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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"
f76701bf 29#include "AliESDVertex.h"
6c94f330 30#include "AliLog.h"
51ad6848 31
32ClassImp(AliExternalTrackParam)
33
51ad6848 34//_____________________________________________________________________________
90e48c0c 35AliExternalTrackParam::AliExternalTrackParam() :
6c94f330 36 TObject(),
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
6c94f330 47//_____________________________________________________________________________
48AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
49 TObject(track),
50 fX(track.fX),
51 fAlpha(track.fAlpha)
52{
53 //
54 // copy constructor
55 //
56 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
57 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
58}
59
51ad6848 60//_____________________________________________________________________________
61AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
62 const Double_t param[5],
90e48c0c 63 const Double_t covar[15]) :
6c94f330 64 TObject(),
90e48c0c 65 fX(x),
c9ec41e8 66 fAlpha(alpha)
51ad6848 67{
90e48c0c 68 //
69 // create external track parameters from given arguments
70 //
c9ec41e8 71 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
72 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 73}
74
90e48c0c 75//_____________________________________________________________________________
6c94f330 76void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
77 const Double_t p[5], const Double_t cov[15]) {
c9ec41e8 78 //
6c94f330 79 // Sets the parameters
c9ec41e8 80 //
6c94f330 81 fX=x;
82 fAlpha=alpha;
83 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
84 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
51ad6848 85}
86
87//_____________________________________________________________________________
c9ec41e8 88void AliExternalTrackParam::Reset() {
1530f89c 89 //
90 // Resets all the parameters to 0
91 //
c9ec41e8 92 fX=fAlpha=0.;
93 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
94 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 95}
96
c9ec41e8 97Double_t AliExternalTrackParam::GetP() const {
98 //---------------------------------------------------------------------
99 // This function returns the track momentum
100 // Results for (nearly) straight tracks are meaningless !
101 //---------------------------------------------------------------------
06fb4a2f 102 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 103 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 104}
105
1d99986f 106Double_t AliExternalTrackParam::Get1P() const {
107 //---------------------------------------------------------------------
108 // This function returns the 1/(track momentum)
109 //---------------------------------------------------------------------
110 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
111}
112
c9ec41e8 113//_______________________________________________________________________
c7bafca9 114Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 115 //------------------------------------------------------------------
116 // This function calculates the transverse impact parameter
117 // with respect to a point with global coordinates (x,y)
118 // in the magnetic field "b" (kG)
119 //------------------------------------------------------------------
5773defd 120 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 121 Double_t rp4=GetC(b);
c9ec41e8 122
123 Double_t xt=fX, yt=fP[0];
124
125 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
126 Double_t a = x*cs + y*sn;
127 y = -x*sn + y*cs; x=a;
128 xt-=x; yt-=y;
129
130 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
131 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 132 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
133}
134
135//_______________________________________________________________________
136void AliExternalTrackParam::
137GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
138 //------------------------------------------------------------------
139 // This function calculates the transverse and longitudinal impact parameters
140 // with respect to a point with global coordinates (x,y)
141 // in the magnetic field "b" (kG)
142 //------------------------------------------------------------------
143 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
144 Double_t xt=fX, yt=fP[0];
145 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
146 Double_t a = x*cs + y*sn;
147 y = -x*sn + y*cs; x=a;
148 xt-=x; yt-=y;
149
150 Double_t rp4=GetC(b);
151 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
152 dz[0] = -(xt*f1 - yt*r1);
153 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
154 return;
155 }
156
157 sn=rp4*xt - f1; cs=rp4*yt + r1;
158 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
159 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
160 dz[0] = -a/(1 + rr);
161 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
162 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 163}
164
49d13e89 165//_______________________________________________________________________
166Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
167 //------------------------------------------------------------------
168 // This function calculates the transverse impact parameter
169 // with respect to a point with global coordinates (xv,yv)
170 // neglecting the track curvature.
171 //------------------------------------------------------------------
172 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
173 Double_t x= xv*cs + yv*sn;
174 Double_t y=-xv*sn + yv*cs;
175
176 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
177
1530f89c 178 return -d;
49d13e89 179}
180
c7bafca9 181Bool_t AliExternalTrackParam::
182CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) {
183 //------------------------------------------------------------------
184 // This function corrects the track parameters for the crossed material
185 // "d" - the thickness (fraction of the radiation length)
186 // "x0" - the radiation length (g/cm^2)
187 // "mass" - the mass of this particle (GeV/c^2)
188 //------------------------------------------------------------------
189 Double_t &fP2=fP[2];
190 Double_t &fP3=fP[3];
191 Double_t &fP4=fP[4];
192
193 Double_t &fC22=fC[5];
194 Double_t &fC33=fC[9];
195 Double_t &fC43=fC[13];
196 Double_t &fC44=fC[14];
197
7b5ef2e6 198 Double_t p=GetP();
199 Double_t p2=p*p;
c7bafca9 200 Double_t beta2=p2/(p2 + mass*mass);
201 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
202
203 //Multiple scattering******************
204 if (d!=0) {
205 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
206 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
207 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
208 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
209 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
210 fC44 += theta2*fP3*fP4*fP3*fP4;
211 }
212
213 //Energy losses************************
8fc1985d 214 if (x0!=0. && beta2<1) {
c7bafca9 215 d*=x0;
216 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
217 if (beta2/(1-beta2)>3.5*3.5)
218 dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
219
220 fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE);
221 }
222
223 return kTRUE;
224}
225
49d13e89 226Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
227 //------------------------------------------------------------------
228 // Transform this track to the local coord. system rotated
229 // by angle "alpha" (rad) with respect to the global coord. system.
230 //------------------------------------------------------------------
dfcef74c 231 if (TMath::Abs(fP[2]) >= kAlmost1) {
232 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
233 return kFALSE;
234 }
235
49d13e89 236 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
237 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
238
239 Double_t &fP0=fP[0];
240 Double_t &fP2=fP[2];
241 Double_t &fC00=fC[0];
242 Double_t &fC10=fC[1];
243 Double_t &fC20=fC[3];
244 Double_t &fC21=fC[4];
245 Double_t &fC22=fC[5];
246 Double_t &fC30=fC[6];
247 Double_t &fC32=fC[8];
248 Double_t &fC40=fC[10];
249 Double_t &fC42=fC[12];
250
251 Double_t x=fX;
252 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
253 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
254
dfcef74c 255 Double_t tmp=sf*ca - cf*sa;
256 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
257
49d13e89 258 fAlpha = alpha;
259 fX = x*ca + fP0*sa;
260 fP0= -x*sa + fP0*ca;
dfcef74c 261 fP2= tmp;
49d13e89 262
06fb4a2f 263 if (TMath::Abs(cf)<kAlmost0) {
264 AliError(Form("Too small cosine value %f",cf));
265 cf = kAlmost0;
266 }
267
49d13e89 268 Double_t rr=(ca+sf/cf*sa);
269
270 fC00 *= (ca*ca);
271 fC10 *= ca;
272 fC20 *= ca*rr;
273 fC21 *= rr;
274 fC22 *= rr*rr;
275 fC30 *= ca;
276 fC32 *= rr;
277 fC40 *= ca;
278 fC42 *= rr;
279
280 return kTRUE;
281}
282
283Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
284 //----------------------------------------------------------------
285 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
286 //----------------------------------------------------------------
49d13e89 287 Double_t dx=xk-fX;
e421f556 288 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 289
1530f89c 290 Double_t crv=GetC(b);
5773defd 291 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
292
49d13e89 293 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 294 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 295 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
296
297 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
298 Double_t
299 &fC00=fC[0],
300 &fC10=fC[1], &fC11=fC[2],
301 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
302 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
303 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
304
305 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
306
307 fX=xk;
308 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 309 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 310 fP2 += dx*crv;
311
312 //f = F - 1
313
314 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
315 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
316 Double_t f12= dx*fP3*f1/(r1*r1*r1);
317 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
318 Double_t f13= dx/r1;
319 Double_t f24= dx; f24*=cc;
320
321 //b = C*ft
322 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
323 Double_t b02=f24*fC40;
324 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
325 Double_t b12=f24*fC41;
326 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
327 Double_t b22=f24*fC42;
328 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
329 Double_t b42=f24*fC44;
330 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
331 Double_t b32=f24*fC43;
332
333 //a = f*b = f*C*ft
334 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
335 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
336 Double_t a22=f24*b42;
337
338 //F*C*Ft = C + (b + bt + a)
339 fC00 += b00 + b00 + a00;
340 fC10 += b10 + b01 + a01;
341 fC20 += b20 + b02 + a02;
342 fC30 += b30;
343 fC40 += b40;
344 fC11 += b11 + b11 + a11;
345 fC21 += b21 + b12 + a12;
346 fC31 += b31;
347 fC41 += b41;
348 fC22 += b22 + b22 + a22;
349 fC32 += b32;
350 fC42 += b42;
351
352 return kTRUE;
353}
354
355Double_t
356AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
357 //----------------------------------------------------------------
358 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
359 //----------------------------------------------------------------
360 Double_t sdd = fC[0] + cov[0];
361 Double_t sdz = fC[1] + cov[1];
362 Double_t szz = fC[2] + cov[2];
363 Double_t det = sdd*szz - sdz*sdz;
364
365 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
366
367 Double_t d = fP[0] - p[0];
368 Double_t z = fP[1] - p[1];
369
370 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
371}
372
373Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
374 //------------------------------------------------------------------
375 // Update the track parameters with the space point "p" having
376 // the covariance matrix "cov"
377 //------------------------------------------------------------------
378 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
379 Double_t
380 &fC00=fC[0],
381 &fC10=fC[1], &fC11=fC[2],
382 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
383 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
384 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
385
386 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
387 r00+=fC00; r01+=fC10; r11+=fC11;
388 Double_t det=r00*r11 - r01*r01;
389
390 if (TMath::Abs(det) < kAlmost0) return kFALSE;
391
392
393 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
394
395 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
396 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
397 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
398 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
399 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
400
401 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
402 Double_t sf=fP2 + k20*dy + k21*dz;
403 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
404
405 fP0 += k00*dy + k01*dz;
406 fP1 += k10*dy + k11*dz;
407 fP2 = sf;
408 fP3 += k30*dy + k31*dz;
409 fP4 += k40*dy + k41*dz;
410
411 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
412 Double_t c12=fC21, c13=fC31, c14=fC41;
413
414 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
415 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
416 fC40-=k00*c04+k01*c14;
417
418 fC11-=k10*c01+k11*fC11;
419 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
420 fC41-=k10*c04+k11*c14;
421
422 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
423 fC42-=k20*c04+k21*c14;
424
425 fC33-=k30*c03+k31*c13;
426 fC43-=k30*c04+k31*c14;
427
428 fC44-=k40*c04+k41*c14;
429
430 return kTRUE;
431}
432
c7bafca9 433void
434AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
435 //--------------------------------------------------------------------
436 // External track parameters -> helix parameters
437 // "b" - magnetic field (kG)
438 //--------------------------------------------------------------------
439 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
440
1530f89c 441 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 442
443 hlx[5]=fX*cs - hlx[0]*sn; // x0
444 hlx[0]=fX*sn + hlx[0]*cs; // y0
445//hlx[1]= // z0
446 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
447//hlx[3]= // tgl
1530f89c 448 hlx[4]=GetC(b); // C
c7bafca9 449}
450
451
452static void Evaluate(const Double_t *h, Double_t t,
453 Double_t r[3], //radius vector
454 Double_t g[3], //first defivatives
455 Double_t gg[3]) //second derivatives
456{
457 //--------------------------------------------------------------------
458 // Calculate position of a point on a track and some derivatives
459 //--------------------------------------------------------------------
460 Double_t phase=h[4]*t+h[2];
461 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
462
463 r[0] = h[5] + (sn - h[6])/h[4];
464 r[1] = h[0] - (cs - h[7])/h[4];
465 r[2] = h[1] + h[3]*t;
466
467 g[0] = cs; g[1]=sn; g[2]=h[3];
468
469 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
470}
471
472Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
473Double_t b, Double_t &xthis, Double_t &xp) const {
474 //------------------------------------------------------------
475 // Returns the (weighed !) distance of closest approach between
476 // this track and the track "p".
477 // Other returned values:
478 // xthis, xt - coordinates of tracks' reference planes at the DCA
479 //-----------------------------------------------------------
480 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
481 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
482 Double_t dx2=dy2;
483
484 //dx2=dy2=dz2=1.;
485
486 Double_t p1[8]; GetHelixParameters(p1,b);
487 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
488 Double_t p2[8]; p->GetHelixParameters(p2,b);
489 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
490
491
492 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
493 Evaluate(p1,t1,r1,g1,gg1);
494 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
495 Evaluate(p2,t2,r2,g2,gg2);
496
497 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
498 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
499
500 Int_t max=27;
501 while (max--) {
502 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
503 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
504 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
505 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
506 (g1[2]*g1[2] - dz*gg1[2])/dz2;
507 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
508 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
509 (g2[2]*g2[2] + dz*gg2[2])/dz2;
510 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
511
512 Double_t det=h11*h22-h12*h12;
513
514 Double_t dt1,dt2;
515 if (TMath::Abs(det)<1.e-33) {
516 //(quasi)singular Hessian
517 dt1=-gt1; dt2=-gt2;
518 } else {
519 dt1=-(gt1*h22 - gt2*h12)/det;
520 dt2=-(h11*gt2 - h12*gt1)/det;
521 }
522
523 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
524
525 //check delta(phase1) ?
526 //check delta(phase2) ?
527
528 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
529 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
530 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
531 AliWarning(" stopped at not a stationary point !");
532 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
533 if (lmb < 0.)
534 AliWarning(" stopped at not a minimum !");
535 break;
536 }
537
538 Double_t dd=dm;
539 for (Int_t div=1 ; ; div*=2) {
540 Evaluate(p1,t1+dt1,r1,g1,gg1);
541 Evaluate(p2,t2+dt2,r2,g2,gg2);
542 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
543 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
544 if (dd<dm) break;
545 dt1*=0.5; dt2*=0.5;
546 if (div>512) {
547 AliWarning(" overshoot !"); break;
548 }
549 }
550 dm=dd;
551
552 t1+=dt1;
553 t2+=dt2;
554
555 }
556
557 if (max<=0) AliWarning(" too many iterations !");
558
559 Double_t cs=TMath::Cos(GetAlpha());
560 Double_t sn=TMath::Sin(GetAlpha());
561 xthis=r1[0]*cs + r1[1]*sn;
562
563 cs=TMath::Cos(p->GetAlpha());
564 sn=TMath::Sin(p->GetAlpha());
565 xp=r2[0]*cs + r2[1]*sn;
566
567 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
568}
569
570Double_t AliExternalTrackParam::
571PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
572 //--------------------------------------------------------------
573 // Propagates this track and the argument track to the position of the
574 // distance of closest approach.
575 // Returns the (weighed !) distance of closest approach.
576 //--------------------------------------------------------------
577 Double_t xthis,xp;
578 Double_t dca=GetDCA(p,b,xthis,xp);
579
580 if (!PropagateTo(xthis,b)) {
581 //AliWarning(" propagation failed !");
582 return 1e+33;
583 }
584
585 if (!p->PropagateTo(xp,b)) {
586 //AliWarning(" propagation failed !";
587 return 1e+33;
588 }
589
590 return dca;
591}
592
593
594
f76701bf 595
596Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
597 //
598 // Try to relate this track to the vertex "vtx",
599 // if the (rough) transverse impact parameter is not bigger then "maxd".
600 // Magnetic field is "b" (kG).
601 //
602 // a) The track gets extapolated to the DCA to the vertex.
603 // b) The impact parameters and their covariance matrix are calculated.
604 //
605 // In the case of success, the returned value is kTRUE
606 // (otherwise, it's kFALSE)
607 //
608 Double_t alpha=GetAlpha();
609 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
610 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
611 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 612 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 613 x-=xv; y-=yv;
614
615 //Estimate the impact parameter neglecting the track curvature
616 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
617 if (d > maxd) return kFALSE;
618
619 //Propagate to the DCA
620 Double_t crv=0.299792458e-3*b*GetParameter()[4];
621 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
622 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
623
624 x = xv*cs + yv*sn;
625 yv=-xv*sn + yv*cs; xv=x;
626
627 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 628 return kTRUE;
f76701bf 629}
630
631
632
633
c9ec41e8 634Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
635 //----------------------------------------------------------------
636 // This function performs local->global transformation of the
637 // track momentum.
638 // When called, the arguments are:
639 // p[0] = 1/pt of the track;
640 // p[1] = sine of local azim. angle of the track momentum;
641 // p[2] = tangent of the track momentum dip angle;
642 // alpha - rotation angle.
643 // The result is returned as:
644 // p[0] = px
645 // p[1] = py
646 // p[2] = pz
647 // Results for (nearly) straight tracks are meaningless !
648 //----------------------------------------------------------------
e421f556 649 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 650 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 651
652 Double_t pt=1./TMath::Abs(p[0]);
653 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
654 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
655 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 656
657 return kTRUE;
658}
659
c9ec41e8 660Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
661 //----------------------------------------------------------------
662 // This function performs local->global transformation of the
663 // track position.
664 // When called, the arguments are:
665 // r[0] = local x
666 // r[1] = local y
667 // r[2] = local z
668 // alpha - rotation angle.
669 // The result is returned as:
670 // r[0] = global x
671 // r[1] = global y
672 // r[2] = global z
673 //----------------------------------------------------------------
674 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
675 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 676
a5e407e9 677 return kTRUE;
51ad6848 678}
679
c9ec41e8 680Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
681 //---------------------------------------------------------------------
682 // This function returns the global track momentum components
683 // Results for (nearly) straight tracks are meaningless !
684 //---------------------------------------------------------------------
685 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
686 return Local2GlobalMomentum(p,fAlpha);
687}
a5e407e9 688
c9ec41e8 689Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
690 //---------------------------------------------------------------------
691 // This function returns the global track position
692 //---------------------------------------------------------------------
693 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
694 return Local2GlobalPosition(r,fAlpha);
51ad6848 695}
696
c9ec41e8 697Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
698 //---------------------------------------------------------------------
699 // This function returns the global covariance matrix of the track params
700 //
701 // Cov(x,x) ... : cv[0]
702 // Cov(y,x) ... : cv[1] cv[2]
703 // Cov(z,x) ... : cv[3] cv[4] cv[5]
704 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
705 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
706 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 707 //
c9ec41e8 708 // Results for (nearly) straight tracks are meaningless !
709 //---------------------------------------------------------------------
e421f556 710 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 711 for (Int_t i=0; i<21; i++) cv[i]=0.;
712 return kFALSE;
a5e407e9 713 }
49d13e89 714 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 715 for (Int_t i=0; i<21; i++) cv[i]=0.;
716 return kFALSE;
717 }
718 Double_t pt=1./TMath::Abs(fP[4]);
719 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
720 Double_t r=TMath::Sqrt(1-fP[2]*fP[2]);
721
722 Double_t m00=-sn, m10=cs;
723 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
724 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
725 Double_t m35=pt, m45=-pt*pt*fP[3];
726
727 cv[0 ] = fC[0]*m00*m00;
728 cv[1 ] = fC[0]*m00*m10;
729 cv[2 ] = fC[0]*m10*m10;
730 cv[3 ] = fC[1]*m00;
731 cv[4 ] = fC[1]*m10;
732 cv[5 ] = fC[2];
733 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
734 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
735 cv[8 ] = fC[4]*m23 + fC[11]*m43;
736 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
737 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
738 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
739 cv[12] = fC[4]*m24 + fC[11]*m44;
740 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
741 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
742 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
743 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
744 cv[17] = fC[7]*m35 + fC[11]*m45;
745 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
746 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
747 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 748
c9ec41e8 749 return kTRUE;
51ad6848 750}
751
51ad6848 752
c9ec41e8 753Bool_t
754AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
755 //---------------------------------------------------------------------
756 // This function returns the global track momentum extrapolated to
757 // the radial position "x" (cm) in the magnetic field "b" (kG)
758 //---------------------------------------------------------------------
c9ec41e8 759 p[0]=fP[4];
1530f89c 760 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 761 p[2]=fP[3];
762 return Local2GlobalMomentum(p,fAlpha);
51ad6848 763}
764
7cf7bb6c 765Bool_t
766AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
767 //---------------------------------------------------------------------
768 // This function returns the local Y-coordinate of the intersection
769 // point between this track and the reference plane "x" (cm).
770 // Magnetic field "b" (kG)
771 //---------------------------------------------------------------------
772 Double_t dx=x-fX;
773 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
774
1530f89c 775 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 776
777 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
778 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
779
780 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
781 y = fP[0] + dx*(f1+f2)/(r1+r2);
782 return kTRUE;
783}
784
6c94f330 785Bool_t
786AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
787 //---------------------------------------------------------------------
788 // This function returns the local Z-coordinate of the intersection
789 // point between this track and the reference plane "x" (cm).
790 // Magnetic field "b" (kG)
791 //---------------------------------------------------------------------
792 Double_t dx=x-fX;
793 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
794
795 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
796
797 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
798 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
799
800 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
801 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
802 return kTRUE;
803}
804
c9ec41e8 805Bool_t
806AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
807 //---------------------------------------------------------------------
808 // This function returns the global track position extrapolated to
809 // the radial position "x" (cm) in the magnetic field "b" (kG)
810 //---------------------------------------------------------------------
c9ec41e8 811 Double_t dx=x-fX;
e421f556 812 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
813
1530f89c 814 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 815
e421f556 816 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 817 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 818
819 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
820 r[0] = x;
821 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 822 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 823 return Local2GlobalPosition(r,fAlpha);
51ad6848 824}
825
51ad6848 826//_____________________________________________________________________________
827void AliExternalTrackParam::Print(Option_t* /*option*/) const
828{
829// print the parameters and the covariance matrix
830
831 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
832 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 833 fP[0], fP[1], fP[2], fP[3], fP[4]);
834 printf(" covariance: %12g\n", fC[0]);
835 printf(" %12g %12g\n", fC[1], fC[2]);
836 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 837 printf(" %12g %12g %12g %12g\n",
c9ec41e8 838 fC[6], fC[7], fC[8], fC[9]);
51ad6848 839 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 840 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 841}
5b77d93c 842
c194ba83 843Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
844 //
845 // Get sinus at given x
846 //
1530f89c 847 Double_t crv=GetC(b);
c194ba83 848 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
849 Double_t dx = x-fX;
850 Double_t res = fP[2]+dx*crv;
851 return res;
852}