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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" |
58e536c5 | 30 | #include "AliVVertex.h" |
0c19adf7 | 31 | #include "TPolyMarker3D.h" |
da4e3deb | 32 | #include "TVector3.h" |
6c94f330 | 33 | #include "AliLog.h" |
51ad6848 | 34 | |
35 | ClassImp(AliExternalTrackParam) | |
36 | ||
ed5f2849 | 37 | Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; |
38 | ||
51ad6848 | 39 | //_____________________________________________________________________________ |
90e48c0c | 40 | AliExternalTrackParam::AliExternalTrackParam() : |
def9660e | 41 | AliVParticle(), |
90e48c0c | 42 | fX(0), |
c9ec41e8 | 43 | fAlpha(0) |
51ad6848 | 44 | { |
90e48c0c | 45 | // |
46 | // default constructor | |
47 | // | |
c9ec41e8 | 48 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
49 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 50 | } |
51 | ||
6c94f330 | 52 | //_____________________________________________________________________________ |
53 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
def9660e | 54 | AliVParticle(track), |
6c94f330 | 55 | fX(track.fX), |
56 | fAlpha(track.fAlpha) | |
57 | { | |
58 | // | |
59 | // copy constructor | |
60 | // | |
61 | for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i]; | |
62 | for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i]; | |
63 | } | |
64 | ||
def9660e | 65 | //_____________________________________________________________________________ |
66 | AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar) | |
67 | { | |
68 | // | |
69 | // assignment operator | |
70 | // | |
71 | ||
72 | if (this!=&trkPar) { | |
73 | AliVParticle::operator=(trkPar); | |
74 | fX = trkPar.fX; | |
75 | fAlpha = trkPar.fAlpha; | |
76 | ||
77 | for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i]; | |
78 | for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i]; | |
79 | } | |
80 | ||
81 | return *this; | |
82 | } | |
83 | ||
51ad6848 | 84 | //_____________________________________________________________________________ |
85 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
86 | const Double_t param[5], | |
90e48c0c | 87 | const Double_t covar[15]) : |
def9660e | 88 | AliVParticle(), |
90e48c0c | 89 | fX(x), |
c9ec41e8 | 90 | fAlpha(alpha) |
51ad6848 | 91 | { |
90e48c0c | 92 | // |
93 | // create external track parameters from given arguments | |
94 | // | |
c9ec41e8 | 95 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
96 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 97 | } |
98 | ||
90e48c0c | 99 | //_____________________________________________________________________________ |
da4e3deb | 100 | AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], |
101 | Double_t cv[21],Short_t sign) : | |
102 | AliVParticle(), | |
103 | fX(0.), | |
104 | fAlpha(0.) | |
105 | { | |
106 | // | |
107 | // create external track parameters from the global parameters | |
108 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
109 | // A.Dainese 10.10.08 | |
110 | ||
111 | // Calculate alpha: the rotation angle of the corresponding local system | |
112 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); | |
113 | ||
114 | // Get the vertex of origin and the momentum | |
115 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
116 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
117 | ||
118 | // Rotate to the local coordinate system | |
119 | ver.RotateZ(-fAlpha); | |
120 | mom.RotateZ(-fAlpha); | |
121 | ||
122 | // x of the reference plane | |
123 | fX = ver.X(); | |
124 | ||
125 | Double_t charge = (Double_t)sign; | |
126 | ||
127 | fP[0] = ver.Y(); | |
128 | fP[1] = ver.Z(); | |
129 | fP[2] = TMath::Sin(mom.Phi()); | |
130 | fP[3] = mom.Pz()/mom.Pt(); | |
131 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
132 | ||
133 | // Covariance matrix (formulas to be simplified) | |
134 | ||
135 | Double_t pt=1./TMath::Abs(fP[4]); | |
136 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
137 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); | |
138 | ||
139 | Double_t m00=-sn;// m10=cs; | |
140 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
141 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
142 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
143 | ||
144 | m43*=GetSign(); | |
145 | m44*=GetSign(); | |
146 | m45*=GetSign(); | |
147 | ||
148 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
149 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
150 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
151 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
152 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
153 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
154 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
155 | ||
156 | fC[0 ] = cv[0 ]+cv[2 ]; | |
157 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
158 | fC[2 ] = cv[5 ]; | |
159 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
160 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
161 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
162 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
163 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
164 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
165 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
166 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
167 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
168 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
169 | Double_t b2=m23*m35; | |
170 | Double_t b3=m43*m35; | |
171 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
172 | Double_t b5=m24*m35; | |
173 | Double_t b6=m44*m35; | |
174 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
175 | fC[13] = b1/b3-b2*fC[8]/b3; | |
176 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
177 | } | |
178 | ||
179 | //_____________________________________________________________________________ | |
6c94f330 | 180 | void AliExternalTrackParam::Set(Double_t x, Double_t alpha, |
181 | const Double_t p[5], const Double_t cov[15]) { | |
c9ec41e8 | 182 | // |
6c94f330 | 183 | // Sets the parameters |
c9ec41e8 | 184 | // |
6c94f330 | 185 | fX=x; |
186 | fAlpha=alpha; | |
187 | for (Int_t i = 0; i < 5; i++) fP[i] = p[i]; | |
188 | for (Int_t i = 0; i < 15; i++) fC[i] = cov[i]; | |
51ad6848 | 189 | } |
190 | ||
191 | //_____________________________________________________________________________ | |
c9ec41e8 | 192 | void AliExternalTrackParam::Reset() { |
1530f89c | 193 | // |
194 | // Resets all the parameters to 0 | |
195 | // | |
c9ec41e8 | 196 | fX=fAlpha=0.; |
197 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
198 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 199 | } |
200 | ||
3775b0ca | 201 | //_____________________________________________________________________________ |
202 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
203 | // | |
204 | // Add "something" to the track covarince matrix. | |
205 | // May be needed to account for unknown mis-calibration/mis-alignment | |
206 | // | |
207 | fC[0] +=c[0]; | |
208 | fC[1] +=c[1]; fC[2] +=c[2]; | |
209 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
210 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
211 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
212 | } | |
213 | ||
214 | ||
c9ec41e8 | 215 | Double_t AliExternalTrackParam::GetP() const { |
216 | //--------------------------------------------------------------------- | |
217 | // This function returns the track momentum | |
218 | // Results for (nearly) straight tracks are meaningless ! | |
219 | //--------------------------------------------------------------------- | |
06fb4a2f | 220 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 221 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 222 | } |
223 | ||
1d99986f | 224 | Double_t AliExternalTrackParam::Get1P() const { |
225 | //--------------------------------------------------------------------- | |
226 | // This function returns the 1/(track momentum) | |
227 | //--------------------------------------------------------------------- | |
228 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
229 | } | |
230 | ||
c9ec41e8 | 231 | //_______________________________________________________________________ |
c7bafca9 | 232 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 233 | //------------------------------------------------------------------ |
234 | // This function calculates the transverse impact parameter | |
235 | // with respect to a point with global coordinates (x,y) | |
236 | // in the magnetic field "b" (kG) | |
237 | //------------------------------------------------------------------ | |
5773defd | 238 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 239 | Double_t rp4=GetC(b); |
c9ec41e8 | 240 | |
241 | Double_t xt=fX, yt=fP[0]; | |
242 | ||
243 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
244 | Double_t a = x*cs + y*sn; | |
245 | y = -x*sn + y*cs; x=a; | |
246 | xt-=x; yt-=y; | |
247 | ||
248 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
249 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
1530f89c | 250 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
251 | } | |
252 | ||
253 | //_______________________________________________________________________ | |
254 | void AliExternalTrackParam:: | |
255 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
256 | //------------------------------------------------------------------ | |
257 | // This function calculates the transverse and longitudinal impact parameters | |
258 | // with respect to a point with global coordinates (x,y) | |
259 | // in the magnetic field "b" (kG) | |
260 | //------------------------------------------------------------------ | |
261 | Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1); | |
262 | Double_t xt=fX, yt=fP[0]; | |
263 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
264 | Double_t a = x*cs + y*sn; | |
265 | y = -x*sn + y*cs; x=a; | |
266 | xt-=x; yt-=y; | |
267 | ||
268 | Double_t rp4=GetC(b); | |
269 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
270 | dz[0] = -(xt*f1 - yt*r1); | |
271 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
272 | return; | |
273 | } | |
274 | ||
275 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
276 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
277 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
278 | dz[0] = -a/(1 + rr); | |
279 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2); | |
280 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; | |
51ad6848 | 281 | } |
282 | ||
49d13e89 | 283 | //_______________________________________________________________________ |
284 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
285 | //------------------------------------------------------------------ | |
286 | // This function calculates the transverse impact parameter | |
287 | // with respect to a point with global coordinates (xv,yv) | |
288 | // neglecting the track curvature. | |
289 | //------------------------------------------------------------------ | |
290 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
291 | Double_t x= xv*cs + yv*sn; | |
292 | Double_t y=-xv*sn + yv*cs; | |
293 | ||
294 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
295 | ||
1530f89c | 296 | return -d; |
49d13e89 | 297 | } |
298 | ||
116b445b | 299 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
7dded1d5 | 300 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr, |
301 | Double_t (*Bethe)(Double_t)) { | |
116b445b | 302 | //------------------------------------------------------------------ |
303 | // This function corrects the track parameters for the crossed material. | |
304 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
305 | // "xTimesRho" - is the product length*density (g/cm^2). | |
306 | // "mass" - the mass of this particle (GeV/c^2). | |
307 | //------------------------------------------------------------------ | |
308 | Double_t &fP2=fP[2]; | |
309 | Double_t &fP3=fP[3]; | |
310 | Double_t &fP4=fP[4]; | |
311 | ||
312 | Double_t &fC22=fC[5]; | |
313 | Double_t &fC33=fC[9]; | |
314 | Double_t &fC43=fC[13]; | |
315 | Double_t &fC44=fC[14]; | |
316 | ||
7dded1d5 | 317 | //Apply angle correction, if requested |
318 | if(anglecorr) { | |
319 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
320 | xOverX0 *=angle; | |
321 | xTimesRho *=angle; | |
322 | } | |
323 | ||
116b445b | 324 | Double_t p=GetP(); |
325 | Double_t p2=p*p; | |
326 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 327 | |
328 | //Multiple scattering****************** | |
329 | if (xOverX0 != 0) { | |
330 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
9a53dcc6 | 331 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
116b445b | 332 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
333 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
334 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
335 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
336 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
337 | } | |
338 | ||
339 | //Energy losses************************ | |
340 | if ((xTimesRho != 0.) && (beta2 < 1.)) { | |
341 | Double_t dE=Bethe(beta2)*xTimesRho; | |
342 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
343 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
344 | fP4*=(1.- e/p2*dE); | |
4b2fa3ce | 345 | if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c |
346 | ||
116b445b | 347 | |
348 | // Approximate energy loss fluctuation (M.Ivanov) | |
349 | const Double_t knst=0.07; // To be tuned. | |
350 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
351 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); | |
352 | ||
353 | } | |
354 | ||
355 | return kTRUE; | |
356 | } | |
357 | ||
358 | ||
ee5dba5e | 359 | Bool_t AliExternalTrackParam::CorrectForMaterial |
360 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 361 | //------------------------------------------------------------------ |
116b445b | 362 | // Deprecated function ! |
363 | // Better use CorrectForMeanMaterial instead of it. | |
364 | // | |
c7bafca9 | 365 | // This function corrects the track parameters for the crossed material |
366 | // "d" - the thickness (fraction of the radiation length) | |
367 | // "x0" - the radiation length (g/cm^2) | |
368 | // "mass" - the mass of this particle (GeV/c^2) | |
369 | //------------------------------------------------------------------ | |
370 | Double_t &fP2=fP[2]; | |
371 | Double_t &fP3=fP[3]; | |
372 | Double_t &fP4=fP[4]; | |
373 | ||
374 | Double_t &fC22=fC[5]; | |
375 | Double_t &fC33=fC[9]; | |
376 | Double_t &fC43=fC[13]; | |
377 | Double_t &fC44=fC[14]; | |
378 | ||
7b5ef2e6 | 379 | Double_t p=GetP(); |
380 | Double_t p2=p*p; | |
c7bafca9 | 381 | Double_t beta2=p2/(p2 + mass*mass); |
382 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
383 | ||
384 | //Multiple scattering****************** | |
385 | if (d!=0) { | |
386 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
9a53dcc6 | 387 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
c7bafca9 | 388 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
389 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
390 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
391 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
392 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
393 | } | |
394 | ||
395 | //Energy losses************************ | |
8fc1985d | 396 | if (x0!=0. && beta2<1) { |
c7bafca9 | 397 | d*=x0; |
ee5dba5e | 398 | Double_t dE=Bethe(beta2)*d; |
399 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
ae666100 | 400 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! |
ee5dba5e | 401 | fP4*=(1.- e/p2*dE); |
402 | ||
403 | // Approximate energy loss fluctuation (M.Ivanov) | |
ed5f2849 | 404 | const Double_t knst=0.07; // To be tuned. |
405 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
ee5dba5e | 406 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
407 | ||
c7bafca9 | 408 | } |
409 | ||
410 | return kTRUE; | |
411 | } | |
412 | ||
ee5dba5e | 413 | Double_t ApproximateBetheBloch(Double_t beta2) { |
414 | //------------------------------------------------------------------ | |
415 | // This is an approximation of the Bethe-Bloch formula with | |
416 | // the density effect taken into account at beta*gamma > 3.5 | |
417 | // (the approximation is reasonable only for solid materials) | |
418 | //------------------------------------------------------------------ | |
a821848c | 419 | if (beta2 >= 1) return kVeryBig; |
420 | ||
ee5dba5e | 421 | if (beta2/(1-beta2)>3.5*3.5) |
422 | return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); | |
423 | ||
424 | return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); | |
425 | } | |
426 | ||
49d13e89 | 427 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
428 | //------------------------------------------------------------------ | |
429 | // Transform this track to the local coord. system rotated | |
430 | // by angle "alpha" (rad) with respect to the global coord. system. | |
431 | //------------------------------------------------------------------ | |
dfcef74c | 432 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
433 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
434 | return kFALSE; | |
435 | } | |
436 | ||
49d13e89 | 437 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
438 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
439 | ||
440 | Double_t &fP0=fP[0]; | |
441 | Double_t &fP2=fP[2]; | |
442 | Double_t &fC00=fC[0]; | |
443 | Double_t &fC10=fC[1]; | |
444 | Double_t &fC20=fC[3]; | |
445 | Double_t &fC21=fC[4]; | |
446 | Double_t &fC22=fC[5]; | |
447 | Double_t &fC30=fC[6]; | |
448 | Double_t &fC32=fC[8]; | |
449 | Double_t &fC40=fC[10]; | |
450 | Double_t &fC42=fC[12]; | |
451 | ||
452 | Double_t x=fX; | |
453 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
454 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
455 | ||
dfcef74c | 456 | Double_t tmp=sf*ca - cf*sa; |
457 | if (TMath::Abs(tmp) >= kAlmost1) return kFALSE; | |
458 | ||
49d13e89 | 459 | fAlpha = alpha; |
460 | fX = x*ca + fP0*sa; | |
461 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 462 | fP2= tmp; |
49d13e89 | 463 | |
06fb4a2f | 464 | if (TMath::Abs(cf)<kAlmost0) { |
465 | AliError(Form("Too small cosine value %f",cf)); | |
466 | cf = kAlmost0; | |
467 | } | |
468 | ||
49d13e89 | 469 | Double_t rr=(ca+sf/cf*sa); |
470 | ||
471 | fC00 *= (ca*ca); | |
472 | fC10 *= ca; | |
473 | fC20 *= ca*rr; | |
474 | fC21 *= rr; | |
475 | fC22 *= rr*rr; | |
476 | fC30 *= ca; | |
477 | fC32 *= rr; | |
478 | fC40 *= ca; | |
479 | fC42 *= rr; | |
480 | ||
481 | return kTRUE; | |
482 | } | |
483 | ||
484 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
485 | //---------------------------------------------------------------- | |
486 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
487 | //---------------------------------------------------------------- | |
49d13e89 | 488 | Double_t dx=xk-fX; |
e421f556 | 489 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 490 | |
1530f89c | 491 | Double_t crv=GetC(b); |
5773defd | 492 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
493 | ||
49d13e89 | 494 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 495 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 496 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
497 | ||
498 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
499 | Double_t | |
500 | &fC00=fC[0], | |
501 | &fC10=fC[1], &fC11=fC[2], | |
502 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
503 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
504 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
505 | ||
506 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
507 | ||
508 | fX=xk; | |
509 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 510 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 511 | fP2 += dx*crv; |
512 | ||
513 | //f = F - 1 | |
514 | ||
515 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
516 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
517 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
518 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
519 | Double_t f13= dx/r1; | |
520 | Double_t f24= dx; f24*=cc; | |
521 | ||
522 | //b = C*ft | |
523 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
524 | Double_t b02=f24*fC40; | |
525 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
526 | Double_t b12=f24*fC41; | |
527 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
528 | Double_t b22=f24*fC42; | |
529 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
530 | Double_t b42=f24*fC44; | |
531 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
532 | Double_t b32=f24*fC43; | |
533 | ||
534 | //a = f*b = f*C*ft | |
535 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
536 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
537 | Double_t a22=f24*b42; | |
538 | ||
539 | //F*C*Ft = C + (b + bt + a) | |
540 | fC00 += b00 + b00 + a00; | |
541 | fC10 += b10 + b01 + a01; | |
542 | fC20 += b20 + b02 + a02; | |
543 | fC30 += b30; | |
544 | fC40 += b40; | |
545 | fC11 += b11 + b11 + a11; | |
546 | fC21 += b21 + b12 + a12; | |
547 | fC31 += b31; | |
548 | fC41 += b41; | |
549 | fC22 += b22 + b22 + a22; | |
550 | fC32 += b32; | |
551 | fC42 += b42; | |
552 | ||
553 | return kTRUE; | |
554 | } | |
555 | ||
052daaff | 556 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
557 | Double_t p[3], Double_t bz) const { | |
558 | //+++++++++++++++++++++++++++++++++++++++++ | |
559 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
560 | // Extrapolate track along simple helix in magnetic field | |
561 | // Arguments: len -distance alogn helix, [cm] | |
562 | // bz - mag field, [kGaus] | |
563 | // Returns: x and p contain extrapolated positon and momentum | |
564 | // The momentum returned for straight-line tracks is meaningless ! | |
565 | //+++++++++++++++++++++++++++++++++++++++++ | |
566 | GetXYZ(x); | |
567 | ||
def9660e | 568 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks |
052daaff | 569 | Double_t unit[3]; GetDirection(unit); |
570 | x[0]+=unit[0]*len; | |
571 | x[1]+=unit[1]*len; | |
572 | x[2]+=unit[2]*len; | |
573 | ||
574 | p[0]=unit[0]/kAlmost0; | |
575 | p[1]=unit[1]/kAlmost0; | |
576 | p[2]=unit[2]/kAlmost0; | |
577 | } else { | |
578 | GetPxPyPz(p); | |
579 | Double_t pp=GetP(); | |
580 | Double_t a = -kB2C*bz*GetSign(); | |
581 | Double_t rho = a/pp; | |
582 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
583 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
584 | x[2] += p[2]*len/pp; | |
585 | ||
586 | Double_t p0=p[0]; | |
587 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
588 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
589 | } | |
590 | } | |
591 | ||
592 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
593 | Double_t bz) const { | |
594 | //+++++++++++++++++++++++++++++++++++++++++ | |
595 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
596 | // Finds point of intersection (if exists) of the helix with the plane. | |
597 | // Stores result in fX and fP. | |
598 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
599 | // and vector, normal to the plane | |
600 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
601 | //+++++++++++++++++++++++++++++++++++++++++ | |
602 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
603 | ||
604 | //estimates initial helix length up to plane | |
605 | Double_t s= | |
606 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
607 | Double_t dist=99999,distPrev=dist; | |
608 | Double_t x[3],p[3]; | |
609 | while(TMath::Abs(dist)>0.00001){ | |
610 | //calculates helix at the distance s from x0 ALONG the helix | |
611 | Propagate(s,x,p,bz); | |
612 | ||
613 | //distance between current helix position and plane | |
614 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
615 | ||
616 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
617 | distPrev=dist; | |
618 | s-=dist; | |
619 | } | |
620 | //on exit pnt is intersection point,norm is track vector at that point, | |
621 | //all in MARS | |
622 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
623 | return kTRUE; | |
624 | } | |
625 | ||
49d13e89 | 626 | Double_t |
627 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
628 | //---------------------------------------------------------------- | |
629 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
630 | //---------------------------------------------------------------- | |
631 | Double_t sdd = fC[0] + cov[0]; | |
632 | Double_t sdz = fC[1] + cov[1]; | |
633 | Double_t szz = fC[2] + cov[2]; | |
634 | Double_t det = sdd*szz - sdz*sdz; | |
635 | ||
636 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
637 | ||
638 | Double_t d = fP[0] - p[0]; | |
639 | Double_t z = fP[1] - p[1]; | |
640 | ||
641 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
642 | } | |
643 | ||
4b189f98 | 644 | Double_t AliExternalTrackParam:: |
645 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
646 | //---------------------------------------------------------------- | |
647 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 648 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 649 | // |
650 | // Cov(x,x) ... : covxyz[0] | |
651 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
652 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
653 | //---------------------------------------------------------------- | |
654 | ||
655 | Double_t res[3] = { | |
656 | GetX() - p[0], | |
657 | GetY() - p[1], | |
658 | GetZ() - p[2] | |
659 | }; | |
660 | ||
661 | Double_t f=GetSnp(); | |
662 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
663 | Double_t r=TMath::Sqrt(1.- f*f); | |
664 | Double_t a=f/r, b=GetTgl()/r; | |
665 | ||
666 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
667 | ||
668 | TMatrixDSym v(3); | |
669 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
670 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
671 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
672 | ||
673 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
674 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
675 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
676 | ||
677 | v.Invert(); | |
678 | if (!v.IsValid()) return kVeryBig; | |
679 | ||
680 | Double_t chi2=0.; | |
681 | for (Int_t i = 0; i < 3; i++) | |
682 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
683 | ||
684 | return chi2; | |
685 | ||
686 | ||
687 | } | |
688 | ||
1e023a36 | 689 | Bool_t AliExternalTrackParam:: |
690 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
691 | //---------------------------------------------------------------- | |
692 | // Propagate this track to the plane | |
693 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
694 | // belongs to. | |
695 | // The magnetic field is "bz" (kG) | |
696 | // | |
697 | // The track curvature and the change of the covariance matrix | |
698 | // of the track parameters are negleted ! | |
699 | // (So the "step" should be small compared with 1/curvature) | |
700 | //---------------------------------------------------------------- | |
701 | ||
702 | Double_t f=GetSnp(); | |
703 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
704 | Double_t r=TMath::Sqrt(1.- f*f); | |
705 | Double_t a=f/r, b=GetTgl()/r; | |
706 | ||
707 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
708 | ||
709 | TMatrixDSym tV(3); | |
710 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
711 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
712 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
713 | ||
714 | TMatrixDSym pV(3); | |
715 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
716 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
717 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
718 | ||
719 | TMatrixDSym tpV(tV); | |
720 | tpV+=pV; | |
721 | tpV.Invert(); | |
722 | if (!tpV.IsValid()) return kFALSE; | |
723 | ||
724 | TMatrixDSym pW(3),tW(3); | |
725 | for (Int_t i=0; i<3; i++) | |
726 | for (Int_t j=0; j<3; j++) { | |
727 | pW(i,j)=tW(i,j)=0.; | |
728 | for (Int_t k=0; k<3; k++) { | |
729 | pW(i,j) += tV(i,k)*tpV(k,j); | |
730 | tW(i,j) += pV(i,k)*tpV(k,j); | |
731 | } | |
732 | } | |
733 | ||
734 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
735 | ||
736 | Double_t x=0.; | |
737 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
738 | Double_t crv=GetC(bz); | |
739 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
740 | f += crv*(x-fX); | |
741 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
742 | fX=x; | |
743 | ||
744 | fP[0]=0.; | |
745 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
746 | fP[1]=0.; | |
747 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
748 | ||
749 | return kTRUE; | |
750 | } | |
751 | ||
e23a38cb | 752 | Double_t *AliExternalTrackParam::GetResiduals( |
753 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
754 | //------------------------------------------------------------------ | |
755 | // Returns the track residuals with the space point "p" having | |
756 | // the covariance matrix "cov". | |
757 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
758 | // otherwise they must be predicted. | |
759 | //------------------------------------------------------------------ | |
760 | static Double_t res[2]; | |
761 | ||
762 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
763 | if (updated) { | |
764 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
765 | } else { | |
766 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
767 | } | |
768 | Double_t det=r00*r11 - r01*r01; | |
769 | ||
770 | if (TMath::Abs(det) < kAlmost0) return 0; | |
771 | ||
772 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 773 | |
774 | if (r00 < 0.) return 0; | |
775 | if (r11 < 0.) return 0; | |
776 | ||
e23a38cb | 777 | Double_t dy = fP[0] - p[0]; |
778 | Double_t dz = fP[1] - p[1]; | |
779 | ||
780 | res[0]=dy*TMath::Sqrt(r00); | |
781 | res[1]=dz*TMath::Sqrt(r11); | |
782 | ||
783 | return res; | |
784 | } | |
785 | ||
49d13e89 | 786 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
787 | //------------------------------------------------------------------ | |
788 | // Update the track parameters with the space point "p" having | |
789 | // the covariance matrix "cov" | |
790 | //------------------------------------------------------------------ | |
791 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
792 | Double_t | |
793 | &fC00=fC[0], | |
794 | &fC10=fC[1], &fC11=fC[2], | |
795 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
796 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
797 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
798 | ||
799 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
800 | r00+=fC00; r01+=fC10; r11+=fC11; | |
801 | Double_t det=r00*r11 - r01*r01; | |
802 | ||
803 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
804 | ||
805 | ||
806 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
807 | ||
808 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
809 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
810 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
811 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
812 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
813 | ||
814 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
815 | Double_t sf=fP2 + k20*dy + k21*dz; | |
816 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
817 | ||
818 | fP0 += k00*dy + k01*dz; | |
819 | fP1 += k10*dy + k11*dz; | |
820 | fP2 = sf; | |
821 | fP3 += k30*dy + k31*dz; | |
822 | fP4 += k40*dy + k41*dz; | |
823 | ||
824 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
825 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
826 | ||
827 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
828 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
829 | fC40-=k00*c04+k01*c14; | |
830 | ||
831 | fC11-=k10*c01+k11*fC11; | |
832 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
833 | fC41-=k10*c04+k11*c14; | |
834 | ||
835 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
836 | fC42-=k20*c04+k21*c14; | |
837 | ||
838 | fC33-=k30*c03+k31*c13; | |
839 | fC43-=k30*c04+k31*c14; | |
840 | ||
841 | fC44-=k40*c04+k41*c14; | |
842 | ||
843 | return kTRUE; | |
844 | } | |
845 | ||
c7bafca9 | 846 | void |
847 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
848 | //-------------------------------------------------------------------- | |
849 | // External track parameters -> helix parameters | |
850 | // "b" - magnetic field (kG) | |
851 | //-------------------------------------------------------------------- | |
852 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
853 | ||
1530f89c | 854 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 855 | |
856 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
857 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
858 | //hlx[1]= // z0 | |
859 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
860 | //hlx[3]= // tgl | |
1530f89c | 861 | hlx[4]=GetC(b); // C |
c7bafca9 | 862 | } |
863 | ||
864 | ||
865 | static void Evaluate(const Double_t *h, Double_t t, | |
866 | Double_t r[3], //radius vector | |
867 | Double_t g[3], //first defivatives | |
868 | Double_t gg[3]) //second derivatives | |
869 | { | |
870 | //-------------------------------------------------------------------- | |
871 | // Calculate position of a point on a track and some derivatives | |
872 | //-------------------------------------------------------------------- | |
873 | Double_t phase=h[4]*t+h[2]; | |
874 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
875 | ||
876 | r[0] = h[5] + (sn - h[6])/h[4]; | |
877 | r[1] = h[0] - (cs - h[7])/h[4]; | |
878 | r[2] = h[1] + h[3]*t; | |
879 | ||
880 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
881 | ||
882 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
883 | } | |
884 | ||
885 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
886 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
887 | //------------------------------------------------------------ | |
888 | // Returns the (weighed !) distance of closest approach between | |
889 | // this track and the track "p". | |
890 | // Other returned values: | |
891 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
892 | //----------------------------------------------------------- | |
893 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
894 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
895 | Double_t dx2=dy2; | |
896 | ||
897 | //dx2=dy2=dz2=1.; | |
898 | ||
899 | Double_t p1[8]; GetHelixParameters(p1,b); | |
900 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
901 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
902 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
903 | ||
904 | ||
905 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
906 | Evaluate(p1,t1,r1,g1,gg1); | |
907 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
908 | Evaluate(p2,t2,r2,g2,gg2); | |
909 | ||
910 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
911 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
912 | ||
913 | Int_t max=27; | |
914 | while (max--) { | |
915 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
916 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
917 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
918 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
919 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
920 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
921 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
922 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
923 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
924 | ||
925 | Double_t det=h11*h22-h12*h12; | |
926 | ||
927 | Double_t dt1,dt2; | |
928 | if (TMath::Abs(det)<1.e-33) { | |
929 | //(quasi)singular Hessian | |
930 | dt1=-gt1; dt2=-gt2; | |
931 | } else { | |
932 | dt1=-(gt1*h22 - gt2*h12)/det; | |
933 | dt2=-(h11*gt2 - h12*gt1)/det; | |
934 | } | |
935 | ||
936 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
937 | ||
938 | //check delta(phase1) ? | |
939 | //check delta(phase2) ? | |
940 | ||
941 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
942 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
943 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 944 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 945 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
946 | if (lmb < 0.) | |
358f16ae | 947 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 948 | break; |
949 | } | |
950 | ||
951 | Double_t dd=dm; | |
952 | for (Int_t div=1 ; ; div*=2) { | |
953 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
954 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
955 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
956 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
957 | if (dd<dm) break; | |
958 | dt1*=0.5; dt2*=0.5; | |
959 | if (div>512) { | |
358f16ae | 960 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 961 | } |
962 | } | |
963 | dm=dd; | |
964 | ||
965 | t1+=dt1; | |
966 | t2+=dt2; | |
967 | ||
968 | } | |
969 | ||
358f16ae | 970 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 971 | |
972 | Double_t cs=TMath::Cos(GetAlpha()); | |
973 | Double_t sn=TMath::Sin(GetAlpha()); | |
974 | xthis=r1[0]*cs + r1[1]*sn; | |
975 | ||
976 | cs=TMath::Cos(p->GetAlpha()); | |
977 | sn=TMath::Sin(p->GetAlpha()); | |
978 | xp=r2[0]*cs + r2[1]*sn; | |
979 | ||
980 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
981 | } | |
982 | ||
983 | Double_t AliExternalTrackParam:: | |
984 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
985 | //-------------------------------------------------------------- | |
986 | // Propagates this track and the argument track to the position of the | |
987 | // distance of closest approach. | |
988 | // Returns the (weighed !) distance of closest approach. | |
989 | //-------------------------------------------------------------- | |
990 | Double_t xthis,xp; | |
991 | Double_t dca=GetDCA(p,b,xthis,xp); | |
992 | ||
993 | if (!PropagateTo(xthis,b)) { | |
994 | //AliWarning(" propagation failed !"); | |
995 | return 1e+33; | |
996 | } | |
997 | ||
998 | if (!p->PropagateTo(xp,b)) { | |
999 | //AliWarning(" propagation failed !"; | |
1000 | return 1e+33; | |
1001 | } | |
1002 | ||
1003 | return dca; | |
1004 | } | |
1005 | ||
1006 | ||
58e536c5 | 1007 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1008 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1009 | // |
e99a34df | 1010 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1011 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1012 | // Magnetic field is "b" (kG). | |
1013 | // | |
1014 | // a) The track gets extapolated to the DCA to the vertex. | |
1015 | // b) The impact parameters and their covariance matrix are calculated. | |
1016 | // | |
1017 | // In the case of success, the returned value is kTRUE | |
1018 | // (otherwise, it's kFALSE) | |
1019 | // | |
1020 | Double_t alpha=GetAlpha(); | |
1021 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1022 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1023 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1024 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1025 | x-=xv; y-=yv; |
1026 | ||
1027 | //Estimate the impact parameter neglecting the track curvature | |
1028 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
1029 | if (d > maxd) return kFALSE; | |
1030 | ||
1031 | //Propagate to the DCA | |
e99a34df | 1032 | Double_t crv=kB2C*b*GetParameter()[4]; |
1033 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1034 | ||
f76701bf | 1035 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); |
1036 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
e99a34df | 1037 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1038 | else cs=1.; | |
f76701bf | 1039 | |
1040 | x = xv*cs + yv*sn; | |
1041 | yv=-xv*sn + yv*cs; xv=x; | |
1042 | ||
1043 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1044 | |
1045 | if (dz==0) return kTRUE; | |
1046 | dz[0] = GetParameter()[0] - yv; | |
1047 | dz[1] = GetParameter()[1] - zv; | |
1048 | ||
1049 | if (covar==0) return kTRUE; | |
58e536c5 | 1050 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1051 | |
1052 | //***** Improvements by A.Dainese | |
1053 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1054 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1055 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1056 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1057 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1058 | //***** | |
1059 | ||
29fbcc93 | 1060 | return kTRUE; |
f76701bf | 1061 | } |
1062 | ||
1063 | ||
b1149664 | 1064 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1065 | //---------------------------------------------------------------- | |
1066 | // This function returns a unit vector along the track direction | |
1067 | // in the global coordinate system. | |
1068 | //---------------------------------------------------------------- | |
1069 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1070 | Double_t snp=fP[2]; | |
92934324 | 1071 | Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp)); |
b1149664 | 1072 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1073 | d[0]=(csp*cs - snp*sn)/norm; | |
1074 | d[1]=(snp*cs + csp*sn)/norm; | |
1075 | d[2]=fP[3]/norm; | |
1076 | } | |
1077 | ||
c683ddc2 | 1078 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1079 | //--------------------------------------------------------------------- |
1080 | // This function returns the global track momentum components | |
1081 | // Results for (nearly) straight tracks are meaningless ! | |
1082 | //--------------------------------------------------------------------- | |
1083 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1084 | return Local2GlobalMomentum(p,fAlpha); | |
1085 | } | |
a5e407e9 | 1086 | |
def9660e | 1087 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1088 | //--------------------------------------------------------------------- |
1089 | // Returns x-component of momentum | |
1090 | // Result for (nearly) straight tracks is meaningless ! | |
1091 | //--------------------------------------------------------------------- | |
def9660e | 1092 | |
957fb479 | 1093 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1094 | GetPxPyPz(p); |
1095 | ||
1096 | return p[0]; | |
1097 | } | |
1098 | ||
1099 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1100 | //--------------------------------------------------------------------- |
1101 | // Returns y-component of momentum | |
1102 | // Result for (nearly) straight tracks is meaningless ! | |
1103 | //--------------------------------------------------------------------- | |
def9660e | 1104 | |
957fb479 | 1105 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1106 | GetPxPyPz(p); |
1107 | ||
1108 | return p[1]; | |
1109 | } | |
1110 | ||
1111 | Double_t AliExternalTrackParam::Pz() const { | |
957fb479 | 1112 | //--------------------------------------------------------------------- |
1113 | // Returns z-component of momentum | |
1114 | // Result for (nearly) straight tracks is meaningless ! | |
1115 | //--------------------------------------------------------------------- | |
def9660e | 1116 | |
957fb479 | 1117 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1118 | GetPxPyPz(p); |
1119 | ||
1120 | return p[2]; | |
1121 | } | |
1122 | ||
c683ddc2 | 1123 | Double_t AliExternalTrackParam::Xv() const { |
1124 | //--------------------------------------------------------------------- | |
1125 | // Returns x-component of first track point | |
1126 | //--------------------------------------------------------------------- | |
1127 | ||
1128 | Double_t r[3]={0.,0.,0.}; | |
1129 | GetXYZ(r); | |
1130 | ||
1131 | return r[0]; | |
1132 | } | |
1133 | ||
1134 | Double_t AliExternalTrackParam::Yv() const { | |
1135 | //--------------------------------------------------------------------- | |
1136 | // Returns y-component of first track point | |
1137 | //--------------------------------------------------------------------- | |
1138 | ||
1139 | Double_t r[3]={0.,0.,0.}; | |
1140 | GetXYZ(r); | |
1141 | ||
1142 | return r[1]; | |
1143 | } | |
1144 | ||
1145 | Double_t AliExternalTrackParam::Zv() const { | |
1146 | //--------------------------------------------------------------------- | |
1147 | // Returns z-component of first track point | |
1148 | //--------------------------------------------------------------------- | |
1149 | ||
1150 | Double_t r[3]={0.,0.,0.}; | |
1151 | GetXYZ(r); | |
1152 | ||
1153 | return r[2]; | |
1154 | } | |
1155 | ||
def9660e | 1156 | Double_t AliExternalTrackParam::Theta() const { |
1157 | // return theta angle of momentum | |
1158 | ||
7cdd0c20 | 1159 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1160 | } |
1161 | ||
1162 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1163 | //--------------------------------------------------------------------- |
1164 | // Returns the azimuthal angle of momentum | |
1165 | // 0 <= phi < 2*pi | |
1166 | //--------------------------------------------------------------------- | |
def9660e | 1167 | |
957fb479 | 1168 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1169 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1170 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1171 | ||
1172 | return phi; | |
def9660e | 1173 | } |
1174 | ||
1175 | Double_t AliExternalTrackParam::M() const { | |
1176 | // return particle mass | |
1177 | ||
1178 | // No mass information available so far. | |
1179 | // Redifine in derived class! | |
1180 | ||
1181 | return -999.; | |
1182 | } | |
1183 | ||
1184 | Double_t AliExternalTrackParam::E() const { | |
1185 | // return particle energy | |
1186 | ||
1187 | // No PID information available so far. | |
1188 | // Redifine in derived class! | |
1189 | ||
1190 | return -999.; | |
1191 | } | |
1192 | ||
1193 | Double_t AliExternalTrackParam::Eta() const { | |
1194 | // return pseudorapidity | |
1195 | ||
1196 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1197 | } | |
1198 | ||
1199 | Double_t AliExternalTrackParam::Y() const { | |
1200 | // return rapidity | |
1201 | ||
1202 | // No PID information available so far. | |
1203 | // Redifine in derived class! | |
1204 | ||
1205 | return -999.; | |
1206 | } | |
1207 | ||
c9ec41e8 | 1208 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1209 | //--------------------------------------------------------------------- | |
1210 | // This function returns the global track position | |
1211 | //--------------------------------------------------------------------- | |
1212 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1213 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1214 | } |
1215 | ||
c9ec41e8 | 1216 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1217 | //--------------------------------------------------------------------- | |
1218 | // This function returns the global covariance matrix of the track params | |
1219 | // | |
1220 | // Cov(x,x) ... : cv[0] | |
1221 | // Cov(y,x) ... : cv[1] cv[2] | |
1222 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1223 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1224 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1225 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1226 | // |
c9ec41e8 | 1227 | // Results for (nearly) straight tracks are meaningless ! |
1228 | //--------------------------------------------------------------------- | |
e421f556 | 1229 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1230 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1231 | return kFALSE; | |
a5e407e9 | 1232 | } |
49d13e89 | 1233 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1234 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1235 | return kFALSE; | |
1236 | } | |
1237 | Double_t pt=1./TMath::Abs(fP[4]); | |
1238 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1239 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1240 | |
1241 | Double_t m00=-sn, m10=cs; | |
1242 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1243 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1244 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1245 | ||
854d5d49 | 1246 | m43*=GetSign(); |
1247 | m44*=GetSign(); | |
1248 | m45*=GetSign(); | |
1249 | ||
c9ec41e8 | 1250 | cv[0 ] = fC[0]*m00*m00; |
1251 | cv[1 ] = fC[0]*m00*m10; | |
1252 | cv[2 ] = fC[0]*m10*m10; | |
1253 | cv[3 ] = fC[1]*m00; | |
1254 | cv[4 ] = fC[1]*m10; | |
1255 | cv[5 ] = fC[2]; | |
1256 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1257 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1258 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1259 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1260 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1261 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1262 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1263 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1264 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1265 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1266 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1267 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1268 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1269 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1270 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1271 | |
c9ec41e8 | 1272 | return kTRUE; |
51ad6848 | 1273 | } |
1274 | ||
51ad6848 | 1275 | |
c9ec41e8 | 1276 | Bool_t |
1277 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1278 | //--------------------------------------------------------------------- | |
1279 | // This function returns the global track momentum extrapolated to | |
1280 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1281 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1282 | p[0]=fP[4]; |
1530f89c | 1283 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1284 | p[2]=fP[3]; |
1285 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1286 | } |
1287 | ||
7cf7bb6c | 1288 | Bool_t |
1289 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1290 | //--------------------------------------------------------------------- | |
1291 | // This function returns the local Y-coordinate of the intersection | |
1292 | // point between this track and the reference plane "x" (cm). | |
1293 | // Magnetic field "b" (kG) | |
1294 | //--------------------------------------------------------------------- | |
1295 | Double_t dx=x-fX; | |
1296 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1297 | ||
1530f89c | 1298 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1299 | |
1300 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1301 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1302 | ||
1303 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1304 | y = fP[0] + dx*(f1+f2)/(r1+r2); | |
1305 | return kTRUE; | |
1306 | } | |
1307 | ||
6c94f330 | 1308 | Bool_t |
1309 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1310 | //--------------------------------------------------------------------- | |
1311 | // This function returns the local Z-coordinate of the intersection | |
1312 | // point between this track and the reference plane "x" (cm). | |
1313 | // Magnetic field "b" (kG) | |
1314 | //--------------------------------------------------------------------- | |
1315 | Double_t dx=x-fX; | |
1316 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1317 | ||
1318 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; | |
1319 | ||
1320 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1321 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1322 | ||
1323 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); | |
1324 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! | |
1325 | return kTRUE; | |
1326 | } | |
1327 | ||
c9ec41e8 | 1328 | Bool_t |
1329 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1330 | //--------------------------------------------------------------------- | |
1331 | // This function returns the global track position extrapolated to | |
1332 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1333 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1334 | Double_t dx=x-fX; |
e421f556 | 1335 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1336 | ||
1530f89c | 1337 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1338 | |
e421f556 | 1339 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1340 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1341 | |
1342 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1343 | r[0] = x; | |
1344 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
6c94f330 | 1345 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; |
c9ec41e8 | 1346 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1347 | } |
1348 | ||
51ad6848 | 1349 | //_____________________________________________________________________________ |
1350 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1351 | { | |
1352 | // print the parameters and the covariance matrix | |
1353 | ||
1354 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1355 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1356 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1357 | printf(" covariance: %12g\n", fC[0]); | |
1358 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1359 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1360 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1361 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1362 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1363 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1364 | } |
5b77d93c | 1365 | |
c194ba83 | 1366 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1367 | // | |
1368 | // Get sinus at given x | |
1369 | // | |
1530f89c | 1370 | Double_t crv=GetC(b); |
c194ba83 | 1371 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1372 | Double_t dx = x-fX; | |
1373 | Double_t res = fP[2]+dx*crv; | |
1374 | return res; | |
1375 | } | |
bf00ebb8 | 1376 | |
1377 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1378 | //------------------------------------------------------------------------ | |
1379 | // Get the distance between two tracks at the local position x | |
1380 | // working in the local frame of this track. | |
1381 | // Origin : Marian.Ivanov@cern.ch | |
1382 | //----------------------------------------------------------------------- | |
1383 | Double_t xyz[3]; | |
1384 | Double_t xyz2[3]; | |
1385 | xyz[0]=x; | |
1386 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1387 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1388 | // | |
1389 | // | |
1390 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1391 | xyz2[0]=x; | |
1392 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1393 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1394 | }else{ | |
1395 | // | |
1396 | Double_t xyz1[3]; | |
1397 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1398 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1399 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1400 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1401 | // | |
1402 | xyz1[0]=xyz2[0]; | |
1403 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1404 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1405 | // | |
1406 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1407 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1408 | xyz2[2] = xyz1[2]; | |
1409 | } | |
1410 | dist[0] = xyz[0]-xyz2[0]; | |
1411 | dist[1] = xyz[1]-xyz2[1]; | |
1412 | dist[2] = xyz[2]-xyz2[2]; | |
1413 | ||
1414 | return kTRUE; | |
1415 | } | |
0c19adf7 | 1416 | |
1417 | ||
1418 | // | |
1419 | // Draw functionality. | |
1420 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1421 | // | |
1422 | ||
1423 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1424 | // | |
1425 | // Draw track line | |
1426 | // | |
1427 | if (minR>maxR) return ; | |
1428 | if (stepR<=0) return ; | |
1429 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1430 | if (npoints<1) return; | |
1431 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1432 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1433 | polymarker->Draw(); | |
1434 | } | |
1435 | ||
1436 | // | |
1437 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1438 | // | |
1439 | // Fill points in the polymarker | |
1440 | // | |
1441 | Int_t counter=0; | |
1442 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1443 | Double_t point[3]; | |
1444 | GetXYZAt(r,magF,point); | |
1445 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
1446 | printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); | |
1447 | counter++; | |
1448 | } | |
1449 | } |