]> git.uio.no Git - u/mrichter/AliRoot.git/blame_incremental - STEER/AliExternalTrackParam.cxx
git://git.uio.no / u / mrichter / AliRoot.git / blame_incremental
? search:
summary | shortlog | log | commit | commitdiff | tree
blob | blame (non-incremental) | history | HEAD
Removing the dependence on AliCluster3D
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
... / ...
CommitLineData
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// //
20// Implementation of the external track parameterisation class. //
21// //
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 //
27///////////////////////////////////////////////////////////////////////////////
28#include <TMatrixDSym.h>
29#include "AliExternalTrackParam.h"
30#include "AliESDVertex.h"
31#include "AliLog.h"
32
33ClassImp(AliExternalTrackParam)
34
35Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
36
37//_____________________________________________________________________________
38AliExternalTrackParam::AliExternalTrackParam() :
39 TObject(),
40 fX(0),
41 fAlpha(0)
42{
43 //
44 // default constructor
45 //
46 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
47 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
48}
49
50//_____________________________________________________________________________
51AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
52 TObject(track),
53 fX(track.fX),
54 fAlpha(track.fAlpha)
55{
56 //
57 // copy constructor
58 //
59 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
60 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
61}
62
63//_____________________________________________________________________________
64AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
65 const Double_t param[5],
66 const Double_t covar[15]) :
67 TObject(),
68 fX(x),
69 fAlpha(alpha)
70{
71 //
72 // create external track parameters from given arguments
73 //
74 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
75 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
76}
77
78//_____________________________________________________________________________
79void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
80 const Double_t p[5], const Double_t cov[15]) {
81 //
82 // Sets the parameters
83 //
84 fX=x;
85 fAlpha=alpha;
86 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
87 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
88}
89
90//_____________________________________________________________________________
91void AliExternalTrackParam::Reset() {
92 //
93 // Resets all the parameters to 0
94 //
95 fX=fAlpha=0.;
96 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
97 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
98}
99
100Double_t AliExternalTrackParam::GetP() const {
101 //---------------------------------------------------------------------
102 // This function returns the track momentum
103 // Results for (nearly) straight tracks are meaningless !
104 //---------------------------------------------------------------------
105 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
106 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
107}
108
109Double_t AliExternalTrackParam::Get1P() const {
110 //---------------------------------------------------------------------
111 // This function returns the 1/(track momentum)
112 //---------------------------------------------------------------------
113 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
114}
115
116//_______________________________________________________________________
117Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
118 //------------------------------------------------------------------
119 // This function calculates the transverse impact parameter
120 // with respect to a point with global coordinates (x,y)
121 // in the magnetic field "b" (kG)
122 //------------------------------------------------------------------
123 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
124 Double_t rp4=GetC(b);
125
126 Double_t xt=fX, yt=fP[0];
127
128 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
129 Double_t a = x*cs + y*sn;
130 y = -x*sn + y*cs; x=a;
131 xt-=x; yt-=y;
132
133 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
134 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
135 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
136}
137
138//_______________________________________________________________________
139void AliExternalTrackParam::
140GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
141 //------------------------------------------------------------------
142 // This function calculates the transverse and longitudinal impact parameters
143 // with respect to a point with global coordinates (x,y)
144 // in the magnetic field "b" (kG)
145 //------------------------------------------------------------------
146 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
147 Double_t xt=fX, yt=fP[0];
148 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
149 Double_t a = x*cs + y*sn;
150 y = -x*sn + y*cs; x=a;
151 xt-=x; yt-=y;
152
153 Double_t rp4=GetC(b);
154 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
155 dz[0] = -(xt*f1 - yt*r1);
156 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
157 return;
158 }
159
160 sn=rp4*xt - f1; cs=rp4*yt + r1;
161 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
162 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
163 dz[0] = -a/(1 + rr);
164 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
165 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
166}
167
168//_______________________________________________________________________
169Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
170 //------------------------------------------------------------------
171 // This function calculates the transverse impact parameter
172 // with respect to a point with global coordinates (xv,yv)
173 // neglecting the track curvature.
174 //------------------------------------------------------------------
175 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
176 Double_t x= xv*cs + yv*sn;
177 Double_t y=-xv*sn + yv*cs;
178
179 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
180
181 return -d;
182}
183
184Bool_t AliExternalTrackParam::CorrectForMaterial
185(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
186 //------------------------------------------------------------------
187 // This function corrects the track parameters for the crossed material
188 // "d" - the thickness (fraction of the radiation length)
189 // "x0" - the radiation length (g/cm^2)
190 // "mass" - the mass of this particle (GeV/c^2)
191 //------------------------------------------------------------------
192 Double_t &fP2=fP[2];
193 Double_t &fP3=fP[3];
194 Double_t &fP4=fP[4];
195
196 Double_t &fC22=fC[5];
197 Double_t &fC33=fC[9];
198 Double_t &fC43=fC[13];
199 Double_t &fC44=fC[14];
200
201 Double_t p=GetP();
202 Double_t p2=p*p;
203 Double_t beta2=p2/(p2 + mass*mass);
204 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
205
206 //Multiple scattering******************
207 if (d!=0) {
208 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
209 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
210 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
211 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
212 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
213 fC44 += theta2*fP3*fP4*fP3*fP4;
214 }
215
216 //Energy losses************************
217 if (x0!=0. && beta2<1) {
218 d*=x0;
219 Double_t dE=Bethe(beta2)*d;
220 Double_t e=TMath::Sqrt(p2 + mass*mass);
221 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
222 fP4*=(1.- e/p2*dE);
223
224 // Approximate energy loss fluctuation (M.Ivanov)
225 const Double_t knst=0.07; // To be tuned.
226 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
227 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
228
229 }
230
231 return kTRUE;
232}
233
234Double_t ApproximateBetheBloch(Double_t beta2) {
235 //------------------------------------------------------------------
236 // This is an approximation of the Bethe-Bloch formula with
237 // the density effect taken into account at beta*gamma > 3.5
238 // (the approximation is reasonable only for solid materials)
239 //------------------------------------------------------------------
240 if (beta2/(1-beta2)>3.5*3.5)
241 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
242
243 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
244}
245
246Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
247 //------------------------------------------------------------------
248 // Transform this track to the local coord. system rotated
249 // by angle "alpha" (rad) with respect to the global coord. system.
250 //------------------------------------------------------------------
251 if (TMath::Abs(fP[2]) >= kAlmost1) {
252 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
253 return kFALSE;
254 }
255
256 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
257 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
258
259 Double_t &fP0=fP[0];
260 Double_t &fP2=fP[2];
261 Double_t &fC00=fC[0];
262 Double_t &fC10=fC[1];
263 Double_t &fC20=fC[3];
264 Double_t &fC21=fC[4];
265 Double_t &fC22=fC[5];
266 Double_t &fC30=fC[6];
267 Double_t &fC32=fC[8];
268 Double_t &fC40=fC[10];
269 Double_t &fC42=fC[12];
270
271 Double_t x=fX;
272 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
273 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
274
275 Double_t tmp=sf*ca - cf*sa;
276 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
277
278 fAlpha = alpha;
279 fX = x*ca + fP0*sa;
280 fP0= -x*sa + fP0*ca;
281 fP2= tmp;
282
283 if (TMath::Abs(cf)<kAlmost0) {
284 AliError(Form("Too small cosine value %f",cf));
285 cf = kAlmost0;
286 }
287
288 Double_t rr=(ca+sf/cf*sa);
289
290 fC00 *= (ca*ca);
291 fC10 *= ca;
292 fC20 *= ca*rr;
293 fC21 *= rr;
294 fC22 *= rr*rr;
295 fC30 *= ca;
296 fC32 *= rr;
297 fC40 *= ca;
298 fC42 *= rr;
299
300 return kTRUE;
301}
302
303Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
304 //----------------------------------------------------------------
305 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
306 //----------------------------------------------------------------
307 Double_t dx=xk-fX;
308 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
309
310 Double_t crv=GetC(b);
311 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
312
313 Double_t f1=fP[2], f2=f1 + crv*dx;
314 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
315 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
316
317 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
318 Double_t
319 &fC00=fC[0],
320 &fC10=fC[1], &fC11=fC[2],
321 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
322 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
323 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
324
325 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
326
327 fX=xk;
328 fP0 += dx*(f1+f2)/(r1+r2);
329 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
330 fP2 += dx*crv;
331
332 //f = F - 1
333
334 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
335 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
336 Double_t f12= dx*fP3*f1/(r1*r1*r1);
337 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
338 Double_t f13= dx/r1;
339 Double_t f24= dx; f24*=cc;
340
341 //b = C*ft
342 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
343 Double_t b02=f24*fC40;
344 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
345 Double_t b12=f24*fC41;
346 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
347 Double_t b22=f24*fC42;
348 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
349 Double_t b42=f24*fC44;
350 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
351 Double_t b32=f24*fC43;
352
353 //a = f*b = f*C*ft
354 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
355 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
356 Double_t a22=f24*b42;
357
358 //F*C*Ft = C + (b + bt + a)
359 fC00 += b00 + b00 + a00;
360 fC10 += b10 + b01 + a01;
361 fC20 += b20 + b02 + a02;
362 fC30 += b30;
363 fC40 += b40;
364 fC11 += b11 + b11 + a11;
365 fC21 += b21 + b12 + a12;
366 fC31 += b31;
367 fC41 += b41;
368 fC22 += b22 + b22 + a22;
369 fC32 += b32;
370 fC42 += b42;
371
372 return kTRUE;
373}
374
375void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
376Double_t p[3], Double_t bz) const {
377 //+++++++++++++++++++++++++++++++++++++++++
378 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
379 // Extrapolate track along simple helix in magnetic field
380 // Arguments: len -distance alogn helix, [cm]
381 // bz - mag field, [kGaus]
382 // Returns: x and p contain extrapolated positon and momentum
383 // The momentum returned for straight-line tracks is meaningless !
384 //+++++++++++++++++++++++++++++++++++++++++
385 GetXYZ(x);
386
387 if (TMath::Abs(Get1Pt()) < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
388 Double_t unit[3]; GetDirection(unit);
389 x[0]+=unit[0]*len;
390 x[1]+=unit[1]*len;
391 x[2]+=unit[2]*len;
392
393 p[0]=unit[0]/kAlmost0;
394 p[1]=unit[1]/kAlmost0;
395 p[2]=unit[2]/kAlmost0;
396 } else {
397 GetPxPyPz(p);
398 Double_t pp=GetP();
399 Double_t a = -kB2C*bz*GetSign();
400 Double_t rho = a/pp;
401 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
402 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
403 x[2] += p[2]*len/pp;
404
405 Double_t p0=p[0];
406 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
407 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
408 }
409}
410
411Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
412Double_t bz) const {
413 //+++++++++++++++++++++++++++++++++++++++++
414 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
415 // Finds point of intersection (if exists) of the helix with the plane.
416 // Stores result in fX and fP.
417 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
418 // and vector, normal to the plane
419 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
420 //+++++++++++++++++++++++++++++++++++++++++
421 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
422
423 //estimates initial helix length up to plane
424 Double_t s=
425 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
426 Double_t dist=99999,distPrev=dist;
427 Double_t x[3],p[3];
428 while(TMath::Abs(dist)>0.00001){
429 //calculates helix at the distance s from x0 ALONG the helix
430 Propagate(s,x,p,bz);
431
432 //distance between current helix position and plane
433 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
434
435 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
436 distPrev=dist;
437 s-=dist;
438 }
439 //on exit pnt is intersection point,norm is track vector at that point,
440 //all in MARS
441 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
442 return kTRUE;
443}
444
445Double_t
446AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
447 //----------------------------------------------------------------
448 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
449 //----------------------------------------------------------------
450 Double_t sdd = fC[0] + cov[0];
451 Double_t sdz = fC[1] + cov[1];
452 Double_t szz = fC[2] + cov[2];
453 Double_t det = sdd*szz - sdz*sdz;
454
455 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
456
457 Double_t d = fP[0] - p[0];
458 Double_t z = fP[1] - p[1];
459
460 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
461}
462
463Double_t AliExternalTrackParam::
464GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
465 //----------------------------------------------------------------
466 // Estimate the chi2 of the 3D space point "p" and
467 // the fill covariance matrix "covyz" and "covxyz"
468 //
469 // Cov(x,x) ... : covxyz[0]
470 // Cov(y,x) ... : covxyz[1] covyz[0]
471 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
472 //----------------------------------------------------------------
473
474 Double_t res[3] = {
475 GetX() - p[0],
476 GetY() - p[1],
477 GetZ() - p[2]
478 };
479
480 Double_t f=GetSnp();
481 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
482 Double_t r=TMath::Sqrt(1.- f*f);
483 Double_t a=f/r, b=GetTgl()/r;
484
485 Double_t s2=333.*333.; //something reasonably big (cm^2)
486
487 TMatrixDSym v(3);
488 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
489 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
490 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
491
492 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
493 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
494 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
495
496 v.Invert();
497 if (!v.IsValid()) return kVeryBig;
498
499 Double_t chi2=0.;
500 for (Int_t i = 0; i < 3; i++)
501 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
502
503 return chi2;
504
505
506}
507
508Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
509 //------------------------------------------------------------------
510 // Update the track parameters with the space point "p" having
511 // the covariance matrix "cov"
512 //------------------------------------------------------------------
513 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
514 Double_t
515 &fC00=fC[0],
516 &fC10=fC[1], &fC11=fC[2],
517 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
518 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
519 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
520
521 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
522 r00+=fC00; r01+=fC10; r11+=fC11;
523 Double_t det=r00*r11 - r01*r01;
524
525 if (TMath::Abs(det) < kAlmost0) return kFALSE;
526
527
528 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
529
530 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
531 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
532 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
533 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
534 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
535
536 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
537 Double_t sf=fP2 + k20*dy + k21*dz;
538 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
539
540 fP0 += k00*dy + k01*dz;
541 fP1 += k10*dy + k11*dz;
542 fP2 = sf;
543 fP3 += k30*dy + k31*dz;
544 fP4 += k40*dy + k41*dz;
545
546 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
547 Double_t c12=fC21, c13=fC31, c14=fC41;
548
549 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
550 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
551 fC40-=k00*c04+k01*c14;
552
553 fC11-=k10*c01+k11*fC11;
554 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
555 fC41-=k10*c04+k11*c14;
556
557 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
558 fC42-=k20*c04+k21*c14;
559
560 fC33-=k30*c03+k31*c13;
561 fC43-=k30*c04+k31*c14;
562
563 fC44-=k40*c04+k41*c14;
564
565 return kTRUE;
566}
567
568void
569AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
570 //--------------------------------------------------------------------
571 // External track parameters -> helix parameters
572 // "b" - magnetic field (kG)
573 //--------------------------------------------------------------------
574 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
575
576 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
577
578 hlx[5]=fX*cs - hlx[0]*sn; // x0
579 hlx[0]=fX*sn + hlx[0]*cs; // y0
580//hlx[1]= // z0
581 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
582//hlx[3]= // tgl
583 hlx[4]=GetC(b); // C
584}
585
586
587static void Evaluate(const Double_t *h, Double_t t,
588 Double_t r[3], //radius vector
589 Double_t g[3], //first defivatives
590 Double_t gg[3]) //second derivatives
591{
592 //--------------------------------------------------------------------
593 // Calculate position of a point on a track and some derivatives
594 //--------------------------------------------------------------------
595 Double_t phase=h[4]*t+h[2];
596 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
597
598 r[0] = h[5] + (sn - h[6])/h[4];
599 r[1] = h[0] - (cs - h[7])/h[4];
600 r[2] = h[1] + h[3]*t;
601
602 g[0] = cs; g[1]=sn; g[2]=h[3];
603
604 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
605}
606
607Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
608Double_t b, Double_t &xthis, Double_t &xp) const {
609 //------------------------------------------------------------
610 // Returns the (weighed !) distance of closest approach between
611 // this track and the track "p".
612 // Other returned values:
613 // xthis, xt - coordinates of tracks' reference planes at the DCA
614 //-----------------------------------------------------------
615 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
616 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
617 Double_t dx2=dy2;
618
619 //dx2=dy2=dz2=1.;
620
621 Double_t p1[8]; GetHelixParameters(p1,b);
622 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
623 Double_t p2[8]; p->GetHelixParameters(p2,b);
624 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
625
626
627 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
628 Evaluate(p1,t1,r1,g1,gg1);
629 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
630 Evaluate(p2,t2,r2,g2,gg2);
631
632 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
633 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
634
635 Int_t max=27;
636 while (max--) {
637 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
638 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
639 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
640 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
641 (g1[2]*g1[2] - dz*gg1[2])/dz2;
642 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
643 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
644 (g2[2]*g2[2] + dz*gg2[2])/dz2;
645 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
646
647 Double_t det=h11*h22-h12*h12;
648
649 Double_t dt1,dt2;
650 if (TMath::Abs(det)<1.e-33) {
651 //(quasi)singular Hessian
652 dt1=-gt1; dt2=-gt2;
653 } else {
654 dt1=-(gt1*h22 - gt2*h12)/det;
655 dt2=-(h11*gt2 - h12*gt1)/det;
656 }
657
658 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
659
660 //check delta(phase1) ?
661 //check delta(phase2) ?
662
663 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
664 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
665 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
666 AliWarning(" stopped at not a stationary point !");
667 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
668 if (lmb < 0.)
669 AliWarning(" stopped at not a minimum !");
670 break;
671 }
672
673 Double_t dd=dm;
674 for (Int_t div=1 ; ; div*=2) {
675 Evaluate(p1,t1+dt1,r1,g1,gg1);
676 Evaluate(p2,t2+dt2,r2,g2,gg2);
677 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
678 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
679 if (dd<dm) break;
680 dt1*=0.5; dt2*=0.5;
681 if (div>512) {
682 AliWarning(" overshoot !"); break;
683 }
684 }
685 dm=dd;
686
687 t1+=dt1;
688 t2+=dt2;
689
690 }
691
692 if (max<=0) AliWarning(" too many iterations !");
693
694 Double_t cs=TMath::Cos(GetAlpha());
695 Double_t sn=TMath::Sin(GetAlpha());
696 xthis=r1[0]*cs + r1[1]*sn;
697
698 cs=TMath::Cos(p->GetAlpha());
699 sn=TMath::Sin(p->GetAlpha());
700 xp=r2[0]*cs + r2[1]*sn;
701
702 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
703}
704
705Double_t AliExternalTrackParam::
706PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
707 //--------------------------------------------------------------
708 // Propagates this track and the argument track to the position of the
709 // distance of closest approach.
710 // Returns the (weighed !) distance of closest approach.
711 //--------------------------------------------------------------
712 Double_t xthis,xp;
713 Double_t dca=GetDCA(p,b,xthis,xp);
714
715 if (!PropagateTo(xthis,b)) {
716 //AliWarning(" propagation failed !");
717 return 1e+33;
718 }
719
720 if (!p->PropagateTo(xp,b)) {
721 //AliWarning(" propagation failed !";
722 return 1e+33;
723 }
724
725 return dca;
726}
727
728
729
730
731Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
732 //
733 // Try to relate this track to the vertex "vtx",
734 // if the (rough) transverse impact parameter is not bigger then "maxd".
735 // Magnetic field is "b" (kG).
736 //
737 // a) The track gets extapolated to the DCA to the vertex.
738 // b) The impact parameters and their covariance matrix are calculated.
739 //
740 // In the case of success, the returned value is kTRUE
741 // (otherwise, it's kFALSE)
742 //
743 Double_t alpha=GetAlpha();
744 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
745 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
746 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
747 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
748 x-=xv; y-=yv;
749
750 //Estimate the impact parameter neglecting the track curvature
751 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
752 if (d > maxd) return kFALSE;
753
754 //Propagate to the DCA
755 Double_t crv=0.299792458e-3*b*GetParameter()[4];
756 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
757 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
758
759 x = xv*cs + yv*sn;
760 yv=-xv*sn + yv*cs; xv=x;
761
762 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
763 return kTRUE;
764}
765
766
767
768
769Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
770 //----------------------------------------------------------------
771 // This function performs local->global transformation of the
772 // track momentum.
773 // When called, the arguments are:
774 // p[0] = 1/pt of the track;
775 // p[1] = sine of local azim. angle of the track momentum;
776 // p[2] = tangent of the track momentum dip angle;
777 // alpha - rotation angle.
778 // The result is returned as:
779 // p[0] = px
780 // p[1] = py
781 // p[2] = pz
782 // Results for (nearly) straight tracks are meaningless !
783 //----------------------------------------------------------------
784 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
785 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
786
787 Double_t pt=1./TMath::Abs(p[0]);
788 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
789 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
790 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
791
792 return kTRUE;
793}
794
795Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
796 //----------------------------------------------------------------
797 // This function performs local->global transformation of the
798 // track position.
799 // When called, the arguments are:
800 // r[0] = local x
801 // r[1] = local y
802 // r[2] = local z
803 // alpha - rotation angle.
804 // The result is returned as:
805 // r[0] = global x
806 // r[1] = global y
807 // r[2] = global z
808 //----------------------------------------------------------------
809 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
810 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
811
812 return kTRUE;
813}
814
815void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
816 //----------------------------------------------------------------
817 // This function returns a unit vector along the track direction
818 // in the global coordinate system.
819 //----------------------------------------------------------------
820 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
821 Double_t snp=fP[2];
822 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
823 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
824 d[0]=(csp*cs - snp*sn)/norm;
825 d[1]=(snp*cs + csp*sn)/norm;
826 d[2]=fP[3]/norm;
827}
828
829Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
830 //---------------------------------------------------------------------
831 // This function returns the global track momentum components
832 // Results for (nearly) straight tracks are meaningless !
833 //---------------------------------------------------------------------
834 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
835 return Local2GlobalMomentum(p,fAlpha);
836}
837
838Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
839 //---------------------------------------------------------------------
840 // This function returns the global track position
841 //---------------------------------------------------------------------
842 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
843 return Local2GlobalPosition(r,fAlpha);
844}
845
846Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
847 //---------------------------------------------------------------------
848 // This function returns the global covariance matrix of the track params
849 //
850 // Cov(x,x) ... : cv[0]
851 // Cov(y,x) ... : cv[1] cv[2]
852 // Cov(z,x) ... : cv[3] cv[4] cv[5]
853 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
854 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
855 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
856 //
857 // Results for (nearly) straight tracks are meaningless !
858 //---------------------------------------------------------------------
859 if (TMath::Abs(fP[4])<=kAlmost0) {
860 for (Int_t i=0; i<21; i++) cv[i]=0.;
861 return kFALSE;
862 }
863 if (TMath::Abs(fP[2]) > kAlmost1) {
864 for (Int_t i=0; i<21; i++) cv[i]=0.;
865 return kFALSE;
866 }
867 Double_t pt=1./TMath::Abs(fP[4]);
868 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
869 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
870
871 Double_t m00=-sn, m10=cs;
872 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
873 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
874 Double_t m35=pt, m45=-pt*pt*fP[3];
875
876 cv[0 ] = fC[0]*m00*m00;
877 cv[1 ] = fC[0]*m00*m10;
878 cv[2 ] = fC[0]*m10*m10;
879 cv[3 ] = fC[1]*m00;
880 cv[4 ] = fC[1]*m10;
881 cv[5 ] = fC[2];
882 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
883 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
884 cv[8 ] = fC[4]*m23 + fC[11]*m43;
885 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
886 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
887 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
888 cv[12] = fC[4]*m24 + fC[11]*m44;
889 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
890 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
891 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
892 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
893 cv[17] = fC[7]*m35 + fC[11]*m45;
894 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
895 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
896 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
897
898 return kTRUE;
899}
900
901
902Bool_t
903AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
904 //---------------------------------------------------------------------
905 // This function returns the global track momentum extrapolated to
906 // the radial position "x" (cm) in the magnetic field "b" (kG)
907 //---------------------------------------------------------------------
908 p[0]=fP[4];
909 p[1]=fP[2]+(x-fX)*GetC(b);
910 p[2]=fP[3];
911 return Local2GlobalMomentum(p,fAlpha);
912}
913
914Bool_t
915AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
916 //---------------------------------------------------------------------
917 // This function returns the local Y-coordinate of the intersection
918 // point between this track and the reference plane "x" (cm).
919 // Magnetic field "b" (kG)
920 //---------------------------------------------------------------------
921 Double_t dx=x-fX;
922 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
923
924 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
925
926 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
927 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
928
929 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
930 y = fP[0] + dx*(f1+f2)/(r1+r2);
931 return kTRUE;
932}
933
934Bool_t
935AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
936 //---------------------------------------------------------------------
937 // This function returns the local Z-coordinate of the intersection
938 // point between this track and the reference plane "x" (cm).
939 // Magnetic field "b" (kG)
940 //---------------------------------------------------------------------
941 Double_t dx=x-fX;
942 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
943
944 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
945
946 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
947 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
948
949 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
950 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
951 return kTRUE;
952}
953
954Bool_t
955AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
956 //---------------------------------------------------------------------
957 // This function returns the global track position extrapolated to
958 // the radial position "x" (cm) in the magnetic field "b" (kG)
959 //---------------------------------------------------------------------
960 Double_t dx=x-fX;
961 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
962
963 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
964
965 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
966 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
967
968 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
969 r[0] = x;
970 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
971 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
972 return Local2GlobalPosition(r,fAlpha);
973}
974
975//_____________________________________________________________________________
976void AliExternalTrackParam::Print(Option_t* /*option*/) const
977{
978// print the parameters and the covariance matrix
979
980 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
981 printf(" parameters: %12g %12g %12g %12g %12g\n",
982 fP[0], fP[1], fP[2], fP[3], fP[4]);
983 printf(" covariance: %12g\n", fC[0]);
984 printf(" %12g %12g\n", fC[1], fC[2]);
985 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
986 printf(" %12g %12g %12g %12g\n",
987 fC[6], fC[7], fC[8], fC[9]);
988 printf(" %12g %12g %12g %12g %12g\n",
989 fC[10], fC[11], fC[12], fC[13], fC[14]);
990}
991
992Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
993 //
994 // Get sinus at given x
995 //
996 Double_t crv=GetC(b);
997 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
998 Double_t dx = x-fX;
999 Double_t res = fP[2]+dx*crv;
1000 return res;
1001}