Added methods for finding a given module in the DDL map (F. Prino)
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
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51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
4b189f98 28#include <TMatrixDSym.h>
51ad6848 29#include "AliExternalTrackParam.h"
f76701bf 30#include "AliESDVertex.h"
0c19adf7 31#include "TPolyMarker3D.h"
6c94f330 32#include "AliLog.h"
51ad6848 33
34ClassImp(AliExternalTrackParam)
35
ed5f2849 36Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
37
51ad6848 38//_____________________________________________________________________________
90e48c0c 39AliExternalTrackParam::AliExternalTrackParam() :
def9660e 40 AliVParticle(),
90e48c0c 41 fX(0),
c9ec41e8 42 fAlpha(0)
51ad6848 43{
90e48c0c 44 //
45 // default constructor
46 //
c9ec41e8 47 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
48 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 49}
50
51//_____________________________________________________________________________
6c94f330 52AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
def9660e 53 AliVParticle(track),
6c94f330 54 fX(track.fX),
55 fAlpha(track.fAlpha)
56{
57 //
58 // copy constructor
59 //
60 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
61 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
62}
63
64//_____________________________________________________________________________
def9660e 65AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
66{
67 //
68 // assignment operator
69 //
70
71 if (this!=&trkPar) {
72 AliVParticle::operator=(trkPar);
73 fX = trkPar.fX;
74 fAlpha = trkPar.fAlpha;
75
76 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
77 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
78 }
79
80 return *this;
81}
82
83//_____________________________________________________________________________
51ad6848 84AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
85 const Double_t param[5],
90e48c0c 86 const Double_t covar[15]) :
def9660e 87 AliVParticle(),
90e48c0c 88 fX(x),
c9ec41e8 89 fAlpha(alpha)
51ad6848 90{
90e48c0c 91 //
92 // create external track parameters from given arguments
93 //
c9ec41e8 94 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
95 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 96}
97
90e48c0c 98//_____________________________________________________________________________
6c94f330 99void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
100 const Double_t p[5], const Double_t cov[15]) {
c9ec41e8 101 //
6c94f330 102 // Sets the parameters
c9ec41e8 103 //
6c94f330 104 fX=x;
105 fAlpha=alpha;
106 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
107 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
51ad6848 108}
109
110//_____________________________________________________________________________
c9ec41e8 111void AliExternalTrackParam::Reset() {
1530f89c 112 //
113 // Resets all the parameters to 0
114 //
c9ec41e8 115 fX=fAlpha=0.;
116 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
117 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 118}
119
c9ec41e8 120Double_t AliExternalTrackParam::GetP() const {
121 //---------------------------------------------------------------------
122 // This function returns the track momentum
123 // Results for (nearly) straight tracks are meaningless !
124 //---------------------------------------------------------------------
06fb4a2f 125 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 126 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 127}
128
1d99986f 129Double_t AliExternalTrackParam::Get1P() const {
130 //---------------------------------------------------------------------
131 // This function returns the 1/(track momentum)
132 //---------------------------------------------------------------------
133 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
134}
135
c9ec41e8 136//_______________________________________________________________________
c7bafca9 137Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 138 //------------------------------------------------------------------
139 // This function calculates the transverse impact parameter
140 // with respect to a point with global coordinates (x,y)
141 // in the magnetic field "b" (kG)
142 //------------------------------------------------------------------
5773defd 143 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 144 Double_t rp4=GetC(b);
c9ec41e8 145
146 Double_t xt=fX, yt=fP[0];
147
148 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
149 Double_t a = x*cs + y*sn;
150 y = -x*sn + y*cs; x=a;
151 xt-=x; yt-=y;
152
153 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
154 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 155 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
156}
157
158//_______________________________________________________________________
159void AliExternalTrackParam::
160GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
161 //------------------------------------------------------------------
162 // This function calculates the transverse and longitudinal impact parameters
163 // with respect to a point with global coordinates (x,y)
164 // in the magnetic field "b" (kG)
165 //------------------------------------------------------------------
166 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
167 Double_t xt=fX, yt=fP[0];
168 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
169 Double_t a = x*cs + y*sn;
170 y = -x*sn + y*cs; x=a;
171 xt-=x; yt-=y;
172
173 Double_t rp4=GetC(b);
174 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
175 dz[0] = -(xt*f1 - yt*r1);
176 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
177 return;
178 }
179
180 sn=rp4*xt - f1; cs=rp4*yt + r1;
181 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
182 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
183 dz[0] = -a/(1 + rr);
184 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
185 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 186}
187
49d13e89 188//_______________________________________________________________________
189Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
190 //------------------------------------------------------------------
191 // This function calculates the transverse impact parameter
192 // with respect to a point with global coordinates (xv,yv)
193 // neglecting the track curvature.
194 //------------------------------------------------------------------
195 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
196 Double_t x= xv*cs + yv*sn;
197 Double_t y=-xv*sn + yv*cs;
198
199 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
200
1530f89c 201 return -d;
49d13e89 202}
203
116b445b 204Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 205(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
206 Double_t (*Bethe)(Double_t)) {
116b445b 207 //------------------------------------------------------------------
208 // This function corrects the track parameters for the crossed material.
209 // "xOverX0" - X/X0, the thickness in units of the radiation length.
210 // "xTimesRho" - is the product length*density (g/cm^2).
211 // "mass" - the mass of this particle (GeV/c^2).
212 //------------------------------------------------------------------
213 Double_t &fP2=fP[2];
214 Double_t &fP3=fP[3];
215 Double_t &fP4=fP[4];
216
217 Double_t &fC22=fC[5];
218 Double_t &fC33=fC[9];
219 Double_t &fC43=fC[13];
220 Double_t &fC44=fC[14];
221
7dded1d5 222 //Apply angle correction, if requested
223 if(anglecorr) {
224 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
225 xOverX0 *=angle;
226 xTimesRho *=angle;
227 }
228
116b445b 229 Double_t p=GetP();
230 Double_t p2=p*p;
231 Double_t beta2=p2/(p2 + mass*mass);
116b445b 232
233 //Multiple scattering******************
234 if (xOverX0 != 0) {
235 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
236 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
237 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
238 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
239 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
240 fC44 += theta2*fP3*fP4*fP3*fP4;
241 }
242
243 //Energy losses************************
244 if ((xTimesRho != 0.) && (beta2 < 1.)) {
245 Double_t dE=Bethe(beta2)*xTimesRho;
246 Double_t e=TMath::Sqrt(p2 + mass*mass);
247 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
248 fP4*=(1.- e/p2*dE);
249
250 // Approximate energy loss fluctuation (M.Ivanov)
251 const Double_t knst=0.07; // To be tuned.
252 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
253 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
254
255 }
256
257 return kTRUE;
258}
259
260
ee5dba5e 261Bool_t AliExternalTrackParam::CorrectForMaterial
262(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 263 //------------------------------------------------------------------
116b445b 264 // Deprecated function !
265 // Better use CorrectForMeanMaterial instead of it.
266 //
c7bafca9 267 // This function corrects the track parameters for the crossed material
268 // "d" - the thickness (fraction of the radiation length)
269 // "x0" - the radiation length (g/cm^2)
270 // "mass" - the mass of this particle (GeV/c^2)
271 //------------------------------------------------------------------
272 Double_t &fP2=fP[2];
273 Double_t &fP3=fP[3];
274 Double_t &fP4=fP[4];
275
276 Double_t &fC22=fC[5];
277 Double_t &fC33=fC[9];
278 Double_t &fC43=fC[13];
279 Double_t &fC44=fC[14];
280
7b5ef2e6 281 Double_t p=GetP();
282 Double_t p2=p*p;
c7bafca9 283 Double_t beta2=p2/(p2 + mass*mass);
284 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
285
286 //Multiple scattering******************
287 if (d!=0) {
288 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
289 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
290 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
291 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
292 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
293 fC44 += theta2*fP3*fP4*fP3*fP4;
294 }
295
296 //Energy losses************************
8fc1985d 297 if (x0!=0. && beta2<1) {
c7bafca9 298 d*=x0;
ee5dba5e 299 Double_t dE=Bethe(beta2)*d;
300 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 301 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 302 fP4*=(1.- e/p2*dE);
303
304 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 305 const Double_t knst=0.07; // To be tuned.
306 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 307 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
308
c7bafca9 309 }
310
311 return kTRUE;
312}
313
ee5dba5e 314Double_t ApproximateBetheBloch(Double_t beta2) {
315 //------------------------------------------------------------------
316 // This is an approximation of the Bethe-Bloch formula with
317 // the density effect taken into account at beta*gamma > 3.5
318 // (the approximation is reasonable only for solid materials)
319 //------------------------------------------------------------------
a821848c 320 if (beta2 >= 1) return kVeryBig;
321
ee5dba5e 322 if (beta2/(1-beta2)>3.5*3.5)
323 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
324
325 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
326}
327
49d13e89 328Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
329 //------------------------------------------------------------------
330 // Transform this track to the local coord. system rotated
331 // by angle "alpha" (rad) with respect to the global coord. system.
332 //------------------------------------------------------------------
dfcef74c 333 if (TMath::Abs(fP[2]) >= kAlmost1) {
334 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
335 return kFALSE;
336 }
337
49d13e89 338 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
339 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
340
341 Double_t &fP0=fP[0];
342 Double_t &fP2=fP[2];
343 Double_t &fC00=fC[0];
344 Double_t &fC10=fC[1];
345 Double_t &fC20=fC[3];
346 Double_t &fC21=fC[4];
347 Double_t &fC22=fC[5];
348 Double_t &fC30=fC[6];
349 Double_t &fC32=fC[8];
350 Double_t &fC40=fC[10];
351 Double_t &fC42=fC[12];
352
353 Double_t x=fX;
354 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
355 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
356
dfcef74c 357 Double_t tmp=sf*ca - cf*sa;
358 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
359
49d13e89 360 fAlpha = alpha;
361 fX = x*ca + fP0*sa;
362 fP0= -x*sa + fP0*ca;
dfcef74c 363 fP2= tmp;
49d13e89 364
06fb4a2f 365 if (TMath::Abs(cf)<kAlmost0) {
366 AliError(Form("Too small cosine value %f",cf));
367 cf = kAlmost0;
368 }
369
49d13e89 370 Double_t rr=(ca+sf/cf*sa);
371
372 fC00 *= (ca*ca);
373 fC10 *= ca;
374 fC20 *= ca*rr;
375 fC21 *= rr;
376 fC22 *= rr*rr;
377 fC30 *= ca;
378 fC32 *= rr;
379 fC40 *= ca;
380 fC42 *= rr;
381
382 return kTRUE;
383}
384
385Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
386 //----------------------------------------------------------------
387 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
388 //----------------------------------------------------------------
49d13e89 389 Double_t dx=xk-fX;
e421f556 390 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 391
1530f89c 392 Double_t crv=GetC(b);
5773defd 393 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
394
49d13e89 395 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 396 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 397 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
398
399 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
400 Double_t
401 &fC00=fC[0],
402 &fC10=fC[1], &fC11=fC[2],
403 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
404 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
405 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
406
407 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
408
409 fX=xk;
410 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 411 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 412 fP2 += dx*crv;
413
414 //f = F - 1
415
416 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
417 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
418 Double_t f12= dx*fP3*f1/(r1*r1*r1);
419 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
420 Double_t f13= dx/r1;
421 Double_t f24= dx; f24*=cc;
422
423 //b = C*ft
424 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
425 Double_t b02=f24*fC40;
426 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
427 Double_t b12=f24*fC41;
428 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
429 Double_t b22=f24*fC42;
430 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
431 Double_t b42=f24*fC44;
432 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
433 Double_t b32=f24*fC43;
434
435 //a = f*b = f*C*ft
436 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
437 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
438 Double_t a22=f24*b42;
439
440 //F*C*Ft = C + (b + bt + a)
441 fC00 += b00 + b00 + a00;
442 fC10 += b10 + b01 + a01;
443 fC20 += b20 + b02 + a02;
444 fC30 += b30;
445 fC40 += b40;
446 fC11 += b11 + b11 + a11;
447 fC21 += b21 + b12 + a12;
448 fC31 += b31;
449 fC41 += b41;
450 fC22 += b22 + b22 + a22;
451 fC32 += b32;
452 fC42 += b42;
453
454 return kTRUE;
455}
456
052daaff 457void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
458Double_t p[3], Double_t bz) const {
459 //+++++++++++++++++++++++++++++++++++++++++
460 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
461 // Extrapolate track along simple helix in magnetic field
462 // Arguments: len -distance alogn helix, [cm]
463 // bz - mag field, [kGaus]
464 // Returns: x and p contain extrapolated positon and momentum
465 // The momentum returned for straight-line tracks is meaningless !
466 //+++++++++++++++++++++++++++++++++++++++++
467 GetXYZ(x);
468
def9660e 469 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 470 Double_t unit[3]; GetDirection(unit);
471 x[0]+=unit[0]*len;
472 x[1]+=unit[1]*len;
473 x[2]+=unit[2]*len;
474
475 p[0]=unit[0]/kAlmost0;
476 p[1]=unit[1]/kAlmost0;
477 p[2]=unit[2]/kAlmost0;
478 } else {
479 GetPxPyPz(p);
480 Double_t pp=GetP();
481 Double_t a = -kB2C*bz*GetSign();
482 Double_t rho = a/pp;
483 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
484 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
485 x[2] += p[2]*len/pp;
486
487 Double_t p0=p[0];
488 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
489 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
490 }
491}
492
493Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
494Double_t bz) const {
495 //+++++++++++++++++++++++++++++++++++++++++
496 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
497 // Finds point of intersection (if exists) of the helix with the plane.
498 // Stores result in fX and fP.
499 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
500 // and vector, normal to the plane
501 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
502 //+++++++++++++++++++++++++++++++++++++++++
503 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
504
505 //estimates initial helix length up to plane
506 Double_t s=
507 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
508 Double_t dist=99999,distPrev=dist;
509 Double_t x[3],p[3];
510 while(TMath::Abs(dist)>0.00001){
511 //calculates helix at the distance s from x0 ALONG the helix
512 Propagate(s,x,p,bz);
513
514 //distance between current helix position and plane
515 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
516
517 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
518 distPrev=dist;
519 s-=dist;
520 }
521 //on exit pnt is intersection point,norm is track vector at that point,
522 //all in MARS
523 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
524 return kTRUE;
525}
526
49d13e89 527Double_t
528AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
529 //----------------------------------------------------------------
530 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
531 //----------------------------------------------------------------
532 Double_t sdd = fC[0] + cov[0];
533 Double_t sdz = fC[1] + cov[1];
534 Double_t szz = fC[2] + cov[2];
535 Double_t det = sdd*szz - sdz*sdz;
536
537 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
538
539 Double_t d = fP[0] - p[0];
540 Double_t z = fP[1] - p[1];
541
542 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
543}
544
4b189f98 545Double_t AliExternalTrackParam::
546GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
547 //----------------------------------------------------------------
548 // Estimate the chi2 of the 3D space point "p" and
1e023a36 549 // the full covariance matrix "covyz" and "covxyz"
4b189f98 550 //
551 // Cov(x,x) ... : covxyz[0]
552 // Cov(y,x) ... : covxyz[1] covyz[0]
553 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
554 //----------------------------------------------------------------
555
556 Double_t res[3] = {
557 GetX() - p[0],
558 GetY() - p[1],
559 GetZ() - p[2]
560 };
561
562 Double_t f=GetSnp();
563 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
564 Double_t r=TMath::Sqrt(1.- f*f);
565 Double_t a=f/r, b=GetTgl()/r;
566
567 Double_t s2=333.*333.; //something reasonably big (cm^2)
568
569 TMatrixDSym v(3);
570 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
571 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
572 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
573
574 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
575 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
576 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
577
578 v.Invert();
579 if (!v.IsValid()) return kVeryBig;
580
581 Double_t chi2=0.;
582 for (Int_t i = 0; i < 3; i++)
583 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
584
585 return chi2;
586
587
588}
589
1e023a36 590Bool_t AliExternalTrackParam::
591PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
592 //----------------------------------------------------------------
593 // Propagate this track to the plane
594 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
595 // belongs to.
596 // The magnetic field is "bz" (kG)
597 //
598 // The track curvature and the change of the covariance matrix
599 // of the track parameters are negleted !
600 // (So the "step" should be small compared with 1/curvature)
601 //----------------------------------------------------------------
602
603 Double_t f=GetSnp();
604 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
605 Double_t r=TMath::Sqrt(1.- f*f);
606 Double_t a=f/r, b=GetTgl()/r;
607
608 Double_t s2=333.*333.; //something reasonably big (cm^2)
609
610 TMatrixDSym tV(3);
611 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
612 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
613 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
614
615 TMatrixDSym pV(3);
616 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
617 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
618 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
619
620 TMatrixDSym tpV(tV);
621 tpV+=pV;
622 tpV.Invert();
623 if (!tpV.IsValid()) return kFALSE;
624
625 TMatrixDSym pW(3),tW(3);
626 for (Int_t i=0; i<3; i++)
627 for (Int_t j=0; j<3; j++) {
628 pW(i,j)=tW(i,j)=0.;
629 for (Int_t k=0; k<3; k++) {
630 pW(i,j) += tV(i,k)*tpV(k,j);
631 tW(i,j) += pV(i,k)*tpV(k,j);
632 }
633 }
634
635 Double_t t[3] = {GetX(), GetY(), GetZ()};
636
637 Double_t x=0.;
638 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
639 Double_t crv=GetC(bz);
640 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
641 f += crv*(x-fX);
642 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
643 fX=x;
644
645 fP[0]=0.;
646 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
647 fP[1]=0.;
648 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
649
650 return kTRUE;
651}
652
e23a38cb 653Double_t *AliExternalTrackParam::GetResiduals(
654Double_t *p,Double_t *cov,Bool_t updated) const {
655 //------------------------------------------------------------------
656 // Returns the track residuals with the space point "p" having
657 // the covariance matrix "cov".
658 // If "updated" is kTRUE, the track parameters expected to be updated,
659 // otherwise they must be predicted.
660 //------------------------------------------------------------------
661 static Double_t res[2];
662
663 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
664 if (updated) {
665 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
666 } else {
667 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
668 }
669 Double_t det=r00*r11 - r01*r01;
670
671 if (TMath::Abs(det) < kAlmost0) return 0;
672
673 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 674
675 if (r00 < 0.) return 0;
676 if (r11 < 0.) return 0;
677
e23a38cb 678 Double_t dy = fP[0] - p[0];
679 Double_t dz = fP[1] - p[1];
680
681 res[0]=dy*TMath::Sqrt(r00);
682 res[1]=dz*TMath::Sqrt(r11);
683
684 return res;
685}
686
49d13e89 687Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
688 //------------------------------------------------------------------
689 // Update the track parameters with the space point "p" having
690 // the covariance matrix "cov"
691 //------------------------------------------------------------------
692 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
693 Double_t
694 &fC00=fC[0],
695 &fC10=fC[1], &fC11=fC[2],
696 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
697 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
698 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
699
700 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
701 r00+=fC00; r01+=fC10; r11+=fC11;
702 Double_t det=r00*r11 - r01*r01;
703
704 if (TMath::Abs(det) < kAlmost0) return kFALSE;
705
706
707 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
708
709 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
710 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
711 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
712 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
713 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
714
715 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
716 Double_t sf=fP2 + k20*dy + k21*dz;
717 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
718
719 fP0 += k00*dy + k01*dz;
720 fP1 += k10*dy + k11*dz;
721 fP2 = sf;
722 fP3 += k30*dy + k31*dz;
723 fP4 += k40*dy + k41*dz;
724
725 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
726 Double_t c12=fC21, c13=fC31, c14=fC41;
727
728 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
729 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
730 fC40-=k00*c04+k01*c14;
731
732 fC11-=k10*c01+k11*fC11;
733 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
734 fC41-=k10*c04+k11*c14;
735
736 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
737 fC42-=k20*c04+k21*c14;
738
739 fC33-=k30*c03+k31*c13;
740 fC43-=k30*c04+k31*c14;
741
742 fC44-=k40*c04+k41*c14;
743
744 return kTRUE;
745}
746
c7bafca9 747void
748AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
749 //--------------------------------------------------------------------
750 // External track parameters -> helix parameters
751 // "b" - magnetic field (kG)
752 //--------------------------------------------------------------------
753 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
754
1530f89c 755 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 756
757 hlx[5]=fX*cs - hlx[0]*sn; // x0
758 hlx[0]=fX*sn + hlx[0]*cs; // y0
759//hlx[1]= // z0
760 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
761//hlx[3]= // tgl
1530f89c 762 hlx[4]=GetC(b); // C
c7bafca9 763}
764
765
766static void Evaluate(const Double_t *h, Double_t t,
767 Double_t r[3], //radius vector
768 Double_t g[3], //first defivatives
769 Double_t gg[3]) //second derivatives
770{
771 //--------------------------------------------------------------------
772 // Calculate position of a point on a track and some derivatives
773 //--------------------------------------------------------------------
774 Double_t phase=h[4]*t+h[2];
775 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
776
777 r[0] = h[5] + (sn - h[6])/h[4];
778 r[1] = h[0] - (cs - h[7])/h[4];
779 r[2] = h[1] + h[3]*t;
780
781 g[0] = cs; g[1]=sn; g[2]=h[3];
782
783 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
784}
785
786Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
787Double_t b, Double_t &xthis, Double_t &xp) const {
788 //------------------------------------------------------------
789 // Returns the (weighed !) distance of closest approach between
790 // this track and the track "p".
791 // Other returned values:
792 // xthis, xt - coordinates of tracks' reference planes at the DCA
793 //-----------------------------------------------------------
794 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
795 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
796 Double_t dx2=dy2;
797
798 //dx2=dy2=dz2=1.;
799
800 Double_t p1[8]; GetHelixParameters(p1,b);
801 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
802 Double_t p2[8]; p->GetHelixParameters(p2,b);
803 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
804
805
806 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
807 Evaluate(p1,t1,r1,g1,gg1);
808 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
809 Evaluate(p2,t2,r2,g2,gg2);
810
811 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
812 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
813
814 Int_t max=27;
815 while (max--) {
816 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
817 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
818 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
819 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
820 (g1[2]*g1[2] - dz*gg1[2])/dz2;
821 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
822 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
823 (g2[2]*g2[2] + dz*gg2[2])/dz2;
824 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
825
826 Double_t det=h11*h22-h12*h12;
827
828 Double_t dt1,dt2;
829 if (TMath::Abs(det)<1.e-33) {
830 //(quasi)singular Hessian
831 dt1=-gt1; dt2=-gt2;
832 } else {
833 dt1=-(gt1*h22 - gt2*h12)/det;
834 dt2=-(h11*gt2 - h12*gt1)/det;
835 }
836
837 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
838
839 //check delta(phase1) ?
840 //check delta(phase2) ?
841
842 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
843 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
844 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
845 AliWarning(" stopped at not a stationary point !");
846 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
847 if (lmb < 0.)
848 AliWarning(" stopped at not a minimum !");
849 break;
850 }
851
852 Double_t dd=dm;
853 for (Int_t div=1 ; ; div*=2) {
854 Evaluate(p1,t1+dt1,r1,g1,gg1);
855 Evaluate(p2,t2+dt2,r2,g2,gg2);
856 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
857 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
858 if (dd<dm) break;
859 dt1*=0.5; dt2*=0.5;
860 if (div>512) {
861 AliWarning(" overshoot !"); break;
862 }
863 }
864 dm=dd;
865
866 t1+=dt1;
867 t2+=dt2;
868
869 }
870
871 if (max<=0) AliWarning(" too many iterations !");
872
873 Double_t cs=TMath::Cos(GetAlpha());
874 Double_t sn=TMath::Sin(GetAlpha());
875 xthis=r1[0]*cs + r1[1]*sn;
876
877 cs=TMath::Cos(p->GetAlpha());
878 sn=TMath::Sin(p->GetAlpha());
879 xp=r2[0]*cs + r2[1]*sn;
880
881 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
882}
883
884Double_t AliExternalTrackParam::
885PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
886 //--------------------------------------------------------------
887 // Propagates this track and the argument track to the position of the
888 // distance of closest approach.
889 // Returns the (weighed !) distance of closest approach.
890 //--------------------------------------------------------------
891 Double_t xthis,xp;
892 Double_t dca=GetDCA(p,b,xthis,xp);
893
894 if (!PropagateTo(xthis,b)) {
895 //AliWarning(" propagation failed !");
896 return 1e+33;
897 }
898
899 if (!p->PropagateTo(xp,b)) {
900 //AliWarning(" propagation failed !";
901 return 1e+33;
902 }
903
904 return dca;
905}
906
907
e99a34df 908Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx,
909Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 910 //
e99a34df 911 // Propagate this track to the DCA to vertex "vtx",
f76701bf 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;
e99a34df 925 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs, zv=vtx->GetZv();
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
e99a34df 933 Double_t crv=kB2C*b*GetParameter()[4];
934 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
935
f76701bf 936 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
937 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 938 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
939 else cs=1.;
f76701bf 940
941 x = xv*cs + yv*sn;
942 yv=-xv*sn + yv*cs; xv=x;
943
944 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 945
946 if (dz==0) return kTRUE;
947 dz[0] = GetParameter()[0] - yv;
948 dz[1] = GetParameter()[1] - zv;
949
950 if (covar==0) return kTRUE;
951 Double_t cov[6]; vtx->GetCovMatrix(cov);
952
953 //***** Improvements by A.Dainese
954 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
955 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
956 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
957 covar[1] = GetCovariance()[1]; // between (x,y) and z
958 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
959 //*****
960
29fbcc93 961 return kTRUE;
f76701bf 962}
963
964
b1149664 965void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
966 //----------------------------------------------------------------
967 // This function returns a unit vector along the track direction
968 // in the global coordinate system.
969 //----------------------------------------------------------------
970 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
971 Double_t snp=fP[2];
92934324 972 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 973 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
974 d[0]=(csp*cs - snp*sn)/norm;
975 d[1]=(snp*cs + csp*sn)/norm;
976 d[2]=fP[3]/norm;
977}
978
c683ddc2 979Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 980 //---------------------------------------------------------------------
981 // This function returns the global track momentum components
982 // Results for (nearly) straight tracks are meaningless !
983 //---------------------------------------------------------------------
984 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
985 return Local2GlobalMomentum(p,fAlpha);
986}
a5e407e9 987
def9660e 988Double_t AliExternalTrackParam::Px() const {
957fb479 989 //---------------------------------------------------------------------
990 // Returns x-component of momentum
991 // Result for (nearly) straight tracks is meaningless !
992 //---------------------------------------------------------------------
def9660e 993
957fb479 994 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 995 GetPxPyPz(p);
996
997 return p[0];
998}
999
1000Double_t AliExternalTrackParam::Py() const {
957fb479 1001 //---------------------------------------------------------------------
1002 // Returns y-component of momentum
1003 // Result for (nearly) straight tracks is meaningless !
1004 //---------------------------------------------------------------------
def9660e 1005
957fb479 1006 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1007 GetPxPyPz(p);
1008
1009 return p[1];
1010}
1011
1012Double_t AliExternalTrackParam::Pz() const {
957fb479 1013 //---------------------------------------------------------------------
1014 // Returns z-component of momentum
1015 // Result for (nearly) straight tracks is meaningless !
1016 //---------------------------------------------------------------------
def9660e 1017
957fb479 1018 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1019 GetPxPyPz(p);
1020
1021 return p[2];
1022}
1023
c683ddc2 1024Double_t AliExternalTrackParam::Xv() const {
1025 //---------------------------------------------------------------------
1026 // Returns x-component of first track point
1027 //---------------------------------------------------------------------
1028
1029 Double_t r[3]={0.,0.,0.};
1030 GetXYZ(r);
1031
1032 return r[0];
1033}
1034
1035Double_t AliExternalTrackParam::Yv() const {
1036 //---------------------------------------------------------------------
1037 // Returns y-component of first track point
1038 //---------------------------------------------------------------------
1039
1040 Double_t r[3]={0.,0.,0.};
1041 GetXYZ(r);
1042
1043 return r[1];
1044}
1045
1046Double_t AliExternalTrackParam::Zv() const {
1047 //---------------------------------------------------------------------
1048 // Returns z-component of first track point
1049 //---------------------------------------------------------------------
1050
1051 Double_t r[3]={0.,0.,0.};
1052 GetXYZ(r);
1053
1054 return r[2];
1055}
1056
def9660e 1057Double_t AliExternalTrackParam::Theta() const {
1058 // return theta angle of momentum
1059
7cdd0c20 1060 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1061}
1062
1063Double_t AliExternalTrackParam::Phi() const {
957fb479 1064 //---------------------------------------------------------------------
1065 // Returns the azimuthal angle of momentum
1066 // 0 <= phi < 2*pi
1067 //---------------------------------------------------------------------
def9660e 1068
957fb479 1069 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1070 if (phi<0.) phi+=2.*TMath::Pi();
1071 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1072
1073 return phi;
def9660e 1074}
1075
1076Double_t AliExternalTrackParam::M() const {
1077 // return particle mass
1078
1079 // No mass information available so far.
1080 // Redifine in derived class!
1081
1082 return -999.;
1083}
1084
1085Double_t AliExternalTrackParam::E() const {
1086 // return particle energy
1087
1088 // No PID information available so far.
1089 // Redifine in derived class!
1090
1091 return -999.;
1092}
1093
1094Double_t AliExternalTrackParam::Eta() const {
1095 // return pseudorapidity
1096
1097 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1098}
1099
1100Double_t AliExternalTrackParam::Y() const {
1101 // return rapidity
1102
1103 // No PID information available so far.
1104 // Redifine in derived class!
1105
1106 return -999.;
1107}
1108
c9ec41e8 1109Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1110 //---------------------------------------------------------------------
1111 // This function returns the global track position
1112 //---------------------------------------------------------------------
1113 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1114 return Local2GlobalPosition(r,fAlpha);
51ad6848 1115}
1116
c9ec41e8 1117Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1118 //---------------------------------------------------------------------
1119 // This function returns the global covariance matrix of the track params
1120 //
1121 // Cov(x,x) ... : cv[0]
1122 // Cov(y,x) ... : cv[1] cv[2]
1123 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1124 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1125 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1126 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1127 //
c9ec41e8 1128 // Results for (nearly) straight tracks are meaningless !
1129 //---------------------------------------------------------------------
e421f556 1130 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1131 for (Int_t i=0; i<21; i++) cv[i]=0.;
1132 return kFALSE;
a5e407e9 1133 }
49d13e89 1134 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1135 for (Int_t i=0; i<21; i++) cv[i]=0.;
1136 return kFALSE;
1137 }
1138 Double_t pt=1./TMath::Abs(fP[4]);
1139 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1140 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1141
1142 Double_t m00=-sn, m10=cs;
1143 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1144 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1145 Double_t m35=pt, m45=-pt*pt*fP[3];
1146
854d5d49 1147 m43*=GetSign();
1148 m44*=GetSign();
1149 m45*=GetSign();
1150
c9ec41e8 1151 cv[0 ] = fC[0]*m00*m00;
1152 cv[1 ] = fC[0]*m00*m10;
1153 cv[2 ] = fC[0]*m10*m10;
1154 cv[3 ] = fC[1]*m00;
1155 cv[4 ] = fC[1]*m10;
1156 cv[5 ] = fC[2];
1157 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1158 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1159 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1160 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1161 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1162 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1163 cv[12] = fC[4]*m24 + fC[11]*m44;
1164 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1165 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1166 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1167 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1168 cv[17] = fC[7]*m35 + fC[11]*m45;
1169 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1170 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1171 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1172
c9ec41e8 1173 return kTRUE;
51ad6848 1174}
1175
51ad6848 1176
c9ec41e8 1177Bool_t
1178AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1179 //---------------------------------------------------------------------
1180 // This function returns the global track momentum extrapolated to
1181 // the radial position "x" (cm) in the magnetic field "b" (kG)
1182 //---------------------------------------------------------------------
c9ec41e8 1183 p[0]=fP[4];
1530f89c 1184 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1185 p[2]=fP[3];
1186 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1187}
1188
c9ec41e8 1189Bool_t
7cf7bb6c 1190AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1191 //---------------------------------------------------------------------
1192 // This function returns the local Y-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) {y=fP[0]; return kTRUE;}
1198
1530f89c 1199 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1200
1201 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1202 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1203
1204 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1205 y = fP[0] + dx*(f1+f2)/(r1+r2);
1206 return kTRUE;
1207}
1208
1209Bool_t
6c94f330 1210AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1211 //---------------------------------------------------------------------
1212 // This function returns the local Z-coordinate of the intersection
1213 // point between this track and the reference plane "x" (cm).
1214 // Magnetic field "b" (kG)
1215 //---------------------------------------------------------------------
1216 Double_t dx=x-fX;
1217 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1218
1219 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1220
1221 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1222 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1223
1224 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1225 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1226 return kTRUE;
1227}
1228
1229Bool_t
c9ec41e8 1230AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1231 //---------------------------------------------------------------------
1232 // This function returns the global track position extrapolated to
1233 // the radial position "x" (cm) in the magnetic field "b" (kG)
1234 //---------------------------------------------------------------------
c9ec41e8 1235 Double_t dx=x-fX;
e421f556 1236 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1237
1530f89c 1238 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1239
e421f556 1240 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1241 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1242
1243 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1244 r[0] = x;
1245 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 1246 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 1247 return Local2GlobalPosition(r,fAlpha);
51ad6848 1248}
1249
edc97986 1250//_____________________________________________________________________________
51ad6848 1251void AliExternalTrackParam::Print(Option_t* /*option*/) const
1252{
1253// print the parameters and the covariance matrix
1254
1255 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1256 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1257 fP[0], fP[1], fP[2], fP[3], fP[4]);
1258 printf(" covariance: %12g\n", fC[0]);
1259 printf(" %12g %12g\n", fC[1], fC[2]);
1260 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1261 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1262 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1263 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1264 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1265}
5b77d93c 1266
c194ba83 1267Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1268 //
1269 // Get sinus at given x
1270 //
1530f89c 1271 Double_t crv=GetC(b);
c194ba83 1272 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1273 Double_t dx = x-fX;
1274 Double_t res = fP[2]+dx*crv;
1275 return res;
1276}
bf00ebb8 1277
1278Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1279 //------------------------------------------------------------------------
1280 // Get the distance between two tracks at the local position x
1281 // working in the local frame of this track.
1282 // Origin : Marian.Ivanov@cern.ch
1283 //-----------------------------------------------------------------------
1284 Double_t xyz[3];
1285 Double_t xyz2[3];
1286 xyz[0]=x;
1287 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1288 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1289 //
1290 //
1291 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1292 xyz2[0]=x;
1293 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1294 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1295 }else{
1296 //
1297 Double_t xyz1[3];
1298 Double_t dfi = param2->GetAlpha()-GetAlpha();
1299 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1300 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1301 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1302 //
1303 xyz1[0]=xyz2[0];
1304 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1305 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1306 //
1307 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1308 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1309 xyz2[2] = xyz1[2];
1310 }
1311 dist[0] = xyz[0]-xyz2[0];
1312 dist[1] = xyz[1]-xyz2[1];
1313 dist[2] = xyz[2]-xyz2[2];
1314
1315 return kTRUE;
1316}
0c19adf7 1317
1318
1319//
1320// Draw functionality.
1321// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1322//
1323
1324void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1325 //
1326 // Draw track line
1327 //
1328 if (minR>maxR) return ;
1329 if (stepR<=0) return ;
1330 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1331 if (npoints<1) return;
1332 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1333 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1334 polymarker->Draw();
1335}
1336
1337//
1338void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1339 //
1340 // Fill points in the polymarker
1341 //
1342 Int_t counter=0;
1343 for (Double_t r=minR; r<maxR; r+=stepR){
1344 Double_t point[3];
1345 GetXYZAt(r,magF,point);
1346 pol->SetPoint(counter,point[0],point[1], point[2]);
1347 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1348 counter++;
1349 }
1350}