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1023 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1024 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1025 x-=xv; y-=yv;
1026
1027 //Estimate the impact parameter neglecting the track curvature
1028 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
1029 if (d > maxd) return kFALSE;
1030
1031 //Propagate to the DCA
e99a34df 1032 Double_t crv=kB2C*b*GetParameter()[4];
1033 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1034
f76701bf 1035 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
1036 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 1037 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1038 else cs=1.;
f76701bf 1039
1040 x = xv*cs + yv*sn;
1041 yv=-xv*sn + yv*cs; xv=x;
1042
1043 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1044
1045 if (dz==0) return kTRUE;
1046 dz[0] = GetParameter()[0] - yv;
1047 dz[1] = GetParameter()[1] - zv;
1048
1049 if (covar==0) return kTRUE;
58e536c5 1050 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1051
1052 //***** Improvements by A.Dainese
1053 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1054 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1055 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1056 covar[1] = GetCovariance()[1]; // between (x,y) and z
1057 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1058 //*****
1059
29fbcc93 1060 return kTRUE;
f76701bf 1061}
1062
1063
b1149664 1064void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1065 //----------------------------------------------------------------
1066 // This function returns a unit vector along the track direction
1067 // in the global coordinate system.
1068 //----------------------------------------------------------------
1069 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1070 Double_t snp=fP[2];
92934324 1071 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 1072 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1073 d[0]=(csp*cs - snp*sn)/norm;
1074 d[1]=(snp*cs + csp*sn)/norm;
1075 d[2]=fP[3]/norm;
1076}
1077
c683ddc2 1078Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1079 //---------------------------------------------------------------------
1080 // This function returns the global track momentum components
1081 // Results for (nearly) straight tracks are meaningless !
1082 //---------------------------------------------------------------------
1083 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1084 return Local2GlobalMomentum(p,fAlpha);
1085}
a5e407e9 1086
def9660e 1087Double_t AliExternalTrackParam::Px() const {
957fb479 1088 //---------------------------------------------------------------------
1089 // Returns x-component of momentum
1090 // Result for (nearly) straight tracks is meaningless !
1091 //---------------------------------------------------------------------
def9660e 1092
957fb479 1093 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1094 GetPxPyPz(p);
1095
1096 return p[0];
1097}
1098
1099Double_t AliExternalTrackParam::Py() const {
957fb479 1100 //---------------------------------------------------------------------
1101 // Returns y-component of momentum
1102 // Result for (nearly) straight tracks is meaningless !
1103 //---------------------------------------------------------------------
def9660e 1104
957fb479 1105 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1106 GetPxPyPz(p);
1107
1108 return p[1];
1109}
1110
1111Double_t AliExternalTrackParam::Pz() const {
957fb479 1112 //---------------------------------------------------------------------
1113 // Returns z-component of momentum
1114 // Result for (nearly) straight tracks is meaningless !
1115 //---------------------------------------------------------------------
def9660e 1116
957fb479 1117 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1118 GetPxPyPz(p);
1119
1120 return p[2];
1121}
1122
c683ddc2 1123Double_t AliExternalTrackParam::Xv() const {
1124 //---------------------------------------------------------------------
1125 // Returns x-component of first track point
1126 //---------------------------------------------------------------------
1127
1128 Double_t r[3]={0.,0.,0.};
1129 GetXYZ(r);
1130
1131 return r[0];
1132}
1133
1134Double_t AliExternalTrackParam::Yv() const {
1135 //---------------------------------------------------------------------
1136 // Returns y-component of first track point
1137 //---------------------------------------------------------------------
1138
1139 Double_t r[3]={0.,0.,0.};
1140 GetXYZ(r);
1141
1142 return r[1];
1143}
1144
1145Double_t AliExternalTrackParam::Zv() const {
1146 //---------------------------------------------------------------------
1147 // Returns z-component of first track point
1148 //---------------------------------------------------------------------
1149
1150 Double_t r[3]={0.,0.,0.};
1151 GetXYZ(r);
1152
1153 return r[2];
1154}
1155
def9660e 1156Double_t AliExternalTrackParam::Theta() const {
1157 // return theta angle of momentum
1158
7cdd0c20 1159 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1160}
1161
1162Double_t AliExternalTrackParam::Phi() const {
957fb479 1163 //---------------------------------------------------------------------
1164 // Returns the azimuthal angle of momentum
1165 // 0 <= phi < 2*pi
1166 //---------------------------------------------------------------------
def9660e 1167
957fb479 1168 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1169 if (phi<0.) phi+=2.*TMath::Pi();
1170 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1171
1172 return phi;
def9660e 1173}
1174
1175Double_t AliExternalTrackParam::M() const {
1176 // return particle mass
1177
1178 // No mass information available so far.
1179 // Redifine in derived class!
1180
1181 return -999.;
1182}
1183
1184Double_t AliExternalTrackParam::E() const {
1185 // return particle energy
1186
1187 // No PID information available so far.
1188 // Redifine in derived class!
1189
1190 return -999.;
1191}
1192
1193Double_t AliExternalTrackParam::Eta() const {
1194 // return pseudorapidity
1195
1196 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1197}
1198
1199Double_t AliExternalTrackParam::Y() const {
1200 // return rapidity
1201
1202 // No PID information available so far.
1203 // Redifine in derived class!
1204
1205 return -999.;
1206}
1207
c9ec41e8 1208Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1209 //---------------------------------------------------------------------
1210 // This function returns the global track position
1211 //---------------------------------------------------------------------
1212 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1213 return Local2GlobalPosition(r,fAlpha);
51ad6848 1214}
1215
c9ec41e8 1216Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1217 //---------------------------------------------------------------------
1218 // This function returns the global covariance matrix of the track params
1219 //
1220 // Cov(x,x) ... : cv[0]
1221 // Cov(y,x) ... : cv[1] cv[2]
1222 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1223 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1224 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1225 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1226 //
c9ec41e8 1227 // Results for (nearly) straight tracks are meaningless !
1228 //---------------------------------------------------------------------
e421f556 1229 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1230 for (Int_t i=0; i<21; i++) cv[i]=0.;
1231 return kFALSE;
a5e407e9 1232 }
49d13e89 1233 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1234 for (Int_t i=0; i<21; i++) cv[i]=0.;
1235 return kFALSE;
1236 }
1237 Double_t pt=1./TMath::Abs(fP[4]);
1238 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1239 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1240
1241 Double_t m00=-sn, m10=cs;
1242 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1243 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1244 Double_t m35=pt, m45=-pt*pt*fP[3];
1245
854d5d49 1246 m43*=GetSign();
1247 m44*=GetSign();
1248 m45*=GetSign();
1249
c9ec41e8 1250 cv[0 ] = fC[0]*m00*m00;
1251 cv[1 ] = fC[0]*m00*m10;
1252 cv[2 ] = fC[0]*m10*m10;
1253 cv[3 ] = fC[1]*m00;
1254 cv[4 ] = fC[1]*m10;
1255 cv[5 ] = fC[2];
1256 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1257 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1258 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1259 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1260 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1261 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1262 cv[12] = fC[4]*m24 + fC[11]*m44;
1263 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1264 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1265 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1266 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1267 cv[17] = fC[7]*m35 + fC[11]*m45;
1268 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1269 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1270 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1271
c9ec41e8 1272 return kTRUE;
51ad6848 1273}
1274
51ad6848 1275
c9ec41e8 1276Bool_t
1277AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1278 //---------------------------------------------------------------------
1279 // This function returns the global track momentum extrapolated to
1280 // the radial position "x" (cm) in the magnetic field "b" (kG)
1281 //---------------------------------------------------------------------
c9ec41e8 1282 p[0]=fP[4];
1530f89c 1283 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1284 p[2]=fP[3];
1285 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1286}
1287
7cf7bb6c 1288Bool_t
1289AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1290 //---------------------------------------------------------------------
1291 // This function returns the local Y-coordinate of the intersection
1292 // point between this track and the reference plane "x" (cm).
1293 // Magnetic field "b" (kG)
1294 //---------------------------------------------------------------------
1295 Double_t dx=x-fX;
1296 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1297
1530f89c 1298 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1299
1300 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1301 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1302
1303 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1304 y = fP[0] + dx*(f1+f2)/(r1+r2);
1305 return kTRUE;
1306}
1307
6c94f330 1308Bool_t
1309AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1310 //---------------------------------------------------------------------
1311 // This function returns the local Z-coordinate of the intersection
1312 // point between this track and the reference plane "x" (cm).
1313 // Magnetic field "b" (kG)
1314 //---------------------------------------------------------------------
1315 Double_t dx=x-fX;
1316 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1317
1318 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1319
1320 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1321 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1322
1323 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1324 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1325 return kTRUE;
1326}
1327
c9ec41e8 1328Bool_t
1329AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1330 //---------------------------------------------------------------------
1331 // This function returns the global track position extrapolated to
1332 // the radial position "x" (cm) in the magnetic field "b" (kG)
1333 //---------------------------------------------------------------------
c9ec41e8 1334 Double_t dx=x-fX;
e421f556 1335 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1336
1530f89c 1337 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1338
e421f556 1339 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1340 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1341
1342 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1343 r[0] = x;
1344 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 1345 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 1346 return Local2GlobalPosition(r,fAlpha);
51ad6848 1347}
1348
51ad6848 1349//_____________________________________________________________________________
1350void AliExternalTrackParam::Print(Option_t* /*option*/) const
1351{
1352// print the parameters and the covariance matrix
1353
1354 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1355 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1356 fP[0], fP[1], fP[2], fP[3], fP[4]);
1357 printf(" covariance: %12g\n", fC[0]);
1358 printf(" %12g %12g\n", fC[1], fC[2]);
1359 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1360 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1361 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1362 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1363 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1364}
5b77d93c 1365
c194ba83 1366Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1367 //
1368 // Get sinus at given x
1369 //
1530f89c 1370 Double_t crv=GetC(b);
c194ba83 1371 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1372 Double_t dx = x-fX;
1373 Double_t res = fP[2]+dx*crv;
1374 return res;
1375}
bf00ebb8 1376
1377Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1378 //------------------------------------------------------------------------
1379 // Get the distance between two tracks at the local position x
1380 // working in the local frame of this track.
1381 // Origin : Marian.Ivanov@cern.ch
1382 //-----------------------------------------------------------------------
1383 Double_t xyz[3];
1384 Double_t xyz2[3];
1385 xyz[0]=x;
1386 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1387 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1388 //
1389 //
1390 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1391 xyz2[0]=x;
1392 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1393 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1394 }else{
1395 //
1396 Double_t xyz1[3];
1397 Double_t dfi = param2->GetAlpha()-GetAlpha();
1398 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1399 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1400 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1401 //
1402 xyz1[0]=xyz2[0];
1403 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1404 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1405 //
1406 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1407 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1408 xyz2[2] = xyz1[2];
1409 }
1410 dist[0] = xyz[0]-xyz2[0];
1411 dist[1] = xyz[1]-xyz2[1];
1412 dist[2] = xyz[2]-xyz2[2];
1413
1414 return kTRUE;
1415}
0c19adf7 1416
1417
1418//
1419// Draw functionality.
1420// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1421//
1422
1423void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1424 //
1425 // Draw track line
1426 //
1427 if (minR>maxR) return ;
1428 if (stepR<=0) return ;
1429 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1430 if (npoints<1) return;
1431 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1432 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1433 polymarker->Draw();
1434}
1435
1436//
1437void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1438 //
1439 // Fill points in the polymarker
1440 //
1441 Int_t counter=0;
1442 for (Double_t r=minR; r<maxR; r+=stepR){
1443 Double_t point[3];
1444 GetXYZAt(r,magF,point);
1445 pol->SetPoint(counter,point[0],point[1], point[2]);
1446 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1447 counter++;
1448 }
1449}