Adding the reconstructor component for trigger DDL data streams. (Indra)
[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"
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
50//_____________________________________________________________________________
6c94f330 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
63//_____________________________________________________________________________
def9660e 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
82//_____________________________________________________________________________
51ad6848 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);
116b445b 224
225 //Multiple scattering******************
226 if (xOverX0 != 0) {
227 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
228 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
229 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
230 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
231 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
232 fC44 += theta2*fP3*fP4*fP3*fP4;
233 }
234
235 //Energy losses************************
236 if ((xTimesRho != 0.) && (beta2 < 1.)) {
237 Double_t dE=Bethe(beta2)*xTimesRho;
238 Double_t e=TMath::Sqrt(p2 + mass*mass);
239 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
240 fP4*=(1.- e/p2*dE);
241
242 // Approximate energy loss fluctuation (M.Ivanov)
243 const Double_t knst=0.07; // To be tuned.
244 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
245 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
246
247 }
248
249 return kTRUE;
250}
251
252
ee5dba5e 253Bool_t AliExternalTrackParam::CorrectForMaterial
254(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 255 //------------------------------------------------------------------
116b445b 256 // Deprecated function !
257 // Better use CorrectForMeanMaterial instead of it.
258 //
c7bafca9 259 // This function corrects the track parameters for the crossed material
260 // "d" - the thickness (fraction of the radiation length)
261 // "x0" - the radiation length (g/cm^2)
262 // "mass" - the mass of this particle (GeV/c^2)
263 //------------------------------------------------------------------
264 Double_t &fP2=fP[2];
265 Double_t &fP3=fP[3];
266 Double_t &fP4=fP[4];
267
268 Double_t &fC22=fC[5];
269 Double_t &fC33=fC[9];
270 Double_t &fC43=fC[13];
271 Double_t &fC44=fC[14];
272
7b5ef2e6 273 Double_t p=GetP();
274 Double_t p2=p*p;
c7bafca9 275 Double_t beta2=p2/(p2 + mass*mass);
276 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
277
278 //Multiple scattering******************
279 if (d!=0) {
280 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
281 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
282 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
283 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
284 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
285 fC44 += theta2*fP3*fP4*fP3*fP4;
286 }
287
288 //Energy losses************************
8fc1985d 289 if (x0!=0. && beta2<1) {
c7bafca9 290 d*=x0;
ee5dba5e 291 Double_t dE=Bethe(beta2)*d;
292 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 293 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 294 fP4*=(1.- e/p2*dE);
295
296 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 297 const Double_t knst=0.07; // To be tuned.
298 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 299 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
300
c7bafca9 301 }
302
303 return kTRUE;
304}
305
ee5dba5e 306Double_t ApproximateBetheBloch(Double_t beta2) {
307 //------------------------------------------------------------------
308 // This is an approximation of the Bethe-Bloch formula with
309 // the density effect taken into account at beta*gamma > 3.5
310 // (the approximation is reasonable only for solid materials)
311 //------------------------------------------------------------------
312 if (beta2/(1-beta2)>3.5*3.5)
313 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
314
315 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
316}
317
49d13e89 318Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
319 //------------------------------------------------------------------
320 // Transform this track to the local coord. system rotated
321 // by angle "alpha" (rad) with respect to the global coord. system.
322 //------------------------------------------------------------------
dfcef74c 323 if (TMath::Abs(fP[2]) >= kAlmost1) {
324 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
325 return kFALSE;
326 }
327
49d13e89 328 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
329 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
330
331 Double_t &fP0=fP[0];
332 Double_t &fP2=fP[2];
333 Double_t &fC00=fC[0];
334 Double_t &fC10=fC[1];
335 Double_t &fC20=fC[3];
336 Double_t &fC21=fC[4];
337 Double_t &fC22=fC[5];
338 Double_t &fC30=fC[6];
339 Double_t &fC32=fC[8];
340 Double_t &fC40=fC[10];
341 Double_t &fC42=fC[12];
342
343 Double_t x=fX;
344 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
345 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
346
dfcef74c 347 Double_t tmp=sf*ca - cf*sa;
348 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
349
49d13e89 350 fAlpha = alpha;
351 fX = x*ca + fP0*sa;
352 fP0= -x*sa + fP0*ca;
dfcef74c 353 fP2= tmp;
49d13e89 354
06fb4a2f 355 if (TMath::Abs(cf)<kAlmost0) {
356 AliError(Form("Too small cosine value %f",cf));
357 cf = kAlmost0;
358 }
359
49d13e89 360 Double_t rr=(ca+sf/cf*sa);
361
362 fC00 *= (ca*ca);
363 fC10 *= ca;
364 fC20 *= ca*rr;
365 fC21 *= rr;
366 fC22 *= rr*rr;
367 fC30 *= ca;
368 fC32 *= rr;
369 fC40 *= ca;
370 fC42 *= rr;
371
372 return kTRUE;
373}
374
375Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
376 //----------------------------------------------------------------
377 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
378 //----------------------------------------------------------------
49d13e89 379 Double_t dx=xk-fX;
e421f556 380 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 381
1530f89c 382 Double_t crv=GetC(b);
5773defd 383 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
384
49d13e89 385 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 386 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 387 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
388
389 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
390 Double_t
391 &fC00=fC[0],
392 &fC10=fC[1], &fC11=fC[2],
393 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
394 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
395 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
396
397 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
398
399 fX=xk;
400 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 401 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 402 fP2 += dx*crv;
403
404 //f = F - 1
405
406 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
407 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
408 Double_t f12= dx*fP3*f1/(r1*r1*r1);
409 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
410 Double_t f13= dx/r1;
411 Double_t f24= dx; f24*=cc;
412
413 //b = C*ft
414 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
415 Double_t b02=f24*fC40;
416 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
417 Double_t b12=f24*fC41;
418 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
419 Double_t b22=f24*fC42;
420 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
421 Double_t b42=f24*fC44;
422 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
423 Double_t b32=f24*fC43;
424
425 //a = f*b = f*C*ft
426 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
427 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
428 Double_t a22=f24*b42;
429
430 //F*C*Ft = C + (b + bt + a)
431 fC00 += b00 + b00 + a00;
432 fC10 += b10 + b01 + a01;
433 fC20 += b20 + b02 + a02;
434 fC30 += b30;
435 fC40 += b40;
436 fC11 += b11 + b11 + a11;
437 fC21 += b21 + b12 + a12;
438 fC31 += b31;
439 fC41 += b41;
440 fC22 += b22 + b22 + a22;
441 fC32 += b32;
442 fC42 += b42;
443
444 return kTRUE;
445}
446
052daaff 447void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
448Double_t p[3], Double_t bz) const {
449 //+++++++++++++++++++++++++++++++++++++++++
450 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
451 // Extrapolate track along simple helix in magnetic field
452 // Arguments: len -distance alogn helix, [cm]
453 // bz - mag field, [kGaus]
454 // Returns: x and p contain extrapolated positon and momentum
455 // The momentum returned for straight-line tracks is meaningless !
456 //+++++++++++++++++++++++++++++++++++++++++
457 GetXYZ(x);
458
def9660e 459 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 460 Double_t unit[3]; GetDirection(unit);
461 x[0]+=unit[0]*len;
462 x[1]+=unit[1]*len;
463 x[2]+=unit[2]*len;
464
465 p[0]=unit[0]/kAlmost0;
466 p[1]=unit[1]/kAlmost0;
467 p[2]=unit[2]/kAlmost0;
468 } else {
469 GetPxPyPz(p);
470 Double_t pp=GetP();
471 Double_t a = -kB2C*bz*GetSign();
472 Double_t rho = a/pp;
473 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
474 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
475 x[2] += p[2]*len/pp;
476
477 Double_t p0=p[0];
478 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
479 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
480 }
481}
482
483Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
484Double_t bz) const {
485 //+++++++++++++++++++++++++++++++++++++++++
486 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
487 // Finds point of intersection (if exists) of the helix with the plane.
488 // Stores result in fX and fP.
489 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
490 // and vector, normal to the plane
491 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
492 //+++++++++++++++++++++++++++++++++++++++++
493 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
494
495 //estimates initial helix length up to plane
496 Double_t s=
497 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
498 Double_t dist=99999,distPrev=dist;
499 Double_t x[3],p[3];
500 while(TMath::Abs(dist)>0.00001){
501 //calculates helix at the distance s from x0 ALONG the helix
502 Propagate(s,x,p,bz);
503
504 //distance between current helix position and plane
505 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
506
507 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
508 distPrev=dist;
509 s-=dist;
510 }
511 //on exit pnt is intersection point,norm is track vector at that point,
512 //all in MARS
513 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
514 return kTRUE;
515}
516
49d13e89 517Double_t
518AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
519 //----------------------------------------------------------------
520 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
521 //----------------------------------------------------------------
522 Double_t sdd = fC[0] + cov[0];
523 Double_t sdz = fC[1] + cov[1];
524 Double_t szz = fC[2] + cov[2];
525 Double_t det = sdd*szz - sdz*sdz;
526
527 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
528
529 Double_t d = fP[0] - p[0];
530 Double_t z = fP[1] - p[1];
531
532 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
533}
534
4b189f98 535Double_t AliExternalTrackParam::
536GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
537 //----------------------------------------------------------------
538 // Estimate the chi2 of the 3D space point "p" and
1e023a36 539 // the full covariance matrix "covyz" and "covxyz"
4b189f98 540 //
541 // Cov(x,x) ... : covxyz[0]
542 // Cov(y,x) ... : covxyz[1] covyz[0]
543 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
544 //----------------------------------------------------------------
545
546 Double_t res[3] = {
547 GetX() - p[0],
548 GetY() - p[1],
549 GetZ() - p[2]
550 };
551
552 Double_t f=GetSnp();
553 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
554 Double_t r=TMath::Sqrt(1.- f*f);
555 Double_t a=f/r, b=GetTgl()/r;
556
557 Double_t s2=333.*333.; //something reasonably big (cm^2)
558
559 TMatrixDSym v(3);
560 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
561 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
562 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
563
564 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
565 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
566 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
567
568 v.Invert();
569 if (!v.IsValid()) return kVeryBig;
570
571 Double_t chi2=0.;
572 for (Int_t i = 0; i < 3; i++)
573 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
574
575 return chi2;
576
577
578}
579
1e023a36 580Bool_t AliExternalTrackParam::
581PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
582 //----------------------------------------------------------------
583 // Propagate this track to the plane
584 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
585 // belongs to.
586 // The magnetic field is "bz" (kG)
587 //
588 // The track curvature and the change of the covariance matrix
589 // of the track parameters are negleted !
590 // (So the "step" should be small compared with 1/curvature)
591 //----------------------------------------------------------------
592
593 Double_t f=GetSnp();
594 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
595 Double_t r=TMath::Sqrt(1.- f*f);
596 Double_t a=f/r, b=GetTgl()/r;
597
598 Double_t s2=333.*333.; //something reasonably big (cm^2)
599
600 TMatrixDSym tV(3);
601 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
602 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
603 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
604
605 TMatrixDSym pV(3);
606 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
607 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
608 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
609
610 TMatrixDSym tpV(tV);
611 tpV+=pV;
612 tpV.Invert();
613 if (!tpV.IsValid()) return kFALSE;
614
615 TMatrixDSym pW(3),tW(3);
616 for (Int_t i=0; i<3; i++)
617 for (Int_t j=0; j<3; j++) {
618 pW(i,j)=tW(i,j)=0.;
619 for (Int_t k=0; k<3; k++) {
620 pW(i,j) += tV(i,k)*tpV(k,j);
621 tW(i,j) += pV(i,k)*tpV(k,j);
622 }
623 }
624
625 Double_t t[3] = {GetX(), GetY(), GetZ()};
626
627 Double_t x=0.;
628 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
629 Double_t crv=GetC(bz);
630 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
631 f += crv*(x-fX);
632 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
633 fX=x;
634
635 fP[0]=0.;
636 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
637 fP[1]=0.;
638 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
639
640 return kTRUE;
641}
642
49d13e89 643Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
644 //------------------------------------------------------------------
645 // Update the track parameters with the space point "p" having
646 // the covariance matrix "cov"
647 //------------------------------------------------------------------
648 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
649 Double_t
650 &fC00=fC[0],
651 &fC10=fC[1], &fC11=fC[2],
652 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
653 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
654 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
655
656 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
657 r00+=fC00; r01+=fC10; r11+=fC11;
658 Double_t det=r00*r11 - r01*r01;
659
660 if (TMath::Abs(det) < kAlmost0) return kFALSE;
661
662
663 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
664
665 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
666 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
667 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
668 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
669 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
670
671 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
672 Double_t sf=fP2 + k20*dy + k21*dz;
673 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
674
675 fP0 += k00*dy + k01*dz;
676 fP1 += k10*dy + k11*dz;
677 fP2 = sf;
678 fP3 += k30*dy + k31*dz;
679 fP4 += k40*dy + k41*dz;
680
681 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
682 Double_t c12=fC21, c13=fC31, c14=fC41;
683
684 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
685 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
686 fC40-=k00*c04+k01*c14;
687
688 fC11-=k10*c01+k11*fC11;
689 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
690 fC41-=k10*c04+k11*c14;
691
692 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
693 fC42-=k20*c04+k21*c14;
694
695 fC33-=k30*c03+k31*c13;
696 fC43-=k30*c04+k31*c14;
697
698 fC44-=k40*c04+k41*c14;
699
700 return kTRUE;
701}
702
c7bafca9 703void
704AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
705 //--------------------------------------------------------------------
706 // External track parameters -> helix parameters
707 // "b" - magnetic field (kG)
708 //--------------------------------------------------------------------
709 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
710
1530f89c 711 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 712
713 hlx[5]=fX*cs - hlx[0]*sn; // x0
714 hlx[0]=fX*sn + hlx[0]*cs; // y0
715//hlx[1]= // z0
716 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
717//hlx[3]= // tgl
1530f89c 718 hlx[4]=GetC(b); // C
c7bafca9 719}
720
721
722static void Evaluate(const Double_t *h, Double_t t,
723 Double_t r[3], //radius vector
724 Double_t g[3], //first defivatives
725 Double_t gg[3]) //second derivatives
726{
727 //--------------------------------------------------------------------
728 // Calculate position of a point on a track and some derivatives
729 //--------------------------------------------------------------------
730 Double_t phase=h[4]*t+h[2];
731 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
732
733 r[0] = h[5] + (sn - h[6])/h[4];
734 r[1] = h[0] - (cs - h[7])/h[4];
735 r[2] = h[1] + h[3]*t;
736
737 g[0] = cs; g[1]=sn; g[2]=h[3];
738
739 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
740}
741
742Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
743Double_t b, Double_t &xthis, Double_t &xp) const {
744 //------------------------------------------------------------
745 // Returns the (weighed !) distance of closest approach between
746 // this track and the track "p".
747 // Other returned values:
748 // xthis, xt - coordinates of tracks' reference planes at the DCA
749 //-----------------------------------------------------------
750 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
751 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
752 Double_t dx2=dy2;
753
754 //dx2=dy2=dz2=1.;
755
756 Double_t p1[8]; GetHelixParameters(p1,b);
757 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
758 Double_t p2[8]; p->GetHelixParameters(p2,b);
759 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
760
761
762 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
763 Evaluate(p1,t1,r1,g1,gg1);
764 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
765 Evaluate(p2,t2,r2,g2,gg2);
766
767 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
768 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
769
770 Int_t max=27;
771 while (max--) {
772 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
773 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
774 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
775 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
776 (g1[2]*g1[2] - dz*gg1[2])/dz2;
777 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
778 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
779 (g2[2]*g2[2] + dz*gg2[2])/dz2;
780 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
781
782 Double_t det=h11*h22-h12*h12;
783
784 Double_t dt1,dt2;
785 if (TMath::Abs(det)<1.e-33) {
786 //(quasi)singular Hessian
787 dt1=-gt1; dt2=-gt2;
788 } else {
789 dt1=-(gt1*h22 - gt2*h12)/det;
790 dt2=-(h11*gt2 - h12*gt1)/det;
791 }
792
793 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
794
795 //check delta(phase1) ?
796 //check delta(phase2) ?
797
798 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
799 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
800 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
801 AliWarning(" stopped at not a stationary point !");
802 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
803 if (lmb < 0.)
804 AliWarning(" stopped at not a minimum !");
805 break;
806 }
807
808 Double_t dd=dm;
809 for (Int_t div=1 ; ; div*=2) {
810 Evaluate(p1,t1+dt1,r1,g1,gg1);
811 Evaluate(p2,t2+dt2,r2,g2,gg2);
812 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
813 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
814 if (dd<dm) break;
815 dt1*=0.5; dt2*=0.5;
816 if (div>512) {
817 AliWarning(" overshoot !"); break;
818 }
819 }
820 dm=dd;
821
822 t1+=dt1;
823 t2+=dt2;
824
825 }
826
827 if (max<=0) AliWarning(" too many iterations !");
828
829 Double_t cs=TMath::Cos(GetAlpha());
830 Double_t sn=TMath::Sin(GetAlpha());
831 xthis=r1[0]*cs + r1[1]*sn;
832
833 cs=TMath::Cos(p->GetAlpha());
834 sn=TMath::Sin(p->GetAlpha());
835 xp=r2[0]*cs + r2[1]*sn;
836
837 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
838}
839
840Double_t AliExternalTrackParam::
841PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
842 //--------------------------------------------------------------
843 // Propagates this track and the argument track to the position of the
844 // distance of closest approach.
845 // Returns the (weighed !) distance of closest approach.
846 //--------------------------------------------------------------
847 Double_t xthis,xp;
848 Double_t dca=GetDCA(p,b,xthis,xp);
849
850 if (!PropagateTo(xthis,b)) {
851 //AliWarning(" propagation failed !");
852 return 1e+33;
853 }
854
855 if (!p->PropagateTo(xp,b)) {
856 //AliWarning(" propagation failed !";
857 return 1e+33;
858 }
859
860 return dca;
861}
862
863
864
f76701bf 865
866Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
867 //
868 // Try to relate this track to the vertex "vtx",
869 // if the (rough) transverse impact parameter is not bigger then "maxd".
870 // Magnetic field is "b" (kG).
871 //
872 // a) The track gets extapolated to the DCA to the vertex.
873 // b) The impact parameters and their covariance matrix are calculated.
874 //
875 // In the case of success, the returned value is kTRUE
876 // (otherwise, it's kFALSE)
877 //
878 Double_t alpha=GetAlpha();
879 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
880 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
881 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 882 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 883 x-=xv; y-=yv;
884
885 //Estimate the impact parameter neglecting the track curvature
886 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
887 if (d > maxd) return kFALSE;
888
889 //Propagate to the DCA
890 Double_t crv=0.299792458e-3*b*GetParameter()[4];
891 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
892 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
893
894 x = xv*cs + yv*sn;
895 yv=-xv*sn + yv*cs; xv=x;
896
897 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 898 return kTRUE;
f76701bf 899}
900
901
902
903
c9ec41e8 904Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
905 //----------------------------------------------------------------
906 // This function performs local->global transformation of the
907 // track momentum.
908 // When called, the arguments are:
909 // p[0] = 1/pt of the track;
910 // p[1] = sine of local azim. angle of the track momentum;
911 // p[2] = tangent of the track momentum dip angle;
912 // alpha - rotation angle.
913 // The result is returned as:
914 // p[0] = px
915 // p[1] = py
916 // p[2] = pz
917 // Results for (nearly) straight tracks are meaningless !
918 //----------------------------------------------------------------
e421f556 919 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 920 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 921
922 Double_t pt=1./TMath::Abs(p[0]);
923 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
924 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
925 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 926
927 return kTRUE;
928}
929
c9ec41e8 930Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
931 //----------------------------------------------------------------
932 // This function performs local->global transformation of the
933 // track position.
934 // When called, the arguments are:
935 // r[0] = local x
936 // r[1] = local y
937 // r[2] = local z
938 // alpha - rotation angle.
939 // The result is returned as:
940 // r[0] = global x
941 // r[1] = global y
942 // r[2] = global z
943 //----------------------------------------------------------------
944 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
945 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 946
a5e407e9 947 return kTRUE;
51ad6848 948}
949
b1149664 950void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
951 //----------------------------------------------------------------
952 // This function returns a unit vector along the track direction
953 // in the global coordinate system.
954 //----------------------------------------------------------------
955 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
956 Double_t snp=fP[2];
92934324 957 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 958 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
959 d[0]=(csp*cs - snp*sn)/norm;
960 d[1]=(snp*cs + csp*sn)/norm;
961 d[2]=fP[3]/norm;
962}
963
c9ec41e8 964Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
965 //---------------------------------------------------------------------
966 // This function returns the global track momentum components
967 // Results for (nearly) straight tracks are meaningless !
968 //---------------------------------------------------------------------
969 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
970 return Local2GlobalMomentum(p,fAlpha);
971}
a5e407e9 972
def9660e 973Double_t AliExternalTrackParam::Px() const {
957fb479 974 //---------------------------------------------------------------------
975 // Returns x-component of momentum
976 // Result for (nearly) straight tracks is meaningless !
977 //---------------------------------------------------------------------
def9660e 978
957fb479 979 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 980 GetPxPyPz(p);
981
982 return p[0];
983}
984
985Double_t AliExternalTrackParam::Py() const {
957fb479 986 //---------------------------------------------------------------------
987 // Returns y-component of momentum
988 // Result for (nearly) straight tracks is meaningless !
989 //---------------------------------------------------------------------
def9660e 990
957fb479 991 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 992 GetPxPyPz(p);
993
994 return p[1];
995}
996
997Double_t AliExternalTrackParam::Pz() const {
957fb479 998 //---------------------------------------------------------------------
999 // Returns z-component of momentum
1000 // Result for (nearly) straight tracks is meaningless !
1001 //---------------------------------------------------------------------
def9660e 1002
957fb479 1003 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1004 GetPxPyPz(p);
1005
1006 return p[2];
1007}
1008
1009Double_t AliExternalTrackParam::Theta() const {
1010 // return theta angle of momentum
1011
1012 return TMath::ATan2(Pt(), Pz());
1013}
1014
1015Double_t AliExternalTrackParam::Phi() const {
957fb479 1016 //---------------------------------------------------------------------
1017 // Returns the azimuthal angle of momentum
1018 // 0 <= phi < 2*pi
1019 //---------------------------------------------------------------------
def9660e 1020
957fb479 1021 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1022 if (phi<0.) phi+=2.*TMath::Pi();
1023 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1024
1025 return phi;
def9660e 1026}
1027
1028Double_t AliExternalTrackParam::M() const {
1029 // return particle mass
1030
1031 // No mass information available so far.
1032 // Redifine in derived class!
1033
1034 return -999.;
1035}
1036
1037Double_t AliExternalTrackParam::E() const {
1038 // return particle energy
1039
1040 // No PID information available so far.
1041 // Redifine in derived class!
1042
1043 return -999.;
1044}
1045
1046Double_t AliExternalTrackParam::Eta() const {
1047 // return pseudorapidity
1048
1049 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1050}
1051
1052Double_t AliExternalTrackParam::Y() const {
1053 // return rapidity
1054
1055 // No PID information available so far.
1056 // Redifine in derived class!
1057
1058 return -999.;
1059}
1060
c9ec41e8 1061Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1062 //---------------------------------------------------------------------
1063 // This function returns the global track position
1064 //---------------------------------------------------------------------
1065 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1066 return Local2GlobalPosition(r,fAlpha);
51ad6848 1067}
1068
c9ec41e8 1069Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1070 //---------------------------------------------------------------------
1071 // This function returns the global covariance matrix of the track params
1072 //
1073 // Cov(x,x) ... : cv[0]
1074 // Cov(y,x) ... : cv[1] cv[2]
1075 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1076 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1077 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1078 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1079 //
c9ec41e8 1080 // Results for (nearly) straight tracks are meaningless !
1081 //---------------------------------------------------------------------
e421f556 1082 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1083 for (Int_t i=0; i<21; i++) cv[i]=0.;
1084 return kFALSE;
a5e407e9 1085 }
49d13e89 1086 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1087 for (Int_t i=0; i<21; i++) cv[i]=0.;
1088 return kFALSE;
1089 }
1090 Double_t pt=1./TMath::Abs(fP[4]);
1091 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1092 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1093
1094 Double_t m00=-sn, m10=cs;
1095 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1096 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1097 Double_t m35=pt, m45=-pt*pt*fP[3];
1098
854d5d49 1099 m43*=GetSign();
1100 m44*=GetSign();
1101 m45*=GetSign();
1102
c9ec41e8 1103 cv[0 ] = fC[0]*m00*m00;
1104 cv[1 ] = fC[0]*m00*m10;
1105 cv[2 ] = fC[0]*m10*m10;
1106 cv[3 ] = fC[1]*m00;
1107 cv[4 ] = fC[1]*m10;
1108 cv[5 ] = fC[2];
1109 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1110 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1111 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1112 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1113 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1114 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1115 cv[12] = fC[4]*m24 + fC[11]*m44;
1116 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1117 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1118 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1119 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1120 cv[17] = fC[7]*m35 + fC[11]*m45;
1121 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1122 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1123 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1124
c9ec41e8 1125 return kTRUE;
51ad6848 1126}
1127
51ad6848 1128
c9ec41e8 1129Bool_t
1130AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1131 //---------------------------------------------------------------------
1132 // This function returns the global track momentum extrapolated to
1133 // the radial position "x" (cm) in the magnetic field "b" (kG)
1134 //---------------------------------------------------------------------
c9ec41e8 1135 p[0]=fP[4];
1530f89c 1136 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1137 p[2]=fP[3];
1138 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1139}
1140
c9ec41e8 1141Bool_t
7cf7bb6c 1142AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1143 //---------------------------------------------------------------------
1144 // This function returns the local Y-coordinate of the intersection
1145 // point between this track and the reference plane "x" (cm).
1146 // Magnetic field "b" (kG)
1147 //---------------------------------------------------------------------
1148 Double_t dx=x-fX;
1149 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1150
1530f89c 1151 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1152
1153 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1154 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1155
1156 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1157 y = fP[0] + dx*(f1+f2)/(r1+r2);
1158 return kTRUE;
1159}
1160
1161Bool_t
6c94f330 1162AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1163 //---------------------------------------------------------------------
1164 // This function returns the local Z-coordinate of the intersection
1165 // point between this track and the reference plane "x" (cm).
1166 // Magnetic field "b" (kG)
1167 //---------------------------------------------------------------------
1168 Double_t dx=x-fX;
1169 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1170
1171 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1172
1173 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1174 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1175
1176 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1177 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1178 return kTRUE;
1179}
1180
1181Bool_t
c9ec41e8 1182AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1183 //---------------------------------------------------------------------
1184 // This function returns the global track position extrapolated to
1185 // the radial position "x" (cm) in the magnetic field "b" (kG)
1186 //---------------------------------------------------------------------
c9ec41e8 1187 Double_t dx=x-fX;
e421f556 1188 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1189
1530f89c 1190 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1191
e421f556 1192 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1193 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1194
1195 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1196 r[0] = x;
1197 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 1198 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 1199 return Local2GlobalPosition(r,fAlpha);
51ad6848 1200}
1201
edc97986 1202//_____________________________________________________________________________
51ad6848 1203void AliExternalTrackParam::Print(Option_t* /*option*/) const
1204{
1205// print the parameters and the covariance matrix
1206
1207 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1208 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1209 fP[0], fP[1], fP[2], fP[3], fP[4]);
1210 printf(" covariance: %12g\n", fC[0]);
1211 printf(" %12g %12g\n", fC[1], fC[2]);
1212 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1213 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1214 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1215 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1216 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1217}
5b77d93c 1218
c194ba83 1219Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1220 //
1221 // Get sinus at given x
1222 //
1530f89c 1223 Double_t crv=GetC(b);
c194ba83 1224 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1225 Double_t dx = x-fX;
1226 Double_t res = fP[2]+dx*crv;
1227 return res;
1228}