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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> |
d46683db | 29 | #include <TPolyMarker3D.h> |
30 | #include <TVector3.h> | |
31 | ||
51ad6848 | 32 | #include "AliExternalTrackParam.h" |
58e536c5 | 33 | #include "AliVVertex.h" |
6c94f330 | 34 | #include "AliLog.h" |
51ad6848 | 35 | |
36 | ClassImp(AliExternalTrackParam) | |
37 | ||
ed5f2849 | 38 | Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; |
39 | ||
51ad6848 | 40 | //_____________________________________________________________________________ |
90e48c0c | 41 | AliExternalTrackParam::AliExternalTrackParam() : |
4f6e22bd | 42 | AliVTrack(), |
90e48c0c | 43 | fX(0), |
c9ec41e8 | 44 | fAlpha(0) |
51ad6848 | 45 | { |
90e48c0c | 46 | // |
47 | // default constructor | |
48 | // | |
c9ec41e8 | 49 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
50 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 51 | } |
52 | ||
6c94f330 | 53 | //_____________________________________________________________________________ |
54 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
4f6e22bd | 55 | AliVTrack(track), |
6c94f330 | 56 | fX(track.fX), |
57 | fAlpha(track.fAlpha) | |
58 | { | |
59 | // | |
60 | // copy constructor | |
61 | // | |
62 | for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i]; | |
63 | for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i]; | |
64 | } | |
65 | ||
def9660e | 66 | //_____________________________________________________________________________ |
67 | AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar) | |
68 | { | |
69 | // | |
70 | // assignment operator | |
71 | // | |
72 | ||
73 | if (this!=&trkPar) { | |
4f6e22bd | 74 | AliVTrack::operator=(trkPar); |
def9660e | 75 | fX = trkPar.fX; |
76 | fAlpha = trkPar.fAlpha; | |
77 | ||
78 | for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i]; | |
79 | for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i]; | |
80 | } | |
81 | ||
82 | return *this; | |
83 | } | |
84 | ||
51ad6848 | 85 | //_____________________________________________________________________________ |
86 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
87 | const Double_t param[5], | |
90e48c0c | 88 | const Double_t covar[15]) : |
4f6e22bd | 89 | AliVTrack(), |
90e48c0c | 90 | fX(x), |
c9ec41e8 | 91 | fAlpha(alpha) |
51ad6848 | 92 | { |
90e48c0c | 93 | // |
94 | // create external track parameters from given arguments | |
95 | // | |
c9ec41e8 | 96 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
97 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 98 | } |
99 | ||
4f6e22bd | 100 | //_____________________________________________________________________________ |
101 | AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) : | |
102 | AliVTrack(), | |
103 | fX(0.), | |
104 | fAlpha(0.) | |
105 | { | |
106 | // | |
610e3088 | 107 | // Constructor from virtual track, |
108 | // This is not a copy contructor ! | |
4f6e22bd | 109 | // |
610e3088 | 110 | |
111 | if (vTrack->InheritsFrom("AliExternalTrackParam")) { | |
112 | AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !"); | |
113 | AliWarning("Calling the default constructor..."); | |
114 | AliExternalTrackParam(); | |
115 | return; | |
116 | } | |
117 | ||
892be05f | 118 | Double_t xyz[3],pxpypz[3],cv[21]; |
119 | vTrack->GetXYZ(xyz); | |
120 | pxpypz[0]=vTrack->Px(); | |
121 | pxpypz[1]=vTrack->Py(); | |
122 | pxpypz[2]=vTrack->Pz(); | |
4f6e22bd | 123 | vTrack->GetCovarianceXYZPxPyPz(cv); |
124 | Short_t sign = (Short_t)vTrack->Charge(); | |
125 | ||
126 | Set(xyz,pxpypz,cv,sign); | |
127 | } | |
128 | ||
90e48c0c | 129 | //_____________________________________________________________________________ |
da4e3deb | 130 | AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], |
131 | Double_t cv[21],Short_t sign) : | |
4f6e22bd | 132 | AliVTrack(), |
da4e3deb | 133 | fX(0.), |
134 | fAlpha(0.) | |
4f6e22bd | 135 | { |
136 | // | |
137 | // constructor from the global parameters | |
138 | // | |
139 | ||
140 | Set(xyz,pxpypz,cv,sign); | |
141 | } | |
142 | ||
143 | //_____________________________________________________________________________ | |
144 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
145 | Double_t cv[21],Short_t sign) | |
da4e3deb | 146 | { |
147 | // | |
148 | // create external track parameters from the global parameters | |
149 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
150 | // A.Dainese 10.10.08 | |
151 | ||
aff56ff7 | 152 | // Calculate alpha: the rotation angle of the corresponding local system. |
153 | // | |
154 | // For global radial position inside the beam pipe, alpha is the | |
155 | // azimuthal angle of the momentum projected on (x,y). | |
156 | // | |
157 | // For global radial position outside the beam pipe, alpha is the | |
158 | // azimuthal angle of the centre of the TPC sector in which the point | |
159 | // xyz lies | |
160 | // | |
161 | Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1]; | |
162 | if (radPos2 < 3.*3.) { // inside beam pipe | |
163 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); | |
164 | } else { // outside beam pipe | |
165 | Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]); | |
166 | fAlpha = | |
167 | TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10); | |
168 | } | |
da4e3deb | 169 | |
170 | // Get the vertex of origin and the momentum | |
171 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
172 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
173 | ||
174 | // Rotate to the local coordinate system | |
175 | ver.RotateZ(-fAlpha); | |
176 | mom.RotateZ(-fAlpha); | |
177 | ||
178 | // x of the reference plane | |
179 | fX = ver.X(); | |
180 | ||
181 | Double_t charge = (Double_t)sign; | |
182 | ||
183 | fP[0] = ver.Y(); | |
184 | fP[1] = ver.Z(); | |
185 | fP[2] = TMath::Sin(mom.Phi()); | |
186 | fP[3] = mom.Pz()/mom.Pt(); | |
187 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
188 | ||
189 | // Covariance matrix (formulas to be simplified) | |
190 | ||
191 | Double_t pt=1./TMath::Abs(fP[4]); | |
192 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
193 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); | |
194 | ||
195 | Double_t m00=-sn;// m10=cs; | |
196 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
197 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
198 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
199 | ||
200 | m43*=GetSign(); | |
201 | m44*=GetSign(); | |
202 | m45*=GetSign(); | |
203 | ||
204 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
205 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
206 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
207 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
208 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
209 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
210 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
211 | ||
212 | fC[0 ] = cv[0 ]+cv[2 ]; | |
213 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
214 | fC[2 ] = cv[5 ]; | |
215 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
216 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
217 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
218 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
219 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
220 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
221 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
222 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
223 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
224 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
225 | Double_t b2=m23*m35; | |
226 | Double_t b3=m43*m35; | |
227 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
228 | Double_t b5=m24*m35; | |
229 | Double_t b6=m44*m35; | |
230 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
231 | fC[13] = b1/b3-b2*fC[8]/b3; | |
232 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 233 | |
234 | return; | |
da4e3deb | 235 | } |
236 | ||
51ad6848 | 237 | //_____________________________________________________________________________ |
c9ec41e8 | 238 | void AliExternalTrackParam::Reset() { |
1530f89c | 239 | // |
240 | // Resets all the parameters to 0 | |
241 | // | |
c9ec41e8 | 242 | fX=fAlpha=0.; |
243 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
244 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 245 | } |
246 | ||
3775b0ca | 247 | //_____________________________________________________________________________ |
248 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
249 | // | |
250 | // Add "something" to the track covarince matrix. | |
251 | // May be needed to account for unknown mis-calibration/mis-alignment | |
252 | // | |
253 | fC[0] +=c[0]; | |
254 | fC[1] +=c[1]; fC[2] +=c[2]; | |
255 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
256 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
257 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
258 | } | |
259 | ||
260 | ||
c9ec41e8 | 261 | Double_t AliExternalTrackParam::GetP() const { |
262 | //--------------------------------------------------------------------- | |
263 | // This function returns the track momentum | |
264 | // Results for (nearly) straight tracks are meaningless ! | |
265 | //--------------------------------------------------------------------- | |
06fb4a2f | 266 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 267 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 268 | } |
269 | ||
1d99986f | 270 | Double_t AliExternalTrackParam::Get1P() const { |
271 | //--------------------------------------------------------------------- | |
272 | // This function returns the 1/(track momentum) | |
273 | //--------------------------------------------------------------------- | |
274 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
275 | } | |
276 | ||
c9ec41e8 | 277 | //_______________________________________________________________________ |
c7bafca9 | 278 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 279 | //------------------------------------------------------------------ |
280 | // This function calculates the transverse impact parameter | |
281 | // with respect to a point with global coordinates (x,y) | |
282 | // in the magnetic field "b" (kG) | |
283 | //------------------------------------------------------------------ | |
5773defd | 284 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 285 | Double_t rp4=GetC(b); |
c9ec41e8 | 286 | |
287 | Double_t xt=fX, yt=fP[0]; | |
288 | ||
289 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
290 | Double_t a = x*cs + y*sn; | |
291 | y = -x*sn + y*cs; x=a; | |
292 | xt-=x; yt-=y; | |
293 | ||
294 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
295 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
1530f89c | 296 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
297 | } | |
298 | ||
299 | //_______________________________________________________________________ | |
300 | void AliExternalTrackParam:: | |
301 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
302 | //------------------------------------------------------------------ | |
303 | // This function calculates the transverse and longitudinal impact parameters | |
304 | // with respect to a point with global coordinates (x,y) | |
305 | // in the magnetic field "b" (kG) | |
306 | //------------------------------------------------------------------ | |
307 | Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1); | |
308 | Double_t xt=fX, yt=fP[0]; | |
309 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
310 | Double_t a = x*cs + y*sn; | |
311 | y = -x*sn + y*cs; x=a; | |
312 | xt-=x; yt-=y; | |
313 | ||
314 | Double_t rp4=GetC(b); | |
315 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
316 | dz[0] = -(xt*f1 - yt*r1); | |
317 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
318 | return; | |
319 | } | |
320 | ||
321 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
322 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
323 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
324 | dz[0] = -a/(1 + rr); | |
325 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2); | |
326 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; | |
51ad6848 | 327 | } |
328 | ||
49d13e89 | 329 | //_______________________________________________________________________ |
330 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
331 | //------------------------------------------------------------------ | |
332 | // This function calculates the transverse impact parameter | |
333 | // with respect to a point with global coordinates (xv,yv) | |
334 | // neglecting the track curvature. | |
335 | //------------------------------------------------------------------ | |
336 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
337 | Double_t x= xv*cs + yv*sn; | |
338 | Double_t y=-xv*sn + yv*cs; | |
339 | ||
340 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
341 | ||
1530f89c | 342 | return -d; |
49d13e89 | 343 | } |
344 | ||
116b445b | 345 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
7dded1d5 | 346 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr, |
347 | Double_t (*Bethe)(Double_t)) { | |
116b445b | 348 | //------------------------------------------------------------------ |
349 | // This function corrects the track parameters for the crossed material. | |
350 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
351 | // "xTimesRho" - is the product length*density (g/cm^2). | |
352 | // "mass" - the mass of this particle (GeV/c^2). | |
353 | //------------------------------------------------------------------ | |
354 | Double_t &fP2=fP[2]; | |
355 | Double_t &fP3=fP[3]; | |
356 | Double_t &fP4=fP[4]; | |
357 | ||
358 | Double_t &fC22=fC[5]; | |
359 | Double_t &fC33=fC[9]; | |
360 | Double_t &fC43=fC[13]; | |
361 | Double_t &fC44=fC[14]; | |
362 | ||
7dded1d5 | 363 | //Apply angle correction, if requested |
364 | if(anglecorr) { | |
365 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
366 | xOverX0 *=angle; | |
367 | xTimesRho *=angle; | |
368 | } | |
369 | ||
116b445b | 370 | Double_t p=GetP(); |
371 | Double_t p2=p*p; | |
372 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 373 | |
9f2bec63 | 374 | //Calculating the multiple scattering corrections****************** |
375 | Double_t cC22 = 0.; | |
376 | Double_t cC33 = 0.; | |
377 | Double_t cC43 = 0.; | |
378 | Double_t cC44 = 0.; | |
116b445b | 379 | if (xOverX0 != 0) { |
380 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
381 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
9f2bec63 | 382 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
383 | cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
384 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
385 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
386 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
116b445b | 387 | } |
388 | ||
9f2bec63 | 389 | //Calculating the energy loss corrections************************ |
390 | Double_t cP4=1.; | |
116b445b | 391 | if ((xTimesRho != 0.) && (beta2 < 1.)) { |
d46683db | 392 | Double_t dE=Bethe(p/mass)*xTimesRho; |
116b445b | 393 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
394 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
9f2bec63 | 395 | cP4 = (1.- e/p2*dE); |
396 | if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c | |
4b2fa3ce | 397 | |
116b445b | 398 | |
399 | // Approximate energy loss fluctuation (M.Ivanov) | |
400 | const Double_t knst=0.07; // To be tuned. | |
401 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 402 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
116b445b | 403 | |
404 | } | |
405 | ||
9f2bec63 | 406 | //Applying the corrections***************************** |
407 | fC22 += cC22; | |
408 | fC33 += cC33; | |
409 | fC43 += cC43; | |
410 | fC44 += cC44; | |
411 | fP4 *= cP4; | |
412 | ||
116b445b | 413 | return kTRUE; |
414 | } | |
415 | ||
416 | ||
ee5dba5e | 417 | Bool_t AliExternalTrackParam::CorrectForMaterial |
418 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 419 | //------------------------------------------------------------------ |
116b445b | 420 | // Deprecated function ! |
421 | // Better use CorrectForMeanMaterial instead of it. | |
422 | // | |
c7bafca9 | 423 | // This function corrects the track parameters for the crossed material |
424 | // "d" - the thickness (fraction of the radiation length) | |
425 | // "x0" - the radiation length (g/cm^2) | |
426 | // "mass" - the mass of this particle (GeV/c^2) | |
427 | //------------------------------------------------------------------ | |
428 | Double_t &fP2=fP[2]; | |
429 | Double_t &fP3=fP[3]; | |
430 | Double_t &fP4=fP[4]; | |
431 | ||
432 | Double_t &fC22=fC[5]; | |
433 | Double_t &fC33=fC[9]; | |
434 | Double_t &fC43=fC[13]; | |
435 | Double_t &fC44=fC[14]; | |
436 | ||
7b5ef2e6 | 437 | Double_t p=GetP(); |
438 | Double_t p2=p*p; | |
c7bafca9 | 439 | Double_t beta2=p2/(p2 + mass*mass); |
440 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
441 | ||
442 | //Multiple scattering****************** | |
9f2bec63 | 443 | Double_t cC22 = 0.; |
444 | Double_t cC33 = 0.; | |
445 | Double_t cC43 = 0.; | |
446 | Double_t cC44 = 0.; | |
c7bafca9 | 447 | if (d!=0) { |
448 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
449 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
9f2bec63 | 450 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
451 | cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
452 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
453 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
454 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
c7bafca9 | 455 | } |
456 | ||
457 | //Energy losses************************ | |
9f2bec63 | 458 | Double_t cP4=1.; |
8fc1985d | 459 | if (x0!=0. && beta2<1) { |
c7bafca9 | 460 | d*=x0; |
d46683db | 461 | Double_t dE=Bethe(p/mass)*d; |
ee5dba5e | 462 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
ae666100 | 463 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! |
9f2bec63 | 464 | cP4 = (1.- e/p2*dE); |
ee5dba5e | 465 | |
466 | // Approximate energy loss fluctuation (M.Ivanov) | |
ed5f2849 | 467 | const Double_t knst=0.07; // To be tuned. |
468 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 469 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
ee5dba5e | 470 | |
c7bafca9 | 471 | } |
472 | ||
9f2bec63 | 473 | fC22 += cC22; |
474 | fC33 += cC33; | |
475 | fC43 += cC43; | |
476 | fC44 += cC44; | |
477 | fP4 *= cP4; | |
478 | ||
c7bafca9 | 479 | return kTRUE; |
480 | } | |
481 | ||
9c56b409 | 482 | Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg, |
483 | Double_t kp1, | |
484 | Double_t kp2, | |
485 | Double_t kp3, | |
486 | Double_t kp4, | |
487 | Double_t kp5) { | |
488 | // | |
489 | // This is the empirical ALEPH parameterization of the Bethe-Bloch formula. | |
490 | // It is normalized to 1 at the minimum. | |
491 | // | |
492 | // bg - beta*gamma | |
493 | // | |
494 | // The default values for the kp* parameters are for ALICE TPC. | |
495 | // The returned value is in MIP units | |
496 | // | |
497 | ||
498 | Double_t beta = bg/TMath::Sqrt(1.+ bg*bg); | |
499 | ||
500 | Double_t aa = TMath::Power(beta,kp4); | |
501 | Double_t bb = TMath::Power(1./bg,kp5); | |
502 | ||
503 | bb=TMath::Log(kp3+bb); | |
504 | ||
505 | return (kp2-aa-bb)*kp1/aa; | |
506 | } | |
507 | ||
508 | Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg, | |
509 | Double_t kp0, | |
510 | Double_t kp1, | |
511 | Double_t kp2, | |
512 | Double_t kp3, | |
513 | Double_t kp4) { | |
514 | // | |
515 | // This is the parameterization of the Bethe-Bloch formula inspired by Geant. | |
516 | // | |
517 | // bg - beta*gamma | |
518 | // kp0 - density [g/cm^3] | |
519 | // kp1 - density effect first junction point | |
520 | // kp2 - density effect second junction point | |
521 | // kp3 - mean excitation energy [GeV] | |
522 | // kp4 - mean Z/A | |
523 | // | |
524 | // The default values for the kp* parameters are for silicon. | |
525 | // The returned value is in [GeV/(g/cm^2)]. | |
526 | // | |
527 | ||
528 | const Double_t mK = 0.307075e-3; // [GeV*cm^2/g] | |
529 | const Double_t me = 0.511e-3; // [GeV/c^2] | |
530 | const Double_t rho = kp0; | |
531 | const Double_t x0 = kp1*2.303; | |
532 | const Double_t x1 = kp2*2.303; | |
533 | const Double_t mI = kp3; | |
534 | const Double_t mZA = kp4; | |
535 | const Double_t bg2 = bg*bg; | |
536 | const Double_t maxT= 2*me*bg2; // neglecting the electron mass | |
537 | ||
538 | //*** Density effect | |
539 | Double_t d2=0.; | |
540 | const Double_t x=TMath::Log(bg); | |
541 | const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI); | |
542 | if (x > x1) { | |
543 | d2 = lhwI + x - 0.5; | |
544 | } else if (x > x0) { | |
545 | const Double_t r=(x1-x)/(x1-x0); | |
546 | d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r; | |
547 | } | |
548 | ||
549 | return mK*mZA*(1+bg2)/bg2* | |
550 | (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2); | |
551 | } | |
552 | ||
d46683db | 553 | Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) { |
ee5dba5e | 554 | //------------------------------------------------------------------ |
d46683db | 555 | // This is an approximation of the Bethe-Bloch formula, |
556 | // reasonable for solid materials. | |
557 | // All the parameters are, in fact, for Si. | |
558 | // The returned value is in [GeV] | |
ee5dba5e | 559 | //------------------------------------------------------------------ |
a821848c | 560 | |
9c56b409 | 561 | return BetheBlochGeant(bg); |
d46683db | 562 | } |
ee5dba5e | 563 | |
d46683db | 564 | Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) { |
565 | //------------------------------------------------------------------ | |
566 | // This is an approximation of the Bethe-Bloch formula, | |
567 | // reasonable for gas materials. | |
568 | // All the parameters are, in fact, for Ne. | |
569 | // The returned value is in [GeV] | |
570 | //------------------------------------------------------------------ | |
571 | ||
572 | const Double_t rho = 0.9e-3; | |
573 | const Double_t x0 = 2.; | |
574 | const Double_t x1 = 4.; | |
575 | const Double_t mI = 140.e-9; | |
576 | const Double_t mZA = 0.49555; | |
577 | ||
9c56b409 | 578 | return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); |
ee5dba5e | 579 | } |
580 | ||
49d13e89 | 581 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
582 | //------------------------------------------------------------------ | |
583 | // Transform this track to the local coord. system rotated | |
584 | // by angle "alpha" (rad) with respect to the global coord. system. | |
585 | //------------------------------------------------------------------ | |
dfcef74c | 586 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
587 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
588 | return kFALSE; | |
589 | } | |
590 | ||
49d13e89 | 591 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
592 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
593 | ||
594 | Double_t &fP0=fP[0]; | |
595 | Double_t &fP2=fP[2]; | |
596 | Double_t &fC00=fC[0]; | |
597 | Double_t &fC10=fC[1]; | |
598 | Double_t &fC20=fC[3]; | |
599 | Double_t &fC21=fC[4]; | |
600 | Double_t &fC22=fC[5]; | |
601 | Double_t &fC30=fC[6]; | |
602 | Double_t &fC32=fC[8]; | |
603 | Double_t &fC40=fC[10]; | |
604 | Double_t &fC42=fC[12]; | |
605 | ||
606 | Double_t x=fX; | |
607 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
608 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
609 | ||
dfcef74c | 610 | Double_t tmp=sf*ca - cf*sa; |
0b69bbb2 | 611 | if (TMath::Abs(tmp) >= kAlmost1) { |
612 | AliError(Form("Rotation failed ! %.10e",tmp)); | |
613 | return kFALSE; | |
614 | } | |
dfcef74c | 615 | |
49d13e89 | 616 | fAlpha = alpha; |
617 | fX = x*ca + fP0*sa; | |
618 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 619 | fP2= tmp; |
49d13e89 | 620 | |
06fb4a2f | 621 | if (TMath::Abs(cf)<kAlmost0) { |
622 | AliError(Form("Too small cosine value %f",cf)); | |
623 | cf = kAlmost0; | |
624 | } | |
625 | ||
49d13e89 | 626 | Double_t rr=(ca+sf/cf*sa); |
627 | ||
628 | fC00 *= (ca*ca); | |
629 | fC10 *= ca; | |
630 | fC20 *= ca*rr; | |
631 | fC21 *= rr; | |
632 | fC22 *= rr*rr; | |
633 | fC30 *= ca; | |
634 | fC32 *= rr; | |
635 | fC40 *= ca; | |
636 | fC42 *= rr; | |
637 | ||
638 | return kTRUE; | |
639 | } | |
640 | ||
641 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
642 | //---------------------------------------------------------------- | |
643 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
644 | //---------------------------------------------------------------- | |
49d13e89 | 645 | Double_t dx=xk-fX; |
e421f556 | 646 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 647 | |
1530f89c | 648 | Double_t crv=GetC(b); |
5773defd | 649 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
650 | ||
49d13e89 | 651 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 652 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 653 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
654 | ||
655 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
656 | Double_t | |
657 | &fC00=fC[0], | |
658 | &fC10=fC[1], &fC11=fC[2], | |
659 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
660 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
661 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
662 | ||
663 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
664 | ||
665 | fX=xk; | |
666 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 667 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 668 | fP2 += dx*crv; |
669 | ||
670 | //f = F - 1 | |
671 | ||
672 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
673 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
674 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
675 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
676 | Double_t f13= dx/r1; | |
677 | Double_t f24= dx; f24*=cc; | |
678 | ||
679 | //b = C*ft | |
680 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
681 | Double_t b02=f24*fC40; | |
682 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
683 | Double_t b12=f24*fC41; | |
684 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
685 | Double_t b22=f24*fC42; | |
686 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
687 | Double_t b42=f24*fC44; | |
688 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
689 | Double_t b32=f24*fC43; | |
690 | ||
691 | //a = f*b = f*C*ft | |
692 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
693 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
694 | Double_t a22=f24*b42; | |
695 | ||
696 | //F*C*Ft = C + (b + bt + a) | |
697 | fC00 += b00 + b00 + a00; | |
698 | fC10 += b10 + b01 + a01; | |
699 | fC20 += b20 + b02 + a02; | |
700 | fC30 += b30; | |
701 | fC40 += b40; | |
702 | fC11 += b11 + b11 + a11; | |
703 | fC21 += b21 + b12 + a12; | |
704 | fC31 += b31; | |
705 | fC41 += b41; | |
706 | fC22 += b22 + b22 + a22; | |
707 | fC32 += b32; | |
708 | fC42 += b42; | |
709 | ||
710 | return kTRUE; | |
711 | } | |
712 | ||
9f2bec63 | 713 | Bool_t |
714 | AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) { | |
715 | //------------------------------------------------------------------ | |
716 | // Transform this track to the local coord. system rotated | |
717 | // by angle "alpha" (rad) with respect to the global coord. system, | |
718 | // and propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
719 | //------------------------------------------------------------------ | |
720 | ||
721 | //Save the parameters | |
722 | Double_t as=fAlpha; | |
723 | Double_t xs=fX; | |
724 | Double_t ps[5], cs[15]; | |
725 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
726 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
727 | ||
728 | if (Rotate(alpha)) | |
729 | if (PropagateTo(x,b)) return kTRUE; | |
730 | ||
731 | //Restore the parameters, if the operation failed | |
732 | fAlpha=as; | |
733 | fX=xs; | |
734 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
735 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
736 | return kFALSE; | |
737 | } | |
738 | ||
739 | ||
052daaff | 740 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
741 | Double_t p[3], Double_t bz) const { | |
742 | //+++++++++++++++++++++++++++++++++++++++++ | |
743 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
744 | // Extrapolate track along simple helix in magnetic field | |
745 | // Arguments: len -distance alogn helix, [cm] | |
746 | // bz - mag field, [kGaus] | |
747 | // Returns: x and p contain extrapolated positon and momentum | |
748 | // The momentum returned for straight-line tracks is meaningless ! | |
749 | //+++++++++++++++++++++++++++++++++++++++++ | |
750 | GetXYZ(x); | |
751 | ||
2258e165 | 752 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks |
052daaff | 753 | Double_t unit[3]; GetDirection(unit); |
754 | x[0]+=unit[0]*len; | |
755 | x[1]+=unit[1]*len; | |
756 | x[2]+=unit[2]*len; | |
757 | ||
758 | p[0]=unit[0]/kAlmost0; | |
759 | p[1]=unit[1]/kAlmost0; | |
760 | p[2]=unit[2]/kAlmost0; | |
761 | } else { | |
762 | GetPxPyPz(p); | |
763 | Double_t pp=GetP(); | |
764 | Double_t a = -kB2C*bz*GetSign(); | |
765 | Double_t rho = a/pp; | |
766 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
767 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
768 | x[2] += p[2]*len/pp; | |
769 | ||
770 | Double_t p0=p[0]; | |
771 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
772 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
773 | } | |
774 | } | |
775 | ||
776 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
777 | Double_t bz) const { | |
778 | //+++++++++++++++++++++++++++++++++++++++++ | |
779 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
780 | // Finds point of intersection (if exists) of the helix with the plane. | |
781 | // Stores result in fX and fP. | |
782 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
783 | // and vector, normal to the plane | |
784 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
785 | //+++++++++++++++++++++++++++++++++++++++++ | |
786 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
787 | ||
788 | //estimates initial helix length up to plane | |
789 | Double_t s= | |
790 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
791 | Double_t dist=99999,distPrev=dist; | |
792 | Double_t x[3],p[3]; | |
793 | while(TMath::Abs(dist)>0.00001){ | |
794 | //calculates helix at the distance s from x0 ALONG the helix | |
795 | Propagate(s,x,p,bz); | |
796 | ||
797 | //distance between current helix position and plane | |
798 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
799 | ||
800 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
801 | distPrev=dist; | |
802 | s-=dist; | |
803 | } | |
804 | //on exit pnt is intersection point,norm is track vector at that point, | |
805 | //all in MARS | |
806 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
807 | return kTRUE; | |
808 | } | |
809 | ||
49d13e89 | 810 | Double_t |
811 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
812 | //---------------------------------------------------------------- | |
813 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
814 | //---------------------------------------------------------------- | |
815 | Double_t sdd = fC[0] + cov[0]; | |
816 | Double_t sdz = fC[1] + cov[1]; | |
817 | Double_t szz = fC[2] + cov[2]; | |
818 | Double_t det = sdd*szz - sdz*sdz; | |
819 | ||
820 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
821 | ||
822 | Double_t d = fP[0] - p[0]; | |
823 | Double_t z = fP[1] - p[1]; | |
824 | ||
825 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
826 | } | |
827 | ||
4b189f98 | 828 | Double_t AliExternalTrackParam:: |
829 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
830 | //---------------------------------------------------------------- | |
831 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 832 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 833 | // |
834 | // Cov(x,x) ... : covxyz[0] | |
835 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
836 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
837 | //---------------------------------------------------------------- | |
838 | ||
839 | Double_t res[3] = { | |
840 | GetX() - p[0], | |
841 | GetY() - p[1], | |
842 | GetZ() - p[2] | |
843 | }; | |
844 | ||
845 | Double_t f=GetSnp(); | |
846 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
847 | Double_t r=TMath::Sqrt(1.- f*f); | |
848 | Double_t a=f/r, b=GetTgl()/r; | |
849 | ||
850 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
851 | ||
852 | TMatrixDSym v(3); | |
853 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
854 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
855 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
856 | ||
857 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
858 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
859 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
860 | ||
861 | v.Invert(); | |
862 | if (!v.IsValid()) return kVeryBig; | |
863 | ||
864 | Double_t chi2=0.; | |
865 | for (Int_t i = 0; i < 3; i++) | |
866 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
867 | ||
868 | return chi2; | |
869 | ||
870 | ||
871 | } | |
872 | ||
1e023a36 | 873 | Bool_t AliExternalTrackParam:: |
874 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
875 | //---------------------------------------------------------------- | |
876 | // Propagate this track to the plane | |
877 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
878 | // belongs to. | |
879 | // The magnetic field is "bz" (kG) | |
880 | // | |
881 | // The track curvature and the change of the covariance matrix | |
882 | // of the track parameters are negleted ! | |
883 | // (So the "step" should be small compared with 1/curvature) | |
884 | //---------------------------------------------------------------- | |
885 | ||
886 | Double_t f=GetSnp(); | |
887 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
888 | Double_t r=TMath::Sqrt(1.- f*f); | |
889 | Double_t a=f/r, b=GetTgl()/r; | |
890 | ||
891 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
892 | ||
893 | TMatrixDSym tV(3); | |
894 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
895 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
896 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
897 | ||
898 | TMatrixDSym pV(3); | |
899 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
900 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
901 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
902 | ||
903 | TMatrixDSym tpV(tV); | |
904 | tpV+=pV; | |
905 | tpV.Invert(); | |
906 | if (!tpV.IsValid()) return kFALSE; | |
907 | ||
908 | TMatrixDSym pW(3),tW(3); | |
909 | for (Int_t i=0; i<3; i++) | |
910 | for (Int_t j=0; j<3; j++) { | |
911 | pW(i,j)=tW(i,j)=0.; | |
912 | for (Int_t k=0; k<3; k++) { | |
913 | pW(i,j) += tV(i,k)*tpV(k,j); | |
914 | tW(i,j) += pV(i,k)*tpV(k,j); | |
915 | } | |
916 | } | |
917 | ||
918 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
919 | ||
920 | Double_t x=0.; | |
921 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
922 | Double_t crv=GetC(bz); | |
923 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
924 | f += crv*(x-fX); | |
925 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
926 | fX=x; | |
927 | ||
928 | fP[0]=0.; | |
929 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
930 | fP[1]=0.; | |
931 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
932 | ||
933 | return kTRUE; | |
934 | } | |
935 | ||
e23a38cb | 936 | Double_t *AliExternalTrackParam::GetResiduals( |
937 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
938 | //------------------------------------------------------------------ | |
939 | // Returns the track residuals with the space point "p" having | |
940 | // the covariance matrix "cov". | |
941 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
942 | // otherwise they must be predicted. | |
943 | //------------------------------------------------------------------ | |
944 | static Double_t res[2]; | |
945 | ||
946 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
947 | if (updated) { | |
948 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
949 | } else { | |
950 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
951 | } | |
952 | Double_t det=r00*r11 - r01*r01; | |
953 | ||
954 | if (TMath::Abs(det) < kAlmost0) return 0; | |
955 | ||
956 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 957 | |
958 | if (r00 < 0.) return 0; | |
959 | if (r11 < 0.) return 0; | |
960 | ||
e23a38cb | 961 | Double_t dy = fP[0] - p[0]; |
962 | Double_t dz = fP[1] - p[1]; | |
963 | ||
964 | res[0]=dy*TMath::Sqrt(r00); | |
965 | res[1]=dz*TMath::Sqrt(r11); | |
966 | ||
967 | return res; | |
968 | } | |
969 | ||
49d13e89 | 970 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
971 | //------------------------------------------------------------------ | |
972 | // Update the track parameters with the space point "p" having | |
973 | // the covariance matrix "cov" | |
974 | //------------------------------------------------------------------ | |
975 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
976 | Double_t | |
977 | &fC00=fC[0], | |
978 | &fC10=fC[1], &fC11=fC[2], | |
979 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
980 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
981 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
982 | ||
983 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
984 | r00+=fC00; r01+=fC10; r11+=fC11; | |
985 | Double_t det=r00*r11 - r01*r01; | |
986 | ||
987 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
988 | ||
989 | ||
990 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
991 | ||
992 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
993 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
994 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
995 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
996 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
997 | ||
998 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
999 | Double_t sf=fP2 + k20*dy + k21*dz; | |
1000 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
1001 | ||
1002 | fP0 += k00*dy + k01*dz; | |
1003 | fP1 += k10*dy + k11*dz; | |
1004 | fP2 = sf; | |
1005 | fP3 += k30*dy + k31*dz; | |
1006 | fP4 += k40*dy + k41*dz; | |
1007 | ||
1008 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
1009 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
1010 | ||
1011 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
1012 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
1013 | fC40-=k00*c04+k01*c14; | |
1014 | ||
1015 | fC11-=k10*c01+k11*fC11; | |
1016 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
1017 | fC41-=k10*c04+k11*c14; | |
1018 | ||
1019 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
1020 | fC42-=k20*c04+k21*c14; | |
1021 | ||
1022 | fC33-=k30*c03+k31*c13; | |
1023 | fC43-=k30*c04+k31*c14; | |
1024 | ||
1025 | fC44-=k40*c04+k41*c14; | |
1026 | ||
1027 | return kTRUE; | |
1028 | } | |
1029 | ||
c7bafca9 | 1030 | void |
1031 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
1032 | //-------------------------------------------------------------------- | |
1033 | // External track parameters -> helix parameters | |
1034 | // "b" - magnetic field (kG) | |
1035 | //-------------------------------------------------------------------- | |
1036 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1037 | ||
1530f89c | 1038 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 1039 | |
1040 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
1041 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
1042 | //hlx[1]= // z0 | |
1043 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
1044 | //hlx[3]= // tgl | |
1530f89c | 1045 | hlx[4]=GetC(b); // C |
c7bafca9 | 1046 | } |
1047 | ||
1048 | ||
1049 | static void Evaluate(const Double_t *h, Double_t t, | |
1050 | Double_t r[3], //radius vector | |
1051 | Double_t g[3], //first defivatives | |
1052 | Double_t gg[3]) //second derivatives | |
1053 | { | |
1054 | //-------------------------------------------------------------------- | |
1055 | // Calculate position of a point on a track and some derivatives | |
1056 | //-------------------------------------------------------------------- | |
1057 | Double_t phase=h[4]*t+h[2]; | |
1058 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
1059 | ||
ba4550c4 | 1060 | r[0] = h[5]; |
1061 | r[1] = h[0]; | |
1062 | if (TMath::Abs(h[4])>kAlmost0) { | |
1063 | r[0] += (sn - h[6])/h[4]; | |
1064 | r[1] -= (cs - h[7])/h[4]; | |
1065 | } | |
c7bafca9 | 1066 | r[2] = h[1] + h[3]*t; |
1067 | ||
1068 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
1069 | ||
1070 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
1071 | } | |
1072 | ||
1073 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
1074 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
1075 | //------------------------------------------------------------ | |
1076 | // Returns the (weighed !) distance of closest approach between | |
1077 | // this track and the track "p". | |
1078 | // Other returned values: | |
1079 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
1080 | //----------------------------------------------------------- | |
1081 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
1082 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
1083 | Double_t dx2=dy2; | |
1084 | ||
c7bafca9 | 1085 | Double_t p1[8]; GetHelixParameters(p1,b); |
1086 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
1087 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
1088 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
1089 | ||
1090 | ||
1091 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
1092 | Evaluate(p1,t1,r1,g1,gg1); | |
1093 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
1094 | Evaluate(p2,t2,r2,g2,gg2); | |
1095 | ||
1096 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
1097 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1098 | ||
1099 | Int_t max=27; | |
1100 | while (max--) { | |
1101 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
1102 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
1103 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
1104 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
1105 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
1106 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
1107 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
1108 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
1109 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
1110 | ||
1111 | Double_t det=h11*h22-h12*h12; | |
1112 | ||
1113 | Double_t dt1,dt2; | |
1114 | if (TMath::Abs(det)<1.e-33) { | |
1115 | //(quasi)singular Hessian | |
1116 | dt1=-gt1; dt2=-gt2; | |
1117 | } else { | |
1118 | dt1=-(gt1*h22 - gt2*h12)/det; | |
1119 | dt2=-(h11*gt2 - h12*gt1)/det; | |
1120 | } | |
1121 | ||
1122 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
1123 | ||
1124 | //check delta(phase1) ? | |
1125 | //check delta(phase2) ? | |
1126 | ||
1127 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
1128 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
1129 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 1130 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 1131 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
1132 | if (lmb < 0.) | |
358f16ae | 1133 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 1134 | break; |
1135 | } | |
1136 | ||
1137 | Double_t dd=dm; | |
1138 | for (Int_t div=1 ; ; div*=2) { | |
1139 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
1140 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
1141 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
1142 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1143 | if (dd<dm) break; | |
1144 | dt1*=0.5; dt2*=0.5; | |
1145 | if (div>512) { | |
358f16ae | 1146 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 1147 | } |
1148 | } | |
1149 | dm=dd; | |
1150 | ||
1151 | t1+=dt1; | |
1152 | t2+=dt2; | |
1153 | ||
1154 | } | |
1155 | ||
358f16ae | 1156 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1157 | |
1158 | Double_t cs=TMath::Cos(GetAlpha()); | |
1159 | Double_t sn=TMath::Sin(GetAlpha()); | |
1160 | xthis=r1[0]*cs + r1[1]*sn; | |
1161 | ||
1162 | cs=TMath::Cos(p->GetAlpha()); | |
1163 | sn=TMath::Sin(p->GetAlpha()); | |
1164 | xp=r2[0]*cs + r2[1]*sn; | |
1165 | ||
1166 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1167 | } | |
1168 | ||
1169 | Double_t AliExternalTrackParam:: | |
1170 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1171 | //-------------------------------------------------------------- | |
1172 | // Propagates this track and the argument track to the position of the | |
1173 | // distance of closest approach. | |
1174 | // Returns the (weighed !) distance of closest approach. | |
1175 | //-------------------------------------------------------------- | |
1176 | Double_t xthis,xp; | |
1177 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1178 | ||
1179 | if (!PropagateTo(xthis,b)) { | |
1180 | //AliWarning(" propagation failed !"); | |
1181 | return 1e+33; | |
1182 | } | |
1183 | ||
1184 | if (!p->PropagateTo(xp,b)) { | |
1185 | //AliWarning(" propagation failed !"; | |
1186 | return 1e+33; | |
1187 | } | |
1188 | ||
1189 | return dca; | |
1190 | } | |
1191 | ||
1192 | ||
58e536c5 | 1193 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1194 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1195 | // |
e99a34df | 1196 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1197 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1198 | // Magnetic field is "b" (kG). | |
1199 | // | |
1200 | // a) The track gets extapolated to the DCA to the vertex. | |
1201 | // b) The impact parameters and their covariance matrix are calculated. | |
1202 | // | |
1203 | // In the case of success, the returned value is kTRUE | |
1204 | // (otherwise, it's kFALSE) | |
1205 | // | |
1206 | Double_t alpha=GetAlpha(); | |
1207 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1208 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1209 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1210 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1211 | x-=xv; y-=yv; |
1212 | ||
1213 | //Estimate the impact parameter neglecting the track curvature | |
1214 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
1215 | if (d > maxd) return kFALSE; | |
1216 | ||
1217 | //Propagate to the DCA | |
2258e165 | 1218 | Double_t crv=GetC(b); |
e99a34df | 1219 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1220 | ||
f76701bf | 1221 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); |
1222 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
e99a34df | 1223 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1224 | else cs=1.; | |
f76701bf | 1225 | |
1226 | x = xv*cs + yv*sn; | |
1227 | yv=-xv*sn + yv*cs; xv=x; | |
1228 | ||
1229 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1230 | |
1231 | if (dz==0) return kTRUE; | |
1232 | dz[0] = GetParameter()[0] - yv; | |
1233 | dz[1] = GetParameter()[1] - zv; | |
1234 | ||
1235 | if (covar==0) return kTRUE; | |
58e536c5 | 1236 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1237 | |
1238 | //***** Improvements by A.Dainese | |
1239 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1240 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1241 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1242 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1243 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1244 | //***** | |
1245 | ||
29fbcc93 | 1246 | return kTRUE; |
f76701bf | 1247 | } |
1248 | ||
1249 | ||
b1149664 | 1250 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1251 | //---------------------------------------------------------------- | |
1252 | // This function returns a unit vector along the track direction | |
1253 | // in the global coordinate system. | |
1254 | //---------------------------------------------------------------- | |
1255 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1256 | Double_t snp=fP[2]; | |
92934324 | 1257 | Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp)); |
b1149664 | 1258 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1259 | d[0]=(csp*cs - snp*sn)/norm; | |
1260 | d[1]=(snp*cs + csp*sn)/norm; | |
1261 | d[2]=fP[3]/norm; | |
1262 | } | |
1263 | ||
c683ddc2 | 1264 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1265 | //--------------------------------------------------------------------- |
1266 | // This function returns the global track momentum components | |
1267 | // Results for (nearly) straight tracks are meaningless ! | |
1268 | //--------------------------------------------------------------------- | |
1269 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1270 | return Local2GlobalMomentum(p,fAlpha); | |
1271 | } | |
a5e407e9 | 1272 | |
def9660e | 1273 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1274 | //--------------------------------------------------------------------- |
1275 | // Returns x-component of momentum | |
1276 | // Result for (nearly) straight tracks is meaningless ! | |
1277 | //--------------------------------------------------------------------- | |
def9660e | 1278 | |
957fb479 | 1279 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1280 | GetPxPyPz(p); |
1281 | ||
1282 | return p[0]; | |
1283 | } | |
1284 | ||
1285 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1286 | //--------------------------------------------------------------------- |
1287 | // Returns y-component of momentum | |
1288 | // Result for (nearly) straight tracks is meaningless ! | |
1289 | //--------------------------------------------------------------------- | |
def9660e | 1290 | |
957fb479 | 1291 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1292 | GetPxPyPz(p); |
1293 | ||
1294 | return p[1]; | |
1295 | } | |
1296 | ||
1297 | Double_t AliExternalTrackParam::Pz() const { | |
957fb479 | 1298 | //--------------------------------------------------------------------- |
1299 | // Returns z-component of momentum | |
1300 | // Result for (nearly) straight tracks is meaningless ! | |
1301 | //--------------------------------------------------------------------- | |
def9660e | 1302 | |
957fb479 | 1303 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1304 | GetPxPyPz(p); |
1305 | ||
1306 | return p[2]; | |
1307 | } | |
1308 | ||
c683ddc2 | 1309 | Double_t AliExternalTrackParam::Xv() const { |
1310 | //--------------------------------------------------------------------- | |
1311 | // Returns x-component of first track point | |
1312 | //--------------------------------------------------------------------- | |
1313 | ||
1314 | Double_t r[3]={0.,0.,0.}; | |
1315 | GetXYZ(r); | |
1316 | ||
1317 | return r[0]; | |
1318 | } | |
1319 | ||
1320 | Double_t AliExternalTrackParam::Yv() const { | |
1321 | //--------------------------------------------------------------------- | |
1322 | // Returns y-component of first track point | |
1323 | //--------------------------------------------------------------------- | |
1324 | ||
1325 | Double_t r[3]={0.,0.,0.}; | |
1326 | GetXYZ(r); | |
1327 | ||
1328 | return r[1]; | |
1329 | } | |
1330 | ||
1331 | Double_t AliExternalTrackParam::Zv() const { | |
1332 | //--------------------------------------------------------------------- | |
1333 | // Returns z-component of first track point | |
1334 | //--------------------------------------------------------------------- | |
1335 | ||
1336 | Double_t r[3]={0.,0.,0.}; | |
1337 | GetXYZ(r); | |
1338 | ||
1339 | return r[2]; | |
1340 | } | |
1341 | ||
def9660e | 1342 | Double_t AliExternalTrackParam::Theta() const { |
1343 | // return theta angle of momentum | |
1344 | ||
7cdd0c20 | 1345 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1346 | } |
1347 | ||
1348 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1349 | //--------------------------------------------------------------------- |
1350 | // Returns the azimuthal angle of momentum | |
1351 | // 0 <= phi < 2*pi | |
1352 | //--------------------------------------------------------------------- | |
def9660e | 1353 | |
957fb479 | 1354 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1355 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1356 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1357 | ||
1358 | return phi; | |
def9660e | 1359 | } |
1360 | ||
1361 | Double_t AliExternalTrackParam::M() const { | |
1362 | // return particle mass | |
1363 | ||
1364 | // No mass information available so far. | |
1365 | // Redifine in derived class! | |
1366 | ||
1367 | return -999.; | |
1368 | } | |
1369 | ||
1370 | Double_t AliExternalTrackParam::E() const { | |
1371 | // return particle energy | |
1372 | ||
1373 | // No PID information available so far. | |
1374 | // Redifine in derived class! | |
1375 | ||
1376 | return -999.; | |
1377 | } | |
1378 | ||
1379 | Double_t AliExternalTrackParam::Eta() const { | |
1380 | // return pseudorapidity | |
1381 | ||
1382 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1383 | } | |
1384 | ||
1385 | Double_t AliExternalTrackParam::Y() const { | |
1386 | // return rapidity | |
1387 | ||
1388 | // No PID information available so far. | |
1389 | // Redifine in derived class! | |
1390 | ||
1391 | return -999.; | |
1392 | } | |
1393 | ||
c9ec41e8 | 1394 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1395 | //--------------------------------------------------------------------- | |
1396 | // This function returns the global track position | |
1397 | //--------------------------------------------------------------------- | |
1398 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1399 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1400 | } |
1401 | ||
c9ec41e8 | 1402 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1403 | //--------------------------------------------------------------------- | |
1404 | // This function returns the global covariance matrix of the track params | |
1405 | // | |
1406 | // Cov(x,x) ... : cv[0] | |
1407 | // Cov(y,x) ... : cv[1] cv[2] | |
1408 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1409 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1410 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1411 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1412 | // |
c9ec41e8 | 1413 | // Results for (nearly) straight tracks are meaningless ! |
1414 | //--------------------------------------------------------------------- | |
e421f556 | 1415 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1416 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1417 | return kFALSE; | |
a5e407e9 | 1418 | } |
49d13e89 | 1419 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1420 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1421 | return kFALSE; | |
1422 | } | |
1423 | Double_t pt=1./TMath::Abs(fP[4]); | |
1424 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1425 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1426 | |
1427 | Double_t m00=-sn, m10=cs; | |
1428 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1429 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1430 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1431 | ||
854d5d49 | 1432 | m43*=GetSign(); |
1433 | m44*=GetSign(); | |
1434 | m45*=GetSign(); | |
1435 | ||
c9ec41e8 | 1436 | cv[0 ] = fC[0]*m00*m00; |
1437 | cv[1 ] = fC[0]*m00*m10; | |
1438 | cv[2 ] = fC[0]*m10*m10; | |
1439 | cv[3 ] = fC[1]*m00; | |
1440 | cv[4 ] = fC[1]*m10; | |
1441 | cv[5 ] = fC[2]; | |
1442 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1443 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1444 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1445 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1446 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1447 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1448 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1449 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1450 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1451 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1452 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1453 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1454 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1455 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1456 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1457 | |
c9ec41e8 | 1458 | return kTRUE; |
51ad6848 | 1459 | } |
1460 | ||
51ad6848 | 1461 | |
c9ec41e8 | 1462 | Bool_t |
1463 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1464 | //--------------------------------------------------------------------- | |
1465 | // This function returns the global track momentum extrapolated to | |
1466 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1467 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1468 | p[0]=fP[4]; |
1530f89c | 1469 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1470 | p[2]=fP[3]; |
1471 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1472 | } |
1473 | ||
7cf7bb6c | 1474 | Bool_t |
1475 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1476 | //--------------------------------------------------------------------- | |
1477 | // This function returns the local Y-coordinate of the intersection | |
1478 | // point between this track and the reference plane "x" (cm). | |
1479 | // Magnetic field "b" (kG) | |
1480 | //--------------------------------------------------------------------- | |
1481 | Double_t dx=x-fX; | |
1482 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1483 | ||
1530f89c | 1484 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1485 | |
1486 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1487 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1488 | ||
60e55aee | 1489 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
7cf7bb6c | 1490 | y = fP[0] + dx*(f1+f2)/(r1+r2); |
1491 | return kTRUE; | |
1492 | } | |
1493 | ||
6c94f330 | 1494 | Bool_t |
1495 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1496 | //--------------------------------------------------------------------- | |
1497 | // This function returns the local Z-coordinate of the intersection | |
1498 | // point between this track and the reference plane "x" (cm). | |
1499 | // Magnetic field "b" (kG) | |
1500 | //--------------------------------------------------------------------- | |
1501 | Double_t dx=x-fX; | |
1502 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1503 | ||
2258e165 | 1504 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
6c94f330 | 1505 | |
1506 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1507 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1508 | ||
60e55aee | 1509 | Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2)); |
6c94f330 | 1510 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! |
1511 | return kTRUE; | |
1512 | } | |
1513 | ||
c9ec41e8 | 1514 | Bool_t |
1515 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1516 | //--------------------------------------------------------------------- | |
1517 | // This function returns the global track position extrapolated to | |
1518 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1519 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1520 | Double_t dx=x-fX; |
e421f556 | 1521 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1522 | ||
1530f89c | 1523 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1524 | |
e421f556 | 1525 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1526 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1527 | |
60e55aee | 1528 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
c9ec41e8 | 1529 | r[0] = x; |
1530 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
f90a11c9 | 1531 | r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter |
1532 | ||
c9ec41e8 | 1533 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1534 | } |
1535 | ||
51ad6848 | 1536 | //_____________________________________________________________________________ |
1537 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1538 | { | |
1539 | // print the parameters and the covariance matrix | |
1540 | ||
1541 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1542 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1543 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1544 | printf(" covariance: %12g\n", fC[0]); | |
1545 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1546 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1547 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1548 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1549 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1550 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1551 | } |
5b77d93c | 1552 | |
c194ba83 | 1553 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1554 | // | |
1555 | // Get sinus at given x | |
1556 | // | |
1530f89c | 1557 | Double_t crv=GetC(b); |
c194ba83 | 1558 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1559 | Double_t dx = x-fX; | |
1560 | Double_t res = fP[2]+dx*crv; | |
1561 | return res; | |
1562 | } | |
bf00ebb8 | 1563 | |
1564 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1565 | //------------------------------------------------------------------------ | |
1566 | // Get the distance between two tracks at the local position x | |
1567 | // working in the local frame of this track. | |
1568 | // Origin : Marian.Ivanov@cern.ch | |
1569 | //----------------------------------------------------------------------- | |
1570 | Double_t xyz[3]; | |
1571 | Double_t xyz2[3]; | |
1572 | xyz[0]=x; | |
1573 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1574 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1575 | // | |
1576 | // | |
1577 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1578 | xyz2[0]=x; | |
1579 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1580 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1581 | }else{ | |
1582 | // | |
1583 | Double_t xyz1[3]; | |
1584 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1585 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1586 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1587 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1588 | // | |
1589 | xyz1[0]=xyz2[0]; | |
1590 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1591 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1592 | // | |
1593 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1594 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1595 | xyz2[2] = xyz1[2]; | |
1596 | } | |
1597 | dist[0] = xyz[0]-xyz2[0]; | |
1598 | dist[1] = xyz[1]-xyz2[1]; | |
1599 | dist[2] = xyz[2]-xyz2[2]; | |
1600 | ||
1601 | return kTRUE; | |
1602 | } | |
0c19adf7 | 1603 | |
1604 | ||
1605 | // | |
1606 | // Draw functionality. | |
1607 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1608 | // | |
1609 | ||
1610 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1611 | // | |
1612 | // Draw track line | |
1613 | // | |
1614 | if (minR>maxR) return ; | |
1615 | if (stepR<=0) return ; | |
1616 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1617 | if (npoints<1) return; | |
1618 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1619 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1620 | polymarker->Draw(); | |
1621 | } | |
1622 | ||
1623 | // | |
1624 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1625 | // | |
1626 | // Fill points in the polymarker | |
1627 | // | |
1628 | Int_t counter=0; | |
1629 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1630 | Double_t point[3]; | |
1631 | GetXYZAt(r,magF,point); | |
1632 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
1633 | printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); | |
1634 | counter++; | |
1635 | } | |
1636 | } | |
0e8460af | 1637 | |
1638 | Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const { | |
1639 | // | |
1640 | Int_t min = TMath::Min(i,j); | |
1641 | Int_t max = TMath::Max(i,j); | |
1642 | ||
1643 | return min+(max+1)*max/2; | |
1644 | } |