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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 | /////////////////////////////////////////////////////////////////////////////// |
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 |
204 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
205 | Double_t (*Bethe)(Double_t)) { | |
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 | ||
221 | Double_t p=GetP(); | |
222 | Double_t p2=p*p; | |
223 | Double_t beta2=p2/(p2 + mass*mass); | |
224 | xOverX0*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
225 | ||
226 | //Multiple scattering****************** | |
227 | if (xOverX0 != 0) { | |
228 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
229 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
230 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
231 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
232 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
233 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
234 | } | |
235 | ||
236 | //Energy losses************************ | |
237 | if ((xTimesRho != 0.) && (beta2 < 1.)) { | |
238 | Double_t dE=Bethe(beta2)*xTimesRho; | |
239 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
240 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
241 | fP4*=(1.- e/p2*dE); | |
242 | ||
243 | // Approximate energy loss fluctuation (M.Ivanov) | |
244 | const Double_t knst=0.07; // To be tuned. | |
245 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
246 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); | |
247 | ||
248 | } | |
249 | ||
250 | return kTRUE; | |
251 | } | |
252 | ||
253 | ||
ee5dba5e | 254 | Bool_t AliExternalTrackParam::CorrectForMaterial |
255 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 256 | //------------------------------------------------------------------ |
116b445b | 257 | // Deprecated function ! |
258 | // Better use CorrectForMeanMaterial instead of it. | |
259 | // | |
c7bafca9 | 260 | // This function corrects the track parameters for the crossed material |
261 | // "d" - the thickness (fraction of the radiation length) | |
262 | // "x0" - the radiation length (g/cm^2) | |
263 | // "mass" - the mass of this particle (GeV/c^2) | |
264 | //------------------------------------------------------------------ | |
265 | Double_t &fP2=fP[2]; | |
266 | Double_t &fP3=fP[3]; | |
267 | Double_t &fP4=fP[4]; | |
268 | ||
269 | Double_t &fC22=fC[5]; | |
270 | Double_t &fC33=fC[9]; | |
271 | Double_t &fC43=fC[13]; | |
272 | Double_t &fC44=fC[14]; | |
273 | ||
7b5ef2e6 | 274 | Double_t p=GetP(); |
275 | Double_t p2=p*p; | |
c7bafca9 | 276 | Double_t beta2=p2/(p2 + mass*mass); |
277 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
278 | ||
279 | //Multiple scattering****************** | |
280 | if (d!=0) { | |
281 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
282 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
283 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
284 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
285 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
286 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
287 | } | |
288 | ||
289 | //Energy losses************************ | |
8fc1985d | 290 | if (x0!=0. && beta2<1) { |
c7bafca9 | 291 | d*=x0; |
ee5dba5e | 292 | Double_t dE=Bethe(beta2)*d; |
293 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
ae666100 | 294 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! |
ee5dba5e | 295 | fP4*=(1.- e/p2*dE); |
296 | ||
297 | // Approximate energy loss fluctuation (M.Ivanov) | |
ed5f2849 | 298 | const Double_t knst=0.07; // To be tuned. |
299 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
ee5dba5e | 300 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
301 | ||
c7bafca9 | 302 | } |
303 | ||
304 | return kTRUE; | |
305 | } | |
306 | ||
ee5dba5e | 307 | Double_t ApproximateBetheBloch(Double_t beta2) { |
308 | //------------------------------------------------------------------ | |
309 | // This is an approximation of the Bethe-Bloch formula with | |
310 | // the density effect taken into account at beta*gamma > 3.5 | |
311 | // (the approximation is reasonable only for solid materials) | |
312 | //------------------------------------------------------------------ | |
313 | if (beta2/(1-beta2)>3.5*3.5) | |
314 | return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); | |
315 | ||
316 | return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); | |
317 | } | |
318 | ||
49d13e89 | 319 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
320 | //------------------------------------------------------------------ | |
321 | // Transform this track to the local coord. system rotated | |
322 | // by angle "alpha" (rad) with respect to the global coord. system. | |
323 | //------------------------------------------------------------------ | |
dfcef74c | 324 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
325 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
326 | return kFALSE; | |
327 | } | |
328 | ||
49d13e89 | 329 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
330 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
331 | ||
332 | Double_t &fP0=fP[0]; | |
333 | Double_t &fP2=fP[2]; | |
334 | Double_t &fC00=fC[0]; | |
335 | Double_t &fC10=fC[1]; | |
336 | Double_t &fC20=fC[3]; | |
337 | Double_t &fC21=fC[4]; | |
338 | Double_t &fC22=fC[5]; | |
339 | Double_t &fC30=fC[6]; | |
340 | Double_t &fC32=fC[8]; | |
341 | Double_t &fC40=fC[10]; | |
342 | Double_t &fC42=fC[12]; | |
343 | ||
344 | Double_t x=fX; | |
345 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
346 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
347 | ||
dfcef74c | 348 | Double_t tmp=sf*ca - cf*sa; |
349 | if (TMath::Abs(tmp) >= kAlmost1) return kFALSE; | |
350 | ||
49d13e89 | 351 | fAlpha = alpha; |
352 | fX = x*ca + fP0*sa; | |
353 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 354 | fP2= tmp; |
49d13e89 | 355 | |
06fb4a2f | 356 | if (TMath::Abs(cf)<kAlmost0) { |
357 | AliError(Form("Too small cosine value %f",cf)); | |
358 | cf = kAlmost0; | |
359 | } | |
360 | ||
49d13e89 | 361 | Double_t rr=(ca+sf/cf*sa); |
362 | ||
363 | fC00 *= (ca*ca); | |
364 | fC10 *= ca; | |
365 | fC20 *= ca*rr; | |
366 | fC21 *= rr; | |
367 | fC22 *= rr*rr; | |
368 | fC30 *= ca; | |
369 | fC32 *= rr; | |
370 | fC40 *= ca; | |
371 | fC42 *= rr; | |
372 | ||
373 | return kTRUE; | |
374 | } | |
375 | ||
376 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
377 | //---------------------------------------------------------------- | |
378 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
379 | //---------------------------------------------------------------- | |
49d13e89 | 380 | Double_t dx=xk-fX; |
e421f556 | 381 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 382 | |
1530f89c | 383 | Double_t crv=GetC(b); |
5773defd | 384 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
385 | ||
49d13e89 | 386 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 387 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 388 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
389 | ||
390 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
391 | Double_t | |
392 | &fC00=fC[0], | |
393 | &fC10=fC[1], &fC11=fC[2], | |
394 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
395 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
396 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
397 | ||
398 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
399 | ||
400 | fX=xk; | |
401 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 402 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 403 | fP2 += dx*crv; |
404 | ||
405 | //f = F - 1 | |
406 | ||
407 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
408 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
409 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
410 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
411 | Double_t f13= dx/r1; | |
412 | Double_t f24= dx; f24*=cc; | |
413 | ||
414 | //b = C*ft | |
415 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
416 | Double_t b02=f24*fC40; | |
417 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
418 | Double_t b12=f24*fC41; | |
419 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
420 | Double_t b22=f24*fC42; | |
421 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
422 | Double_t b42=f24*fC44; | |
423 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
424 | Double_t b32=f24*fC43; | |
425 | ||
426 | //a = f*b = f*C*ft | |
427 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
428 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
429 | Double_t a22=f24*b42; | |
430 | ||
431 | //F*C*Ft = C + (b + bt + a) | |
432 | fC00 += b00 + b00 + a00; | |
433 | fC10 += b10 + b01 + a01; | |
434 | fC20 += b20 + b02 + a02; | |
435 | fC30 += b30; | |
436 | fC40 += b40; | |
437 | fC11 += b11 + b11 + a11; | |
438 | fC21 += b21 + b12 + a12; | |
439 | fC31 += b31; | |
440 | fC41 += b41; | |
441 | fC22 += b22 + b22 + a22; | |
442 | fC32 += b32; | |
443 | fC42 += b42; | |
444 | ||
445 | return kTRUE; | |
446 | } | |
447 | ||
052daaff | 448 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
449 | Double_t p[3], Double_t bz) const { | |
450 | //+++++++++++++++++++++++++++++++++++++++++ | |
451 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
452 | // Extrapolate track along simple helix in magnetic field | |
453 | // Arguments: len -distance alogn helix, [cm] | |
454 | // bz - mag field, [kGaus] | |
455 | // Returns: x and p contain extrapolated positon and momentum | |
456 | // The momentum returned for straight-line tracks is meaningless ! | |
457 | //+++++++++++++++++++++++++++++++++++++++++ | |
458 | GetXYZ(x); | |
459 | ||
def9660e | 460 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks |
052daaff | 461 | Double_t unit[3]; GetDirection(unit); |
462 | x[0]+=unit[0]*len; | |
463 | x[1]+=unit[1]*len; | |
464 | x[2]+=unit[2]*len; | |
465 | ||
466 | p[0]=unit[0]/kAlmost0; | |
467 | p[1]=unit[1]/kAlmost0; | |
468 | p[2]=unit[2]/kAlmost0; | |
469 | } else { | |
470 | GetPxPyPz(p); | |
471 | Double_t pp=GetP(); | |
472 | Double_t a = -kB2C*bz*GetSign(); | |
473 | Double_t rho = a/pp; | |
474 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
475 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
476 | x[2] += p[2]*len/pp; | |
477 | ||
478 | Double_t p0=p[0]; | |
479 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
480 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
481 | } | |
482 | } | |
483 | ||
484 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
485 | Double_t bz) const { | |
486 | //+++++++++++++++++++++++++++++++++++++++++ | |
487 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
488 | // Finds point of intersection (if exists) of the helix with the plane. | |
489 | // Stores result in fX and fP. | |
490 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
491 | // and vector, normal to the plane | |
492 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
493 | //+++++++++++++++++++++++++++++++++++++++++ | |
494 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
495 | ||
496 | //estimates initial helix length up to plane | |
497 | Double_t s= | |
498 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
499 | Double_t dist=99999,distPrev=dist; | |
500 | Double_t x[3],p[3]; | |
501 | while(TMath::Abs(dist)>0.00001){ | |
502 | //calculates helix at the distance s from x0 ALONG the helix | |
503 | Propagate(s,x,p,bz); | |
504 | ||
505 | //distance between current helix position and plane | |
506 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
507 | ||
508 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
509 | distPrev=dist; | |
510 | s-=dist; | |
511 | } | |
512 | //on exit pnt is intersection point,norm is track vector at that point, | |
513 | //all in MARS | |
514 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
515 | return kTRUE; | |
516 | } | |
517 | ||
49d13e89 | 518 | Double_t |
519 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
520 | //---------------------------------------------------------------- | |
521 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
522 | //---------------------------------------------------------------- | |
523 | Double_t sdd = fC[0] + cov[0]; | |
524 | Double_t sdz = fC[1] + cov[1]; | |
525 | Double_t szz = fC[2] + cov[2]; | |
526 | Double_t det = sdd*szz - sdz*sdz; | |
527 | ||
528 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
529 | ||
530 | Double_t d = fP[0] - p[0]; | |
531 | Double_t z = fP[1] - p[1]; | |
532 | ||
533 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
534 | } | |
535 | ||
4b189f98 | 536 | Double_t AliExternalTrackParam:: |
537 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
538 | //---------------------------------------------------------------- | |
539 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 540 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 541 | // |
542 | // Cov(x,x) ... : covxyz[0] | |
543 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
544 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
545 | //---------------------------------------------------------------- | |
546 | ||
547 | Double_t res[3] = { | |
548 | GetX() - p[0], | |
549 | GetY() - p[1], | |
550 | GetZ() - p[2] | |
551 | }; | |
552 | ||
553 | Double_t f=GetSnp(); | |
554 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
555 | Double_t r=TMath::Sqrt(1.- f*f); | |
556 | Double_t a=f/r, b=GetTgl()/r; | |
557 | ||
558 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
559 | ||
560 | TMatrixDSym v(3); | |
561 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
562 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
563 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
564 | ||
565 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
566 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
567 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
568 | ||
569 | v.Invert(); | |
570 | if (!v.IsValid()) return kVeryBig; | |
571 | ||
572 | Double_t chi2=0.; | |
573 | for (Int_t i = 0; i < 3; i++) | |
574 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
575 | ||
576 | return chi2; | |
577 | ||
578 | ||
579 | } | |
580 | ||
1e023a36 | 581 | Bool_t AliExternalTrackParam:: |
582 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
583 | //---------------------------------------------------------------- | |
584 | // Propagate this track to the plane | |
585 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
586 | // belongs to. | |
587 | // The magnetic field is "bz" (kG) | |
588 | // | |
589 | // The track curvature and the change of the covariance matrix | |
590 | // of the track parameters are negleted ! | |
591 | // (So the "step" should be small compared with 1/curvature) | |
592 | //---------------------------------------------------------------- | |
593 | ||
594 | Double_t f=GetSnp(); | |
595 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
596 | Double_t r=TMath::Sqrt(1.- f*f); | |
597 | Double_t a=f/r, b=GetTgl()/r; | |
598 | ||
599 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
600 | ||
601 | TMatrixDSym tV(3); | |
602 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
603 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
604 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
605 | ||
606 | TMatrixDSym pV(3); | |
607 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
608 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
609 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
610 | ||
611 | TMatrixDSym tpV(tV); | |
612 | tpV+=pV; | |
613 | tpV.Invert(); | |
614 | if (!tpV.IsValid()) return kFALSE; | |
615 | ||
616 | TMatrixDSym pW(3),tW(3); | |
617 | for (Int_t i=0; i<3; i++) | |
618 | for (Int_t j=0; j<3; j++) { | |
619 | pW(i,j)=tW(i,j)=0.; | |
620 | for (Int_t k=0; k<3; k++) { | |
621 | pW(i,j) += tV(i,k)*tpV(k,j); | |
622 | tW(i,j) += pV(i,k)*tpV(k,j); | |
623 | } | |
624 | } | |
625 | ||
626 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
627 | ||
628 | Double_t x=0.; | |
629 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
630 | Double_t crv=GetC(bz); | |
631 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
632 | f += crv*(x-fX); | |
633 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
634 | fX=x; | |
635 | ||
636 | fP[0]=0.; | |
637 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
638 | fP[1]=0.; | |
639 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
640 | ||
641 | return kTRUE; | |
642 | } | |
643 | ||
49d13e89 | 644 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
645 | //------------------------------------------------------------------ | |
646 | // Update the track parameters with the space point "p" having | |
647 | // the covariance matrix "cov" | |
648 | //------------------------------------------------------------------ | |
649 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
650 | Double_t | |
651 | &fC00=fC[0], | |
652 | &fC10=fC[1], &fC11=fC[2], | |
653 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
654 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
655 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
656 | ||
657 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
658 | r00+=fC00; r01+=fC10; r11+=fC11; | |
659 | Double_t det=r00*r11 - r01*r01; | |
660 | ||
661 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
662 | ||
663 | ||
664 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
665 | ||
666 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
667 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
668 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
669 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
670 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
671 | ||
672 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
673 | Double_t sf=fP2 + k20*dy + k21*dz; | |
674 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
675 | ||
676 | fP0 += k00*dy + k01*dz; | |
677 | fP1 += k10*dy + k11*dz; | |
678 | fP2 = sf; | |
679 | fP3 += k30*dy + k31*dz; | |
680 | fP4 += k40*dy + k41*dz; | |
681 | ||
682 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
683 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
684 | ||
685 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
686 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
687 | fC40-=k00*c04+k01*c14; | |
688 | ||
689 | fC11-=k10*c01+k11*fC11; | |
690 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
691 | fC41-=k10*c04+k11*c14; | |
692 | ||
693 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
694 | fC42-=k20*c04+k21*c14; | |
695 | ||
696 | fC33-=k30*c03+k31*c13; | |
697 | fC43-=k30*c04+k31*c14; | |
698 | ||
699 | fC44-=k40*c04+k41*c14; | |
700 | ||
701 | return kTRUE; | |
702 | } | |
703 | ||
c7bafca9 | 704 | void |
705 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
706 | //-------------------------------------------------------------------- | |
707 | // External track parameters -> helix parameters | |
708 | // "b" - magnetic field (kG) | |
709 | //-------------------------------------------------------------------- | |
710 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
711 | ||
1530f89c | 712 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 713 | |
714 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
715 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
716 | //hlx[1]= // z0 | |
717 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
718 | //hlx[3]= // tgl | |
1530f89c | 719 | hlx[4]=GetC(b); // C |
c7bafca9 | 720 | } |
721 | ||
722 | ||
723 | static void Evaluate(const Double_t *h, Double_t t, | |
724 | Double_t r[3], //radius vector | |
725 | Double_t g[3], //first defivatives | |
726 | Double_t gg[3]) //second derivatives | |
727 | { | |
728 | //-------------------------------------------------------------------- | |
729 | // Calculate position of a point on a track and some derivatives | |
730 | //-------------------------------------------------------------------- | |
731 | Double_t phase=h[4]*t+h[2]; | |
732 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
733 | ||
734 | r[0] = h[5] + (sn - h[6])/h[4]; | |
735 | r[1] = h[0] - (cs - h[7])/h[4]; | |
736 | r[2] = h[1] + h[3]*t; | |
737 | ||
738 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
739 | ||
740 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
741 | } | |
742 | ||
743 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
744 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
745 | //------------------------------------------------------------ | |
746 | // Returns the (weighed !) distance of closest approach between | |
747 | // this track and the track "p". | |
748 | // Other returned values: | |
749 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
750 | //----------------------------------------------------------- | |
751 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
752 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
753 | Double_t dx2=dy2; | |
754 | ||
755 | //dx2=dy2=dz2=1.; | |
756 | ||
757 | Double_t p1[8]; GetHelixParameters(p1,b); | |
758 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
759 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
760 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
761 | ||
762 | ||
763 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
764 | Evaluate(p1,t1,r1,g1,gg1); | |
765 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
766 | Evaluate(p2,t2,r2,g2,gg2); | |
767 | ||
768 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
769 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
770 | ||
771 | Int_t max=27; | |
772 | while (max--) { | |
773 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
774 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
775 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
776 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
777 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
778 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
779 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
780 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
781 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
782 | ||
783 | Double_t det=h11*h22-h12*h12; | |
784 | ||
785 | Double_t dt1,dt2; | |
786 | if (TMath::Abs(det)<1.e-33) { | |
787 | //(quasi)singular Hessian | |
788 | dt1=-gt1; dt2=-gt2; | |
789 | } else { | |
790 | dt1=-(gt1*h22 - gt2*h12)/det; | |
791 | dt2=-(h11*gt2 - h12*gt1)/det; | |
792 | } | |
793 | ||
794 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
795 | ||
796 | //check delta(phase1) ? | |
797 | //check delta(phase2) ? | |
798 | ||
799 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
800 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
801 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
802 | AliWarning(" stopped at not a stationary point !"); | |
803 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); | |
804 | if (lmb < 0.) | |
805 | AliWarning(" stopped at not a minimum !"); | |
806 | break; | |
807 | } | |
808 | ||
809 | Double_t dd=dm; | |
810 | for (Int_t div=1 ; ; div*=2) { | |
811 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
812 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
813 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
814 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
815 | if (dd<dm) break; | |
816 | dt1*=0.5; dt2*=0.5; | |
817 | if (div>512) { | |
818 | AliWarning(" overshoot !"); break; | |
819 | } | |
820 | } | |
821 | dm=dd; | |
822 | ||
823 | t1+=dt1; | |
824 | t2+=dt2; | |
825 | ||
826 | } | |
827 | ||
828 | if (max<=0) AliWarning(" too many iterations !"); | |
829 | ||
830 | Double_t cs=TMath::Cos(GetAlpha()); | |
831 | Double_t sn=TMath::Sin(GetAlpha()); | |
832 | xthis=r1[0]*cs + r1[1]*sn; | |
833 | ||
834 | cs=TMath::Cos(p->GetAlpha()); | |
835 | sn=TMath::Sin(p->GetAlpha()); | |
836 | xp=r2[0]*cs + r2[1]*sn; | |
837 | ||
838 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
839 | } | |
840 | ||
841 | Double_t AliExternalTrackParam:: | |
842 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
843 | //-------------------------------------------------------------- | |
844 | // Propagates this track and the argument track to the position of the | |
845 | // distance of closest approach. | |
846 | // Returns the (weighed !) distance of closest approach. | |
847 | //-------------------------------------------------------------- | |
848 | Double_t xthis,xp; | |
849 | Double_t dca=GetDCA(p,b,xthis,xp); | |
850 | ||
851 | if (!PropagateTo(xthis,b)) { | |
852 | //AliWarning(" propagation failed !"); | |
853 | return 1e+33; | |
854 | } | |
855 | ||
856 | if (!p->PropagateTo(xp,b)) { | |
857 | //AliWarning(" propagation failed !"; | |
858 | return 1e+33; | |
859 | } | |
860 | ||
861 | return dca; | |
862 | } | |
863 | ||
864 | ||
865 | ||
f76701bf | 866 | |
867 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){ | |
868 | // | |
869 | // Try to relate this track to the vertex "vtx", | |
870 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
871 | // Magnetic field is "b" (kG). | |
872 | // | |
873 | // a) The track gets extapolated to the DCA to the vertex. | |
874 | // b) The impact parameters and their covariance matrix are calculated. | |
875 | // | |
876 | // In the case of success, the returned value is kTRUE | |
877 | // (otherwise, it's kFALSE) | |
878 | // | |
879 | Double_t alpha=GetAlpha(); | |
880 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
881 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
882 | Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn; | |
29fbcc93 | 883 | Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs; |
f76701bf | 884 | x-=xv; y-=yv; |
885 | ||
886 | //Estimate the impact parameter neglecting the track curvature | |
887 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
888 | if (d > maxd) return kFALSE; | |
889 | ||
890 | //Propagate to the DCA | |
891 | Double_t crv=0.299792458e-3*b*GetParameter()[4]; | |
892 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); | |
893 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
894 | ||
895 | x = xv*cs + yv*sn; | |
896 | yv=-xv*sn + yv*cs; xv=x; | |
897 | ||
898 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
29fbcc93 | 899 | return kTRUE; |
f76701bf | 900 | } |
901 | ||
902 | ||
903 | ||
904 | ||
c9ec41e8 | 905 | Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) { |
906 | //---------------------------------------------------------------- | |
907 | // This function performs local->global transformation of the | |
908 | // track momentum. | |
909 | // When called, the arguments are: | |
910 | // p[0] = 1/pt of the track; | |
911 | // p[1] = sine of local azim. angle of the track momentum; | |
912 | // p[2] = tangent of the track momentum dip angle; | |
913 | // alpha - rotation angle. | |
914 | // The result is returned as: | |
915 | // p[0] = px | |
916 | // p[1] = py | |
917 | // p[2] = pz | |
918 | // Results for (nearly) straight tracks are meaningless ! | |
919 | //---------------------------------------------------------------- | |
e421f556 | 920 | if (TMath::Abs(p[0])<=kAlmost0) return kFALSE; |
49d13e89 | 921 | if (TMath::Abs(p[1])> kAlmost1) return kFALSE; |
c9ec41e8 | 922 | |
923 | Double_t pt=1./TMath::Abs(p[0]); | |
924 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha); | |
925 | Double_t r=TMath::Sqrt(1 - p[1]*p[1]); | |
926 | p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2]; | |
a5e407e9 | 927 | |
928 | return kTRUE; | |
929 | } | |
930 | ||
c9ec41e8 | 931 | Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) { |
932 | //---------------------------------------------------------------- | |
933 | // This function performs local->global transformation of the | |
934 | // track position. | |
935 | // When called, the arguments are: | |
936 | // r[0] = local x | |
937 | // r[1] = local y | |
938 | // r[2] = local z | |
939 | // alpha - rotation angle. | |
940 | // The result is returned as: | |
941 | // r[0] = global x | |
942 | // r[1] = global y | |
943 | // r[2] = global z | |
944 | //---------------------------------------------------------------- | |
945 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0]; | |
946 | r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs; | |
a5e407e9 | 947 | |
a5e407e9 | 948 | return kTRUE; |
51ad6848 | 949 | } |
950 | ||
b1149664 | 951 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
952 | //---------------------------------------------------------------- | |
953 | // This function returns a unit vector along the track direction | |
954 | // in the global coordinate system. | |
955 | //---------------------------------------------------------------- | |
956 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
957 | Double_t snp=fP[2]; | |
92934324 | 958 | Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp)); |
b1149664 | 959 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
960 | d[0]=(csp*cs - snp*sn)/norm; | |
961 | d[1]=(snp*cs + csp*sn)/norm; | |
962 | d[2]=fP[3]/norm; | |
963 | } | |
964 | ||
c9ec41e8 | 965 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const { |
966 | //--------------------------------------------------------------------- | |
967 | // This function returns the global track momentum components | |
968 | // Results for (nearly) straight tracks are meaningless ! | |
969 | //--------------------------------------------------------------------- | |
970 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
971 | return Local2GlobalMomentum(p,fAlpha); | |
972 | } | |
a5e407e9 | 973 | |
def9660e | 974 | Double_t AliExternalTrackParam::Px() const { |
975 | // return x-component of momentum | |
976 | ||
977 | Double_t p[3]; | |
978 | GetPxPyPz(p); | |
979 | ||
980 | return p[0]; | |
981 | } | |
982 | ||
983 | Double_t AliExternalTrackParam::Py() const { | |
984 | // return y-component of momentum | |
985 | ||
986 | Double_t p[3]; | |
987 | GetPxPyPz(p); | |
988 | ||
989 | return p[1]; | |
990 | } | |
991 | ||
992 | Double_t AliExternalTrackParam::Pz() const { | |
993 | // return z-component of momentum | |
994 | ||
995 | Double_t p[3]; | |
996 | GetPxPyPz(p); | |
997 | ||
998 | return p[2]; | |
999 | } | |
1000 | ||
1001 | Double_t AliExternalTrackParam::Theta() const { | |
1002 | // return theta angle of momentum | |
1003 | ||
1004 | return TMath::ATan2(Pt(), Pz()); | |
1005 | } | |
1006 | ||
1007 | Double_t AliExternalTrackParam::Phi() const { | |
1008 | // return phi angle of momentum | |
1009 | ||
1010 | Double_t p[3]; | |
1011 | GetPxPyPz(p); | |
1012 | ||
1013 | return TMath::ATan2(p[1], p[0]); | |
1014 | } | |
1015 | ||
1016 | Double_t AliExternalTrackParam::M() const { | |
1017 | // return particle mass | |
1018 | ||
1019 | // No mass information available so far. | |
1020 | // Redifine in derived class! | |
1021 | ||
1022 | return -999.; | |
1023 | } | |
1024 | ||
1025 | Double_t AliExternalTrackParam::E() const { | |
1026 | // return particle energy | |
1027 | ||
1028 | // No PID information available so far. | |
1029 | // Redifine in derived class! | |
1030 | ||
1031 | return -999.; | |
1032 | } | |
1033 | ||
1034 | Double_t AliExternalTrackParam::Eta() const { | |
1035 | // return pseudorapidity | |
1036 | ||
1037 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1038 | } | |
1039 | ||
1040 | Double_t AliExternalTrackParam::Y() const { | |
1041 | // return rapidity | |
1042 | ||
1043 | // No PID information available so far. | |
1044 | // Redifine in derived class! | |
1045 | ||
1046 | return -999.; | |
1047 | } | |
1048 | ||
c9ec41e8 | 1049 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1050 | //--------------------------------------------------------------------- | |
1051 | // This function returns the global track position | |
1052 | //--------------------------------------------------------------------- | |
1053 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1054 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1055 | } |
1056 | ||
c9ec41e8 | 1057 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1058 | //--------------------------------------------------------------------- | |
1059 | // This function returns the global covariance matrix of the track params | |
1060 | // | |
1061 | // Cov(x,x) ... : cv[0] | |
1062 | // Cov(y,x) ... : cv[1] cv[2] | |
1063 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1064 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1065 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1066 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1067 | // |
c9ec41e8 | 1068 | // Results for (nearly) straight tracks are meaningless ! |
1069 | //--------------------------------------------------------------------- | |
e421f556 | 1070 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1071 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1072 | return kFALSE; | |
a5e407e9 | 1073 | } |
49d13e89 | 1074 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1075 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1076 | return kFALSE; | |
1077 | } | |
1078 | Double_t pt=1./TMath::Abs(fP[4]); | |
1079 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1080 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1081 | |
1082 | Double_t m00=-sn, m10=cs; | |
1083 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1084 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1085 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1086 | ||
854d5d49 | 1087 | m43*=GetSign(); |
1088 | m44*=GetSign(); | |
1089 | m45*=GetSign(); | |
1090 | ||
c9ec41e8 | 1091 | cv[0 ] = fC[0]*m00*m00; |
1092 | cv[1 ] = fC[0]*m00*m10; | |
1093 | cv[2 ] = fC[0]*m10*m10; | |
1094 | cv[3 ] = fC[1]*m00; | |
1095 | cv[4 ] = fC[1]*m10; | |
1096 | cv[5 ] = fC[2]; | |
1097 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1098 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1099 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1100 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1101 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1102 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1103 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1104 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1105 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1106 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1107 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1108 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1109 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1110 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1111 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1112 | |
c9ec41e8 | 1113 | return kTRUE; |
51ad6848 | 1114 | } |
1115 | ||
51ad6848 | 1116 | |
c9ec41e8 | 1117 | Bool_t |
1118 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1119 | //--------------------------------------------------------------------- | |
1120 | // This function returns the global track momentum extrapolated to | |
1121 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1122 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1123 | p[0]=fP[4]; |
1530f89c | 1124 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1125 | p[2]=fP[3]; |
1126 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1127 | } |
1128 | ||
7cf7bb6c | 1129 | Bool_t |
1130 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1131 | //--------------------------------------------------------------------- | |
1132 | // This function returns the local Y-coordinate of the intersection | |
1133 | // point between this track and the reference plane "x" (cm). | |
1134 | // Magnetic field "b" (kG) | |
1135 | //--------------------------------------------------------------------- | |
1136 | Double_t dx=x-fX; | |
1137 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1138 | ||
1530f89c | 1139 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1140 | |
1141 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1142 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1143 | ||
1144 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1145 | y = fP[0] + dx*(f1+f2)/(r1+r2); | |
1146 | return kTRUE; | |
1147 | } | |
1148 | ||
6c94f330 | 1149 | Bool_t |
1150 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1151 | //--------------------------------------------------------------------- | |
1152 | // This function returns the local Z-coordinate of the intersection | |
1153 | // point between this track and the reference plane "x" (cm). | |
1154 | // Magnetic field "b" (kG) | |
1155 | //--------------------------------------------------------------------- | |
1156 | Double_t dx=x-fX; | |
1157 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1158 | ||
1159 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; | |
1160 | ||
1161 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1162 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1163 | ||
1164 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); | |
1165 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! | |
1166 | return kTRUE; | |
1167 | } | |
1168 | ||
c9ec41e8 | 1169 | Bool_t |
1170 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1171 | //--------------------------------------------------------------------- | |
1172 | // This function returns the global track position extrapolated to | |
1173 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1174 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1175 | Double_t dx=x-fX; |
e421f556 | 1176 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1177 | ||
1530f89c | 1178 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1179 | |
e421f556 | 1180 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1181 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1182 | |
1183 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1184 | r[0] = x; | |
1185 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
6c94f330 | 1186 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; |
c9ec41e8 | 1187 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1188 | } |
1189 | ||
51ad6848 | 1190 | //_____________________________________________________________________________ |
1191 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1192 | { | |
1193 | // print the parameters and the covariance matrix | |
1194 | ||
1195 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1196 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1197 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1198 | printf(" covariance: %12g\n", fC[0]); | |
1199 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1200 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1201 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1202 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1203 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1204 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1205 | } |
5b77d93c | 1206 | |
c194ba83 | 1207 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1208 | // | |
1209 | // Get sinus at given x | |
1210 | // | |
1530f89c | 1211 | Double_t crv=GetC(b); |
c194ba83 | 1212 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1213 | Double_t dx = x-fX; | |
1214 | Double_t res = fP[2]+dx*crv; | |
1215 | return res; | |
1216 | } |