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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
204(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
205Double_t (*Bethe)(Double_t)) {
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
221 Double_t p=GetP();
222 Double_t p2=p*p;
223 Double_t beta2=p2/(p2 + mass*mass);
224 xOverX0*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
225
226 //Multiple scattering******************
227 if (xOverX0 != 0) {
228 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
229 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
230 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
231 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
232 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
233 fC44 += theta2*fP3*fP4*fP3*fP4;
234 }
235
236 //Energy losses************************
237 if ((xTimesRho != 0.) && (beta2 < 1.)) {
238 Double_t dE=Bethe(beta2)*xTimesRho;
239 Double_t e=TMath::Sqrt(p2 + mass*mass);
240 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
241 fP4*=(1.- e/p2*dE);
242
243 // Approximate energy loss fluctuation (M.Ivanov)
244 const Double_t knst=0.07; // To be tuned.
245 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
246 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
247
248 }
249
250 return kTRUE;
251}
252
253
ee5dba5e 254Bool_t AliExternalTrackParam::CorrectForMaterial
255(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 256 //------------------------------------------------------------------
116b445b 257 // Deprecated function !
258 // Better use CorrectForMeanMaterial instead of it.
259 //
c7bafca9 260 // This function corrects the track parameters for the crossed material
261 // "d" - the thickness (fraction of the radiation length)
262 // "x0" - the radiation length (g/cm^2)
263 // "mass" - the mass of this particle (GeV/c^2)
264 //------------------------------------------------------------------
265 Double_t &fP2=fP[2];
266 Double_t &fP3=fP[3];
267 Double_t &fP4=fP[4];
268
269 Double_t &fC22=fC[5];
270 Double_t &fC33=fC[9];
271 Double_t &fC43=fC[13];
272 Double_t &fC44=fC[14];
273
7b5ef2e6 274 Double_t p=GetP();
275 Double_t p2=p*p;
c7bafca9 276 Double_t beta2=p2/(p2 + mass*mass);
277 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
278
279 //Multiple scattering******************
280 if (d!=0) {
281 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
282 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
283 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
284 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
285 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
286 fC44 += theta2*fP3*fP4*fP3*fP4;
287 }
288
289 //Energy losses************************
8fc1985d 290 if (x0!=0. && beta2<1) {
c7bafca9 291 d*=x0;
ee5dba5e 292 Double_t dE=Bethe(beta2)*d;
293 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 294 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 295 fP4*=(1.- e/p2*dE);
296
297 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 298 const Double_t knst=0.07; // To be tuned.
299 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 300 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
301
c7bafca9 302 }
303
304 return kTRUE;
305}
306
ee5dba5e 307Double_t ApproximateBetheBloch(Double_t beta2) {
308 //------------------------------------------------------------------
309 // This is an approximation of the Bethe-Bloch formula with
310 // the density effect taken into account at beta*gamma > 3.5
311 // (the approximation is reasonable only for solid materials)
312 //------------------------------------------------------------------
313 if (beta2/(1-beta2)>3.5*3.5)
314 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
315
316 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
317}
318
49d13e89 319Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
320 //------------------------------------------------------------------
321 // Transform this track to the local coord. system rotated
322 // by angle "alpha" (rad) with respect to the global coord. system.
323 //------------------------------------------------------------------
dfcef74c 324 if (TMath::Abs(fP[2]) >= kAlmost1) {
325 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
326 return kFALSE;
327 }
328
49d13e89 329 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
330 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
331
332 Double_t &fP0=fP[0];
333 Double_t &fP2=fP[2];
334 Double_t &fC00=fC[0];
335 Double_t &fC10=fC[1];
336 Double_t &fC20=fC[3];
337 Double_t &fC21=fC[4];
338 Double_t &fC22=fC[5];
339 Double_t &fC30=fC[6];
340 Double_t &fC32=fC[8];
341 Double_t &fC40=fC[10];
342 Double_t &fC42=fC[12];
343
344 Double_t x=fX;
345 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
346 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
347
dfcef74c 348 Double_t tmp=sf*ca - cf*sa;
349 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
350
49d13e89 351 fAlpha = alpha;
352 fX = x*ca + fP0*sa;
353 fP0= -x*sa + fP0*ca;
dfcef74c 354 fP2= tmp;
49d13e89 355
06fb4a2f 356 if (TMath::Abs(cf)<kAlmost0) {
357 AliError(Form("Too small cosine value %f",cf));
358 cf = kAlmost0;
359 }
360
49d13e89 361 Double_t rr=(ca+sf/cf*sa);
362
363 fC00 *= (ca*ca);
364 fC10 *= ca;
365 fC20 *= ca*rr;
366 fC21 *= rr;
367 fC22 *= rr*rr;
368 fC30 *= ca;
369 fC32 *= rr;
370 fC40 *= ca;
371 fC42 *= rr;
372
373 return kTRUE;
374}
375
376Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
377 //----------------------------------------------------------------
378 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
379 //----------------------------------------------------------------
49d13e89 380 Double_t dx=xk-fX;
e421f556 381 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 382
1530f89c 383 Double_t crv=GetC(b);
5773defd 384 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
385
49d13e89 386 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 387 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 388 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
389
390 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
391 Double_t
392 &fC00=fC[0],
393 &fC10=fC[1], &fC11=fC[2],
394 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
395 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
396 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
397
398 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
399
400 fX=xk;
401 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 402 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 403 fP2 += dx*crv;
404
405 //f = F - 1
406
407 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
408 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
409 Double_t f12= dx*fP3*f1/(r1*r1*r1);
410 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
411 Double_t f13= dx/r1;
412 Double_t f24= dx; f24*=cc;
413
414 //b = C*ft
415 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
416 Double_t b02=f24*fC40;
417 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
418 Double_t b12=f24*fC41;
419 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
420 Double_t b22=f24*fC42;
421 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
422 Double_t b42=f24*fC44;
423 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
424 Double_t b32=f24*fC43;
425
426 //a = f*b = f*C*ft
427 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
428 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
429 Double_t a22=f24*b42;
430
431 //F*C*Ft = C + (b + bt + a)
432 fC00 += b00 + b00 + a00;
433 fC10 += b10 + b01 + a01;
434 fC20 += b20 + b02 + a02;
435 fC30 += b30;
436 fC40 += b40;
437 fC11 += b11 + b11 + a11;
438 fC21 += b21 + b12 + a12;
439 fC31 += b31;
440 fC41 += b41;
441 fC22 += b22 + b22 + a22;
442 fC32 += b32;
443 fC42 += b42;
444
445 return kTRUE;
446}
447
052daaff 448void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
449Double_t p[3], Double_t bz) const {
450 //+++++++++++++++++++++++++++++++++++++++++
451 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
452 // Extrapolate track along simple helix in magnetic field
453 // Arguments: len -distance alogn helix, [cm]
454 // bz - mag field, [kGaus]
455 // Returns: x and p contain extrapolated positon and momentum
456 // The momentum returned for straight-line tracks is meaningless !
457 //+++++++++++++++++++++++++++++++++++++++++
458 GetXYZ(x);
459
def9660e 460 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 461 Double_t unit[3]; GetDirection(unit);
462 x[0]+=unit[0]*len;
463 x[1]+=unit[1]*len;
464 x[2]+=unit[2]*len;
465
466 p[0]=unit[0]/kAlmost0;
467 p[1]=unit[1]/kAlmost0;
468 p[2]=unit[2]/kAlmost0;
469 } else {
470 GetPxPyPz(p);
471 Double_t pp=GetP();
472 Double_t a = -kB2C*bz*GetSign();
473 Double_t rho = a/pp;
474 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
475 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
476 x[2] += p[2]*len/pp;
477
478 Double_t p0=p[0];
479 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
480 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
481 }
482}
483
484Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
485Double_t bz) const {
486 //+++++++++++++++++++++++++++++++++++++++++
487 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
488 // Finds point of intersection (if exists) of the helix with the plane.
489 // Stores result in fX and fP.
490 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
491 // and vector, normal to the plane
492 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
493 //+++++++++++++++++++++++++++++++++++++++++
494 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
495
496 //estimates initial helix length up to plane
497 Double_t s=
498 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
499 Double_t dist=99999,distPrev=dist;
500 Double_t x[3],p[3];
501 while(TMath::Abs(dist)>0.00001){
502 //calculates helix at the distance s from x0 ALONG the helix
503 Propagate(s,x,p,bz);
504
505 //distance between current helix position and plane
506 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
507
508 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
509 distPrev=dist;
510 s-=dist;
511 }
512 //on exit pnt is intersection point,norm is track vector at that point,
513 //all in MARS
514 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
515 return kTRUE;
516}
517
49d13e89 518Double_t
519AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
520 //----------------------------------------------------------------
521 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
522 //----------------------------------------------------------------
523 Double_t sdd = fC[0] + cov[0];
524 Double_t sdz = fC[1] + cov[1];
525 Double_t szz = fC[2] + cov[2];
526 Double_t det = sdd*szz - sdz*sdz;
527
528 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
529
530 Double_t d = fP[0] - p[0];
531 Double_t z = fP[1] - p[1];
532
533 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
534}
535
4b189f98 536Double_t AliExternalTrackParam::
537GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
538 //----------------------------------------------------------------
539 // Estimate the chi2 of the 3D space point "p" and
1e023a36 540 // the full covariance matrix "covyz" and "covxyz"
4b189f98 541 //
542 // Cov(x,x) ... : covxyz[0]
543 // Cov(y,x) ... : covxyz[1] covyz[0]
544 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
545 //----------------------------------------------------------------
546
547 Double_t res[3] = {
548 GetX() - p[0],
549 GetY() - p[1],
550 GetZ() - p[2]
551 };
552
553 Double_t f=GetSnp();
554 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
555 Double_t r=TMath::Sqrt(1.- f*f);
556 Double_t a=f/r, b=GetTgl()/r;
557
558 Double_t s2=333.*333.; //something reasonably big (cm^2)
559
560 TMatrixDSym v(3);
561 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
562 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
563 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
564
565 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
566 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
567 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
568
569 v.Invert();
570 if (!v.IsValid()) return kVeryBig;
571
572 Double_t chi2=0.;
573 for (Int_t i = 0; i < 3; i++)
574 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
575
576 return chi2;
577
578
579}
580
1e023a36 581Bool_t AliExternalTrackParam::
582PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
583 //----------------------------------------------------------------
584 // Propagate this track to the plane
585 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
586 // belongs to.
587 // The magnetic field is "bz" (kG)
588 //
589 // The track curvature and the change of the covariance matrix
590 // of the track parameters are negleted !
591 // (So the "step" should be small compared with 1/curvature)
592 //----------------------------------------------------------------
593
594 Double_t f=GetSnp();
595 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
596 Double_t r=TMath::Sqrt(1.- f*f);
597 Double_t a=f/r, b=GetTgl()/r;
598
599 Double_t s2=333.*333.; //something reasonably big (cm^2)
600
601 TMatrixDSym tV(3);
602 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
603 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
604 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
605
606 TMatrixDSym pV(3);
607 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
608 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
609 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
610
611 TMatrixDSym tpV(tV);
612 tpV+=pV;
613 tpV.Invert();
614 if (!tpV.IsValid()) return kFALSE;
615
616 TMatrixDSym pW(3),tW(3);
617 for (Int_t i=0; i<3; i++)
618 for (Int_t j=0; j<3; j++) {
619 pW(i,j)=tW(i,j)=0.;
620 for (Int_t k=0; k<3; k++) {
621 pW(i,j) += tV(i,k)*tpV(k,j);
622 tW(i,j) += pV(i,k)*tpV(k,j);
623 }
624 }
625
626 Double_t t[3] = {GetX(), GetY(), GetZ()};
627
628 Double_t x=0.;
629 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
630 Double_t crv=GetC(bz);
631 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
632 f += crv*(x-fX);
633 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
634 fX=x;
635
636 fP[0]=0.;
637 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
638 fP[1]=0.;
639 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
640
641 return kTRUE;
642}
643
49d13e89 644Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
645 //------------------------------------------------------------------
646 // Update the track parameters with the space point "p" having
647 // the covariance matrix "cov"
648 //------------------------------------------------------------------
649 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
650 Double_t
651 &fC00=fC[0],
652 &fC10=fC[1], &fC11=fC[2],
653 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
654 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
655 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
656
657 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
658 r00+=fC00; r01+=fC10; r11+=fC11;
659 Double_t det=r00*r11 - r01*r01;
660
661 if (TMath::Abs(det) < kAlmost0) return kFALSE;
662
663
664 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
665
666 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
667 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
668 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
669 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
670 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
671
672 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
673 Double_t sf=fP2 + k20*dy + k21*dz;
674 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
675
676 fP0 += k00*dy + k01*dz;
677 fP1 += k10*dy + k11*dz;
678 fP2 = sf;
679 fP3 += k30*dy + k31*dz;
680 fP4 += k40*dy + k41*dz;
681
682 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
683 Double_t c12=fC21, c13=fC31, c14=fC41;
684
685 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
686 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
687 fC40-=k00*c04+k01*c14;
688
689 fC11-=k10*c01+k11*fC11;
690 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
691 fC41-=k10*c04+k11*c14;
692
693 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
694 fC42-=k20*c04+k21*c14;
695
696 fC33-=k30*c03+k31*c13;
697 fC43-=k30*c04+k31*c14;
698
699 fC44-=k40*c04+k41*c14;
700
701 return kTRUE;
702}
703
c7bafca9 704void
705AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
706 //--------------------------------------------------------------------
707 // External track parameters -> helix parameters
708 // "b" - magnetic field (kG)
709 //--------------------------------------------------------------------
710 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
711
1530f89c 712 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 713
714 hlx[5]=fX*cs - hlx[0]*sn; // x0
715 hlx[0]=fX*sn + hlx[0]*cs; // y0
716//hlx[1]= // z0
717 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
718//hlx[3]= // tgl
1530f89c 719 hlx[4]=GetC(b); // C
c7bafca9 720}
721
722
723static void Evaluate(const Double_t *h, Double_t t,
724 Double_t r[3], //radius vector
725 Double_t g[3], //first defivatives
726 Double_t gg[3]) //second derivatives
727{
728 //--------------------------------------------------------------------
729 // Calculate position of a point on a track and some derivatives
730 //--------------------------------------------------------------------
731 Double_t phase=h[4]*t+h[2];
732 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
733
734 r[0] = h[5] + (sn - h[6])/h[4];
735 r[1] = h[0] - (cs - h[7])/h[4];
736 r[2] = h[1] + h[3]*t;
737
738 g[0] = cs; g[1]=sn; g[2]=h[3];
739
740 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
741}
742
743Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
744Double_t b, Double_t &xthis, Double_t &xp) const {
745 //------------------------------------------------------------
746 // Returns the (weighed !) distance of closest approach between
747 // this track and the track "p".
748 // Other returned values:
749 // xthis, xt - coordinates of tracks' reference planes at the DCA
750 //-----------------------------------------------------------
751 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
752 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
753 Double_t dx2=dy2;
754
755 //dx2=dy2=dz2=1.;
756
757 Double_t p1[8]; GetHelixParameters(p1,b);
758 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
759 Double_t p2[8]; p->GetHelixParameters(p2,b);
760 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
761
762
763 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
764 Evaluate(p1,t1,r1,g1,gg1);
765 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
766 Evaluate(p2,t2,r2,g2,gg2);
767
768 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
769 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
770
771 Int_t max=27;
772 while (max--) {
773 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
774 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
775 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
776 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
777 (g1[2]*g1[2] - dz*gg1[2])/dz2;
778 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
779 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
780 (g2[2]*g2[2] + dz*gg2[2])/dz2;
781 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
782
783 Double_t det=h11*h22-h12*h12;
784
785 Double_t dt1,dt2;
786 if (TMath::Abs(det)<1.e-33) {
787 //(quasi)singular Hessian
788 dt1=-gt1; dt2=-gt2;
789 } else {
790 dt1=-(gt1*h22 - gt2*h12)/det;
791 dt2=-(h11*gt2 - h12*gt1)/det;
792 }
793
794 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
795
796 //check delta(phase1) ?
797 //check delta(phase2) ?
798
799 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
800 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
801 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
802 AliWarning(" stopped at not a stationary point !");
803 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
804 if (lmb < 0.)
805 AliWarning(" stopped at not a minimum !");
806 break;
807 }
808
809 Double_t dd=dm;
810 for (Int_t div=1 ; ; div*=2) {
811 Evaluate(p1,t1+dt1,r1,g1,gg1);
812 Evaluate(p2,t2+dt2,r2,g2,gg2);
813 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
814 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
815 if (dd<dm) break;
816 dt1*=0.5; dt2*=0.5;
817 if (div>512) {
818 AliWarning(" overshoot !"); break;
819 }
820 }
821 dm=dd;
822
823 t1+=dt1;
824 t2+=dt2;
825
826 }
827
828 if (max<=0) AliWarning(" too many iterations !");
829
830 Double_t cs=TMath::Cos(GetAlpha());
831 Double_t sn=TMath::Sin(GetAlpha());
832 xthis=r1[0]*cs + r1[1]*sn;
833
834 cs=TMath::Cos(p->GetAlpha());
835 sn=TMath::Sin(p->GetAlpha());
836 xp=r2[0]*cs + r2[1]*sn;
837
838 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
839}
840
841Double_t AliExternalTrackParam::
842PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
843 //--------------------------------------------------------------
844 // Propagates this track and the argument track to the position of the
845 // distance of closest approach.
846 // Returns the (weighed !) distance of closest approach.
847 //--------------------------------------------------------------
848 Double_t xthis,xp;
849 Double_t dca=GetDCA(p,b,xthis,xp);
850
851 if (!PropagateTo(xthis,b)) {
852 //AliWarning(" propagation failed !");
853 return 1e+33;
854 }
855
856 if (!p->PropagateTo(xp,b)) {
857 //AliWarning(" propagation failed !";
858 return 1e+33;
859 }
860
861 return dca;
862}
863
864
865
f76701bf 866
867Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
868 //
869 // Try to relate this track to the vertex "vtx",
870 // if the (rough) transverse impact parameter is not bigger then "maxd".
871 // Magnetic field is "b" (kG).
872 //
873 // a) The track gets extapolated to the DCA to the vertex.
874 // b) The impact parameters and their covariance matrix are calculated.
875 //
876 // In the case of success, the returned value is kTRUE
877 // (otherwise, it's kFALSE)
878 //
879 Double_t alpha=GetAlpha();
880 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
881 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
882 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 883 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 884 x-=xv; y-=yv;
885
886 //Estimate the impact parameter neglecting the track curvature
887 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
888 if (d > maxd) return kFALSE;
889
890 //Propagate to the DCA
891 Double_t crv=0.299792458e-3*b*GetParameter()[4];
892 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
893 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
894
895 x = xv*cs + yv*sn;
896 yv=-xv*sn + yv*cs; xv=x;
897
898 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 899 return kTRUE;
f76701bf 900}
901
902
903
904
c9ec41e8 905Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
906 //----------------------------------------------------------------
907 // This function performs local->global transformation of the
908 // track momentum.
909 // When called, the arguments are:
910 // p[0] = 1/pt of the track;
911 // p[1] = sine of local azim. angle of the track momentum;
912 // p[2] = tangent of the track momentum dip angle;
913 // alpha - rotation angle.
914 // The result is returned as:
915 // p[0] = px
916 // p[1] = py
917 // p[2] = pz
918 // Results for (nearly) straight tracks are meaningless !
919 //----------------------------------------------------------------
e421f556 920 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 921 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 922
923 Double_t pt=1./TMath::Abs(p[0]);
924 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
925 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
926 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 927
928 return kTRUE;
929}
930
c9ec41e8 931Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
932 //----------------------------------------------------------------
933 // This function performs local->global transformation of the
934 // track position.
935 // When called, the arguments are:
936 // r[0] = local x
937 // r[1] = local y
938 // r[2] = local z
939 // alpha - rotation angle.
940 // The result is returned as:
941 // r[0] = global x
942 // r[1] = global y
943 // r[2] = global z
944 //----------------------------------------------------------------
945 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
946 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 947
a5e407e9 948 return kTRUE;
51ad6848 949}
950
b1149664 951void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
952 //----------------------------------------------------------------
953 // This function returns a unit vector along the track direction
954 // in the global coordinate system.
955 //----------------------------------------------------------------
956 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
957 Double_t snp=fP[2];
92934324 958 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 959 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
960 d[0]=(csp*cs - snp*sn)/norm;
961 d[1]=(snp*cs + csp*sn)/norm;
962 d[2]=fP[3]/norm;
963}
964
c9ec41e8 965Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
966 //---------------------------------------------------------------------
967 // This function returns the global track momentum components
968 // Results for (nearly) straight tracks are meaningless !
969 //---------------------------------------------------------------------
970 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
971 return Local2GlobalMomentum(p,fAlpha);
972}
a5e407e9 973
def9660e 974Double_t AliExternalTrackParam::Px() const {
975 // return x-component of momentum
976
977 Double_t p[3];
978 GetPxPyPz(p);
979
980 return p[0];
981}
982
983Double_t AliExternalTrackParam::Py() const {
984 // return y-component of momentum
985
986 Double_t p[3];
987 GetPxPyPz(p);
988
989 return p[1];
990}
991
992Double_t AliExternalTrackParam::Pz() const {
993 // return z-component of momentum
994
995 Double_t p[3];
996 GetPxPyPz(p);
997
998 return p[2];
999}
1000
1001Double_t AliExternalTrackParam::Theta() const {
1002 // return theta angle of momentum
1003
1004 return TMath::ATan2(Pt(), Pz());
1005}
1006
1007Double_t AliExternalTrackParam::Phi() const {
1008 // return phi angle of momentum
1009
1010 Double_t p[3];
1011 GetPxPyPz(p);
1012
1013 return TMath::ATan2(p[1], p[0]);
1014}
1015
1016Double_t AliExternalTrackParam::M() const {
1017 // return particle mass
1018
1019 // No mass information available so far.
1020 // Redifine in derived class!
1021
1022 return -999.;
1023}
1024
1025Double_t AliExternalTrackParam::E() const {
1026 // return particle energy
1027
1028 // No PID information available so far.
1029 // Redifine in derived class!
1030
1031 return -999.;
1032}
1033
1034Double_t AliExternalTrackParam::Eta() const {
1035 // return pseudorapidity
1036
1037 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1038}
1039
1040Double_t AliExternalTrackParam::Y() const {
1041 // return rapidity
1042
1043 // No PID information available so far.
1044 // Redifine in derived class!
1045
1046 return -999.;
1047}
1048
c9ec41e8 1049Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1050 //---------------------------------------------------------------------
1051 // This function returns the global track position
1052 //---------------------------------------------------------------------
1053 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1054 return Local2GlobalPosition(r,fAlpha);
51ad6848 1055}
1056
c9ec41e8 1057Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1058 //---------------------------------------------------------------------
1059 // This function returns the global covariance matrix of the track params
1060 //
1061 // Cov(x,x) ... : cv[0]
1062 // Cov(y,x) ... : cv[1] cv[2]
1063 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1064 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1065 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1066 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1067 //
c9ec41e8 1068 // Results for (nearly) straight tracks are meaningless !
1069 //---------------------------------------------------------------------
e421f556 1070 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1071 for (Int_t i=0; i<21; i++) cv[i]=0.;
1072 return kFALSE;
a5e407e9 1073 }
49d13e89 1074 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1075 for (Int_t i=0; i<21; i++) cv[i]=0.;
1076 return kFALSE;
1077 }
1078 Double_t pt=1./TMath::Abs(fP[4]);
1079 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1080 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1081
1082 Double_t m00=-sn, m10=cs;
1083 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1084 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1085 Double_t m35=pt, m45=-pt*pt*fP[3];
1086
854d5d49 1087 m43*=GetSign();
1088 m44*=GetSign();
1089 m45*=GetSign();
1090
c9ec41e8 1091 cv[0 ] = fC[0]*m00*m00;
1092 cv[1 ] = fC[0]*m00*m10;
1093 cv[2 ] = fC[0]*m10*m10;
1094 cv[3 ] = fC[1]*m00;
1095 cv[4 ] = fC[1]*m10;
1096 cv[5 ] = fC[2];
1097 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1098 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1099 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1100 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1101 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1102 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1103 cv[12] = fC[4]*m24 + fC[11]*m44;
1104 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1105 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1106 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1107 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1108 cv[17] = fC[7]*m35 + fC[11]*m45;
1109 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1110 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1111 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1112
c9ec41e8 1113 return kTRUE;
51ad6848 1114}
1115
51ad6848 1116
c9ec41e8 1117Bool_t
1118AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1119 //---------------------------------------------------------------------
1120 // This function returns the global track momentum extrapolated to
1121 // the radial position "x" (cm) in the magnetic field "b" (kG)
1122 //---------------------------------------------------------------------
c9ec41e8 1123 p[0]=fP[4];
1530f89c 1124 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1125 p[2]=fP[3];
1126 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1127}
1128
7cf7bb6c 1129Bool_t
1130AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1131 //---------------------------------------------------------------------
1132 // This function returns the local Y-coordinate of the intersection
1133 // point between this track and the reference plane "x" (cm).
1134 // Magnetic field "b" (kG)
1135 //---------------------------------------------------------------------
1136 Double_t dx=x-fX;
1137 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1138
1530f89c 1139 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1140
1141 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1142 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1143
1144 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1145 y = fP[0] + dx*(f1+f2)/(r1+r2);
1146 return kTRUE;
1147}
1148
6c94f330 1149Bool_t
1150AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1151 //---------------------------------------------------------------------
1152 // This function returns the local Z-coordinate of the intersection
1153 // point between this track and the reference plane "x" (cm).
1154 // Magnetic field "b" (kG)
1155 //---------------------------------------------------------------------
1156 Double_t dx=x-fX;
1157 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1158
1159 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1160
1161 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1162 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1163
1164 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1165 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1166 return kTRUE;
1167}
1168
c9ec41e8 1169Bool_t
1170AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1171 //---------------------------------------------------------------------
1172 // This function returns the global track position extrapolated to
1173 // the radial position "x" (cm) in the magnetic field "b" (kG)
1174 //---------------------------------------------------------------------
c9ec41e8 1175 Double_t dx=x-fX;
e421f556 1176 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1177
1530f89c 1178 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1179
e421f556 1180 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1181 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1182
1183 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1184 r[0] = x;
1185 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 1186 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 1187 return Local2GlobalPosition(r,fAlpha);
51ad6848 1188}
1189
51ad6848 1190//_____________________________________________________________________________
1191void AliExternalTrackParam::Print(Option_t* /*option*/) const
1192{
1193// print the parameters and the covariance matrix
1194
1195 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1196 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1197 fP[0], fP[1], fP[2], fP[3], fP[4]);
1198 printf(" covariance: %12g\n", fC[0]);
1199 printf(" %12g %12g\n", fC[1], fC[2]);
1200 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1201 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1202 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1203 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1204 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1205}
5b77d93c 1206
c194ba83 1207Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1208 //
1209 // Get sinus at given x
1210 //
1530f89c 1211 Double_t crv=GetC(b);
c194ba83 1212 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1213 Double_t dx = x-fX;
1214 Double_t res = fP[2]+dx*crv;
1215 return res;
1216}