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