bugfix: translation from readout partition no to ddl no
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
CommitLineData
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"
f76701bf 29#include "AliESDVertex.h"
6c94f330 30#include "AliLog.h"
51ad6848 31
32ClassImp(AliExternalTrackParam)
33
ed5f2849 34Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
35
51ad6848 36//_____________________________________________________________________________
90e48c0c 37AliExternalTrackParam::AliExternalTrackParam() :
6c94f330 38 TObject(),
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//_____________________________________________________________________________
6c94f330 50AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
51 TObject(track),
52 fX(track.fX),
53 fAlpha(track.fAlpha)
54{
55 //
56 // copy constructor
57 //
58 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
59 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
60}
61
62//_____________________________________________________________________________
51ad6848 63AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
64 const Double_t param[5],
90e48c0c 65 const Double_t covar[15]) :
6c94f330 66 TObject(),
90e48c0c 67 fX(x),
c9ec41e8 68 fAlpha(alpha)
51ad6848 69{
90e48c0c 70 //
71 // create external track parameters from given arguments
72 //
c9ec41e8 73 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
74 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 75}
76
90e48c0c 77//_____________________________________________________________________________
6c94f330 78void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
79 const Double_t p[5], const Double_t cov[15]) {
c9ec41e8 80 //
6c94f330 81 // Sets the parameters
c9ec41e8 82 //
6c94f330 83 fX=x;
84 fAlpha=alpha;
85 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
86 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
51ad6848 87}
88
89//_____________________________________________________________________________
c9ec41e8 90void AliExternalTrackParam::Reset() {
1530f89c 91 //
92 // Resets all the parameters to 0
93 //
c9ec41e8 94 fX=fAlpha=0.;
95 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
96 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 97}
98
c9ec41e8 99Double_t AliExternalTrackParam::GetP() const {
100 //---------------------------------------------------------------------
101 // This function returns the track momentum
102 // Results for (nearly) straight tracks are meaningless !
103 //---------------------------------------------------------------------
06fb4a2f 104 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 105 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 106}
107
1d99986f 108Double_t AliExternalTrackParam::Get1P() const {
109 //---------------------------------------------------------------------
110 // This function returns the 1/(track momentum)
111 //---------------------------------------------------------------------
112 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
113}
114
c9ec41e8 115//_______________________________________________________________________
c7bafca9 116Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 117 //------------------------------------------------------------------
118 // This function calculates the transverse impact parameter
119 // with respect to a point with global coordinates (x,y)
120 // in the magnetic field "b" (kG)
121 //------------------------------------------------------------------
5773defd 122 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 123 Double_t rp4=GetC(b);
c9ec41e8 124
125 Double_t xt=fX, yt=fP[0];
126
127 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
128 Double_t a = x*cs + y*sn;
129 y = -x*sn + y*cs; x=a;
130 xt-=x; yt-=y;
131
132 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
133 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 134 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
135}
136
137//_______________________________________________________________________
138void AliExternalTrackParam::
139GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
140 //------------------------------------------------------------------
141 // This function calculates the transverse and longitudinal impact parameters
142 // with respect to a point with global coordinates (x,y)
143 // in the magnetic field "b" (kG)
144 //------------------------------------------------------------------
145 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
146 Double_t xt=fX, yt=fP[0];
147 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
148 Double_t a = x*cs + y*sn;
149 y = -x*sn + y*cs; x=a;
150 xt-=x; yt-=y;
151
152 Double_t rp4=GetC(b);
153 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
154 dz[0] = -(xt*f1 - yt*r1);
155 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
156 return;
157 }
158
159 sn=rp4*xt - f1; cs=rp4*yt + r1;
160 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
161 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
162 dz[0] = -a/(1 + rr);
163 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
164 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 165}
166
49d13e89 167//_______________________________________________________________________
168Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
169 //------------------------------------------------------------------
170 // This function calculates the transverse impact parameter
171 // with respect to a point with global coordinates (xv,yv)
172 // neglecting the track curvature.
173 //------------------------------------------------------------------
174 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
175 Double_t x= xv*cs + yv*sn;
176 Double_t y=-xv*sn + yv*cs;
177
178 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
179
1530f89c 180 return -d;
49d13e89 181}
182
ee5dba5e 183Bool_t AliExternalTrackParam::CorrectForMaterial
184(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 185 //------------------------------------------------------------------
186 // This function corrects the track parameters for the crossed material
187 // "d" - the thickness (fraction of the radiation length)
188 // "x0" - the radiation length (g/cm^2)
189 // "mass" - the mass of this particle (GeV/c^2)
190 //------------------------------------------------------------------
191 Double_t &fP2=fP[2];
192 Double_t &fP3=fP[3];
193 Double_t &fP4=fP[4];
194
195 Double_t &fC22=fC[5];
196 Double_t &fC33=fC[9];
197 Double_t &fC43=fC[13];
198 Double_t &fC44=fC[14];
199
7b5ef2e6 200 Double_t p=GetP();
201 Double_t p2=p*p;
c7bafca9 202 Double_t beta2=p2/(p2 + mass*mass);
203 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
204
205 //Multiple scattering******************
206 if (d!=0) {
207 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
208 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
209 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
210 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
211 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
212 fC44 += theta2*fP3*fP4*fP3*fP4;
213 }
214
215 //Energy losses************************
8fc1985d 216 if (x0!=0. && beta2<1) {
c7bafca9 217 d*=x0;
ee5dba5e 218 Double_t dE=Bethe(beta2)*d;
219 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 220 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 221 fP4*=(1.- e/p2*dE);
222
223 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 224 const Double_t knst=0.07; // To be tuned.
225 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 226 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
227
c7bafca9 228 }
229
230 return kTRUE;
231}
232
ee5dba5e 233Double_t ApproximateBetheBloch(Double_t beta2) {
234 //------------------------------------------------------------------
235 // This is an approximation of the Bethe-Bloch formula with
236 // the density effect taken into account at beta*gamma > 3.5
237 // (the approximation is reasonable only for solid materials)
238 //------------------------------------------------------------------
239 if (beta2/(1-beta2)>3.5*3.5)
240 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
241
242 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
243}
244
49d13e89 245Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
246 //------------------------------------------------------------------
247 // Transform this track to the local coord. system rotated
248 // by angle "alpha" (rad) with respect to the global coord. system.
249 //------------------------------------------------------------------
dfcef74c 250 if (TMath::Abs(fP[2]) >= kAlmost1) {
251 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
252 return kFALSE;
253 }
254
49d13e89 255 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
256 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
257
258 Double_t &fP0=fP[0];
259 Double_t &fP2=fP[2];
260 Double_t &fC00=fC[0];
261 Double_t &fC10=fC[1];
262 Double_t &fC20=fC[3];
263 Double_t &fC21=fC[4];
264 Double_t &fC22=fC[5];
265 Double_t &fC30=fC[6];
266 Double_t &fC32=fC[8];
267 Double_t &fC40=fC[10];
268 Double_t &fC42=fC[12];
269
270 Double_t x=fX;
271 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
272 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
273
dfcef74c 274 Double_t tmp=sf*ca - cf*sa;
275 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
276
49d13e89 277 fAlpha = alpha;
278 fX = x*ca + fP0*sa;
279 fP0= -x*sa + fP0*ca;
dfcef74c 280 fP2= tmp;
49d13e89 281
06fb4a2f 282 if (TMath::Abs(cf)<kAlmost0) {
283 AliError(Form("Too small cosine value %f",cf));
284 cf = kAlmost0;
285 }
286
49d13e89 287 Double_t rr=(ca+sf/cf*sa);
288
289 fC00 *= (ca*ca);
290 fC10 *= ca;
291 fC20 *= ca*rr;
292 fC21 *= rr;
293 fC22 *= rr*rr;
294 fC30 *= ca;
295 fC32 *= rr;
296 fC40 *= ca;
297 fC42 *= rr;
298
299 return kTRUE;
300}
301
302Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
303 //----------------------------------------------------------------
304 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
305 //----------------------------------------------------------------
49d13e89 306 Double_t dx=xk-fX;
e421f556 307 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 308
1530f89c 309 Double_t crv=GetC(b);
5773defd 310 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
311
49d13e89 312 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 313 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 314 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
315
316 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
317 Double_t
318 &fC00=fC[0],
319 &fC10=fC[1], &fC11=fC[2],
320 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
321 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
322 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
323
324 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
325
326 fX=xk;
327 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 328 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 329 fP2 += dx*crv;
330
331 //f = F - 1
332
333 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
334 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
335 Double_t f12= dx*fP3*f1/(r1*r1*r1);
336 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
337 Double_t f13= dx/r1;
338 Double_t f24= dx; f24*=cc;
339
340 //b = C*ft
341 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
342 Double_t b02=f24*fC40;
343 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
344 Double_t b12=f24*fC41;
345 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
346 Double_t b22=f24*fC42;
347 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
348 Double_t b42=f24*fC44;
349 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
350 Double_t b32=f24*fC43;
351
352 //a = f*b = f*C*ft
353 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
354 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
355 Double_t a22=f24*b42;
356
357 //F*C*Ft = C + (b + bt + a)
358 fC00 += b00 + b00 + a00;
359 fC10 += b10 + b01 + a01;
360 fC20 += b20 + b02 + a02;
361 fC30 += b30;
362 fC40 += b40;
363 fC11 += b11 + b11 + a11;
364 fC21 += b21 + b12 + a12;
365 fC31 += b31;
366 fC41 += b41;
367 fC22 += b22 + b22 + a22;
368 fC32 += b32;
369 fC42 += b42;
370
371 return kTRUE;
372}
373
052daaff 374void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
375Double_t p[3], Double_t bz) const {
376 //+++++++++++++++++++++++++++++++++++++++++
377 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
378 // Extrapolate track along simple helix in magnetic field
379 // Arguments: len -distance alogn helix, [cm]
380 // bz - mag field, [kGaus]
381 // Returns: x and p contain extrapolated positon and momentum
382 // The momentum returned for straight-line tracks is meaningless !
383 //+++++++++++++++++++++++++++++++++++++++++
384 GetXYZ(x);
385
59c0deea 386 if (TMath::Abs(Get1Pt()) < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
052daaff 387 Double_t unit[3]; GetDirection(unit);
388 x[0]+=unit[0]*len;
389 x[1]+=unit[1]*len;
390 x[2]+=unit[2]*len;
391
392 p[0]=unit[0]/kAlmost0;
393 p[1]=unit[1]/kAlmost0;
394 p[2]=unit[2]/kAlmost0;
395 } else {
396 GetPxPyPz(p);
397 Double_t pp=GetP();
398 Double_t a = -kB2C*bz*GetSign();
399 Double_t rho = a/pp;
400 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
401 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
402 x[2] += p[2]*len/pp;
403
404 Double_t p0=p[0];
405 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
406 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
407 }
408}
409
410Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
411Double_t bz) const {
412 //+++++++++++++++++++++++++++++++++++++++++
413 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
414 // Finds point of intersection (if exists) of the helix with the plane.
415 // Stores result in fX and fP.
416 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
417 // and vector, normal to the plane
418 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
419 //+++++++++++++++++++++++++++++++++++++++++
420 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
421
422 //estimates initial helix length up to plane
423 Double_t s=
424 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
425 Double_t dist=99999,distPrev=dist;
426 Double_t x[3],p[3];
427 while(TMath::Abs(dist)>0.00001){
428 //calculates helix at the distance s from x0 ALONG the helix
429 Propagate(s,x,p,bz);
430
431 //distance between current helix position and plane
432 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
433
434 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
435 distPrev=dist;
436 s-=dist;
437 }
438 //on exit pnt is intersection point,norm is track vector at that point,
439 //all in MARS
440 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
441 return kTRUE;
442}
443
49d13e89 444Double_t
445AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
446 //----------------------------------------------------------------
447 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
448 //----------------------------------------------------------------
449 Double_t sdd = fC[0] + cov[0];
450 Double_t sdz = fC[1] + cov[1];
451 Double_t szz = fC[2] + cov[2];
452 Double_t det = sdd*szz - sdz*sdz;
453
454 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
455
456 Double_t d = fP[0] - p[0];
457 Double_t z = fP[1] - p[1];
458
459 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
460}
461
462Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
463 //------------------------------------------------------------------
464 // Update the track parameters with the space point "p" having
465 // the covariance matrix "cov"
466 //------------------------------------------------------------------
467 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
468 Double_t
469 &fC00=fC[0],
470 &fC10=fC[1], &fC11=fC[2],
471 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
472 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
473 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
474
475 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
476 r00+=fC00; r01+=fC10; r11+=fC11;
477 Double_t det=r00*r11 - r01*r01;
478
479 if (TMath::Abs(det) < kAlmost0) return kFALSE;
480
481
482 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
483
484 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
485 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
486 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
487 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
488 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
489
490 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
491 Double_t sf=fP2 + k20*dy + k21*dz;
492 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
493
494 fP0 += k00*dy + k01*dz;
495 fP1 += k10*dy + k11*dz;
496 fP2 = sf;
497 fP3 += k30*dy + k31*dz;
498 fP4 += k40*dy + k41*dz;
499
500 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
501 Double_t c12=fC21, c13=fC31, c14=fC41;
502
503 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
504 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
505 fC40-=k00*c04+k01*c14;
506
507 fC11-=k10*c01+k11*fC11;
508 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
509 fC41-=k10*c04+k11*c14;
510
511 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
512 fC42-=k20*c04+k21*c14;
513
514 fC33-=k30*c03+k31*c13;
515 fC43-=k30*c04+k31*c14;
516
517 fC44-=k40*c04+k41*c14;
518
519 return kTRUE;
520}
521
c7bafca9 522void
523AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
524 //--------------------------------------------------------------------
525 // External track parameters -> helix parameters
526 // "b" - magnetic field (kG)
527 //--------------------------------------------------------------------
528 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
529
1530f89c 530 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 531
532 hlx[5]=fX*cs - hlx[0]*sn; // x0
533 hlx[0]=fX*sn + hlx[0]*cs; // y0
534//hlx[1]= // z0
535 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
536//hlx[3]= // tgl
1530f89c 537 hlx[4]=GetC(b); // C
c7bafca9 538}
539
540
541static void Evaluate(const Double_t *h, Double_t t,
542 Double_t r[3], //radius vector
543 Double_t g[3], //first defivatives
544 Double_t gg[3]) //second derivatives
545{
546 //--------------------------------------------------------------------
547 // Calculate position of a point on a track and some derivatives
548 //--------------------------------------------------------------------
549 Double_t phase=h[4]*t+h[2];
550 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
551
552 r[0] = h[5] + (sn - h[6])/h[4];
553 r[1] = h[0] - (cs - h[7])/h[4];
554 r[2] = h[1] + h[3]*t;
555
556 g[0] = cs; g[1]=sn; g[2]=h[3];
557
558 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
559}
560
561Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
562Double_t b, Double_t &xthis, Double_t &xp) const {
563 //------------------------------------------------------------
564 // Returns the (weighed !) distance of closest approach between
565 // this track and the track "p".
566 // Other returned values:
567 // xthis, xt - coordinates of tracks' reference planes at the DCA
568 //-----------------------------------------------------------
569 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
570 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
571 Double_t dx2=dy2;
572
573 //dx2=dy2=dz2=1.;
574
575 Double_t p1[8]; GetHelixParameters(p1,b);
576 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
577 Double_t p2[8]; p->GetHelixParameters(p2,b);
578 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
579
580
581 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
582 Evaluate(p1,t1,r1,g1,gg1);
583 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
584 Evaluate(p2,t2,r2,g2,gg2);
585
586 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
587 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
588
589 Int_t max=27;
590 while (max--) {
591 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
592 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
593 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
594 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
595 (g1[2]*g1[2] - dz*gg1[2])/dz2;
596 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
597 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
598 (g2[2]*g2[2] + dz*gg2[2])/dz2;
599 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
600
601 Double_t det=h11*h22-h12*h12;
602
603 Double_t dt1,dt2;
604 if (TMath::Abs(det)<1.e-33) {
605 //(quasi)singular Hessian
606 dt1=-gt1; dt2=-gt2;
607 } else {
608 dt1=-(gt1*h22 - gt2*h12)/det;
609 dt2=-(h11*gt2 - h12*gt1)/det;
610 }
611
612 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
613
614 //check delta(phase1) ?
615 //check delta(phase2) ?
616
617 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
618 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
619 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
620 AliWarning(" stopped at not a stationary point !");
621 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
622 if (lmb < 0.)
623 AliWarning(" stopped at not a minimum !");
624 break;
625 }
626
627 Double_t dd=dm;
628 for (Int_t div=1 ; ; div*=2) {
629 Evaluate(p1,t1+dt1,r1,g1,gg1);
630 Evaluate(p2,t2+dt2,r2,g2,gg2);
631 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
632 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
633 if (dd<dm) break;
634 dt1*=0.5; dt2*=0.5;
635 if (div>512) {
636 AliWarning(" overshoot !"); break;
637 }
638 }
639 dm=dd;
640
641 t1+=dt1;
642 t2+=dt2;
643
644 }
645
646 if (max<=0) AliWarning(" too many iterations !");
647
648 Double_t cs=TMath::Cos(GetAlpha());
649 Double_t sn=TMath::Sin(GetAlpha());
650 xthis=r1[0]*cs + r1[1]*sn;
651
652 cs=TMath::Cos(p->GetAlpha());
653 sn=TMath::Sin(p->GetAlpha());
654 xp=r2[0]*cs + r2[1]*sn;
655
656 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
657}
658
659Double_t AliExternalTrackParam::
660PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
661 //--------------------------------------------------------------
662 // Propagates this track and the argument track to the position of the
663 // distance of closest approach.
664 // Returns the (weighed !) distance of closest approach.
665 //--------------------------------------------------------------
666 Double_t xthis,xp;
667 Double_t dca=GetDCA(p,b,xthis,xp);
668
669 if (!PropagateTo(xthis,b)) {
670 //AliWarning(" propagation failed !");
671 return 1e+33;
672 }
673
674 if (!p->PropagateTo(xp,b)) {
675 //AliWarning(" propagation failed !";
676 return 1e+33;
677 }
678
679 return dca;
680}
681
682
683
f76701bf 684
685Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
686 //
687 // Try to relate this track to the vertex "vtx",
688 // if the (rough) transverse impact parameter is not bigger then "maxd".
689 // Magnetic field is "b" (kG).
690 //
691 // a) The track gets extapolated to the DCA to the vertex.
692 // b) The impact parameters and their covariance matrix are calculated.
693 //
694 // In the case of success, the returned value is kTRUE
695 // (otherwise, it's kFALSE)
696 //
697 Double_t alpha=GetAlpha();
698 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
699 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
700 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 701 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 702 x-=xv; y-=yv;
703
704 //Estimate the impact parameter neglecting the track curvature
705 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
706 if (d > maxd) return kFALSE;
707
708 //Propagate to the DCA
709 Double_t crv=0.299792458e-3*b*GetParameter()[4];
710 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
711 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
712
713 x = xv*cs + yv*sn;
714 yv=-xv*sn + yv*cs; xv=x;
715
716 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 717 return kTRUE;
f76701bf 718}
719
720
721
722
c9ec41e8 723Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
724 //----------------------------------------------------------------
725 // This function performs local->global transformation of the
726 // track momentum.
727 // When called, the arguments are:
728 // p[0] = 1/pt of the track;
729 // p[1] = sine of local azim. angle of the track momentum;
730 // p[2] = tangent of the track momentum dip angle;
731 // alpha - rotation angle.
732 // The result is returned as:
733 // p[0] = px
734 // p[1] = py
735 // p[2] = pz
736 // Results for (nearly) straight tracks are meaningless !
737 //----------------------------------------------------------------
e421f556 738 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 739 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 740
741 Double_t pt=1./TMath::Abs(p[0]);
742 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
743 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
744 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 745
746 return kTRUE;
747}
748
c9ec41e8 749Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
750 //----------------------------------------------------------------
751 // This function performs local->global transformation of the
752 // track position.
753 // When called, the arguments are:
754 // r[0] = local x
755 // r[1] = local y
756 // r[2] = local z
757 // alpha - rotation angle.
758 // The result is returned as:
759 // r[0] = global x
760 // r[1] = global y
761 // r[2] = global z
762 //----------------------------------------------------------------
763 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
764 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 765
a5e407e9 766 return kTRUE;
51ad6848 767}
768
b1149664 769void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
770 //----------------------------------------------------------------
771 // This function returns a unit vector along the track direction
772 // in the global coordinate system.
773 //----------------------------------------------------------------
774 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
775 Double_t snp=fP[2];
92934324 776 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 777 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
778 d[0]=(csp*cs - snp*sn)/norm;
779 d[1]=(snp*cs + csp*sn)/norm;
780 d[2]=fP[3]/norm;
781}
782
c9ec41e8 783Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
784 //---------------------------------------------------------------------
785 // This function returns the global track momentum components
786 // Results for (nearly) straight tracks are meaningless !
787 //---------------------------------------------------------------------
788 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
789 return Local2GlobalMomentum(p,fAlpha);
790}
a5e407e9 791
c9ec41e8 792Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
793 //---------------------------------------------------------------------
794 // This function returns the global track position
795 //---------------------------------------------------------------------
796 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
797 return Local2GlobalPosition(r,fAlpha);
51ad6848 798}
799
c9ec41e8 800Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
801 //---------------------------------------------------------------------
802 // This function returns the global covariance matrix of the track params
803 //
804 // Cov(x,x) ... : cv[0]
805 // Cov(y,x) ... : cv[1] cv[2]
806 // Cov(z,x) ... : cv[3] cv[4] cv[5]
807 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
808 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
809 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 810 //
c9ec41e8 811 // Results for (nearly) straight tracks are meaningless !
812 //---------------------------------------------------------------------
e421f556 813 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 814 for (Int_t i=0; i<21; i++) cv[i]=0.;
815 return kFALSE;
a5e407e9 816 }
49d13e89 817 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 818 for (Int_t i=0; i<21; i++) cv[i]=0.;
819 return kFALSE;
820 }
821 Double_t pt=1./TMath::Abs(fP[4]);
822 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 823 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 824
825 Double_t m00=-sn, m10=cs;
826 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
827 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
828 Double_t m35=pt, m45=-pt*pt*fP[3];
829
830 cv[0 ] = fC[0]*m00*m00;
831 cv[1 ] = fC[0]*m00*m10;
832 cv[2 ] = fC[0]*m10*m10;
833 cv[3 ] = fC[1]*m00;
834 cv[4 ] = fC[1]*m10;
835 cv[5 ] = fC[2];
836 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
837 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
838 cv[8 ] = fC[4]*m23 + fC[11]*m43;
839 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
840 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
841 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
842 cv[12] = fC[4]*m24 + fC[11]*m44;
843 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
844 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
845 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
846 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
847 cv[17] = fC[7]*m35 + fC[11]*m45;
848 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
849 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
850 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 851
c9ec41e8 852 return kTRUE;
51ad6848 853}
854
51ad6848 855
c9ec41e8 856Bool_t
857AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
858 //---------------------------------------------------------------------
859 // This function returns the global track momentum extrapolated to
860 // the radial position "x" (cm) in the magnetic field "b" (kG)
861 //---------------------------------------------------------------------
c9ec41e8 862 p[0]=fP[4];
1530f89c 863 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 864 p[2]=fP[3];
865 return Local2GlobalMomentum(p,fAlpha);
51ad6848 866}
867
c9ec41e8 868Bool_t
7cf7bb6c 869AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
870 //---------------------------------------------------------------------
871 // This function returns the local Y-coordinate of the intersection
872 // point between this track and the reference plane "x" (cm).
873 // Magnetic field "b" (kG)
874 //---------------------------------------------------------------------
875 Double_t dx=x-fX;
876 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
877
1530f89c 878 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 879
880 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
881 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
882
883 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
884 y = fP[0] + dx*(f1+f2)/(r1+r2);
885 return kTRUE;
886}
887
888Bool_t
6c94f330 889AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
890 //---------------------------------------------------------------------
891 // This function returns the local Z-coordinate of the intersection
892 // point between this track and the reference plane "x" (cm).
893 // Magnetic field "b" (kG)
894 //---------------------------------------------------------------------
895 Double_t dx=x-fX;
896 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
897
898 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
899
900 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
901 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
902
903 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
904 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
905 return kTRUE;
906}
907
908Bool_t
c9ec41e8 909AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
910 //---------------------------------------------------------------------
911 // This function returns the global track position extrapolated to
912 // the radial position "x" (cm) in the magnetic field "b" (kG)
913 //---------------------------------------------------------------------
c9ec41e8 914 Double_t dx=x-fX;
e421f556 915 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
916
1530f89c 917 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 918
e421f556 919 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 920 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 921
922 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
923 r[0] = x;
924 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 925 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 926 return Local2GlobalPosition(r,fAlpha);
51ad6848 927}
928
edc97986 929//_____________________________________________________________________________
51ad6848 930void AliExternalTrackParam::Print(Option_t* /*option*/) const
931{
932// print the parameters and the covariance matrix
933
934 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
935 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 936 fP[0], fP[1], fP[2], fP[3], fP[4]);
937 printf(" covariance: %12g\n", fC[0]);
938 printf(" %12g %12g\n", fC[1], fC[2]);
939 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 940 printf(" %12g %12g %12g %12g\n",
c9ec41e8 941 fC[6], fC[7], fC[8], fC[9]);
51ad6848 942 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 943 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 944}
5b77d93c 945
c194ba83 946Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
947 //
948 // Get sinus at given x
949 //
1530f89c 950 Double_t crv=GetC(b);
c194ba83 951 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
952 Double_t dx = x-fX;
953 Double_t res = fP[2]+dx*crv;
954 return res;
955}