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