Possibility to read Kalman tracks from a Root file without setting the magnetic field
[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///////////////////////////////////////////////////////////////////////////////
51ad6848 28#include "AliExternalTrackParam.h"
29#include "AliKalmanTrack.h"
5b77d93c 30#include "AliTracker.h"
edc97986 31#include "AliStrLine.h"
f76701bf 32#include "AliESDVertex.h"
5b77d93c 33
51ad6848 34
35ClassImp(AliExternalTrackParam)
36
51ad6848 37//_____________________________________________________________________________
90e48c0c 38AliExternalTrackParam::AliExternalTrackParam() :
90e48c0c 39 fX(0),
c9ec41e8 40 fAlpha(0)
51ad6848 41{
90e48c0c 42 //
43 // default constructor
44 //
c9ec41e8 45 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
46 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 47}
48
49//_____________________________________________________________________________
50AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
51 const Double_t param[5],
90e48c0c 52 const Double_t covar[15]) :
90e48c0c 53 fX(x),
c9ec41e8 54 fAlpha(alpha)
51ad6848 55{
90e48c0c 56 //
57 // create external track parameters from given arguments
58 //
c9ec41e8 59 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
60 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 61}
62
90e48c0c 63//_____________________________________________________________________________
64AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) :
c9ec41e8 65 fAlpha(track.GetAlpha())
51ad6848 66{
67 //
68 //
c9ec41e8 69 track.GetExternalParameters(fX,fP);
70 track.GetExternalCovariance(fC);
51ad6848 71}
72
51ad6848 73//_____________________________________________________________________________
c9ec41e8 74void AliExternalTrackParam::Set(const AliKalmanTrack& track) {
75 //
76 //
77 fAlpha=track.GetAlpha();
78 track.GetExternalParameters(fX,fP);
79 track.GetExternalCovariance(fC);
51ad6848 80}
81
82//_____________________________________________________________________________
c9ec41e8 83void AliExternalTrackParam::Reset() {
84 fX=fAlpha=0.;
85 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
86 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 87}
88
c9ec41e8 89Double_t AliExternalTrackParam::GetP() const {
90 //---------------------------------------------------------------------
91 // This function returns the track momentum
92 // Results for (nearly) straight tracks are meaningless !
93 //---------------------------------------------------------------------
5773defd 94 if (TMath::Abs(fP[4])<=0) return kVeryBig;
c9ec41e8 95 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 96}
97
1d99986f 98Double_t AliExternalTrackParam::Get1P() const {
99 //---------------------------------------------------------------------
100 // This function returns the 1/(track momentum)
101 //---------------------------------------------------------------------
102 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
103}
104
c9ec41e8 105//_______________________________________________________________________
c7bafca9 106Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 107 //------------------------------------------------------------------
108 // This function calculates the transverse impact parameter
109 // with respect to a point with global coordinates (x,y)
110 // in the magnetic field "b" (kG)
111 //------------------------------------------------------------------
5773defd 112 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
49d13e89 113 Double_t rp4=kB2C*b*fP[4];
c9ec41e8 114
115 Double_t xt=fX, yt=fP[0];
116
117 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
118 Double_t a = x*cs + y*sn;
119 y = -x*sn + y*cs; x=a;
120 xt-=x; yt-=y;
121
122 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
123 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
124 if (rp4<0) a=-a;
125 return a/(1 + TMath::Sqrt(sn*sn + cs*cs));
51ad6848 126}
127
49d13e89 128//_______________________________________________________________________
129Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
130 //------------------------------------------------------------------
131 // This function calculates the transverse impact parameter
132 // with respect to a point with global coordinates (xv,yv)
133 // neglecting the track curvature.
134 //------------------------------------------------------------------
135 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
136 Double_t x= xv*cs + yv*sn;
137 Double_t y=-xv*sn + yv*cs;
138
139 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
140
141 return d;
142}
143
c7bafca9 144Bool_t AliExternalTrackParam::
145CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) {
146 //------------------------------------------------------------------
147 // This function corrects the track parameters for the crossed material
148 // "d" - the thickness (fraction of the radiation length)
149 // "x0" - the radiation length (g/cm^2)
150 // "mass" - the mass of this particle (GeV/c^2)
151 //------------------------------------------------------------------
152 Double_t &fP2=fP[2];
153 Double_t &fP3=fP[3];
154 Double_t &fP4=fP[4];
155
156 Double_t &fC22=fC[5];
157 Double_t &fC33=fC[9];
158 Double_t &fC43=fC[13];
159 Double_t &fC44=fC[14];
160
161 Double_t p2=(1.+ fP3*fP3)/(fP4*fP4);
162 Double_t beta2=p2/(p2 + mass*mass);
163 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
164
165 //Multiple scattering******************
166 if (d!=0) {
167 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
168 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
169 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
170 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
171 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
172 fC44 += theta2*fP3*fP4*fP3*fP4;
173 }
174
175 //Energy losses************************
176 if (x0!=0.) {
177 d*=x0;
178 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
179 if (beta2/(1-beta2)>3.5*3.5)
180 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
181
182 fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE);
183 }
184
185 return kTRUE;
186}
187
49d13e89 188Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
189 //------------------------------------------------------------------
190 // Transform this track to the local coord. system rotated
191 // by angle "alpha" (rad) with respect to the global coord. system.
192 //------------------------------------------------------------------
193 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
194 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
195
196 Double_t &fP0=fP[0];
197 Double_t &fP2=fP[2];
198 Double_t &fC00=fC[0];
199 Double_t &fC10=fC[1];
200 Double_t &fC20=fC[3];
201 Double_t &fC21=fC[4];
202 Double_t &fC22=fC[5];
203 Double_t &fC30=fC[6];
204 Double_t &fC32=fC[8];
205 Double_t &fC40=fC[10];
206 Double_t &fC42=fC[12];
207
208 Double_t x=fX;
209 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
210 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
211
212 fAlpha = alpha;
213 fX = x*ca + fP0*sa;
214 fP0= -x*sa + fP0*ca;
215 fP2= sf*ca - cf*sa;
216
217 Double_t rr=(ca+sf/cf*sa);
218
219 fC00 *= (ca*ca);
220 fC10 *= ca;
221 fC20 *= ca*rr;
222 fC21 *= rr;
223 fC22 *= rr*rr;
224 fC30 *= ca;
225 fC32 *= rr;
226 fC40 *= ca;
227 fC42 *= rr;
228
229 return kTRUE;
230}
231
232Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
233 //----------------------------------------------------------------
234 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
235 //----------------------------------------------------------------
49d13e89 236 Double_t dx=xk-fX;
606833e7 237 if (TMath::Abs(dx)<=0) return kTRUE;
18ebc5ef 238
239 Double_t crv=kB2C*b*fP[4];
5773defd 240 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
241
49d13e89 242 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 243 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 244 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
245
246 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
247 Double_t
248 &fC00=fC[0],
249 &fC10=fC[1], &fC11=fC[2],
250 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
251 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
252 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
253
254 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
255
256 fX=xk;
257 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 258 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 259 fP2 += dx*crv;
260
261 //f = F - 1
262
263 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
264 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
265 Double_t f12= dx*fP3*f1/(r1*r1*r1);
266 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
267 Double_t f13= dx/r1;
268 Double_t f24= dx; f24*=cc;
269
270 //b = C*ft
271 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
272 Double_t b02=f24*fC40;
273 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
274 Double_t b12=f24*fC41;
275 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
276 Double_t b22=f24*fC42;
277 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
278 Double_t b42=f24*fC44;
279 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
280 Double_t b32=f24*fC43;
281
282 //a = f*b = f*C*ft
283 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
284 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
285 Double_t a22=f24*b42;
286
287 //F*C*Ft = C + (b + bt + a)
288 fC00 += b00 + b00 + a00;
289 fC10 += b10 + b01 + a01;
290 fC20 += b20 + b02 + a02;
291 fC30 += b30;
292 fC40 += b40;
293 fC11 += b11 + b11 + a11;
294 fC21 += b21 + b12 + a12;
295 fC31 += b31;
296 fC41 += b41;
297 fC22 += b22 + b22 + a22;
298 fC32 += b32;
299 fC42 += b42;
300
301 return kTRUE;
302}
303
304Double_t
305AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
306 //----------------------------------------------------------------
307 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
308 //----------------------------------------------------------------
309 Double_t sdd = fC[0] + cov[0];
310 Double_t sdz = fC[1] + cov[1];
311 Double_t szz = fC[2] + cov[2];
312 Double_t det = sdd*szz - sdz*sdz;
313
314 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
315
316 Double_t d = fP[0] - p[0];
317 Double_t z = fP[1] - p[1];
318
319 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
320}
321
322Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
323 //------------------------------------------------------------------
324 // Update the track parameters with the space point "p" having
325 // the covariance matrix "cov"
326 //------------------------------------------------------------------
327 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
328 Double_t
329 &fC00=fC[0],
330 &fC10=fC[1], &fC11=fC[2],
331 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
332 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
333 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
334
335 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
336 r00+=fC00; r01+=fC10; r11+=fC11;
337 Double_t det=r00*r11 - r01*r01;
338
339 if (TMath::Abs(det) < kAlmost0) return kFALSE;
340
341
342 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
343
344 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
345 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
346 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
347 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
348 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
349
350 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
351 Double_t sf=fP2 + k20*dy + k21*dz;
352 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
353
354 fP0 += k00*dy + k01*dz;
355 fP1 += k10*dy + k11*dz;
356 fP2 = sf;
357 fP3 += k30*dy + k31*dz;
358 fP4 += k40*dy + k41*dz;
359
360 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
361 Double_t c12=fC21, c13=fC31, c14=fC41;
362
363 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
364 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
365 fC40-=k00*c04+k01*c14;
366
367 fC11-=k10*c01+k11*fC11;
368 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
369 fC41-=k10*c04+k11*c14;
370
371 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
372 fC42-=k20*c04+k21*c14;
373
374 fC33-=k30*c03+k31*c13;
375 fC43-=k30*c04+k31*c14;
376
377 fC44-=k40*c04+k41*c14;
378
379 return kTRUE;
380}
381
c7bafca9 382void
383AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
384 //--------------------------------------------------------------------
385 // External track parameters -> helix parameters
386 // "b" - magnetic field (kG)
387 //--------------------------------------------------------------------
388 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
389
390 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; hlx[4]=fP[4];
391
392 hlx[5]=fX*cs - hlx[0]*sn; // x0
393 hlx[0]=fX*sn + hlx[0]*cs; // y0
394//hlx[1]= // z0
395 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
396//hlx[3]= // tgl
397 hlx[4]=hlx[4]*kB2C*b; // C
398}
399
400
401static void Evaluate(const Double_t *h, Double_t t,
402 Double_t r[3], //radius vector
403 Double_t g[3], //first defivatives
404 Double_t gg[3]) //second derivatives
405{
406 //--------------------------------------------------------------------
407 // Calculate position of a point on a track and some derivatives
408 //--------------------------------------------------------------------
409 Double_t phase=h[4]*t+h[2];
410 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
411
412 r[0] = h[5] + (sn - h[6])/h[4];
413 r[1] = h[0] - (cs - h[7])/h[4];
414 r[2] = h[1] + h[3]*t;
415
416 g[0] = cs; g[1]=sn; g[2]=h[3];
417
418 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
419}
420
421Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
422Double_t b, Double_t &xthis, Double_t &xp) const {
423 //------------------------------------------------------------
424 // Returns the (weighed !) distance of closest approach between
425 // this track and the track "p".
426 // Other returned values:
427 // xthis, xt - coordinates of tracks' reference planes at the DCA
428 //-----------------------------------------------------------
429 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
430 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
431 Double_t dx2=dy2;
432
433 //dx2=dy2=dz2=1.;
434
435 Double_t p1[8]; GetHelixParameters(p1,b);
436 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
437 Double_t p2[8]; p->GetHelixParameters(p2,b);
438 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
439
440
441 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
442 Evaluate(p1,t1,r1,g1,gg1);
443 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
444 Evaluate(p2,t2,r2,g2,gg2);
445
446 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
447 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
448
449 Int_t max=27;
450 while (max--) {
451 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
452 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
453 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
454 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
455 (g1[2]*g1[2] - dz*gg1[2])/dz2;
456 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
457 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
458 (g2[2]*g2[2] + dz*gg2[2])/dz2;
459 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
460
461 Double_t det=h11*h22-h12*h12;
462
463 Double_t dt1,dt2;
464 if (TMath::Abs(det)<1.e-33) {
465 //(quasi)singular Hessian
466 dt1=-gt1; dt2=-gt2;
467 } else {
468 dt1=-(gt1*h22 - gt2*h12)/det;
469 dt2=-(h11*gt2 - h12*gt1)/det;
470 }
471
472 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
473
474 //check delta(phase1) ?
475 //check delta(phase2) ?
476
477 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
478 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
479 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
480 AliWarning(" stopped at not a stationary point !");
481 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
482 if (lmb < 0.)
483 AliWarning(" stopped at not a minimum !");
484 break;
485 }
486
487 Double_t dd=dm;
488 for (Int_t div=1 ; ; div*=2) {
489 Evaluate(p1,t1+dt1,r1,g1,gg1);
490 Evaluate(p2,t2+dt2,r2,g2,gg2);
491 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
492 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
493 if (dd<dm) break;
494 dt1*=0.5; dt2*=0.5;
495 if (div>512) {
496 AliWarning(" overshoot !"); break;
497 }
498 }
499 dm=dd;
500
501 t1+=dt1;
502 t2+=dt2;
503
504 }
505
506 if (max<=0) AliWarning(" too many iterations !");
507
508 Double_t cs=TMath::Cos(GetAlpha());
509 Double_t sn=TMath::Sin(GetAlpha());
510 xthis=r1[0]*cs + r1[1]*sn;
511
512 cs=TMath::Cos(p->GetAlpha());
513 sn=TMath::Sin(p->GetAlpha());
514 xp=r2[0]*cs + r2[1]*sn;
515
516 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
517}
518
519Double_t AliExternalTrackParam::
520PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
521 //--------------------------------------------------------------
522 // Propagates this track and the argument track to the position of the
523 // distance of closest approach.
524 // Returns the (weighed !) distance of closest approach.
525 //--------------------------------------------------------------
526 Double_t xthis,xp;
527 Double_t dca=GetDCA(p,b,xthis,xp);
528
529 if (!PropagateTo(xthis,b)) {
530 //AliWarning(" propagation failed !");
531 return 1e+33;
532 }
533
534 if (!p->PropagateTo(xp,b)) {
535 //AliWarning(" propagation failed !";
536 return 1e+33;
537 }
538
539 return dca;
540}
541
542
543
f76701bf 544
545Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
546 //
547 // Try to relate this track to the vertex "vtx",
548 // if the (rough) transverse impact parameter is not bigger then "maxd".
549 // Magnetic field is "b" (kG).
550 //
551 // a) The track gets extapolated to the DCA to the vertex.
552 // b) The impact parameters and their covariance matrix are calculated.
553 //
554 // In the case of success, the returned value is kTRUE
555 // (otherwise, it's kFALSE)
556 //
557 Double_t alpha=GetAlpha();
558 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
559 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
560 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 561 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 562 x-=xv; y-=yv;
563
564 //Estimate the impact parameter neglecting the track curvature
565 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
566 if (d > maxd) return kFALSE;
567
568 //Propagate to the DCA
569 Double_t crv=0.299792458e-3*b*GetParameter()[4];
570 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
571 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
572
573 x = xv*cs + yv*sn;
574 yv=-xv*sn + yv*cs; xv=x;
575
576 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 577 return kTRUE;
f76701bf 578}
579
580
581
582
c9ec41e8 583Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
584 //----------------------------------------------------------------
585 // This function performs local->global transformation of the
586 // track momentum.
587 // When called, the arguments are:
588 // p[0] = 1/pt of the track;
589 // p[1] = sine of local azim. angle of the track momentum;
590 // p[2] = tangent of the track momentum dip angle;
591 // alpha - rotation angle.
592 // The result is returned as:
593 // p[0] = px
594 // p[1] = py
595 // p[2] = pz
596 // Results for (nearly) straight tracks are meaningless !
597 //----------------------------------------------------------------
598 if (TMath::Abs(p[0])<=0) return kFALSE;
49d13e89 599 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 600
601 Double_t pt=1./TMath::Abs(p[0]);
602 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
603 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
604 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 605
606 return kTRUE;
607}
608
c9ec41e8 609Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
610 //----------------------------------------------------------------
611 // This function performs local->global transformation of the
612 // track position.
613 // When called, the arguments are:
614 // r[0] = local x
615 // r[1] = local y
616 // r[2] = local z
617 // alpha - rotation angle.
618 // The result is returned as:
619 // r[0] = global x
620 // r[1] = global y
621 // r[2] = global z
622 //----------------------------------------------------------------
623 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
624 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 625
a5e407e9 626 return kTRUE;
51ad6848 627}
628
c9ec41e8 629Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
630 //---------------------------------------------------------------------
631 // This function returns the global track momentum components
632 // Results for (nearly) straight tracks are meaningless !
633 //---------------------------------------------------------------------
634 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
635 return Local2GlobalMomentum(p,fAlpha);
636}
a5e407e9 637
c9ec41e8 638Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
639 //---------------------------------------------------------------------
640 // This function returns the global track position
641 //---------------------------------------------------------------------
642 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
643 return Local2GlobalPosition(r,fAlpha);
51ad6848 644}
645
c9ec41e8 646Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
647 //---------------------------------------------------------------------
648 // This function returns the global covariance matrix of the track params
649 //
650 // Cov(x,x) ... : cv[0]
651 // Cov(y,x) ... : cv[1] cv[2]
652 // Cov(z,x) ... : cv[3] cv[4] cv[5]
653 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
654 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
655 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 656 //
c9ec41e8 657 // Results for (nearly) straight tracks are meaningless !
658 //---------------------------------------------------------------------
659 if (TMath::Abs(fP[4])<=0) {
660 for (Int_t i=0; i<21; i++) cv[i]=0.;
661 return kFALSE;
a5e407e9 662 }
49d13e89 663 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 664 for (Int_t i=0; i<21; i++) cv[i]=0.;
665 return kFALSE;
666 }
667 Double_t pt=1./TMath::Abs(fP[4]);
668 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
669 Double_t r=TMath::Sqrt(1-fP[2]*fP[2]);
670
671 Double_t m00=-sn, m10=cs;
672 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
673 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
674 Double_t m35=pt, m45=-pt*pt*fP[3];
675
676 cv[0 ] = fC[0]*m00*m00;
677 cv[1 ] = fC[0]*m00*m10;
678 cv[2 ] = fC[0]*m10*m10;
679 cv[3 ] = fC[1]*m00;
680 cv[4 ] = fC[1]*m10;
681 cv[5 ] = fC[2];
682 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
683 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
684 cv[8 ] = fC[4]*m23 + fC[11]*m43;
685 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
686 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
687 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
688 cv[12] = fC[4]*m24 + fC[11]*m44;
689 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
690 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
691 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
692 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
693 cv[17] = fC[7]*m35 + fC[11]*m45;
694 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
695 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
696 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 697
c9ec41e8 698 return kTRUE;
51ad6848 699}
700
51ad6848 701
c9ec41e8 702Bool_t
703AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
704 //---------------------------------------------------------------------
705 // This function returns the global track momentum extrapolated to
706 // the radial position "x" (cm) in the magnetic field "b" (kG)
707 //---------------------------------------------------------------------
c9ec41e8 708 p[0]=fP[4];
49d13e89 709 p[1]=fP[2]+(x-fX)*fP[4]*b*kB2C;
c9ec41e8 710 p[2]=fP[3];
711 return Local2GlobalMomentum(p,fAlpha);
51ad6848 712}
713
c9ec41e8 714Bool_t
715AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
716 //---------------------------------------------------------------------
717 // This function returns the global track position extrapolated to
718 // the radial position "x" (cm) in the magnetic field "b" (kG)
719 //---------------------------------------------------------------------
c9ec41e8 720 Double_t dx=x-fX;
49d13e89 721 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
c9ec41e8 722
49d13e89 723 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 724
725 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
726 r[0] = x;
727 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
728 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
729 return Local2GlobalPosition(r,fAlpha);
51ad6848 730}
731
732
733//_____________________________________________________________________________
edc97986 734void AliExternalTrackParam::ApproximateHelixWithLine(Double_t xk, Double_t b, AliStrLine *line)
735{
736 //------------------------------------------------------------
737 // Approximate the track (helix) with a straight line tangent to the
738 // helix in the point defined by r (F. Prino, prino@to.infn.it)
739 //------------------------------------------------------------
740 Double_t mom[3];
741 Double_t azim = TMath::ASin(fP[2])+fAlpha;
742 Double_t theta = TMath::Pi()/2. - TMath::ATan(fP[3]);
743 mom[0] = TMath::Sin(theta)*TMath::Cos(azim);
744 mom[1] = TMath::Sin(theta)*TMath::Sin(azim);
745 mom[2] = TMath::Cos(theta);
746 Double_t pos[3];
747 GetXYZAt(xk,b,pos);
748 line->SetP0(pos);
749 line->SetCd(mom);
750}
751//_____________________________________________________________________________
51ad6848 752void AliExternalTrackParam::Print(Option_t* /*option*/) const
753{
754// print the parameters and the covariance matrix
755
756 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
757 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 758 fP[0], fP[1], fP[2], fP[3], fP[4]);
759 printf(" covariance: %12g\n", fC[0]);
760 printf(" %12g %12g\n", fC[1], fC[2]);
761 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 762 printf(" %12g %12g %12g %12g\n",
c9ec41e8 763 fC[6], fC[7], fC[8], fC[9]);
51ad6848 764 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 765 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 766}
5b77d93c 767
768
769Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t mass, Double_t maxStep, Bool_t rotateTo){
770 //----------------------------------------------------------------
771 // Propagate this track to the plane X=xk (cm)
772 // correction for unhomogenity of the magnetic field and the
773 // the correction for the material is included
774 //
775 // Require acces to magnetic field and geomanager
776 //
777 // mass - mass used in propagation - used for energy loss correction
778 // maxStep - maximal step for propagation
779 //----------------------------------------------------------------
780 const Double_t kEpsilon = 0.00001;
781 Double_t xpos = GetX();
782 Double_t dir = (xpos<xToGo) ? 1.:-1.;
783 //
784 while ( (xToGo-xpos)*dir > kEpsilon){
785 Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep);
786 Double_t x = xpos+step;
787 Double_t xyz0[3],xyz1[3],param[7];
788 GetXYZ(xyz0); //starting global position
789 Float_t pos0[3] = {xyz0[0],xyz0[1],xyz0[2]};
790 Double_t magZ = AliTracker::GetBz(pos0);
791 if (!GetXYZAt(x,magZ,xyz1)) return kFALSE; // no prolongation
792 AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
793 if (!PropagateTo(x,magZ)) return kFALSE;
794 Double_t distance = param[4];
795 if (!CorrectForMaterial(distance,param[1],param[0],mass)) return kFALSE;
796 if (rotateTo){
797 GetXYZ(xyz0); // global position
798 Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]);
799 if (!Rotate(alphan)) return kFALSE;
800 }
801 xpos = GetX();
802 }
803 return kTRUE;
804}
805
806//_____________________________________________________________________________
807Bool_t AliExternalTrackParam::CorrectForMaterial(Double_t d, Double_t x0, Double_t rho, Double_t mass)
808{
809 //
810 // Take into account material effects assuming:
811 // x0 - mean rad length
812 // rho - mean density
813
814 //
815 // multiple scattering
816 //
817 if (mass<=0) {
818 AliError("Non-positive mass");
819 return kFALSE;
820 }
821 Double_t p2=(1.+ fP[3]*fP[3])/(fP[4]*fP[4]);
822 Double_t beta2=p2/(p2 + mass*mass);
823 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
824 //
825 fC[5] += theta2*(1.- fP[2]*fP[2])*(1. + fP[3]*fP[3]);
826 fC[9] += theta2*(1. + fP[3]*fP[3])*(1. + fP[3]*fP[3]);
827 fC[13] += theta2*fP[3]*fP[4]*(1. + fP[3]*fP[3]);
828 fC[14] += theta2*fP[3]*fP[4]*fP[3]*fP[4];
829 //
830 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho;
831 fP[4] *=(1.- TMath::Sqrt(p2+mass*mass)/p2*dE);
832 //
833 Double_t sigmade = 0.02*TMath::Sqrt(TMath::Abs(dE)); // energy loss fluctuation
834 Double_t sigmac2 = sigmade*sigmade*fP[4]*fP[4]*(p2+mass*mass)/(p2*p2);
835 fC[14] += sigmac2;
836 return kTRUE;
837}
838
839