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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"
6c94f330 31#include "AliLog.h"
51ad6848 32
33ClassImp(AliExternalTrackParam)
34
ed5f2849 35Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
36
51ad6848 37//_____________________________________________________________________________
90e48c0c 38AliExternalTrackParam::AliExternalTrackParam() :
def9660e 39 AliVParticle(),
90e48c0c 40 fX(0),
c9ec41e8 41 fAlpha(0)
51ad6848 42{
90e48c0c 43 //
44 // default constructor
45 //
c9ec41e8 46 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
47 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 48}
49
6c94f330 50//_____________________________________________________________________________
51AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
def9660e 52 AliVParticle(track),
6c94f330 53 fX(track.fX),
54 fAlpha(track.fAlpha)
55{
56 //
57 // copy constructor
58 //
59 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
60 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
61}
62
def9660e 63//_____________________________________________________________________________
64AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
65{
66 //
67 // assignment operator
68 //
69
70 if (this!=&trkPar) {
71 AliVParticle::operator=(trkPar);
72 fX = trkPar.fX;
73 fAlpha = trkPar.fAlpha;
74
75 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
76 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
77 }
78
79 return *this;
80}
81
51ad6848 82//_____________________________________________________________________________
83AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
84 const Double_t param[5],
90e48c0c 85 const Double_t covar[15]) :
def9660e 86 AliVParticle(),
90e48c0c 87 fX(x),
c9ec41e8 88 fAlpha(alpha)
51ad6848 89{
90e48c0c 90 //
91 // create external track parameters from given arguments
92 //
c9ec41e8 93 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
94 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 95}
96
90e48c0c 97//_____________________________________________________________________________
6c94f330 98void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
99 const Double_t p[5], const Double_t cov[15]) {
c9ec41e8 100 //
6c94f330 101 // Sets the parameters
c9ec41e8 102 //
6c94f330 103 fX=x;
104 fAlpha=alpha;
105 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
106 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
51ad6848 107}
108
109//_____________________________________________________________________________
c9ec41e8 110void AliExternalTrackParam::Reset() {
1530f89c 111 //
112 // Resets all the parameters to 0
113 //
c9ec41e8 114 fX=fAlpha=0.;
115 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
116 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 117}
118
c9ec41e8 119Double_t AliExternalTrackParam::GetP() const {
120 //---------------------------------------------------------------------
121 // This function returns the track momentum
122 // Results for (nearly) straight tracks are meaningless !
123 //---------------------------------------------------------------------
06fb4a2f 124 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 125 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 126}
127
1d99986f 128Double_t AliExternalTrackParam::Get1P() const {
129 //---------------------------------------------------------------------
130 // This function returns the 1/(track momentum)
131 //---------------------------------------------------------------------
132 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
133}
134
c9ec41e8 135//_______________________________________________________________________
c7bafca9 136Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 137 //------------------------------------------------------------------
138 // This function calculates the transverse impact parameter
139 // with respect to a point with global coordinates (x,y)
140 // in the magnetic field "b" (kG)
141 //------------------------------------------------------------------
5773defd 142 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 143 Double_t rp4=GetC(b);
c9ec41e8 144
145 Double_t xt=fX, yt=fP[0];
146
147 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
148 Double_t a = x*cs + y*sn;
149 y = -x*sn + y*cs; x=a;
150 xt-=x; yt-=y;
151
152 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
153 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 154 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
155}
156
157//_______________________________________________________________________
158void AliExternalTrackParam::
159GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
160 //------------------------------------------------------------------
161 // This function calculates the transverse and longitudinal impact parameters
162 // with respect to a point with global coordinates (x,y)
163 // in the magnetic field "b" (kG)
164 //------------------------------------------------------------------
165 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
166 Double_t xt=fX, yt=fP[0];
167 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
168 Double_t a = x*cs + y*sn;
169 y = -x*sn + y*cs; x=a;
170 xt-=x; yt-=y;
171
172 Double_t rp4=GetC(b);
173 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
174 dz[0] = -(xt*f1 - yt*r1);
175 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
176 return;
177 }
178
179 sn=rp4*xt - f1; cs=rp4*yt + r1;
180 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
181 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
182 dz[0] = -a/(1 + rr);
183 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
184 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 185}
186
49d13e89 187//_______________________________________________________________________
188Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
189 //------------------------------------------------------------------
190 // This function calculates the transverse impact parameter
191 // with respect to a point with global coordinates (xv,yv)
192 // neglecting the track curvature.
193 //------------------------------------------------------------------
194 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
195 Double_t x= xv*cs + yv*sn;
196 Double_t y=-xv*sn + yv*cs;
197
198 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
199
1530f89c 200 return -d;
49d13e89 201}
202
116b445b 203Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 204(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
205 Double_t (*Bethe)(Double_t)) {
116b445b 206 //------------------------------------------------------------------
207 // This function corrects the track parameters for the crossed material.
208 // "xOverX0" - X/X0, the thickness in units of the radiation length.
209 // "xTimesRho" - is the product length*density (g/cm^2).
210 // "mass" - the mass of this particle (GeV/c^2).
211 //------------------------------------------------------------------
212 Double_t &fP2=fP[2];
213 Double_t &fP3=fP[3];
214 Double_t &fP4=fP[4];
215
216 Double_t &fC22=fC[5];
217 Double_t &fC33=fC[9];
218 Double_t &fC43=fC[13];
219 Double_t &fC44=fC[14];
220
7dded1d5 221 //Apply angle correction, if requested
222 if(anglecorr) {
223 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
224 xOverX0 *=angle;
225 xTimesRho *=angle;
226 }
227
116b445b 228 Double_t p=GetP();
229 Double_t p2=p*p;
230 Double_t beta2=p2/(p2 + mass*mass);
116b445b 231
232 //Multiple scattering******************
233 if (xOverX0 != 0) {
234 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
235 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
236 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
237 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
238 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
239 fC44 += theta2*fP3*fP4*fP3*fP4;
240 }
241
242 //Energy losses************************
243 if ((xTimesRho != 0.) && (beta2 < 1.)) {
244 Double_t dE=Bethe(beta2)*xTimesRho;
245 Double_t e=TMath::Sqrt(p2 + mass*mass);
246 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
247 fP4*=(1.- e/p2*dE);
248
249 // Approximate energy loss fluctuation (M.Ivanov)
250 const Double_t knst=0.07; // To be tuned.
251 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
252 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
253
254 }
255
256 return kTRUE;
257}
258
259
ee5dba5e 260Bool_t AliExternalTrackParam::CorrectForMaterial
261(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 262 //------------------------------------------------------------------
116b445b 263 // Deprecated function !
264 // Better use CorrectForMeanMaterial instead of it.
265 //
c7bafca9 266 // This function corrects the track parameters for the crossed material
267 // "d" - the thickness (fraction of the radiation length)
268 // "x0" - the radiation length (g/cm^2)
269 // "mass" - the mass of this particle (GeV/c^2)
270 //------------------------------------------------------------------
271 Double_t &fP2=fP[2];
272 Double_t &fP3=fP[3];
273 Double_t &fP4=fP[4];
274
275 Double_t &fC22=fC[5];
276 Double_t &fC33=fC[9];
277 Double_t &fC43=fC[13];
278 Double_t &fC44=fC[14];
279
7b5ef2e6 280 Double_t p=GetP();
281 Double_t p2=p*p;
c7bafca9 282 Double_t beta2=p2/(p2 + mass*mass);
283 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
284
285 //Multiple scattering******************
286 if (d!=0) {
287 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
288 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
289 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
290 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
291 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
292 fC44 += theta2*fP3*fP4*fP3*fP4;
293 }
294
295 //Energy losses************************
8fc1985d 296 if (x0!=0. && beta2<1) {
c7bafca9 297 d*=x0;
ee5dba5e 298 Double_t dE=Bethe(beta2)*d;
299 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 300 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 301 fP4*=(1.- e/p2*dE);
302
303 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 304 const Double_t knst=0.07; // To be tuned.
305 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 306 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
307
c7bafca9 308 }
309
310 return kTRUE;
311}
312
ee5dba5e 313Double_t ApproximateBetheBloch(Double_t beta2) {
314 //------------------------------------------------------------------
315 // This is an approximation of the Bethe-Bloch formula with
316 // the density effect taken into account at beta*gamma > 3.5
317 // (the approximation is reasonable only for solid materials)
318 //------------------------------------------------------------------
a821848c 319 if (beta2 >= 1) return kVeryBig;
320
ee5dba5e 321 if (beta2/(1-beta2)>3.5*3.5)
322 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
323
324 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
325}
326
49d13e89 327Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
328 //------------------------------------------------------------------
329 // Transform this track to the local coord. system rotated
330 // by angle "alpha" (rad) with respect to the global coord. system.
331 //------------------------------------------------------------------
dfcef74c 332 if (TMath::Abs(fP[2]) >= kAlmost1) {
333 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
334 return kFALSE;
335 }
336
49d13e89 337 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
338 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
339
340 Double_t &fP0=fP[0];
341 Double_t &fP2=fP[2];
342 Double_t &fC00=fC[0];
343 Double_t &fC10=fC[1];
344 Double_t &fC20=fC[3];
345 Double_t &fC21=fC[4];
346 Double_t &fC22=fC[5];
347 Double_t &fC30=fC[6];
348 Double_t &fC32=fC[8];
349 Double_t &fC40=fC[10];
350 Double_t &fC42=fC[12];
351
352 Double_t x=fX;
353 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
354 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
355
dfcef74c 356 Double_t tmp=sf*ca - cf*sa;
357 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
358
49d13e89 359 fAlpha = alpha;
360 fX = x*ca + fP0*sa;
361 fP0= -x*sa + fP0*ca;
dfcef74c 362 fP2= tmp;
49d13e89 363
06fb4a2f 364 if (TMath::Abs(cf)<kAlmost0) {
365 AliError(Form("Too small cosine value %f",cf));
366 cf = kAlmost0;
367 }
368
49d13e89 369 Double_t rr=(ca+sf/cf*sa);
370
371 fC00 *= (ca*ca);
372 fC10 *= ca;
373 fC20 *= ca*rr;
374 fC21 *= rr;
375 fC22 *= rr*rr;
376 fC30 *= ca;
377 fC32 *= rr;
378 fC40 *= ca;
379 fC42 *= rr;
380
381 return kTRUE;
382}
383
384Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
385 //----------------------------------------------------------------
386 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
387 //----------------------------------------------------------------
49d13e89 388 Double_t dx=xk-fX;
e421f556 389 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 390
1530f89c 391 Double_t crv=GetC(b);
5773defd 392 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
393
49d13e89 394 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 395 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 396 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
397
398 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
399 Double_t
400 &fC00=fC[0],
401 &fC10=fC[1], &fC11=fC[2],
402 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
403 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
404 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
405
406 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
407
408 fX=xk;
409 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 410 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 411 fP2 += dx*crv;
412
413 //f = F - 1
414
415 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
416 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
417 Double_t f12= dx*fP3*f1/(r1*r1*r1);
418 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
419 Double_t f13= dx/r1;
420 Double_t f24= dx; f24*=cc;
421
422 //b = C*ft
423 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
424 Double_t b02=f24*fC40;
425 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
426 Double_t b12=f24*fC41;
427 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
428 Double_t b22=f24*fC42;
429 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
430 Double_t b42=f24*fC44;
431 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
432 Double_t b32=f24*fC43;
433
434 //a = f*b = f*C*ft
435 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
436 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
437 Double_t a22=f24*b42;
438
439 //F*C*Ft = C + (b + bt + a)
440 fC00 += b00 + b00 + a00;
441 fC10 += b10 + b01 + a01;
442 fC20 += b20 + b02 + a02;
443 fC30 += b30;
444 fC40 += b40;
445 fC11 += b11 + b11 + a11;
446 fC21 += b21 + b12 + a12;
447 fC31 += b31;
448 fC41 += b41;
449 fC22 += b22 + b22 + a22;
450 fC32 += b32;
451 fC42 += b42;
452
453 return kTRUE;
454}
455
052daaff 456void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
457Double_t p[3], Double_t bz) const {
458 //+++++++++++++++++++++++++++++++++++++++++
459 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
460 // Extrapolate track along simple helix in magnetic field
461 // Arguments: len -distance alogn helix, [cm]
462 // bz - mag field, [kGaus]
463 // Returns: x and p contain extrapolated positon and momentum
464 // The momentum returned for straight-line tracks is meaningless !
465 //+++++++++++++++++++++++++++++++++++++++++
466 GetXYZ(x);
467
def9660e 468 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 469 Double_t unit[3]; GetDirection(unit);
470 x[0]+=unit[0]*len;
471 x[1]+=unit[1]*len;
472 x[2]+=unit[2]*len;
473
474 p[0]=unit[0]/kAlmost0;
475 p[1]=unit[1]/kAlmost0;
476 p[2]=unit[2]/kAlmost0;
477 } else {
478 GetPxPyPz(p);
479 Double_t pp=GetP();
480 Double_t a = -kB2C*bz*GetSign();
481 Double_t rho = a/pp;
482 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
483 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
484 x[2] += p[2]*len/pp;
485
486 Double_t p0=p[0];
487 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
488 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
489 }
490}
491
492Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
493Double_t bz) const {
494 //+++++++++++++++++++++++++++++++++++++++++
495 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
496 // Finds point of intersection (if exists) of the helix with the plane.
497 // Stores result in fX and fP.
498 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
499 // and vector, normal to the plane
500 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
501 //+++++++++++++++++++++++++++++++++++++++++
502 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
503
504 //estimates initial helix length up to plane
505 Double_t s=
506 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
507 Double_t dist=99999,distPrev=dist;
508 Double_t x[3],p[3];
509 while(TMath::Abs(dist)>0.00001){
510 //calculates helix at the distance s from x0 ALONG the helix
511 Propagate(s,x,p,bz);
512
513 //distance between current helix position and plane
514 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
515
516 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
517 distPrev=dist;
518 s-=dist;
519 }
520 //on exit pnt is intersection point,norm is track vector at that point,
521 //all in MARS
522 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
523 return kTRUE;
524}
525
49d13e89 526Double_t
527AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
528 //----------------------------------------------------------------
529 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
530 //----------------------------------------------------------------
531 Double_t sdd = fC[0] + cov[0];
532 Double_t sdz = fC[1] + cov[1];
533 Double_t szz = fC[2] + cov[2];
534 Double_t det = sdd*szz - sdz*sdz;
535
536 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
537
538 Double_t d = fP[0] - p[0];
539 Double_t z = fP[1] - p[1];
540
541 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
542}
543
4b189f98 544Double_t AliExternalTrackParam::
545GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
546 //----------------------------------------------------------------
547 // Estimate the chi2 of the 3D space point "p" and
1e023a36 548 // the full covariance matrix "covyz" and "covxyz"
4b189f98 549 //
550 // Cov(x,x) ... : covxyz[0]
551 // Cov(y,x) ... : covxyz[1] covyz[0]
552 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
553 //----------------------------------------------------------------
554
555 Double_t res[3] = {
556 GetX() - p[0],
557 GetY() - p[1],
558 GetZ() - p[2]
559 };
560
561 Double_t f=GetSnp();
562 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
563 Double_t r=TMath::Sqrt(1.- f*f);
564 Double_t a=f/r, b=GetTgl()/r;
565
566 Double_t s2=333.*333.; //something reasonably big (cm^2)
567
568 TMatrixDSym v(3);
569 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
570 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
571 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
572
573 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
574 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
575 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
576
577 v.Invert();
578 if (!v.IsValid()) return kVeryBig;
579
580 Double_t chi2=0.;
581 for (Int_t i = 0; i < 3; i++)
582 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
583
584 return chi2;
585
586
587}
588
1e023a36 589Bool_t AliExternalTrackParam::
590PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
591 //----------------------------------------------------------------
592 // Propagate this track to the plane
593 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
594 // belongs to.
595 // The magnetic field is "bz" (kG)
596 //
597 // The track curvature and the change of the covariance matrix
598 // of the track parameters are negleted !
599 // (So the "step" should be small compared with 1/curvature)
600 //----------------------------------------------------------------
601
602 Double_t f=GetSnp();
603 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
604 Double_t r=TMath::Sqrt(1.- f*f);
605 Double_t a=f/r, b=GetTgl()/r;
606
607 Double_t s2=333.*333.; //something reasonably big (cm^2)
608
609 TMatrixDSym tV(3);
610 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
611 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
612 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
613
614 TMatrixDSym pV(3);
615 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
616 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
617 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
618
619 TMatrixDSym tpV(tV);
620 tpV+=pV;
621 tpV.Invert();
622 if (!tpV.IsValid()) return kFALSE;
623
624 TMatrixDSym pW(3),tW(3);
625 for (Int_t i=0; i<3; i++)
626 for (Int_t j=0; j<3; j++) {
627 pW(i,j)=tW(i,j)=0.;
628 for (Int_t k=0; k<3; k++) {
629 pW(i,j) += tV(i,k)*tpV(k,j);
630 tW(i,j) += pV(i,k)*tpV(k,j);
631 }
632 }
633
634 Double_t t[3] = {GetX(), GetY(), GetZ()};
635
636 Double_t x=0.;
637 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
638 Double_t crv=GetC(bz);
639 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
640 f += crv*(x-fX);
641 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
642 fX=x;
643
644 fP[0]=0.;
645 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
646 fP[1]=0.;
647 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
648
649 return kTRUE;
650}
651
e23a38cb 652Double_t *AliExternalTrackParam::GetResiduals(
653Double_t *p,Double_t *cov,Bool_t updated) const {
654 //------------------------------------------------------------------
655 // Returns the track residuals with the space point "p" having
656 // the covariance matrix "cov".
657 // If "updated" is kTRUE, the track parameters expected to be updated,
658 // otherwise they must be predicted.
659 //------------------------------------------------------------------
660 static Double_t res[2];
661
662 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
663 if (updated) {
664 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
665 } else {
666 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
667 }
668 Double_t det=r00*r11 - r01*r01;
669
670 if (TMath::Abs(det) < kAlmost0) return 0;
671
672 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 673
674 if (r00 < 0.) return 0;
675 if (r11 < 0.) return 0;
676
e23a38cb 677 Double_t dy = fP[0] - p[0];
678 Double_t dz = fP[1] - p[1];
679
680 res[0]=dy*TMath::Sqrt(r00);
681 res[1]=dz*TMath::Sqrt(r11);
682
683 return res;
684}
685
49d13e89 686Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
687 //------------------------------------------------------------------
688 // Update the track parameters with the space point "p" having
689 // the covariance matrix "cov"
690 //------------------------------------------------------------------
691 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
692 Double_t
693 &fC00=fC[0],
694 &fC10=fC[1], &fC11=fC[2],
695 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
696 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
697 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
698
699 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
700 r00+=fC00; r01+=fC10; r11+=fC11;
701 Double_t det=r00*r11 - r01*r01;
702
703 if (TMath::Abs(det) < kAlmost0) return kFALSE;
704
705
706 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
707
708 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
709 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
710 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
711 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
712 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
713
714 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
715 Double_t sf=fP2 + k20*dy + k21*dz;
716 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
717
718 fP0 += k00*dy + k01*dz;
719 fP1 += k10*dy + k11*dz;
720 fP2 = sf;
721 fP3 += k30*dy + k31*dz;
722 fP4 += k40*dy + k41*dz;
723
724 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
725 Double_t c12=fC21, c13=fC31, c14=fC41;
726
727 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
728 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
729 fC40-=k00*c04+k01*c14;
730
731 fC11-=k10*c01+k11*fC11;
732 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
733 fC41-=k10*c04+k11*c14;
734
735 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
736 fC42-=k20*c04+k21*c14;
737
738 fC33-=k30*c03+k31*c13;
739 fC43-=k30*c04+k31*c14;
740
741 fC44-=k40*c04+k41*c14;
742
743 return kTRUE;
744}
745
c7bafca9 746void
747AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
748 //--------------------------------------------------------------------
749 // External track parameters -> helix parameters
750 // "b" - magnetic field (kG)
751 //--------------------------------------------------------------------
752 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
753
1530f89c 754 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 755
756 hlx[5]=fX*cs - hlx[0]*sn; // x0
757 hlx[0]=fX*sn + hlx[0]*cs; // y0
758//hlx[1]= // z0
759 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
760//hlx[3]= // tgl
1530f89c 761 hlx[4]=GetC(b); // C
c7bafca9 762}
763
764
765static void Evaluate(const Double_t *h, Double_t t,
766 Double_t r[3], //radius vector
767 Double_t g[3], //first defivatives
768 Double_t gg[3]) //second derivatives
769{
770 //--------------------------------------------------------------------
771 // Calculate position of a point on a track and some derivatives
772 //--------------------------------------------------------------------
773 Double_t phase=h[4]*t+h[2];
774 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
775
776 r[0] = h[5] + (sn - h[6])/h[4];
777 r[1] = h[0] - (cs - h[7])/h[4];
778 r[2] = h[1] + h[3]*t;
779
780 g[0] = cs; g[1]=sn; g[2]=h[3];
781
782 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
783}
784
785Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
786Double_t b, Double_t &xthis, Double_t &xp) const {
787 //------------------------------------------------------------
788 // Returns the (weighed !) distance of closest approach between
789 // this track and the track "p".
790 // Other returned values:
791 // xthis, xt - coordinates of tracks' reference planes at the DCA
792 //-----------------------------------------------------------
793 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
794 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
795 Double_t dx2=dy2;
796
797 //dx2=dy2=dz2=1.;
798
799 Double_t p1[8]; GetHelixParameters(p1,b);
800 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
801 Double_t p2[8]; p->GetHelixParameters(p2,b);
802 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
803
804
805 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
806 Evaluate(p1,t1,r1,g1,gg1);
807 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
808 Evaluate(p2,t2,r2,g2,gg2);
809
810 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
811 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
812
813 Int_t max=27;
814 while (max--) {
815 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
816 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
817 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
818 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
819 (g1[2]*g1[2] - dz*gg1[2])/dz2;
820 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
821 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
822 (g2[2]*g2[2] + dz*gg2[2])/dz2;
823 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
824
825 Double_t det=h11*h22-h12*h12;
826
827 Double_t dt1,dt2;
828 if (TMath::Abs(det)<1.e-33) {
829 //(quasi)singular Hessian
830 dt1=-gt1; dt2=-gt2;
831 } else {
832 dt1=-(gt1*h22 - gt2*h12)/det;
833 dt2=-(h11*gt2 - h12*gt1)/det;
834 }
835
836 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
837
838 //check delta(phase1) ?
839 //check delta(phase2) ?
840
841 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
842 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
843 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
844 AliWarning(" stopped at not a stationary point !");
845 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
846 if (lmb < 0.)
847 AliWarning(" stopped at not a minimum !");
848 break;
849 }
850
851 Double_t dd=dm;
852 for (Int_t div=1 ; ; div*=2) {
853 Evaluate(p1,t1+dt1,r1,g1,gg1);
854 Evaluate(p2,t2+dt2,r2,g2,gg2);
855 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
856 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
857 if (dd<dm) break;
858 dt1*=0.5; dt2*=0.5;
859 if (div>512) {
860 AliWarning(" overshoot !"); break;
861 }
862 }
863 dm=dd;
864
865 t1+=dt1;
866 t2+=dt2;
867
868 }
869
870 if (max<=0) AliWarning(" too many iterations !");
871
872 Double_t cs=TMath::Cos(GetAlpha());
873 Double_t sn=TMath::Sin(GetAlpha());
874 xthis=r1[0]*cs + r1[1]*sn;
875
876 cs=TMath::Cos(p->GetAlpha());
877 sn=TMath::Sin(p->GetAlpha());
878 xp=r2[0]*cs + r2[1]*sn;
879
880 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
881}
882
883Double_t AliExternalTrackParam::
884PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
885 //--------------------------------------------------------------
886 // Propagates this track and the argument track to the position of the
887 // distance of closest approach.
888 // Returns the (weighed !) distance of closest approach.
889 //--------------------------------------------------------------
890 Double_t xthis,xp;
891 Double_t dca=GetDCA(p,b,xthis,xp);
892
893 if (!PropagateTo(xthis,b)) {
894 //AliWarning(" propagation failed !");
895 return 1e+33;
896 }
897
898 if (!p->PropagateTo(xp,b)) {
899 //AliWarning(" propagation failed !";
900 return 1e+33;
901 }
902
903 return dca;
904}
905
906
907
f76701bf 908
909Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
910 //
911 // Try to relate this track to the vertex "vtx",
912 // if the (rough) transverse impact parameter is not bigger then "maxd".
913 // Magnetic field is "b" (kG).
914 //
915 // a) The track gets extapolated to the DCA to the vertex.
916 // b) The impact parameters and their covariance matrix are calculated.
917 //
918 // In the case of success, the returned value is kTRUE
919 // (otherwise, it's kFALSE)
920 //
921 Double_t alpha=GetAlpha();
922 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
923 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
924 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 925 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 926 x-=xv; y-=yv;
927
928 //Estimate the impact parameter neglecting the track curvature
929 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
930 if (d > maxd) return kFALSE;
931
932 //Propagate to the DCA
933 Double_t crv=0.299792458e-3*b*GetParameter()[4];
934 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
935 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
936
937 x = xv*cs + yv*sn;
938 yv=-xv*sn + yv*cs; xv=x;
939
940 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 941 return kTRUE;
f76701bf 942}
943
944
b1149664 945void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
946 //----------------------------------------------------------------
947 // This function returns a unit vector along the track direction
948 // in the global coordinate system.
949 //----------------------------------------------------------------
950 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
951 Double_t snp=fP[2];
92934324 952 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 953 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
954 d[0]=(csp*cs - snp*sn)/norm;
955 d[1]=(snp*cs + csp*sn)/norm;
956 d[2]=fP[3]/norm;
957}
958
c683ddc2 959Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 960 //---------------------------------------------------------------------
961 // This function returns the global track momentum components
962 // Results for (nearly) straight tracks are meaningless !
963 //---------------------------------------------------------------------
964 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
965 return Local2GlobalMomentum(p,fAlpha);
966}
a5e407e9 967
def9660e 968Double_t AliExternalTrackParam::Px() const {
957fb479 969 //---------------------------------------------------------------------
970 // Returns x-component of momentum
971 // Result for (nearly) straight tracks is meaningless !
972 //---------------------------------------------------------------------
def9660e 973
957fb479 974 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 975 GetPxPyPz(p);
976
977 return p[0];
978}
979
980Double_t AliExternalTrackParam::Py() const {
957fb479 981 //---------------------------------------------------------------------
982 // Returns y-component of momentum
983 // Result for (nearly) straight tracks is meaningless !
984 //---------------------------------------------------------------------
def9660e 985
957fb479 986 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 987 GetPxPyPz(p);
988
989 return p[1];
990}
991
992Double_t AliExternalTrackParam::Pz() const {
957fb479 993 //---------------------------------------------------------------------
994 // Returns z-component of momentum
995 // Result for (nearly) straight tracks is meaningless !
996 //---------------------------------------------------------------------
def9660e 997
957fb479 998 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 999 GetPxPyPz(p);
1000
1001 return p[2];
1002}
1003
c683ddc2 1004Double_t AliExternalTrackParam::Xv() const {
1005 //---------------------------------------------------------------------
1006 // Returns x-component of first track point
1007 //---------------------------------------------------------------------
1008
1009 Double_t r[3]={0.,0.,0.};
1010 GetXYZ(r);
1011
1012 return r[0];
1013}
1014
1015Double_t AliExternalTrackParam::Yv() const {
1016 //---------------------------------------------------------------------
1017 // Returns y-component of first track point
1018 //---------------------------------------------------------------------
1019
1020 Double_t r[3]={0.,0.,0.};
1021 GetXYZ(r);
1022
1023 return r[1];
1024}
1025
1026Double_t AliExternalTrackParam::Zv() const {
1027 //---------------------------------------------------------------------
1028 // Returns z-component of first track point
1029 //---------------------------------------------------------------------
1030
1031 Double_t r[3]={0.,0.,0.};
1032 GetXYZ(r);
1033
1034 return r[2];
1035}
1036
def9660e 1037Double_t AliExternalTrackParam::Theta() const {
1038 // return theta angle of momentum
1039
7cdd0c20 1040 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1041}
1042
1043Double_t AliExternalTrackParam::Phi() const {
957fb479 1044 //---------------------------------------------------------------------
1045 // Returns the azimuthal angle of momentum
1046 // 0 <= phi < 2*pi
1047 //---------------------------------------------------------------------
def9660e 1048
957fb479 1049 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1050 if (phi<0.) phi+=2.*TMath::Pi();
1051 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1052
1053 return phi;
def9660e 1054}
1055
1056Double_t AliExternalTrackParam::M() const {
1057 // return particle mass
1058
1059 // No mass information available so far.
1060 // Redifine in derived class!
1061
1062 return -999.;
1063}
1064
1065Double_t AliExternalTrackParam::E() const {
1066 // return particle energy
1067
1068 // No PID information available so far.
1069 // Redifine in derived class!
1070
1071 return -999.;
1072}
1073
1074Double_t AliExternalTrackParam::Eta() const {
1075 // return pseudorapidity
1076
1077 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1078}
1079
1080Double_t AliExternalTrackParam::Y() const {
1081 // return rapidity
1082
1083 // No PID information available so far.
1084 // Redifine in derived class!
1085
1086 return -999.;
1087}
1088
c9ec41e8 1089Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1090 //---------------------------------------------------------------------
1091 // This function returns the global track position
1092 //---------------------------------------------------------------------
1093 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1094 return Local2GlobalPosition(r,fAlpha);
51ad6848 1095}
1096
c9ec41e8 1097Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1098 //---------------------------------------------------------------------
1099 // This function returns the global covariance matrix of the track params
1100 //
1101 // Cov(x,x) ... : cv[0]
1102 // Cov(y,x) ... : cv[1] cv[2]
1103 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1104 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1105 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1106 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1107 //
c9ec41e8 1108 // Results for (nearly) straight tracks are meaningless !
1109 //---------------------------------------------------------------------
e421f556 1110 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1111 for (Int_t i=0; i<21; i++) cv[i]=0.;
1112 return kFALSE;
a5e407e9 1113 }
49d13e89 1114 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1115 for (Int_t i=0; i<21; i++) cv[i]=0.;
1116 return kFALSE;
1117 }
1118 Double_t pt=1./TMath::Abs(fP[4]);
1119 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1120 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1121
1122 Double_t m00=-sn, m10=cs;
1123 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1124 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1125 Double_t m35=pt, m45=-pt*pt*fP[3];
1126
854d5d49 1127 m43*=GetSign();
1128 m44*=GetSign();
1129 m45*=GetSign();
1130
c9ec41e8 1131 cv[0 ] = fC[0]*m00*m00;
1132 cv[1 ] = fC[0]*m00*m10;
1133 cv[2 ] = fC[0]*m10*m10;
1134 cv[3 ] = fC[1]*m00;
1135 cv[4 ] = fC[1]*m10;
1136 cv[5 ] = fC[2];
1137 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1138 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1139 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1140 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1141 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1142 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1143 cv[12] = fC[4]*m24 + fC[11]*m44;
1144 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1145 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1146 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1147 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1148 cv[17] = fC[7]*m35 + fC[11]*m45;
1149 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1150 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1151 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1152
c9ec41e8 1153 return kTRUE;
51ad6848 1154}
1155
51ad6848 1156
c9ec41e8 1157Bool_t
1158AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1159 //---------------------------------------------------------------------
1160 // This function returns the global track momentum extrapolated to
1161 // the radial position "x" (cm) in the magnetic field "b" (kG)
1162 //---------------------------------------------------------------------
c9ec41e8 1163 p[0]=fP[4];
1530f89c 1164 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1165 p[2]=fP[3];
1166 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1167}
1168
7cf7bb6c 1169Bool_t
1170AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1171 //---------------------------------------------------------------------
1172 // This function returns the local Y-coordinate of the intersection
1173 // point between this track and the reference plane "x" (cm).
1174 // Magnetic field "b" (kG)
1175 //---------------------------------------------------------------------
1176 Double_t dx=x-fX;
1177 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1178
1530f89c 1179 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1180
1181 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1182 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1183
1184 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1185 y = fP[0] + dx*(f1+f2)/(r1+r2);
1186 return kTRUE;
1187}
1188
6c94f330 1189Bool_t
1190AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1191 //---------------------------------------------------------------------
1192 // This function returns the local Z-coordinate of the intersection
1193 // point between this track and the reference plane "x" (cm).
1194 // Magnetic field "b" (kG)
1195 //---------------------------------------------------------------------
1196 Double_t dx=x-fX;
1197 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1198
1199 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1200
1201 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1202 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1203
1204 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1205 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1206 return kTRUE;
1207}
1208
c9ec41e8 1209Bool_t
1210AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1211 //---------------------------------------------------------------------
1212 // This function returns the global track position extrapolated to
1213 // the radial position "x" (cm) in the magnetic field "b" (kG)
1214 //---------------------------------------------------------------------
c9ec41e8 1215 Double_t dx=x-fX;
e421f556 1216 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1217
1530f89c 1218 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1219
e421f556 1220 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1221 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1222
1223 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1224 r[0] = x;
1225 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 1226 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 1227 return Local2GlobalPosition(r,fAlpha);
51ad6848 1228}
1229
51ad6848 1230//_____________________________________________________________________________
1231void AliExternalTrackParam::Print(Option_t* /*option*/) const
1232{
1233// print the parameters and the covariance matrix
1234
1235 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1236 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1237 fP[0], fP[1], fP[2], fP[3], fP[4]);
1238 printf(" covariance: %12g\n", fC[0]);
1239 printf(" %12g %12g\n", fC[1], fC[2]);
1240 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1241 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1242 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1243 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1244 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1245}
5b77d93c 1246
c194ba83 1247Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1248 //
1249 // Get sinus at given x
1250 //
1530f89c 1251 Double_t crv=GetC(b);
c194ba83 1252 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1253 Double_t dx = x-fX;
1254 Double_t res = fP[2]+dx*crv;
1255 return res;
1256}
bf00ebb8 1257
1258Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1259 //------------------------------------------------------------------------
1260 // Get the distance between two tracks at the local position x
1261 // working in the local frame of this track.
1262 // Origin : Marian.Ivanov@cern.ch
1263 //-----------------------------------------------------------------------
1264 Double_t xyz[3];
1265 Double_t xyz2[3];
1266 xyz[0]=x;
1267 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1268 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1269 //
1270 //
1271 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1272 xyz2[0]=x;
1273 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1274 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1275 }else{
1276 //
1277 Double_t xyz1[3];
1278 Double_t dfi = param2->GetAlpha()-GetAlpha();
1279 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1280 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1281 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1282 //
1283 xyz1[0]=xyz2[0];
1284 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1285 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1286 //
1287 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1288 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1289 xyz2[2] = xyz1[2];
1290 }
1291 dist[0] = xyz[0]-xyz2[0];
1292 dist[1] = xyz[1]-xyz2[1];
1293 dist[2] = xyz[2]-xyz2[2];
1294
1295 return kTRUE;
1296}