]>
Commit | Line | Data |
---|---|---|
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 | /////////////////////////////////////////////////////////////////////////////// |
4b189f98 | 28 | #include <TMatrixDSym.h> |
51ad6848 | 29 | #include "AliExternalTrackParam.h" |
f76701bf | 30 | #include "AliESDVertex.h" |
6c94f330 | 31 | #include "AliLog.h" |
51ad6848 | 32 | |
33 | ClassImp(AliExternalTrackParam) | |
34 | ||
ed5f2849 | 35 | Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; |
36 | ||
51ad6848 | 37 | //_____________________________________________________________________________ |
90e48c0c | 38 | AliExternalTrackParam::AliExternalTrackParam() : |
def9660e | 39 | AliVParticle(), |
90e48c0c | 40 | fX(0), |
c9ec41e8 | 41 | fAlpha(0) |
51ad6848 | 42 | { |
90e48c0c | 43 | // |
44 | // default constructor | |
45 | // | |
c9ec41e8 | 46 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
47 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 48 | } |
49 | ||
6c94f330 | 50 | //_____________________________________________________________________________ |
51 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
def9660e | 52 | AliVParticle(track), |
6c94f330 | 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 | ||
def9660e | 63 | //_____________________________________________________________________________ |
64 | AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar) | |
65 | { | |
66 | // | |
67 | // assignment operator | |
68 | // | |
69 | ||
70 | if (this!=&trkPar) { | |
71 | AliVParticle::operator=(trkPar); | |
72 | fX = trkPar.fX; | |
73 | fAlpha = trkPar.fAlpha; | |
74 | ||
75 | for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i]; | |
76 | for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i]; | |
77 | } | |
78 | ||
79 | return *this; | |
80 | } | |
81 | ||
51ad6848 | 82 | //_____________________________________________________________________________ |
83 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
84 | const Double_t param[5], | |
90e48c0c | 85 | const Double_t covar[15]) : |
def9660e | 86 | AliVParticle(), |
90e48c0c | 87 | fX(x), |
c9ec41e8 | 88 | fAlpha(alpha) |
51ad6848 | 89 | { |
90e48c0c | 90 | // |
91 | // create external track parameters from given arguments | |
92 | // | |
c9ec41e8 | 93 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
94 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 95 | } |
96 | ||
90e48c0c | 97 | //_____________________________________________________________________________ |
6c94f330 | 98 | void AliExternalTrackParam::Set(Double_t x, Double_t alpha, |
99 | const Double_t p[5], const Double_t cov[15]) { | |
c9ec41e8 | 100 | // |
6c94f330 | 101 | // Sets the parameters |
c9ec41e8 | 102 | // |
6c94f330 | 103 | fX=x; |
104 | fAlpha=alpha; | |
105 | for (Int_t i = 0; i < 5; i++) fP[i] = p[i]; | |
106 | for (Int_t i = 0; i < 15; i++) fC[i] = cov[i]; | |
51ad6848 | 107 | } |
108 | ||
109 | //_____________________________________________________________________________ | |
c9ec41e8 | 110 | void AliExternalTrackParam::Reset() { |
1530f89c | 111 | // |
112 | // Resets all the parameters to 0 | |
113 | // | |
c9ec41e8 | 114 | fX=fAlpha=0.; |
115 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
116 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 117 | } |
118 | ||
c9ec41e8 | 119 | Double_t AliExternalTrackParam::GetP() const { |
120 | //--------------------------------------------------------------------- | |
121 | // This function returns the track momentum | |
122 | // Results for (nearly) straight tracks are meaningless ! | |
123 | //--------------------------------------------------------------------- | |
06fb4a2f | 124 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 125 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 126 | } |
127 | ||
1d99986f | 128 | Double_t AliExternalTrackParam::Get1P() const { |
129 | //--------------------------------------------------------------------- | |
130 | // This function returns the 1/(track momentum) | |
131 | //--------------------------------------------------------------------- | |
132 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
133 | } | |
134 | ||
c9ec41e8 | 135 | //_______________________________________________________________________ |
c7bafca9 | 136 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 137 | //------------------------------------------------------------------ |
138 | // This function calculates the transverse impact parameter | |
139 | // with respect to a point with global coordinates (x,y) | |
140 | // in the magnetic field "b" (kG) | |
141 | //------------------------------------------------------------------ | |
5773defd | 142 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 143 | Double_t rp4=GetC(b); |
c9ec41e8 | 144 | |
145 | Double_t xt=fX, yt=fP[0]; | |
146 | ||
147 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
148 | Double_t a = x*cs + y*sn; | |
149 | y = -x*sn + y*cs; x=a; | |
150 | xt-=x; yt-=y; | |
151 | ||
152 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
153 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
1530f89c | 154 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
155 | } | |
156 | ||
157 | //_______________________________________________________________________ | |
158 | void AliExternalTrackParam:: | |
159 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
160 | //------------------------------------------------------------------ | |
161 | // This function calculates the transverse and longitudinal impact parameters | |
162 | // with respect to a point with global coordinates (x,y) | |
163 | // in the magnetic field "b" (kG) | |
164 | //------------------------------------------------------------------ | |
165 | Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1); | |
166 | Double_t xt=fX, yt=fP[0]; | |
167 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
168 | Double_t a = x*cs + y*sn; | |
169 | y = -x*sn + y*cs; x=a; | |
170 | xt-=x; yt-=y; | |
171 | ||
172 | Double_t rp4=GetC(b); | |
173 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
174 | dz[0] = -(xt*f1 - yt*r1); | |
175 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
176 | return; | |
177 | } | |
178 | ||
179 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
180 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
181 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
182 | dz[0] = -a/(1 + rr); | |
183 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2); | |
184 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; | |
51ad6848 | 185 | } |
186 | ||
49d13e89 | 187 | //_______________________________________________________________________ |
188 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
189 | //------------------------------------------------------------------ | |
190 | // This function calculates the transverse impact parameter | |
191 | // with respect to a point with global coordinates (xv,yv) | |
192 | // neglecting the track curvature. | |
193 | //------------------------------------------------------------------ | |
194 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
195 | Double_t x= xv*cs + yv*sn; | |
196 | Double_t y=-xv*sn + yv*cs; | |
197 | ||
198 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
199 | ||
1530f89c | 200 | return -d; |
49d13e89 | 201 | } |
202 | ||
116b445b | 203 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
7dded1d5 | 204 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr, |
205 | Double_t (*Bethe)(Double_t)) { | |
116b445b | 206 | //------------------------------------------------------------------ |
207 | // This function corrects the track parameters for the crossed material. | |
208 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
209 | // "xTimesRho" - is the product length*density (g/cm^2). | |
210 | // "mass" - the mass of this particle (GeV/c^2). | |
211 | //------------------------------------------------------------------ | |
212 | Double_t &fP2=fP[2]; | |
213 | Double_t &fP3=fP[3]; | |
214 | Double_t &fP4=fP[4]; | |
215 | ||
216 | Double_t &fC22=fC[5]; | |
217 | Double_t &fC33=fC[9]; | |
218 | Double_t &fC43=fC[13]; | |
219 | Double_t &fC44=fC[14]; | |
220 | ||
7dded1d5 | 221 | //Apply angle correction, if requested |
222 | if(anglecorr) { | |
223 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
224 | xOverX0 *=angle; | |
225 | xTimesRho *=angle; | |
226 | } | |
227 | ||
116b445b | 228 | Double_t p=GetP(); |
229 | Double_t p2=p*p; | |
230 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 231 | |
232 | //Multiple scattering****************** | |
233 | if (xOverX0 != 0) { | |
234 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
235 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
236 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
237 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
238 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
239 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
240 | } | |
241 | ||
242 | //Energy losses************************ | |
243 | if ((xTimesRho != 0.) && (beta2 < 1.)) { | |
244 | Double_t dE=Bethe(beta2)*xTimesRho; | |
245 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
246 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
247 | fP4*=(1.- e/p2*dE); | |
248 | ||
249 | // Approximate energy loss fluctuation (M.Ivanov) | |
250 | const Double_t knst=0.07; // To be tuned. | |
251 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
252 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); | |
253 | ||
254 | } | |
255 | ||
256 | return kTRUE; | |
257 | } | |
258 | ||
259 | ||
ee5dba5e | 260 | Bool_t AliExternalTrackParam::CorrectForMaterial |
261 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 262 | //------------------------------------------------------------------ |
116b445b | 263 | // Deprecated function ! |
264 | // Better use CorrectForMeanMaterial instead of it. | |
265 | // | |
c7bafca9 | 266 | // This function corrects the track parameters for the crossed material |
267 | // "d" - the thickness (fraction of the radiation length) | |
268 | // "x0" - the radiation length (g/cm^2) | |
269 | // "mass" - the mass of this particle (GeV/c^2) | |
270 | //------------------------------------------------------------------ | |
271 | Double_t &fP2=fP[2]; | |
272 | Double_t &fP3=fP[3]; | |
273 | Double_t &fP4=fP[4]; | |
274 | ||
275 | Double_t &fC22=fC[5]; | |
276 | Double_t &fC33=fC[9]; | |
277 | Double_t &fC43=fC[13]; | |
278 | Double_t &fC44=fC[14]; | |
279 | ||
7b5ef2e6 | 280 | Double_t p=GetP(); |
281 | Double_t p2=p*p; | |
c7bafca9 | 282 | Double_t beta2=p2/(p2 + mass*mass); |
283 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
284 | ||
285 | //Multiple scattering****************** | |
286 | if (d!=0) { | |
287 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
288 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
289 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
290 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
291 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
292 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
293 | } | |
294 | ||
295 | //Energy losses************************ | |
8fc1985d | 296 | if (x0!=0. && beta2<1) { |
c7bafca9 | 297 | d*=x0; |
ee5dba5e | 298 | Double_t dE=Bethe(beta2)*d; |
299 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
ae666100 | 300 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! |
ee5dba5e | 301 | fP4*=(1.- e/p2*dE); |
302 | ||
303 | // Approximate energy loss fluctuation (M.Ivanov) | |
ed5f2849 | 304 | const Double_t knst=0.07; // To be tuned. |
305 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
ee5dba5e | 306 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
307 | ||
c7bafca9 | 308 | } |
309 | ||
310 | return kTRUE; | |
311 | } | |
312 | ||
ee5dba5e | 313 | Double_t ApproximateBetheBloch(Double_t beta2) { |
314 | //------------------------------------------------------------------ | |
315 | // This is an approximation of the Bethe-Bloch formula with | |
316 | // the density effect taken into account at beta*gamma > 3.5 | |
317 | // (the approximation is reasonable only for solid materials) | |
318 | //------------------------------------------------------------------ | |
319 | if (beta2/(1-beta2)>3.5*3.5) | |
320 | return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); | |
321 | ||
322 | return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); | |
323 | } | |
324 | ||
49d13e89 | 325 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
326 | //------------------------------------------------------------------ | |
327 | // Transform this track to the local coord. system rotated | |
328 | // by angle "alpha" (rad) with respect to the global coord. system. | |
329 | //------------------------------------------------------------------ | |
dfcef74c | 330 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
331 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
332 | return kFALSE; | |
333 | } | |
334 | ||
49d13e89 | 335 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
336 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
337 | ||
338 | Double_t &fP0=fP[0]; | |
339 | Double_t &fP2=fP[2]; | |
340 | Double_t &fC00=fC[0]; | |
341 | Double_t &fC10=fC[1]; | |
342 | Double_t &fC20=fC[3]; | |
343 | Double_t &fC21=fC[4]; | |
344 | Double_t &fC22=fC[5]; | |
345 | Double_t &fC30=fC[6]; | |
346 | Double_t &fC32=fC[8]; | |
347 | Double_t &fC40=fC[10]; | |
348 | Double_t &fC42=fC[12]; | |
349 | ||
350 | Double_t x=fX; | |
351 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
352 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
353 | ||
dfcef74c | 354 | Double_t tmp=sf*ca - cf*sa; |
355 | if (TMath::Abs(tmp) >= kAlmost1) return kFALSE; | |
356 | ||
49d13e89 | 357 | fAlpha = alpha; |
358 | fX = x*ca + fP0*sa; | |
359 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 360 | fP2= tmp; |
49d13e89 | 361 | |
06fb4a2f | 362 | if (TMath::Abs(cf)<kAlmost0) { |
363 | AliError(Form("Too small cosine value %f",cf)); | |
364 | cf = kAlmost0; | |
365 | } | |
366 | ||
49d13e89 | 367 | Double_t rr=(ca+sf/cf*sa); |
368 | ||
369 | fC00 *= (ca*ca); | |
370 | fC10 *= ca; | |
371 | fC20 *= ca*rr; | |
372 | fC21 *= rr; | |
373 | fC22 *= rr*rr; | |
374 | fC30 *= ca; | |
375 | fC32 *= rr; | |
376 | fC40 *= ca; | |
377 | fC42 *= rr; | |
378 | ||
379 | return kTRUE; | |
380 | } | |
381 | ||
382 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
383 | //---------------------------------------------------------------- | |
384 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
385 | //---------------------------------------------------------------- | |
49d13e89 | 386 | Double_t dx=xk-fX; |
e421f556 | 387 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 388 | |
1530f89c | 389 | Double_t crv=GetC(b); |
5773defd | 390 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
391 | ||
49d13e89 | 392 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 393 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 394 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
395 | ||
396 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
397 | Double_t | |
398 | &fC00=fC[0], | |
399 | &fC10=fC[1], &fC11=fC[2], | |
400 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
401 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
402 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
403 | ||
404 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
405 | ||
406 | fX=xk; | |
407 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 408 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 409 | fP2 += dx*crv; |
410 | ||
411 | //f = F - 1 | |
412 | ||
413 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
414 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
415 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
416 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
417 | Double_t f13= dx/r1; | |
418 | Double_t f24= dx; f24*=cc; | |
419 | ||
420 | //b = C*ft | |
421 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
422 | Double_t b02=f24*fC40; | |
423 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
424 | Double_t b12=f24*fC41; | |
425 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
426 | Double_t b22=f24*fC42; | |
427 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
428 | Double_t b42=f24*fC44; | |
429 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
430 | Double_t b32=f24*fC43; | |
431 | ||
432 | //a = f*b = f*C*ft | |
433 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
434 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
435 | Double_t a22=f24*b42; | |
436 | ||
437 | //F*C*Ft = C + (b + bt + a) | |
438 | fC00 += b00 + b00 + a00; | |
439 | fC10 += b10 + b01 + a01; | |
440 | fC20 += b20 + b02 + a02; | |
441 | fC30 += b30; | |
442 | fC40 += b40; | |
443 | fC11 += b11 + b11 + a11; | |
444 | fC21 += b21 + b12 + a12; | |
445 | fC31 += b31; | |
446 | fC41 += b41; | |
447 | fC22 += b22 + b22 + a22; | |
448 | fC32 += b32; | |
449 | fC42 += b42; | |
450 | ||
451 | return kTRUE; | |
452 | } | |
453 | ||
052daaff | 454 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
455 | Double_t p[3], Double_t bz) const { | |
456 | //+++++++++++++++++++++++++++++++++++++++++ | |
457 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
458 | // Extrapolate track along simple helix in magnetic field | |
459 | // Arguments: len -distance alogn helix, [cm] | |
460 | // bz - mag field, [kGaus] | |
461 | // Returns: x and p contain extrapolated positon and momentum | |
462 | // The momentum returned for straight-line tracks is meaningless ! | |
463 | //+++++++++++++++++++++++++++++++++++++++++ | |
464 | GetXYZ(x); | |
465 | ||
def9660e | 466 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks |
052daaff | 467 | Double_t unit[3]; GetDirection(unit); |
468 | x[0]+=unit[0]*len; | |
469 | x[1]+=unit[1]*len; | |
470 | x[2]+=unit[2]*len; | |
471 | ||
472 | p[0]=unit[0]/kAlmost0; | |
473 | p[1]=unit[1]/kAlmost0; | |
474 | p[2]=unit[2]/kAlmost0; | |
475 | } else { | |
476 | GetPxPyPz(p); | |
477 | Double_t pp=GetP(); | |
478 | Double_t a = -kB2C*bz*GetSign(); | |
479 | Double_t rho = a/pp; | |
480 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
481 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
482 | x[2] += p[2]*len/pp; | |
483 | ||
484 | Double_t p0=p[0]; | |
485 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
486 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
487 | } | |
488 | } | |
489 | ||
490 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
491 | Double_t bz) const { | |
492 | //+++++++++++++++++++++++++++++++++++++++++ | |
493 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
494 | // Finds point of intersection (if exists) of the helix with the plane. | |
495 | // Stores result in fX and fP. | |
496 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
497 | // and vector, normal to the plane | |
498 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
499 | //+++++++++++++++++++++++++++++++++++++++++ | |
500 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
501 | ||
502 | //estimates initial helix length up to plane | |
503 | Double_t s= | |
504 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
505 | Double_t dist=99999,distPrev=dist; | |
506 | Double_t x[3],p[3]; | |
507 | while(TMath::Abs(dist)>0.00001){ | |
508 | //calculates helix at the distance s from x0 ALONG the helix | |
509 | Propagate(s,x,p,bz); | |
510 | ||
511 | //distance between current helix position and plane | |
512 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
513 | ||
514 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
515 | distPrev=dist; | |
516 | s-=dist; | |
517 | } | |
518 | //on exit pnt is intersection point,norm is track vector at that point, | |
519 | //all in MARS | |
520 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
521 | return kTRUE; | |
522 | } | |
523 | ||
49d13e89 | 524 | Double_t |
525 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
526 | //---------------------------------------------------------------- | |
527 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
528 | //---------------------------------------------------------------- | |
529 | Double_t sdd = fC[0] + cov[0]; | |
530 | Double_t sdz = fC[1] + cov[1]; | |
531 | Double_t szz = fC[2] + cov[2]; | |
532 | Double_t det = sdd*szz - sdz*sdz; | |
533 | ||
534 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
535 | ||
536 | Double_t d = fP[0] - p[0]; | |
537 | Double_t z = fP[1] - p[1]; | |
538 | ||
539 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
540 | } | |
541 | ||
4b189f98 | 542 | Double_t AliExternalTrackParam:: |
543 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
544 | //---------------------------------------------------------------- | |
545 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 546 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 547 | // |
548 | // Cov(x,x) ... : covxyz[0] | |
549 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
550 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
551 | //---------------------------------------------------------------- | |
552 | ||
553 | Double_t res[3] = { | |
554 | GetX() - p[0], | |
555 | GetY() - p[1], | |
556 | GetZ() - p[2] | |
557 | }; | |
558 | ||
559 | Double_t f=GetSnp(); | |
560 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
561 | Double_t r=TMath::Sqrt(1.- f*f); | |
562 | Double_t a=f/r, b=GetTgl()/r; | |
563 | ||
564 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
565 | ||
566 | TMatrixDSym v(3); | |
567 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
568 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
569 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
570 | ||
571 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
572 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
573 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
574 | ||
575 | v.Invert(); | |
576 | if (!v.IsValid()) return kVeryBig; | |
577 | ||
578 | Double_t chi2=0.; | |
579 | for (Int_t i = 0; i < 3; i++) | |
580 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
581 | ||
582 | return chi2; | |
583 | ||
584 | ||
585 | } | |
586 | ||
1e023a36 | 587 | Bool_t AliExternalTrackParam:: |
588 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
589 | //---------------------------------------------------------------- | |
590 | // Propagate this track to the plane | |
591 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
592 | // belongs to. | |
593 | // The magnetic field is "bz" (kG) | |
594 | // | |
595 | // The track curvature and the change of the covariance matrix | |
596 | // of the track parameters are negleted ! | |
597 | // (So the "step" should be small compared with 1/curvature) | |
598 | //---------------------------------------------------------------- | |
599 | ||
600 | Double_t f=GetSnp(); | |
601 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
602 | Double_t r=TMath::Sqrt(1.- f*f); | |
603 | Double_t a=f/r, b=GetTgl()/r; | |
604 | ||
605 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
606 | ||
607 | TMatrixDSym tV(3); | |
608 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
609 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
610 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
611 | ||
612 | TMatrixDSym pV(3); | |
613 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
614 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
615 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
616 | ||
617 | TMatrixDSym tpV(tV); | |
618 | tpV+=pV; | |
619 | tpV.Invert(); | |
620 | if (!tpV.IsValid()) return kFALSE; | |
621 | ||
622 | TMatrixDSym pW(3),tW(3); | |
623 | for (Int_t i=0; i<3; i++) | |
624 | for (Int_t j=0; j<3; j++) { | |
625 | pW(i,j)=tW(i,j)=0.; | |
626 | for (Int_t k=0; k<3; k++) { | |
627 | pW(i,j) += tV(i,k)*tpV(k,j); | |
628 | tW(i,j) += pV(i,k)*tpV(k,j); | |
629 | } | |
630 | } | |
631 | ||
632 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
633 | ||
634 | Double_t x=0.; | |
635 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
636 | Double_t crv=GetC(bz); | |
637 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
638 | f += crv*(x-fX); | |
639 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
640 | fX=x; | |
641 | ||
642 | fP[0]=0.; | |
643 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
644 | fP[1]=0.; | |
645 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
646 | ||
647 | return kTRUE; | |
648 | } | |
649 | ||
49d13e89 | 650 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
651 | //------------------------------------------------------------------ | |
652 | // Update the track parameters with the space point "p" having | |
653 | // the covariance matrix "cov" | |
654 | //------------------------------------------------------------------ | |
655 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
656 | Double_t | |
657 | &fC00=fC[0], | |
658 | &fC10=fC[1], &fC11=fC[2], | |
659 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
660 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
661 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
662 | ||
663 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
664 | r00+=fC00; r01+=fC10; r11+=fC11; | |
665 | Double_t det=r00*r11 - r01*r01; | |
666 | ||
667 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
668 | ||
669 | ||
670 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
671 | ||
672 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
673 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
674 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
675 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
676 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
677 | ||
678 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
679 | Double_t sf=fP2 + k20*dy + k21*dz; | |
680 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
681 | ||
682 | fP0 += k00*dy + k01*dz; | |
683 | fP1 += k10*dy + k11*dz; | |
684 | fP2 = sf; | |
685 | fP3 += k30*dy + k31*dz; | |
686 | fP4 += k40*dy + k41*dz; | |
687 | ||
688 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
689 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
690 | ||
691 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
692 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
693 | fC40-=k00*c04+k01*c14; | |
694 | ||
695 | fC11-=k10*c01+k11*fC11; | |
696 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
697 | fC41-=k10*c04+k11*c14; | |
698 | ||
699 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
700 | fC42-=k20*c04+k21*c14; | |
701 | ||
702 | fC33-=k30*c03+k31*c13; | |
703 | fC43-=k30*c04+k31*c14; | |
704 | ||
705 | fC44-=k40*c04+k41*c14; | |
706 | ||
707 | return kTRUE; | |
708 | } | |
709 | ||
c7bafca9 | 710 | void |
711 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
712 | //-------------------------------------------------------------------- | |
713 | // External track parameters -> helix parameters | |
714 | // "b" - magnetic field (kG) | |
715 | //-------------------------------------------------------------------- | |
716 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
717 | ||
1530f89c | 718 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 719 | |
720 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
721 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
722 | //hlx[1]= // z0 | |
723 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
724 | //hlx[3]= // tgl | |
1530f89c | 725 | hlx[4]=GetC(b); // C |
c7bafca9 | 726 | } |
727 | ||
728 | ||
729 | static void Evaluate(const Double_t *h, Double_t t, | |
730 | Double_t r[3], //radius vector | |
731 | Double_t g[3], //first defivatives | |
732 | Double_t gg[3]) //second derivatives | |
733 | { | |
734 | //-------------------------------------------------------------------- | |
735 | // Calculate position of a point on a track and some derivatives | |
736 | //-------------------------------------------------------------------- | |
737 | Double_t phase=h[4]*t+h[2]; | |
738 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
739 | ||
740 | r[0] = h[5] + (sn - h[6])/h[4]; | |
741 | r[1] = h[0] - (cs - h[7])/h[4]; | |
742 | r[2] = h[1] + h[3]*t; | |
743 | ||
744 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
745 | ||
746 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
747 | } | |
748 | ||
749 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
750 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
751 | //------------------------------------------------------------ | |
752 | // Returns the (weighed !) distance of closest approach between | |
753 | // this track and the track "p". | |
754 | // Other returned values: | |
755 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
756 | //----------------------------------------------------------- | |
757 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
758 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
759 | Double_t dx2=dy2; | |
760 | ||
761 | //dx2=dy2=dz2=1.; | |
762 | ||
763 | Double_t p1[8]; GetHelixParameters(p1,b); | |
764 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
765 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
766 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
767 | ||
768 | ||
769 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
770 | Evaluate(p1,t1,r1,g1,gg1); | |
771 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
772 | Evaluate(p2,t2,r2,g2,gg2); | |
773 | ||
774 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
775 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
776 | ||
777 | Int_t max=27; | |
778 | while (max--) { | |
779 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
780 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
781 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
782 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
783 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
784 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
785 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
786 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
787 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
788 | ||
789 | Double_t det=h11*h22-h12*h12; | |
790 | ||
791 | Double_t dt1,dt2; | |
792 | if (TMath::Abs(det)<1.e-33) { | |
793 | //(quasi)singular Hessian | |
794 | dt1=-gt1; dt2=-gt2; | |
795 | } else { | |
796 | dt1=-(gt1*h22 - gt2*h12)/det; | |
797 | dt2=-(h11*gt2 - h12*gt1)/det; | |
798 | } | |
799 | ||
800 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
801 | ||
802 | //check delta(phase1) ? | |
803 | //check delta(phase2) ? | |
804 | ||
805 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
806 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
807 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
808 | AliWarning(" stopped at not a stationary point !"); | |
809 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); | |
810 | if (lmb < 0.) | |
811 | AliWarning(" stopped at not a minimum !"); | |
812 | break; | |
813 | } | |
814 | ||
815 | Double_t dd=dm; | |
816 | for (Int_t div=1 ; ; div*=2) { | |
817 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
818 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
819 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
820 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
821 | if (dd<dm) break; | |
822 | dt1*=0.5; dt2*=0.5; | |
823 | if (div>512) { | |
824 | AliWarning(" overshoot !"); break; | |
825 | } | |
826 | } | |
827 | dm=dd; | |
828 | ||
829 | t1+=dt1; | |
830 | t2+=dt2; | |
831 | ||
832 | } | |
833 | ||
834 | if (max<=0) AliWarning(" too many iterations !"); | |
835 | ||
836 | Double_t cs=TMath::Cos(GetAlpha()); | |
837 | Double_t sn=TMath::Sin(GetAlpha()); | |
838 | xthis=r1[0]*cs + r1[1]*sn; | |
839 | ||
840 | cs=TMath::Cos(p->GetAlpha()); | |
841 | sn=TMath::Sin(p->GetAlpha()); | |
842 | xp=r2[0]*cs + r2[1]*sn; | |
843 | ||
844 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
845 | } | |
846 | ||
847 | Double_t AliExternalTrackParam:: | |
848 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
849 | //-------------------------------------------------------------- | |
850 | // Propagates this track and the argument track to the position of the | |
851 | // distance of closest approach. | |
852 | // Returns the (weighed !) distance of closest approach. | |
853 | //-------------------------------------------------------------- | |
854 | Double_t xthis,xp; | |
855 | Double_t dca=GetDCA(p,b,xthis,xp); | |
856 | ||
857 | if (!PropagateTo(xthis,b)) { | |
858 | //AliWarning(" propagation failed !"); | |
859 | return 1e+33; | |
860 | } | |
861 | ||
862 | if (!p->PropagateTo(xp,b)) { | |
863 | //AliWarning(" propagation failed !"; | |
864 | return 1e+33; | |
865 | } | |
866 | ||
867 | return dca; | |
868 | } | |
869 | ||
870 | ||
871 | ||
f76701bf | 872 | |
873 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){ | |
874 | // | |
875 | // Try to relate this track to the vertex "vtx", | |
876 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
877 | // Magnetic field is "b" (kG). | |
878 | // | |
879 | // a) The track gets extapolated to the DCA to the vertex. | |
880 | // b) The impact parameters and their covariance matrix are calculated. | |
881 | // | |
882 | // In the case of success, the returned value is kTRUE | |
883 | // (otherwise, it's kFALSE) | |
884 | // | |
885 | Double_t alpha=GetAlpha(); | |
886 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
887 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
888 | Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn; | |
29fbcc93 | 889 | Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs; |
f76701bf | 890 | x-=xv; y-=yv; |
891 | ||
892 | //Estimate the impact parameter neglecting the track curvature | |
893 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
894 | if (d > maxd) return kFALSE; | |
895 | ||
896 | //Propagate to the DCA | |
897 | Double_t crv=0.299792458e-3*b*GetParameter()[4]; | |
898 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); | |
899 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
900 | ||
901 | x = xv*cs + yv*sn; | |
902 | yv=-xv*sn + yv*cs; xv=x; | |
903 | ||
904 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
29fbcc93 | 905 | return kTRUE; |
f76701bf | 906 | } |
907 | ||
908 | ||
909 | ||
910 | ||
c9ec41e8 | 911 | Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) { |
912 | //---------------------------------------------------------------- | |
913 | // This function performs local->global transformation of the | |
914 | // track momentum. | |
915 | // When called, the arguments are: | |
916 | // p[0] = 1/pt of the track; | |
917 | // p[1] = sine of local azim. angle of the track momentum; | |
918 | // p[2] = tangent of the track momentum dip angle; | |
919 | // alpha - rotation angle. | |
920 | // The result is returned as: | |
921 | // p[0] = px | |
922 | // p[1] = py | |
923 | // p[2] = pz | |
924 | // Results for (nearly) straight tracks are meaningless ! | |
925 | //---------------------------------------------------------------- | |
e421f556 | 926 | if (TMath::Abs(p[0])<=kAlmost0) return kFALSE; |
49d13e89 | 927 | if (TMath::Abs(p[1])> kAlmost1) return kFALSE; |
c9ec41e8 | 928 | |
929 | Double_t pt=1./TMath::Abs(p[0]); | |
930 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha); | |
931 | Double_t r=TMath::Sqrt(1 - p[1]*p[1]); | |
932 | p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2]; | |
a5e407e9 | 933 | |
934 | return kTRUE; | |
935 | } | |
936 | ||
c9ec41e8 | 937 | Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) { |
938 | //---------------------------------------------------------------- | |
939 | // This function performs local->global transformation of the | |
940 | // track position. | |
941 | // When called, the arguments are: | |
942 | // r[0] = local x | |
943 | // r[1] = local y | |
944 | // r[2] = local z | |
945 | // alpha - rotation angle. | |
946 | // The result is returned as: | |
947 | // r[0] = global x | |
948 | // r[1] = global y | |
949 | // r[2] = global z | |
950 | //---------------------------------------------------------------- | |
951 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0]; | |
952 | r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs; | |
a5e407e9 | 953 | |
a5e407e9 | 954 | return kTRUE; |
51ad6848 | 955 | } |
956 | ||
b1149664 | 957 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
958 | //---------------------------------------------------------------- | |
959 | // This function returns a unit vector along the track direction | |
960 | // in the global coordinate system. | |
961 | //---------------------------------------------------------------- | |
962 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
963 | Double_t snp=fP[2]; | |
92934324 | 964 | Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp)); |
b1149664 | 965 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
966 | d[0]=(csp*cs - snp*sn)/norm; | |
967 | d[1]=(snp*cs + csp*sn)/norm; | |
968 | d[2]=fP[3]/norm; | |
969 | } | |
970 | ||
c9ec41e8 | 971 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const { |
972 | //--------------------------------------------------------------------- | |
973 | // This function returns the global track momentum components | |
974 | // Results for (nearly) straight tracks are meaningless ! | |
975 | //--------------------------------------------------------------------- | |
976 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
977 | return Local2GlobalMomentum(p,fAlpha); | |
978 | } | |
a5e407e9 | 979 | |
def9660e | 980 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 981 | //--------------------------------------------------------------------- |
982 | // Returns x-component of momentum | |
983 | // Result for (nearly) straight tracks is meaningless ! | |
984 | //--------------------------------------------------------------------- | |
def9660e | 985 | |
957fb479 | 986 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 987 | GetPxPyPz(p); |
988 | ||
989 | return p[0]; | |
990 | } | |
991 | ||
992 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 993 | //--------------------------------------------------------------------- |
994 | // Returns y-component of momentum | |
995 | // Result for (nearly) straight tracks is meaningless ! | |
996 | //--------------------------------------------------------------------- | |
def9660e | 997 | |
957fb479 | 998 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 999 | GetPxPyPz(p); |
1000 | ||
1001 | return p[1]; | |
1002 | } | |
1003 | ||
1004 | Double_t AliExternalTrackParam::Pz() const { | |
957fb479 | 1005 | //--------------------------------------------------------------------- |
1006 | // Returns z-component of momentum | |
1007 | // Result for (nearly) straight tracks is meaningless ! | |
1008 | //--------------------------------------------------------------------- | |
def9660e | 1009 | |
957fb479 | 1010 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1011 | GetPxPyPz(p); |
1012 | ||
1013 | return p[2]; | |
1014 | } | |
1015 | ||
1016 | Double_t AliExternalTrackParam::Theta() const { | |
1017 | // return theta angle of momentum | |
1018 | ||
7cdd0c20 | 1019 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1020 | } |
1021 | ||
1022 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1023 | //--------------------------------------------------------------------- |
1024 | // Returns the azimuthal angle of momentum | |
1025 | // 0 <= phi < 2*pi | |
1026 | //--------------------------------------------------------------------- | |
def9660e | 1027 | |
957fb479 | 1028 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1029 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1030 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1031 | ||
1032 | return phi; | |
def9660e | 1033 | } |
1034 | ||
1035 | Double_t AliExternalTrackParam::M() const { | |
1036 | // return particle mass | |
1037 | ||
1038 | // No mass information available so far. | |
1039 | // Redifine in derived class! | |
1040 | ||
1041 | return -999.; | |
1042 | } | |
1043 | ||
1044 | Double_t AliExternalTrackParam::E() const { | |
1045 | // return particle energy | |
1046 | ||
1047 | // No PID information available so far. | |
1048 | // Redifine in derived class! | |
1049 | ||
1050 | return -999.; | |
1051 | } | |
1052 | ||
1053 | Double_t AliExternalTrackParam::Eta() const { | |
1054 | // return pseudorapidity | |
1055 | ||
1056 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1057 | } | |
1058 | ||
1059 | Double_t AliExternalTrackParam::Y() const { | |
1060 | // return rapidity | |
1061 | ||
1062 | // No PID information available so far. | |
1063 | // Redifine in derived class! | |
1064 | ||
1065 | return -999.; | |
1066 | } | |
1067 | ||
c9ec41e8 | 1068 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1069 | //--------------------------------------------------------------------- | |
1070 | // This function returns the global track position | |
1071 | //--------------------------------------------------------------------- | |
1072 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1073 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1074 | } |
1075 | ||
c9ec41e8 | 1076 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1077 | //--------------------------------------------------------------------- | |
1078 | // This function returns the global covariance matrix of the track params | |
1079 | // | |
1080 | // Cov(x,x) ... : cv[0] | |
1081 | // Cov(y,x) ... : cv[1] cv[2] | |
1082 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1083 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1084 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1085 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1086 | // |
c9ec41e8 | 1087 | // Results for (nearly) straight tracks are meaningless ! |
1088 | //--------------------------------------------------------------------- | |
e421f556 | 1089 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1090 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1091 | return kFALSE; | |
a5e407e9 | 1092 | } |
49d13e89 | 1093 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1094 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1095 | return kFALSE; | |
1096 | } | |
1097 | Double_t pt=1./TMath::Abs(fP[4]); | |
1098 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1099 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1100 | |
1101 | Double_t m00=-sn, m10=cs; | |
1102 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1103 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1104 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1105 | ||
854d5d49 | 1106 | m43*=GetSign(); |
1107 | m44*=GetSign(); | |
1108 | m45*=GetSign(); | |
1109 | ||
c9ec41e8 | 1110 | cv[0 ] = fC[0]*m00*m00; |
1111 | cv[1 ] = fC[0]*m00*m10; | |
1112 | cv[2 ] = fC[0]*m10*m10; | |
1113 | cv[3 ] = fC[1]*m00; | |
1114 | cv[4 ] = fC[1]*m10; | |
1115 | cv[5 ] = fC[2]; | |
1116 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1117 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1118 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1119 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1120 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1121 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1122 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1123 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1124 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1125 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1126 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1127 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1128 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1129 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1130 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1131 | |
c9ec41e8 | 1132 | return kTRUE; |
51ad6848 | 1133 | } |
1134 | ||
51ad6848 | 1135 | |
c9ec41e8 | 1136 | Bool_t |
1137 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1138 | //--------------------------------------------------------------------- | |
1139 | // This function returns the global track momentum extrapolated to | |
1140 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1141 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1142 | p[0]=fP[4]; |
1530f89c | 1143 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1144 | p[2]=fP[3]; |
1145 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1146 | } |
1147 | ||
7cf7bb6c | 1148 | Bool_t |
1149 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1150 | //--------------------------------------------------------------------- | |
1151 | // This function returns the local Y-coordinate of the intersection | |
1152 | // point between this track and the reference plane "x" (cm). | |
1153 | // Magnetic field "b" (kG) | |
1154 | //--------------------------------------------------------------------- | |
1155 | Double_t dx=x-fX; | |
1156 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1157 | ||
1530f89c | 1158 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1159 | |
1160 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1161 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1162 | ||
1163 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1164 | y = fP[0] + dx*(f1+f2)/(r1+r2); | |
1165 | return kTRUE; | |
1166 | } | |
1167 | ||
6c94f330 | 1168 | Bool_t |
1169 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1170 | //--------------------------------------------------------------------- | |
1171 | // This function returns the local Z-coordinate of the intersection | |
1172 | // point between this track and the reference plane "x" (cm). | |
1173 | // Magnetic field "b" (kG) | |
1174 | //--------------------------------------------------------------------- | |
1175 | Double_t dx=x-fX; | |
1176 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1177 | ||
1178 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; | |
1179 | ||
1180 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1181 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1182 | ||
1183 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); | |
1184 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! | |
1185 | return kTRUE; | |
1186 | } | |
1187 | ||
c9ec41e8 | 1188 | Bool_t |
1189 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1190 | //--------------------------------------------------------------------- | |
1191 | // This function returns the global track position extrapolated to | |
1192 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1193 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1194 | Double_t dx=x-fX; |
e421f556 | 1195 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1196 | ||
1530f89c | 1197 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1198 | |
e421f556 | 1199 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1200 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1201 | |
1202 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1203 | r[0] = x; | |
1204 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
6c94f330 | 1205 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; |
c9ec41e8 | 1206 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1207 | } |
1208 | ||
51ad6848 | 1209 | //_____________________________________________________________________________ |
1210 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1211 | { | |
1212 | // print the parameters and the covariance matrix | |
1213 | ||
1214 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1215 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1216 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1217 | printf(" covariance: %12g\n", fC[0]); | |
1218 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1219 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1220 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1221 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1222 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1223 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1224 | } |
5b77d93c | 1225 | |
c194ba83 | 1226 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1227 | // | |
1228 | // Get sinus at given x | |
1229 | // | |
1530f89c | 1230 | Double_t crv=GetC(b); |
c194ba83 | 1231 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1232 | Double_t dx = x-fX; | |
1233 | Double_t res = fP[2]+dx*crv; | |
1234 | return res; | |
1235 | } | |
bf00ebb8 | 1236 | |
1237 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1238 | //------------------------------------------------------------------------ | |
1239 | // Get the distance between two tracks at the local position x | |
1240 | // working in the local frame of this track. | |
1241 | // Origin : Marian.Ivanov@cern.ch | |
1242 | //----------------------------------------------------------------------- | |
1243 | Double_t xyz[3]; | |
1244 | Double_t xyz2[3]; | |
1245 | xyz[0]=x; | |
1246 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1247 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1248 | // | |
1249 | // | |
1250 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1251 | xyz2[0]=x; | |
1252 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1253 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1254 | }else{ | |
1255 | // | |
1256 | Double_t xyz1[3]; | |
1257 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1258 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1259 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1260 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1261 | // | |
1262 | xyz1[0]=xyz2[0]; | |
1263 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1264 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1265 | // | |
1266 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1267 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1268 | xyz2[2] = xyz1[2]; | |
1269 | } | |
1270 | dist[0] = xyz[0]-xyz2[0]; | |
1271 | dist[1] = xyz[1]-xyz2[1]; | |
1272 | dist[2] = xyz[2]-xyz2[2]; | |
1273 | ||
1274 | return kTRUE; | |
1275 | } |