Bug fix in LTM - initial max sigma^2 (Marian)
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
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51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
51ad6848 28#include "AliExternalTrackParam.h"
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
47//_____________________________________________________________________________
6c94f330 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
60//_____________________________________________________________________________
51ad6848 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
ee5dba5e 181Bool_t AliExternalTrackParam::CorrectForMaterial
182(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 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;
ee5dba5e 216 Double_t dE=Bethe(beta2)*d;
217 Double_t e=TMath::Sqrt(p2 + mass*mass);
218 fP4*=(1.- e/p2*dE);
219
220 // Approximate energy loss fluctuation (M.Ivanov)
221 const Double_t cnst=0.07; // To be tuned.
222 Double_t sigmadE=cnst*TMath::Sqrt(TMath::Abs(dE));
223 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
224
c7bafca9 225 }
226
227 return kTRUE;
228}
229
ee5dba5e 230Double_t ApproximateBetheBloch(Double_t beta2) {
231 //------------------------------------------------------------------
232 // This is an approximation of the Bethe-Bloch formula with
233 // the density effect taken into account at beta*gamma > 3.5
234 // (the approximation is reasonable only for solid materials)
235 //------------------------------------------------------------------
236 if (beta2/(1-beta2)>3.5*3.5)
237 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
238
239 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
240}
241
49d13e89 242Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
243 //------------------------------------------------------------------
244 // Transform this track to the local coord. system rotated
245 // by angle "alpha" (rad) with respect to the global coord. system.
246 //------------------------------------------------------------------
dfcef74c 247 if (TMath::Abs(fP[2]) >= kAlmost1) {
248 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
249 return kFALSE;
250 }
251
49d13e89 252 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
253 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
254
255 Double_t &fP0=fP[0];
256 Double_t &fP2=fP[2];
257 Double_t &fC00=fC[0];
258 Double_t &fC10=fC[1];
259 Double_t &fC20=fC[3];
260 Double_t &fC21=fC[4];
261 Double_t &fC22=fC[5];
262 Double_t &fC30=fC[6];
263 Double_t &fC32=fC[8];
264 Double_t &fC40=fC[10];
265 Double_t &fC42=fC[12];
266
267 Double_t x=fX;
268 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
269 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
270
dfcef74c 271 Double_t tmp=sf*ca - cf*sa;
272 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
273
49d13e89 274 fAlpha = alpha;
275 fX = x*ca + fP0*sa;
276 fP0= -x*sa + fP0*ca;
dfcef74c 277 fP2= tmp;
49d13e89 278
06fb4a2f 279 if (TMath::Abs(cf)<kAlmost0) {
280 AliError(Form("Too small cosine value %f",cf));
281 cf = kAlmost0;
282 }
283
49d13e89 284 Double_t rr=(ca+sf/cf*sa);
285
286 fC00 *= (ca*ca);
287 fC10 *= ca;
288 fC20 *= ca*rr;
289 fC21 *= rr;
290 fC22 *= rr*rr;
291 fC30 *= ca;
292 fC32 *= rr;
293 fC40 *= ca;
294 fC42 *= rr;
295
296 return kTRUE;
297}
298
299Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
300 //----------------------------------------------------------------
301 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
302 //----------------------------------------------------------------
49d13e89 303 Double_t dx=xk-fX;
e421f556 304 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 305
1530f89c 306 Double_t crv=GetC(b);
5773defd 307 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
308
49d13e89 309 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 310 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 311 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
312
313 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
314 Double_t
315 &fC00=fC[0],
316 &fC10=fC[1], &fC11=fC[2],
317 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
318 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
319 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
320
321 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
322
323 fX=xk;
324 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 325 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 326 fP2 += dx*crv;
327
328 //f = F - 1
329
330 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
331 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
332 Double_t f12= dx*fP3*f1/(r1*r1*r1);
333 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
334 Double_t f13= dx/r1;
335 Double_t f24= dx; f24*=cc;
336
337 //b = C*ft
338 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
339 Double_t b02=f24*fC40;
340 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
341 Double_t b12=f24*fC41;
342 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
343 Double_t b22=f24*fC42;
344 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
345 Double_t b42=f24*fC44;
346 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
347 Double_t b32=f24*fC43;
348
349 //a = f*b = f*C*ft
350 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
351 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
352 Double_t a22=f24*b42;
353
354 //F*C*Ft = C + (b + bt + a)
355 fC00 += b00 + b00 + a00;
356 fC10 += b10 + b01 + a01;
357 fC20 += b20 + b02 + a02;
358 fC30 += b30;
359 fC40 += b40;
360 fC11 += b11 + b11 + a11;
361 fC21 += b21 + b12 + a12;
362 fC31 += b31;
363 fC41 += b41;
364 fC22 += b22 + b22 + a22;
365 fC32 += b32;
366 fC42 += b42;
367
368 return kTRUE;
369}
370
052daaff 371void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
372Double_t p[3], Double_t bz) const {
373 //+++++++++++++++++++++++++++++++++++++++++
374 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
375 // Extrapolate track along simple helix in magnetic field
376 // Arguments: len -distance alogn helix, [cm]
377 // bz - mag field, [kGaus]
378 // Returns: x and p contain extrapolated positon and momentum
379 // The momentum returned for straight-line tracks is meaningless !
380 //+++++++++++++++++++++++++++++++++++++++++
381 GetXYZ(x);
382
383 if (TMath::Abs(Get1Pt()) < kAlmost0){ //straight-line tracks
384 Double_t unit[3]; GetDirection(unit);
385 x[0]+=unit[0]*len;
386 x[1]+=unit[1]*len;
387 x[2]+=unit[2]*len;
388
389 p[0]=unit[0]/kAlmost0;
390 p[1]=unit[1]/kAlmost0;
391 p[2]=unit[2]/kAlmost0;
392 } else {
393 GetPxPyPz(p);
394 Double_t pp=GetP();
395 Double_t a = -kB2C*bz*GetSign();
396 Double_t rho = a/pp;
397 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
398 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
399 x[2] += p[2]*len/pp;
400
401 Double_t p0=p[0];
402 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
403 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
404 }
405}
406
407Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
408Double_t bz) const {
409 //+++++++++++++++++++++++++++++++++++++++++
410 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
411 // Finds point of intersection (if exists) of the helix with the plane.
412 // Stores result in fX and fP.
413 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
414 // and vector, normal to the plane
415 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
416 //+++++++++++++++++++++++++++++++++++++++++
417 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
418
419 //estimates initial helix length up to plane
420 Double_t s=
421 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
422 Double_t dist=99999,distPrev=dist;
423 Double_t x[3],p[3];
424 while(TMath::Abs(dist)>0.00001){
425 //calculates helix at the distance s from x0 ALONG the helix
426 Propagate(s,x,p,bz);
427
428 //distance between current helix position and plane
429 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
430
431 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
432 distPrev=dist;
433 s-=dist;
434 }
435 //on exit pnt is intersection point,norm is track vector at that point,
436 //all in MARS
437 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
438 return kTRUE;
439}
440
49d13e89 441Double_t
442AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
443 //----------------------------------------------------------------
444 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
445 //----------------------------------------------------------------
446 Double_t sdd = fC[0] + cov[0];
447 Double_t sdz = fC[1] + cov[1];
448 Double_t szz = fC[2] + cov[2];
449 Double_t det = sdd*szz - sdz*sdz;
450
451 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
452
453 Double_t d = fP[0] - p[0];
454 Double_t z = fP[1] - p[1];
455
456 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
457}
458
459Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
460 //------------------------------------------------------------------
461 // Update the track parameters with the space point "p" having
462 // the covariance matrix "cov"
463 //------------------------------------------------------------------
464 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
465 Double_t
466 &fC00=fC[0],
467 &fC10=fC[1], &fC11=fC[2],
468 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
469 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
470 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
471
472 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
473 r00+=fC00; r01+=fC10; r11+=fC11;
474 Double_t det=r00*r11 - r01*r01;
475
476 if (TMath::Abs(det) < kAlmost0) return kFALSE;
477
478
479 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
480
481 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
482 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
483 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
484 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
485 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
486
487 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
488 Double_t sf=fP2 + k20*dy + k21*dz;
489 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
490
491 fP0 += k00*dy + k01*dz;
492 fP1 += k10*dy + k11*dz;
493 fP2 = sf;
494 fP3 += k30*dy + k31*dz;
495 fP4 += k40*dy + k41*dz;
496
497 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
498 Double_t c12=fC21, c13=fC31, c14=fC41;
499
500 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
501 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
502 fC40-=k00*c04+k01*c14;
503
504 fC11-=k10*c01+k11*fC11;
505 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
506 fC41-=k10*c04+k11*c14;
507
508 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
509 fC42-=k20*c04+k21*c14;
510
511 fC33-=k30*c03+k31*c13;
512 fC43-=k30*c04+k31*c14;
513
514 fC44-=k40*c04+k41*c14;
515
516 return kTRUE;
517}
518
c7bafca9 519void
520AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
521 //--------------------------------------------------------------------
522 // External track parameters -> helix parameters
523 // "b" - magnetic field (kG)
524 //--------------------------------------------------------------------
525 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
526
1530f89c 527 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 528
529 hlx[5]=fX*cs - hlx[0]*sn; // x0
530 hlx[0]=fX*sn + hlx[0]*cs; // y0
531//hlx[1]= // z0
532 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
533//hlx[3]= // tgl
1530f89c 534 hlx[4]=GetC(b); // C
c7bafca9 535}
536
537
538static void Evaluate(const Double_t *h, Double_t t,
539 Double_t r[3], //radius vector
540 Double_t g[3], //first defivatives
541 Double_t gg[3]) //second derivatives
542{
543 //--------------------------------------------------------------------
544 // Calculate position of a point on a track and some derivatives
545 //--------------------------------------------------------------------
546 Double_t phase=h[4]*t+h[2];
547 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
548
549 r[0] = h[5] + (sn - h[6])/h[4];
550 r[1] = h[0] - (cs - h[7])/h[4];
551 r[2] = h[1] + h[3]*t;
552
553 g[0] = cs; g[1]=sn; g[2]=h[3];
554
555 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
556}
557
558Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
559Double_t b, Double_t &xthis, Double_t &xp) const {
560 //------------------------------------------------------------
561 // Returns the (weighed !) distance of closest approach between
562 // this track and the track "p".
563 // Other returned values:
564 // xthis, xt - coordinates of tracks' reference planes at the DCA
565 //-----------------------------------------------------------
566 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
567 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
568 Double_t dx2=dy2;
569
570 //dx2=dy2=dz2=1.;
571
572 Double_t p1[8]; GetHelixParameters(p1,b);
573 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
574 Double_t p2[8]; p->GetHelixParameters(p2,b);
575 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
576
577
578 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
579 Evaluate(p1,t1,r1,g1,gg1);
580 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
581 Evaluate(p2,t2,r2,g2,gg2);
582
583 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
584 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
585
586 Int_t max=27;
587 while (max--) {
588 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
589 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
590 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
591 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
592 (g1[2]*g1[2] - dz*gg1[2])/dz2;
593 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
594 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
595 (g2[2]*g2[2] + dz*gg2[2])/dz2;
596 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
597
598 Double_t det=h11*h22-h12*h12;
599
600 Double_t dt1,dt2;
601 if (TMath::Abs(det)<1.e-33) {
602 //(quasi)singular Hessian
603 dt1=-gt1; dt2=-gt2;
604 } else {
605 dt1=-(gt1*h22 - gt2*h12)/det;
606 dt2=-(h11*gt2 - h12*gt1)/det;
607 }
608
609 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
610
611 //check delta(phase1) ?
612 //check delta(phase2) ?
613
614 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
615 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
616 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
617 AliWarning(" stopped at not a stationary point !");
618 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
619 if (lmb < 0.)
620 AliWarning(" stopped at not a minimum !");
621 break;
622 }
623
624 Double_t dd=dm;
625 for (Int_t div=1 ; ; div*=2) {
626 Evaluate(p1,t1+dt1,r1,g1,gg1);
627 Evaluate(p2,t2+dt2,r2,g2,gg2);
628 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
629 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
630 if (dd<dm) break;
631 dt1*=0.5; dt2*=0.5;
632 if (div>512) {
633 AliWarning(" overshoot !"); break;
634 }
635 }
636 dm=dd;
637
638 t1+=dt1;
639 t2+=dt2;
640
641 }
642
643 if (max<=0) AliWarning(" too many iterations !");
644
645 Double_t cs=TMath::Cos(GetAlpha());
646 Double_t sn=TMath::Sin(GetAlpha());
647 xthis=r1[0]*cs + r1[1]*sn;
648
649 cs=TMath::Cos(p->GetAlpha());
650 sn=TMath::Sin(p->GetAlpha());
651 xp=r2[0]*cs + r2[1]*sn;
652
653 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
654}
655
656Double_t AliExternalTrackParam::
657PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
658 //--------------------------------------------------------------
659 // Propagates this track and the argument track to the position of the
660 // distance of closest approach.
661 // Returns the (weighed !) distance of closest approach.
662 //--------------------------------------------------------------
663 Double_t xthis,xp;
664 Double_t dca=GetDCA(p,b,xthis,xp);
665
666 if (!PropagateTo(xthis,b)) {
667 //AliWarning(" propagation failed !");
668 return 1e+33;
669 }
670
671 if (!p->PropagateTo(xp,b)) {
672 //AliWarning(" propagation failed !";
673 return 1e+33;
674 }
675
676 return dca;
677}
678
679
680
f76701bf 681
682Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
683 //
684 // Try to relate this track to the vertex "vtx",
685 // if the (rough) transverse impact parameter is not bigger then "maxd".
686 // Magnetic field is "b" (kG).
687 //
688 // a) The track gets extapolated to the DCA to the vertex.
689 // b) The impact parameters and their covariance matrix are calculated.
690 //
691 // In the case of success, the returned value is kTRUE
692 // (otherwise, it's kFALSE)
693 //
694 Double_t alpha=GetAlpha();
695 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
696 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
697 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
29fbcc93 698 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
f76701bf 699 x-=xv; y-=yv;
700
701 //Estimate the impact parameter neglecting the track curvature
702 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
703 if (d > maxd) return kFALSE;
704
705 //Propagate to the DCA
706 Double_t crv=0.299792458e-3*b*GetParameter()[4];
707 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
708 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
709
710 x = xv*cs + yv*sn;
711 yv=-xv*sn + yv*cs; xv=x;
712
713 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
29fbcc93 714 return kTRUE;
f76701bf 715}
716
717
718
719
c9ec41e8 720Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
721 //----------------------------------------------------------------
722 // This function performs local->global transformation of the
723 // track momentum.
724 // When called, the arguments are:
725 // p[0] = 1/pt of the track;
726 // p[1] = sine of local azim. angle of the track momentum;
727 // p[2] = tangent of the track momentum dip angle;
728 // alpha - rotation angle.
729 // The result is returned as:
730 // p[0] = px
731 // p[1] = py
732 // p[2] = pz
733 // Results for (nearly) straight tracks are meaningless !
734 //----------------------------------------------------------------
e421f556 735 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
49d13e89 736 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
c9ec41e8 737
738 Double_t pt=1./TMath::Abs(p[0]);
739 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
740 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
741 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
a5e407e9 742
743 return kTRUE;
744}
745
c9ec41e8 746Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
747 //----------------------------------------------------------------
748 // This function performs local->global transformation of the
749 // track position.
750 // When called, the arguments are:
751 // r[0] = local x
752 // r[1] = local y
753 // r[2] = local z
754 // alpha - rotation angle.
755 // The result is returned as:
756 // r[0] = global x
757 // r[1] = global y
758 // r[2] = global z
759 //----------------------------------------------------------------
760 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
761 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
a5e407e9 762
a5e407e9 763 return kTRUE;
51ad6848 764}
765
b1149664 766void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
767 //----------------------------------------------------------------
768 // This function returns a unit vector along the track direction
769 // in the global coordinate system.
770 //----------------------------------------------------------------
771 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
772 Double_t snp=fP[2];
92934324 773 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 774 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
775 d[0]=(csp*cs - snp*sn)/norm;
776 d[1]=(snp*cs + csp*sn)/norm;
777 d[2]=fP[3]/norm;
778}
779
c9ec41e8 780Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
781 //---------------------------------------------------------------------
782 // This function returns the global track momentum components
783 // Results for (nearly) straight tracks are meaningless !
784 //---------------------------------------------------------------------
785 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
786 return Local2GlobalMomentum(p,fAlpha);
787}
a5e407e9 788
c9ec41e8 789Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
790 //---------------------------------------------------------------------
791 // This function returns the global track position
792 //---------------------------------------------------------------------
793 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
794 return Local2GlobalPosition(r,fAlpha);
51ad6848 795}
796
c9ec41e8 797Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
798 //---------------------------------------------------------------------
799 // This function returns the global covariance matrix of the track params
800 //
801 // Cov(x,x) ... : cv[0]
802 // Cov(y,x) ... : cv[1] cv[2]
803 // Cov(z,x) ... : cv[3] cv[4] cv[5]
804 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
805 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
806 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 807 //
c9ec41e8 808 // Results for (nearly) straight tracks are meaningless !
809 //---------------------------------------------------------------------
e421f556 810 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 811 for (Int_t i=0; i<21; i++) cv[i]=0.;
812 return kFALSE;
a5e407e9 813 }
49d13e89 814 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 815 for (Int_t i=0; i<21; i++) cv[i]=0.;
816 return kFALSE;
817 }
818 Double_t pt=1./TMath::Abs(fP[4]);
819 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 820 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 821
822 Double_t m00=-sn, m10=cs;
823 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
824 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
825 Double_t m35=pt, m45=-pt*pt*fP[3];
826
827 cv[0 ] = fC[0]*m00*m00;
828 cv[1 ] = fC[0]*m00*m10;
829 cv[2 ] = fC[0]*m10*m10;
830 cv[3 ] = fC[1]*m00;
831 cv[4 ] = fC[1]*m10;
832 cv[5 ] = fC[2];
833 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
834 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
835 cv[8 ] = fC[4]*m23 + fC[11]*m43;
836 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
837 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
838 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
839 cv[12] = fC[4]*m24 + fC[11]*m44;
840 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
841 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
842 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
843 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
844 cv[17] = fC[7]*m35 + fC[11]*m45;
845 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
846 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
847 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 848
c9ec41e8 849 return kTRUE;
51ad6848 850}
851
51ad6848 852
c9ec41e8 853Bool_t
854AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
855 //---------------------------------------------------------------------
856 // This function returns the global track momentum extrapolated to
857 // the radial position "x" (cm) in the magnetic field "b" (kG)
858 //---------------------------------------------------------------------
c9ec41e8 859 p[0]=fP[4];
1530f89c 860 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 861 p[2]=fP[3];
862 return Local2GlobalMomentum(p,fAlpha);
51ad6848 863}
864
c9ec41e8 865Bool_t
7cf7bb6c 866AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
867 //---------------------------------------------------------------------
868 // This function returns the local Y-coordinate of the intersection
869 // point between this track and the reference plane "x" (cm).
870 // Magnetic field "b" (kG)
871 //---------------------------------------------------------------------
872 Double_t dx=x-fX;
873 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
874
1530f89c 875 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 876
877 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
878 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
879
880 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
881 y = fP[0] + dx*(f1+f2)/(r1+r2);
882 return kTRUE;
883}
884
885Bool_t
6c94f330 886AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
887 //---------------------------------------------------------------------
888 // This function returns the local Z-coordinate of the intersection
889 // point between this track and the reference plane "x" (cm).
890 // Magnetic field "b" (kG)
891 //---------------------------------------------------------------------
892 Double_t dx=x-fX;
893 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
894
895 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
896
897 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
898 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
899
900 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
901 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
902 return kTRUE;
903}
904
905Bool_t
c9ec41e8 906AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
907 //---------------------------------------------------------------------
908 // This function returns the global track position extrapolated to
909 // the radial position "x" (cm) in the magnetic field "b" (kG)
910 //---------------------------------------------------------------------
c9ec41e8 911 Double_t dx=x-fX;
e421f556 912 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
913
1530f89c 914 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 915
e421f556 916 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 917 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 918
919 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
920 r[0] = x;
921 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
6c94f330 922 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
c9ec41e8 923 return Local2GlobalPosition(r,fAlpha);
51ad6848 924}
925
edc97986 926//_____________________________________________________________________________
51ad6848 927void AliExternalTrackParam::Print(Option_t* /*option*/) const
928{
929// print the parameters and the covariance matrix
930
931 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
932 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 933 fP[0], fP[1], fP[2], fP[3], fP[4]);
934 printf(" covariance: %12g\n", fC[0]);
935 printf(" %12g %12g\n", fC[1], fC[2]);
936 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 937 printf(" %12g %12g %12g %12g\n",
c9ec41e8 938 fC[6], fC[7], fC[8], fC[9]);
51ad6848 939 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 940 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 941}
5b77d93c 942
c194ba83 943Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
944 //
945 // Get sinus at given x
946 //
1530f89c 947 Double_t crv=GetC(b);
c194ba83 948 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
949 Double_t dx = x-fX;
950 Double_t res = fP[2]+dx*crv;
951 return res;
952}