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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 | /////////////////////////////////////////////////////////////////////////////// |
86be8934 | 28 | #include <cassert> |
29 | ||
30 | #include <TVectorD.h> | |
4b189f98 | 31 | #include <TMatrixDSym.h> |
d46683db | 32 | #include <TPolyMarker3D.h> |
33 | #include <TVector3.h> | |
cfdb62d4 | 34 | #include <TMatrixD.h> |
d46683db | 35 | |
51ad6848 | 36 | #include "AliExternalTrackParam.h" |
58e536c5 | 37 | #include "AliVVertex.h" |
6c94f330 | 38 | #include "AliLog.h" |
51ad6848 | 39 | |
40 | ClassImp(AliExternalTrackParam) | |
41 | ||
ed5f2849 | 42 | Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; |
43 | ||
51ad6848 | 44 | //_____________________________________________________________________________ |
90e48c0c | 45 | AliExternalTrackParam::AliExternalTrackParam() : |
4f6e22bd | 46 | AliVTrack(), |
90e48c0c | 47 | fX(0), |
c9ec41e8 | 48 | fAlpha(0) |
51ad6848 | 49 | { |
90e48c0c | 50 | // |
51 | // default constructor | |
52 | // | |
c9ec41e8 | 53 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
54 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 55 | } |
56 | ||
6c94f330 | 57 | //_____________________________________________________________________________ |
58 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
4f6e22bd | 59 | AliVTrack(track), |
6c94f330 | 60 | fX(track.fX), |
61 | fAlpha(track.fAlpha) | |
62 | { | |
63 | // | |
64 | // copy constructor | |
65 | // | |
66 | for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i]; | |
67 | for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i]; | |
86be8934 | 68 | CheckCovariance(); |
6c94f330 | 69 | } |
70 | ||
def9660e | 71 | //_____________________________________________________________________________ |
72 | AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar) | |
73 | { | |
74 | // | |
75 | // assignment operator | |
76 | // | |
77 | ||
78 | if (this!=&trkPar) { | |
4f6e22bd | 79 | AliVTrack::operator=(trkPar); |
def9660e | 80 | fX = trkPar.fX; |
81 | fAlpha = trkPar.fAlpha; | |
82 | ||
83 | for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i]; | |
84 | for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i]; | |
86be8934 | 85 | CheckCovariance(); |
def9660e | 86 | } |
87 | ||
88 | return *this; | |
89 | } | |
90 | ||
51ad6848 | 91 | //_____________________________________________________________________________ |
92 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
93 | const Double_t param[5], | |
90e48c0c | 94 | const Double_t covar[15]) : |
4f6e22bd | 95 | AliVTrack(), |
90e48c0c | 96 | fX(x), |
c9ec41e8 | 97 | fAlpha(alpha) |
51ad6848 | 98 | { |
90e48c0c | 99 | // |
100 | // create external track parameters from given arguments | |
101 | // | |
c9ec41e8 | 102 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
103 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
86be8934 | 104 | CheckCovariance(); |
51ad6848 | 105 | } |
106 | ||
4f6e22bd | 107 | //_____________________________________________________________________________ |
108 | AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) : | |
109 | AliVTrack(), | |
110 | fX(0.), | |
111 | fAlpha(0.) | |
112 | { | |
113 | // | |
610e3088 | 114 | // Constructor from virtual track, |
115 | // This is not a copy contructor ! | |
4f6e22bd | 116 | // |
610e3088 | 117 | |
118 | if (vTrack->InheritsFrom("AliExternalTrackParam")) { | |
119 | AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !"); | |
120 | AliWarning("Calling the default constructor..."); | |
121 | AliExternalTrackParam(); | |
122 | return; | |
123 | } | |
124 | ||
892be05f | 125 | Double_t xyz[3],pxpypz[3],cv[21]; |
126 | vTrack->GetXYZ(xyz); | |
127 | pxpypz[0]=vTrack->Px(); | |
128 | pxpypz[1]=vTrack->Py(); | |
129 | pxpypz[2]=vTrack->Pz(); | |
4f6e22bd | 130 | vTrack->GetCovarianceXYZPxPyPz(cv); |
131 | Short_t sign = (Short_t)vTrack->Charge(); | |
132 | ||
133 | Set(xyz,pxpypz,cv,sign); | |
134 | } | |
135 | ||
90e48c0c | 136 | //_____________________________________________________________________________ |
da4e3deb | 137 | AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], |
138 | Double_t cv[21],Short_t sign) : | |
4f6e22bd | 139 | AliVTrack(), |
da4e3deb | 140 | fX(0.), |
141 | fAlpha(0.) | |
4f6e22bd | 142 | { |
143 | // | |
144 | // constructor from the global parameters | |
145 | // | |
146 | ||
147 | Set(xyz,pxpypz,cv,sign); | |
148 | } | |
149 | ||
150 | //_____________________________________________________________________________ | |
151 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
152 | Double_t cv[21],Short_t sign) | |
da4e3deb | 153 | { |
154 | // | |
155 | // create external track parameters from the global parameters | |
156 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
157 | // A.Dainese 10.10.08 | |
158 | ||
aff56ff7 | 159 | // Calculate alpha: the rotation angle of the corresponding local system. |
160 | // | |
161 | // For global radial position inside the beam pipe, alpha is the | |
162 | // azimuthal angle of the momentum projected on (x,y). | |
163 | // | |
c99948ce | 164 | // For global radial position outside the ITS, alpha is the |
aff56ff7 | 165 | // azimuthal angle of the centre of the TPC sector in which the point |
166 | // xyz lies | |
167 | // | |
168 | Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1]; | |
c99948ce | 169 | Double_t radMax = 45.; // approximately ITS outer radius |
170 | if (radPos2 < radMax*radMax) { // inside the ITS | |
171 | ||
aff56ff7 | 172 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); |
c99948ce | 173 | } else { // outside the ITS |
aff56ff7 | 174 | Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]); |
175 | fAlpha = | |
176 | TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10); | |
177 | } | |
da4e3deb | 178 | |
179 | // Get the vertex of origin and the momentum | |
180 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
181 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
182 | ||
183 | // Rotate to the local coordinate system | |
184 | ver.RotateZ(-fAlpha); | |
185 | mom.RotateZ(-fAlpha); | |
186 | ||
187 | // x of the reference plane | |
188 | fX = ver.X(); | |
189 | ||
190 | Double_t charge = (Double_t)sign; | |
191 | ||
192 | fP[0] = ver.Y(); | |
193 | fP[1] = ver.Z(); | |
194 | fP[2] = TMath::Sin(mom.Phi()); | |
195 | fP[3] = mom.Pz()/mom.Pt(); | |
196 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
197 | ||
198 | // Covariance matrix (formulas to be simplified) | |
199 | ||
200 | Double_t pt=1./TMath::Abs(fP[4]); | |
201 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
202 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); | |
203 | ||
204 | Double_t m00=-sn;// m10=cs; | |
205 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
206 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
207 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
208 | ||
209 | m43*=GetSign(); | |
210 | m44*=GetSign(); | |
211 | m45*=GetSign(); | |
212 | ||
213 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
214 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
215 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
216 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
217 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
218 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
219 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
220 | ||
221 | fC[0 ] = cv[0 ]+cv[2 ]; | |
222 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
223 | fC[2 ] = cv[5 ]; | |
224 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
225 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
226 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
227 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
228 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
229 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
230 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
231 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
232 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
233 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
234 | Double_t b2=m23*m35; | |
235 | Double_t b3=m43*m35; | |
236 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
237 | Double_t b5=m24*m35; | |
238 | Double_t b6=m44*m35; | |
239 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
240 | fC[13] = b1/b3-b2*fC[8]/b3; | |
241 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 242 | |
86be8934 | 243 | CheckCovariance(); |
244 | ||
4f6e22bd | 245 | return; |
da4e3deb | 246 | } |
247 | ||
51ad6848 | 248 | //_____________________________________________________________________________ |
c9ec41e8 | 249 | void AliExternalTrackParam::Reset() { |
1530f89c | 250 | // |
251 | // Resets all the parameters to 0 | |
252 | // | |
c9ec41e8 | 253 | fX=fAlpha=0.; |
254 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
255 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 256 | } |
257 | ||
3775b0ca | 258 | //_____________________________________________________________________________ |
259 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
260 | // | |
261 | // Add "something" to the track covarince matrix. | |
262 | // May be needed to account for unknown mis-calibration/mis-alignment | |
263 | // | |
264 | fC[0] +=c[0]; | |
265 | fC[1] +=c[1]; fC[2] +=c[2]; | |
266 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
267 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
268 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
86be8934 | 269 | CheckCovariance(); |
3775b0ca | 270 | } |
271 | ||
272 | ||
c9ec41e8 | 273 | Double_t AliExternalTrackParam::GetP() const { |
274 | //--------------------------------------------------------------------- | |
275 | // This function returns the track momentum | |
276 | // Results for (nearly) straight tracks are meaningless ! | |
277 | //--------------------------------------------------------------------- | |
06fb4a2f | 278 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 279 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 280 | } |
281 | ||
1d99986f | 282 | Double_t AliExternalTrackParam::Get1P() const { |
283 | //--------------------------------------------------------------------- | |
284 | // This function returns the 1/(track momentum) | |
285 | //--------------------------------------------------------------------- | |
286 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
287 | } | |
288 | ||
c9ec41e8 | 289 | //_______________________________________________________________________ |
c7bafca9 | 290 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 291 | //------------------------------------------------------------------ |
292 | // This function calculates the transverse impact parameter | |
293 | // with respect to a point with global coordinates (x,y) | |
294 | // in the magnetic field "b" (kG) | |
295 | //------------------------------------------------------------------ | |
5773defd | 296 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 297 | Double_t rp4=GetC(b); |
c9ec41e8 | 298 | |
299 | Double_t xt=fX, yt=fP[0]; | |
300 | ||
301 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
302 | Double_t a = x*cs + y*sn; | |
303 | y = -x*sn + y*cs; x=a; | |
304 | xt-=x; yt-=y; | |
305 | ||
bfd20868 | 306 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2])); |
307 | a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt); | |
1530f89c | 308 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
309 | } | |
310 | ||
311 | //_______________________________________________________________________ | |
312 | void AliExternalTrackParam:: | |
313 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
314 | //------------------------------------------------------------------ | |
315 | // This function calculates the transverse and longitudinal impact parameters | |
316 | // with respect to a point with global coordinates (x,y) | |
317 | // in the magnetic field "b" (kG) | |
318 | //------------------------------------------------------------------ | |
bfd20868 | 319 | Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1)); |
1530f89c | 320 | Double_t xt=fX, yt=fP[0]; |
321 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
322 | Double_t a = x*cs + y*sn; | |
323 | y = -x*sn + y*cs; x=a; | |
324 | xt-=x; yt-=y; | |
325 | ||
326 | Double_t rp4=GetC(b); | |
327 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
328 | dz[0] = -(xt*f1 - yt*r1); | |
329 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
330 | return; | |
331 | } | |
332 | ||
333 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
334 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
335 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
336 | dz[0] = -a/(1 + rr); | |
bfd20868 | 337 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2)); |
1530f89c | 338 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; |
51ad6848 | 339 | } |
340 | ||
49d13e89 | 341 | //_______________________________________________________________________ |
342 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
343 | //------------------------------------------------------------------ | |
344 | // This function calculates the transverse impact parameter | |
345 | // with respect to a point with global coordinates (xv,yv) | |
346 | // neglecting the track curvature. | |
347 | //------------------------------------------------------------------ | |
348 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
349 | Double_t x= xv*cs + yv*sn; | |
350 | Double_t y=-xv*sn + yv*cs; | |
351 | ||
bfd20868 | 352 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
49d13e89 | 353 | |
1530f89c | 354 | return -d; |
49d13e89 | 355 | } |
356 | ||
b8e07ed6 | 357 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx |
358 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
359 | Double_t dEdx, | |
360 | Bool_t anglecorr) { | |
116b445b | 361 | //------------------------------------------------------------------ |
362 | // This function corrects the track parameters for the crossed material. | |
363 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
364 | // "xTimesRho" - is the product length*density (g/cm^2). | |
365 | // "mass" - the mass of this particle (GeV/c^2). | |
b8e07ed6 | 366 | // "dEdx" - mean enery loss (GeV/(g/cm^2) |
367 | // "anglecorr" - switch for the angular correction | |
116b445b | 368 | //------------------------------------------------------------------ |
369 | Double_t &fP2=fP[2]; | |
370 | Double_t &fP3=fP[3]; | |
371 | Double_t &fP4=fP[4]; | |
372 | ||
373 | Double_t &fC22=fC[5]; | |
374 | Double_t &fC33=fC[9]; | |
375 | Double_t &fC43=fC[13]; | |
376 | Double_t &fC44=fC[14]; | |
377 | ||
7dded1d5 | 378 | //Apply angle correction, if requested |
379 | if(anglecorr) { | |
bfd20868 | 380 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2))); |
7dded1d5 | 381 | xOverX0 *=angle; |
382 | xTimesRho *=angle; | |
383 | } | |
384 | ||
116b445b | 385 | Double_t p=GetP(); |
386 | Double_t p2=p*p; | |
387 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 388 | |
9f2bec63 | 389 | //Calculating the multiple scattering corrections****************** |
390 | Double_t cC22 = 0.; | |
391 | Double_t cC33 = 0.; | |
392 | Double_t cC43 = 0.; | |
393 | Double_t cC44 = 0.; | |
116b445b | 394 | if (xOverX0 != 0) { |
395 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
396 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
9f2bec63 | 397 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
bfd20868 | 398 | cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3); |
9f2bec63 | 399 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); |
400 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
401 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
116b445b | 402 | } |
403 | ||
9f2bec63 | 404 | //Calculating the energy loss corrections************************ |
405 | Double_t cP4=1.; | |
116b445b | 406 | if ((xTimesRho != 0.) && (beta2 < 1.)) { |
b8e07ed6 | 407 | Double_t dE=dEdx*xTimesRho; |
116b445b | 408 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
409 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
c9038cae | 410 | //cP4 = (1.- e/p2*dE); |
76ece3d8 | 411 | if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE; |
c9038cae | 412 | cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben ! |
9f2bec63 | 413 | if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c |
4b2fa3ce | 414 | |
116b445b | 415 | |
416 | // Approximate energy loss fluctuation (M.Ivanov) | |
417 | const Double_t knst=0.07; // To be tuned. | |
418 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 419 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
116b445b | 420 | |
421 | } | |
422 | ||
9f2bec63 | 423 | //Applying the corrections***************************** |
424 | fC22 += cC22; | |
425 | fC33 += cC33; | |
426 | fC43 += cC43; | |
427 | fC44 += cC44; | |
428 | fP4 *= cP4; | |
429 | ||
86be8934 | 430 | CheckCovariance(); |
431 | ||
116b445b | 432 | return kTRUE; |
433 | } | |
434 | ||
b8e07ed6 | 435 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
436 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
437 | Bool_t anglecorr, | |
438 | Double_t (*Bethe)(Double_t)) { | |
439 | //------------------------------------------------------------------ | |
440 | // This function corrects the track parameters for the crossed material. | |
441 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
442 | // "xTimesRho" - is the product length*density (g/cm^2). | |
443 | // "mass" - the mass of this particle (GeV/c^2). | |
444 | // "anglecorr" - switch for the angular correction | |
445 | // "Bethe" - function calculating the energy loss (GeV/(g/cm^2)) | |
446 | //------------------------------------------------------------------ | |
447 | ||
448 | Double_t bg=GetP()/mass; | |
449 | Double_t dEdx=Bethe(bg); | |
450 | ||
451 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
452 | } | |
453 | ||
454 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA | |
455 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
456 | Double_t zOverA, | |
457 | Double_t density, | |
458 | Double_t exEnergy, | |
459 | Double_t jp1, | |
460 | Double_t jp2, | |
461 | Bool_t anglecorr) { | |
462 | //------------------------------------------------------------------ | |
463 | // This function corrects the track parameters for the crossed material | |
464 | // using the full Geant-like Bethe-Bloch formula parameterization | |
465 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
466 | // "xTimesRho" - is the product length*density (g/cm^2). | |
467 | // "mass" - the mass of this particle (GeV/c^2). | |
468 | // "density" - mean density (g/cm^3) | |
469 | // "zOverA" - mean Z/A | |
470 | // "exEnergy" - mean exitation energy (GeV) | |
471 | // "jp1" - density effect first junction point | |
472 | // "jp2" - density effect second junction point | |
473 | // "anglecorr" - switch for the angular correction | |
474 | // | |
475 | // The default values of the parameters are for silicon | |
476 | // | |
477 | //------------------------------------------------------------------ | |
478 | ||
479 | Double_t bg=GetP()/mass; | |
480 | Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA); | |
481 | ||
482 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
483 | } | |
484 | ||
485 | ||
116b445b | 486 | |
ee5dba5e | 487 | Bool_t AliExternalTrackParam::CorrectForMaterial |
488 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 489 | //------------------------------------------------------------------ |
116b445b | 490 | // Deprecated function ! |
491 | // Better use CorrectForMeanMaterial instead of it. | |
492 | // | |
c7bafca9 | 493 | // This function corrects the track parameters for the crossed material |
494 | // "d" - the thickness (fraction of the radiation length) | |
495 | // "x0" - the radiation length (g/cm^2) | |
496 | // "mass" - the mass of this particle (GeV/c^2) | |
497 | //------------------------------------------------------------------ | |
c7bafca9 | 498 | |
b8e07ed6 | 499 | return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe); |
c7bafca9 | 500 | |
c7bafca9 | 501 | } |
502 | ||
9c56b409 | 503 | Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg, |
504 | Double_t kp1, | |
505 | Double_t kp2, | |
506 | Double_t kp3, | |
507 | Double_t kp4, | |
508 | Double_t kp5) { | |
509 | // | |
510 | // This is the empirical ALEPH parameterization of the Bethe-Bloch formula. | |
511 | // It is normalized to 1 at the minimum. | |
512 | // | |
513 | // bg - beta*gamma | |
514 | // | |
515 | // The default values for the kp* parameters are for ALICE TPC. | |
516 | // The returned value is in MIP units | |
517 | // | |
518 | ||
519 | Double_t beta = bg/TMath::Sqrt(1.+ bg*bg); | |
520 | ||
521 | Double_t aa = TMath::Power(beta,kp4); | |
522 | Double_t bb = TMath::Power(1./bg,kp5); | |
523 | ||
524 | bb=TMath::Log(kp3+bb); | |
525 | ||
526 | return (kp2-aa-bb)*kp1/aa; | |
527 | } | |
528 | ||
529 | Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg, | |
530 | Double_t kp0, | |
531 | Double_t kp1, | |
532 | Double_t kp2, | |
533 | Double_t kp3, | |
534 | Double_t kp4) { | |
535 | // | |
536 | // This is the parameterization of the Bethe-Bloch formula inspired by Geant. | |
537 | // | |
538 | // bg - beta*gamma | |
539 | // kp0 - density [g/cm^3] | |
540 | // kp1 - density effect first junction point | |
541 | // kp2 - density effect second junction point | |
542 | // kp3 - mean excitation energy [GeV] | |
543 | // kp4 - mean Z/A | |
544 | // | |
545 | // The default values for the kp* parameters are for silicon. | |
546 | // The returned value is in [GeV/(g/cm^2)]. | |
547 | // | |
548 | ||
549 | const Double_t mK = 0.307075e-3; // [GeV*cm^2/g] | |
550 | const Double_t me = 0.511e-3; // [GeV/c^2] | |
551 | const Double_t rho = kp0; | |
552 | const Double_t x0 = kp1*2.303; | |
553 | const Double_t x1 = kp2*2.303; | |
554 | const Double_t mI = kp3; | |
555 | const Double_t mZA = kp4; | |
556 | const Double_t bg2 = bg*bg; | |
557 | const Double_t maxT= 2*me*bg2; // neglecting the electron mass | |
558 | ||
559 | //*** Density effect | |
560 | Double_t d2=0.; | |
561 | const Double_t x=TMath::Log(bg); | |
562 | const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI); | |
563 | if (x > x1) { | |
564 | d2 = lhwI + x - 0.5; | |
565 | } else if (x > x0) { | |
566 | const Double_t r=(x1-x)/(x1-x0); | |
567 | d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r; | |
568 | } | |
569 | ||
570 | return mK*mZA*(1+bg2)/bg2* | |
571 | (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2); | |
572 | } | |
573 | ||
d46683db | 574 | Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) { |
ee5dba5e | 575 | //------------------------------------------------------------------ |
d46683db | 576 | // This is an approximation of the Bethe-Bloch formula, |
577 | // reasonable for solid materials. | |
578 | // All the parameters are, in fact, for Si. | |
9b655cba | 579 | // The returned value is in [GeV/(g/cm^2)] |
ee5dba5e | 580 | //------------------------------------------------------------------ |
a821848c | 581 | |
9c56b409 | 582 | return BetheBlochGeant(bg); |
d46683db | 583 | } |
ee5dba5e | 584 | |
d46683db | 585 | Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) { |
586 | //------------------------------------------------------------------ | |
587 | // This is an approximation of the Bethe-Bloch formula, | |
588 | // reasonable for gas materials. | |
589 | // All the parameters are, in fact, for Ne. | |
9b655cba | 590 | // The returned value is in [GeV/(g/cm^2)] |
d46683db | 591 | //------------------------------------------------------------------ |
592 | ||
593 | const Double_t rho = 0.9e-3; | |
594 | const Double_t x0 = 2.; | |
595 | const Double_t x1 = 4.; | |
596 | const Double_t mI = 140.e-9; | |
597 | const Double_t mZA = 0.49555; | |
598 | ||
9c56b409 | 599 | return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); |
ee5dba5e | 600 | } |
601 | ||
49d13e89 | 602 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
603 | //------------------------------------------------------------------ | |
604 | // Transform this track to the local coord. system rotated | |
605 | // by angle "alpha" (rad) with respect to the global coord. system. | |
606 | //------------------------------------------------------------------ | |
dfcef74c | 607 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
608 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
609 | return kFALSE; | |
610 | } | |
611 | ||
49d13e89 | 612 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
613 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
614 | ||
615 | Double_t &fP0=fP[0]; | |
616 | Double_t &fP2=fP[2]; | |
617 | Double_t &fC00=fC[0]; | |
618 | Double_t &fC10=fC[1]; | |
619 | Double_t &fC20=fC[3]; | |
620 | Double_t &fC21=fC[4]; | |
621 | Double_t &fC22=fC[5]; | |
622 | Double_t &fC30=fC[6]; | |
623 | Double_t &fC32=fC[8]; | |
624 | Double_t &fC40=fC[10]; | |
625 | Double_t &fC42=fC[12]; | |
626 | ||
627 | Double_t x=fX; | |
628 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
bfd20868 | 629 | Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision |
49d13e89 | 630 | |
dfcef74c | 631 | Double_t tmp=sf*ca - cf*sa; |
7248cf51 | 632 | if (TMath::Abs(tmp) >= kAlmost1) { |
633 | if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) | |
634 | AliWarning(Form("Rotation failed ! %.10e",tmp)); | |
0b69bbb2 | 635 | return kFALSE; |
636 | } | |
dfcef74c | 637 | |
49d13e89 | 638 | fAlpha = alpha; |
639 | fX = x*ca + fP0*sa; | |
640 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 641 | fP2= tmp; |
49d13e89 | 642 | |
06fb4a2f | 643 | if (TMath::Abs(cf)<kAlmost0) { |
644 | AliError(Form("Too small cosine value %f",cf)); | |
645 | cf = kAlmost0; | |
646 | } | |
647 | ||
49d13e89 | 648 | Double_t rr=(ca+sf/cf*sa); |
649 | ||
650 | fC00 *= (ca*ca); | |
651 | fC10 *= ca; | |
652 | fC20 *= ca*rr; | |
653 | fC21 *= rr; | |
654 | fC22 *= rr*rr; | |
655 | fC30 *= ca; | |
656 | fC32 *= rr; | |
657 | fC40 *= ca; | |
658 | fC42 *= rr; | |
659 | ||
86be8934 | 660 | CheckCovariance(); |
661 | ||
49d13e89 | 662 | return kTRUE; |
663 | } | |
664 | ||
665 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
666 | //---------------------------------------------------------------- | |
667 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
668 | //---------------------------------------------------------------- | |
49d13e89 | 669 | Double_t dx=xk-fX; |
e421f556 | 670 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 671 | |
1530f89c | 672 | Double_t crv=GetC(b); |
5773defd | 673 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
674 | ||
49d13e89 | 675 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 676 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 677 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
678 | ||
679 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
680 | Double_t | |
681 | &fC00=fC[0], | |
682 | &fC10=fC[1], &fC11=fC[2], | |
683 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
684 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
685 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
686 | ||
bfd20868 | 687 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
49d13e89 | 688 | |
689 | fX=xk; | |
690 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 691 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 692 | fP2 += dx*crv; |
693 | ||
694 | //f = F - 1 | |
695 | ||
696 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
697 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
698 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
699 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
700 | Double_t f13= dx/r1; | |
701 | Double_t f24= dx; f24*=cc; | |
702 | ||
703 | //b = C*ft | |
704 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
705 | Double_t b02=f24*fC40; | |
706 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
707 | Double_t b12=f24*fC41; | |
708 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
709 | Double_t b22=f24*fC42; | |
710 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
711 | Double_t b42=f24*fC44; | |
712 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
713 | Double_t b32=f24*fC43; | |
714 | ||
715 | //a = f*b = f*C*ft | |
716 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
717 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
718 | Double_t a22=f24*b42; | |
719 | ||
720 | //F*C*Ft = C + (b + bt + a) | |
721 | fC00 += b00 + b00 + a00; | |
722 | fC10 += b10 + b01 + a01; | |
723 | fC20 += b20 + b02 + a02; | |
724 | fC30 += b30; | |
725 | fC40 += b40; | |
726 | fC11 += b11 + b11 + a11; | |
727 | fC21 += b21 + b12 + a12; | |
728 | fC31 += b31; | |
729 | fC41 += b41; | |
730 | fC22 += b22 + b22 + a22; | |
731 | fC32 += b32; | |
732 | fC42 += b42; | |
733 | ||
86be8934 | 734 | CheckCovariance(); |
735 | ||
49d13e89 | 736 | return kTRUE; |
737 | } | |
738 | ||
9f2bec63 | 739 | Bool_t |
740 | AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) { | |
741 | //------------------------------------------------------------------ | |
742 | // Transform this track to the local coord. system rotated | |
743 | // by angle "alpha" (rad) with respect to the global coord. system, | |
744 | // and propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
745 | //------------------------------------------------------------------ | |
746 | ||
747 | //Save the parameters | |
748 | Double_t as=fAlpha; | |
749 | Double_t xs=fX; | |
750 | Double_t ps[5], cs[15]; | |
751 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
752 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
753 | ||
754 | if (Rotate(alpha)) | |
755 | if (PropagateTo(x,b)) return kTRUE; | |
756 | ||
757 | //Restore the parameters, if the operation failed | |
758 | fAlpha=as; | |
759 | fX=xs; | |
760 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
761 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
762 | return kFALSE; | |
763 | } | |
764 | ||
266a0f9b | 765 | Bool_t AliExternalTrackParam::PropagateBxByBz |
766 | (Double_t alpha, Double_t x, Double_t b[3]) { | |
767 | //------------------------------------------------------------------ | |
768 | // Transform this track to the local coord. system rotated | |
769 | // by angle "alpha" (rad) with respect to the global coord. system, | |
770 | // and propagate this track to the plane X=xk (cm), | |
771 | // taking into account all three components of the B field, "b[3]" (kG) | |
772 | //------------------------------------------------------------------ | |
773 | ||
774 | //Save the parameters | |
775 | Double_t as=fAlpha; | |
776 | Double_t xs=fX; | |
777 | Double_t ps[5], cs[15]; | |
778 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
779 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
780 | ||
781 | if (Rotate(alpha)) | |
782 | if (PropagateToBxByBz(x,b)) return kTRUE; | |
783 | ||
784 | //Restore the parameters, if the operation failed | |
785 | fAlpha=as; | |
786 | fX=xs; | |
787 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
788 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
789 | return kFALSE; | |
790 | } | |
791 | ||
9f2bec63 | 792 | |
052daaff | 793 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
794 | Double_t p[3], Double_t bz) const { | |
795 | //+++++++++++++++++++++++++++++++++++++++++ | |
796 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
797 | // Extrapolate track along simple helix in magnetic field | |
798 | // Arguments: len -distance alogn helix, [cm] | |
799 | // bz - mag field, [kGaus] | |
800 | // Returns: x and p contain extrapolated positon and momentum | |
801 | // The momentum returned for straight-line tracks is meaningless ! | |
802 | //+++++++++++++++++++++++++++++++++++++++++ | |
803 | GetXYZ(x); | |
804 | ||
2258e165 | 805 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks |
052daaff | 806 | Double_t unit[3]; GetDirection(unit); |
807 | x[0]+=unit[0]*len; | |
808 | x[1]+=unit[1]*len; | |
809 | x[2]+=unit[2]*len; | |
810 | ||
811 | p[0]=unit[0]/kAlmost0; | |
812 | p[1]=unit[1]/kAlmost0; | |
813 | p[2]=unit[2]/kAlmost0; | |
814 | } else { | |
815 | GetPxPyPz(p); | |
816 | Double_t pp=GetP(); | |
817 | Double_t a = -kB2C*bz*GetSign(); | |
818 | Double_t rho = a/pp; | |
819 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
820 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
821 | x[2] += p[2]*len/pp; | |
822 | ||
823 | Double_t p0=p[0]; | |
824 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
825 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
826 | } | |
827 | } | |
828 | ||
829 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
830 | Double_t bz) const { | |
831 | //+++++++++++++++++++++++++++++++++++++++++ | |
832 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
833 | // Finds point of intersection (if exists) of the helix with the plane. | |
834 | // Stores result in fX and fP. | |
835 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
836 | // and vector, normal to the plane | |
837 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
838 | //+++++++++++++++++++++++++++++++++++++++++ | |
839 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
840 | ||
841 | //estimates initial helix length up to plane | |
842 | Double_t s= | |
843 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
844 | Double_t dist=99999,distPrev=dist; | |
845 | Double_t x[3],p[3]; | |
846 | while(TMath::Abs(dist)>0.00001){ | |
847 | //calculates helix at the distance s from x0 ALONG the helix | |
848 | Propagate(s,x,p,bz); | |
849 | ||
850 | //distance between current helix position and plane | |
851 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
852 | ||
853 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
854 | distPrev=dist; | |
855 | s-=dist; | |
856 | } | |
857 | //on exit pnt is intersection point,norm is track vector at that point, | |
858 | //all in MARS | |
859 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
860 | return kTRUE; | |
861 | } | |
862 | ||
49d13e89 | 863 | Double_t |
864 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
865 | //---------------------------------------------------------------- | |
866 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
867 | //---------------------------------------------------------------- | |
868 | Double_t sdd = fC[0] + cov[0]; | |
869 | Double_t sdz = fC[1] + cov[1]; | |
870 | Double_t szz = fC[2] + cov[2]; | |
871 | Double_t det = sdd*szz - sdz*sdz; | |
872 | ||
873 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
874 | ||
875 | Double_t d = fP[0] - p[0]; | |
876 | Double_t z = fP[1] - p[1]; | |
877 | ||
878 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
879 | } | |
880 | ||
4b189f98 | 881 | Double_t AliExternalTrackParam:: |
882 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
883 | //---------------------------------------------------------------- | |
884 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 885 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 886 | // |
887 | // Cov(x,x) ... : covxyz[0] | |
888 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
889 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
890 | //---------------------------------------------------------------- | |
891 | ||
892 | Double_t res[3] = { | |
893 | GetX() - p[0], | |
894 | GetY() - p[1], | |
895 | GetZ() - p[2] | |
896 | }; | |
897 | ||
898 | Double_t f=GetSnp(); | |
899 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
bfd20868 | 900 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
4b189f98 | 901 | Double_t a=f/r, b=GetTgl()/r; |
902 | ||
903 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
904 | ||
905 | TMatrixDSym v(3); | |
906 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
907 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
908 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
909 | ||
910 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
911 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
912 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
913 | ||
914 | v.Invert(); | |
915 | if (!v.IsValid()) return kVeryBig; | |
916 | ||
917 | Double_t chi2=0.; | |
918 | for (Int_t i = 0; i < 3; i++) | |
919 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
920 | ||
921 | return chi2; | |
acdfbc78 | 922 | } |
923 | ||
924 | Double_t AliExternalTrackParam:: | |
925 | GetPredictedChi2(const AliExternalTrackParam *t) const { | |
926 | //---------------------------------------------------------------- | |
927 | // Estimate the chi2 (5 dof) of this track with respect to the track | |
928 | // given by the argument. | |
929 | // The two tracks must be in the same reference system | |
930 | // and estimated at the same reference plane. | |
931 | //---------------------------------------------------------------- | |
932 | ||
933 | if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) { | |
934 | AliError("The reference systems of the tracks differ !"); | |
935 | return kVeryBig; | |
936 | } | |
937 | if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) { | |
938 | AliError("The reference of the tracks planes differ !"); | |
939 | return kVeryBig; | |
940 | } | |
941 | ||
942 | TMatrixDSym c(5); | |
943 | c(0,0)=GetSigmaY2(); | |
944 | c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2(); | |
945 | c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2(); | |
946 | c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2(); | |
947 | c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2(); | |
948 | ||
949 | c(0,0)+=t->GetSigmaY2(); | |
950 | c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2(); | |
951 | c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2(); | |
952 | c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2(); | |
953 | c(4,0)+=t->GetSigma1PtY();c(4,1)+=t->GetSigma1PtZ();c(4,2)+=t->GetSigma1PtSnp();c(4,3)+=t->GetSigma1PtTgl();c(4,4)+=t->GetSigma1Pt2(); | |
954 | c(0,1)=c(1,0); | |
955 | c(0,2)=c(2,0); c(1,2)=c(2,1); | |
956 | c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2); | |
957 | c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3); | |
958 | ||
959 | c.Invert(); | |
960 | if (!c.IsValid()) return kVeryBig; | |
961 | ||
962 | ||
963 | Double_t res[5] = { | |
964 | GetY() - t->GetY(), | |
965 | GetZ() - t->GetZ(), | |
966 | GetSnp() - t->GetSnp(), | |
967 | GetTgl() - t->GetTgl(), | |
968 | GetSigned1Pt() - t->GetSigned1Pt() | |
969 | }; | |
4b189f98 | 970 | |
acdfbc78 | 971 | Double_t chi2=0.; |
972 | for (Int_t i = 0; i < 5; i++) | |
973 | for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j); | |
4b189f98 | 974 | |
acdfbc78 | 975 | return chi2; |
4b189f98 | 976 | } |
977 | ||
1e023a36 | 978 | Bool_t AliExternalTrackParam:: |
979 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
980 | //---------------------------------------------------------------- | |
981 | // Propagate this track to the plane | |
982 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
983 | // belongs to. | |
984 | // The magnetic field is "bz" (kG) | |
985 | // | |
986 | // The track curvature and the change of the covariance matrix | |
987 | // of the track parameters are negleted ! | |
988 | // (So the "step" should be small compared with 1/curvature) | |
989 | //---------------------------------------------------------------- | |
990 | ||
991 | Double_t f=GetSnp(); | |
992 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
bfd20868 | 993 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
1e023a36 | 994 | Double_t a=f/r, b=GetTgl()/r; |
995 | ||
996 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
997 | ||
998 | TMatrixDSym tV(3); | |
999 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
1000 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
1001 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
1002 | ||
1003 | TMatrixDSym pV(3); | |
1004 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
1005 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
1006 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
1007 | ||
1008 | TMatrixDSym tpV(tV); | |
1009 | tpV+=pV; | |
1010 | tpV.Invert(); | |
1011 | if (!tpV.IsValid()) return kFALSE; | |
1012 | ||
1013 | TMatrixDSym pW(3),tW(3); | |
1014 | for (Int_t i=0; i<3; i++) | |
1015 | for (Int_t j=0; j<3; j++) { | |
1016 | pW(i,j)=tW(i,j)=0.; | |
1017 | for (Int_t k=0; k<3; k++) { | |
1018 | pW(i,j) += tV(i,k)*tpV(k,j); | |
1019 | tW(i,j) += pV(i,k)*tpV(k,j); | |
1020 | } | |
1021 | } | |
1022 | ||
1023 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
1024 | ||
1025 | Double_t x=0.; | |
1026 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
1027 | Double_t crv=GetC(bz); | |
1028 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1029 | f += crv*(x-fX); | |
1030 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
1031 | fX=x; | |
1032 | ||
1033 | fP[0]=0.; | |
1034 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
1035 | fP[1]=0.; | |
1036 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
1037 | ||
1038 | return kTRUE; | |
1039 | } | |
1040 | ||
e23a38cb | 1041 | Double_t *AliExternalTrackParam::GetResiduals( |
1042 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
1043 | //------------------------------------------------------------------ | |
1044 | // Returns the track residuals with the space point "p" having | |
1045 | // the covariance matrix "cov". | |
1046 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
1047 | // otherwise they must be predicted. | |
1048 | //------------------------------------------------------------------ | |
1049 | static Double_t res[2]; | |
1050 | ||
1051 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1052 | if (updated) { | |
1053 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
1054 | } else { | |
1055 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
1056 | } | |
1057 | Double_t det=r00*r11 - r01*r01; | |
1058 | ||
1059 | if (TMath::Abs(det) < kAlmost0) return 0; | |
1060 | ||
1061 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 1062 | |
1063 | if (r00 < 0.) return 0; | |
1064 | if (r11 < 0.) return 0; | |
1065 | ||
e23a38cb | 1066 | Double_t dy = fP[0] - p[0]; |
1067 | Double_t dz = fP[1] - p[1]; | |
1068 | ||
1069 | res[0]=dy*TMath::Sqrt(r00); | |
1070 | res[1]=dz*TMath::Sqrt(r11); | |
1071 | ||
1072 | return res; | |
1073 | } | |
1074 | ||
49d13e89 | 1075 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
1076 | //------------------------------------------------------------------ | |
1077 | // Update the track parameters with the space point "p" having | |
1078 | // the covariance matrix "cov" | |
1079 | //------------------------------------------------------------------ | |
1080 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
1081 | Double_t | |
1082 | &fC00=fC[0], | |
1083 | &fC10=fC[1], &fC11=fC[2], | |
1084 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1085 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1086 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1087 | ||
1088 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1089 | r00+=fC00; r01+=fC10; r11+=fC11; | |
1090 | Double_t det=r00*r11 - r01*r01; | |
1091 | ||
1092 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
1093 | ||
1094 | ||
1095 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
1096 | ||
1097 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
1098 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
1099 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
1100 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
1101 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
1102 | ||
1103 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
1104 | Double_t sf=fP2 + k20*dy + k21*dz; | |
1105 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
1106 | ||
1107 | fP0 += k00*dy + k01*dz; | |
1108 | fP1 += k10*dy + k11*dz; | |
1109 | fP2 = sf; | |
1110 | fP3 += k30*dy + k31*dz; | |
1111 | fP4 += k40*dy + k41*dz; | |
1112 | ||
1113 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
1114 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
1115 | ||
1116 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
1117 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
1118 | fC40-=k00*c04+k01*c14; | |
1119 | ||
1120 | fC11-=k10*c01+k11*fC11; | |
1121 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
1122 | fC41-=k10*c04+k11*c14; | |
1123 | ||
1124 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
1125 | fC42-=k20*c04+k21*c14; | |
1126 | ||
1127 | fC33-=k30*c03+k31*c13; | |
1128 | fC43-=k30*c04+k31*c14; | |
1129 | ||
1130 | fC44-=k40*c04+k41*c14; | |
1131 | ||
86be8934 | 1132 | CheckCovariance(); |
1133 | ||
49d13e89 | 1134 | return kTRUE; |
1135 | } | |
1136 | ||
c7bafca9 | 1137 | void |
1138 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
1139 | //-------------------------------------------------------------------- | |
1140 | // External track parameters -> helix parameters | |
1141 | // "b" - magnetic field (kG) | |
1142 | //-------------------------------------------------------------------- | |
1143 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1144 | ||
1530f89c | 1145 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 1146 | |
1147 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
1148 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
1149 | //hlx[1]= // z0 | |
1150 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
1151 | //hlx[3]= // tgl | |
1530f89c | 1152 | hlx[4]=GetC(b); // C |
c7bafca9 | 1153 | } |
1154 | ||
1155 | ||
1156 | static void Evaluate(const Double_t *h, Double_t t, | |
1157 | Double_t r[3], //radius vector | |
1158 | Double_t g[3], //first defivatives | |
1159 | Double_t gg[3]) //second derivatives | |
1160 | { | |
1161 | //-------------------------------------------------------------------- | |
1162 | // Calculate position of a point on a track and some derivatives | |
1163 | //-------------------------------------------------------------------- | |
1164 | Double_t phase=h[4]*t+h[2]; | |
1165 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
1166 | ||
ba4550c4 | 1167 | r[0] = h[5]; |
1168 | r[1] = h[0]; | |
1169 | if (TMath::Abs(h[4])>kAlmost0) { | |
1170 | r[0] += (sn - h[6])/h[4]; | |
1171 | r[1] -= (cs - h[7])/h[4]; | |
1172 | } | |
c7bafca9 | 1173 | r[2] = h[1] + h[3]*t; |
1174 | ||
1175 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
1176 | ||
1177 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
1178 | } | |
1179 | ||
1180 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
1181 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
1182 | //------------------------------------------------------------ | |
1183 | // Returns the (weighed !) distance of closest approach between | |
1184 | // this track and the track "p". | |
1185 | // Other returned values: | |
1186 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
1187 | //----------------------------------------------------------- | |
1188 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
1189 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
1190 | Double_t dx2=dy2; | |
1191 | ||
c7bafca9 | 1192 | Double_t p1[8]; GetHelixParameters(p1,b); |
1193 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
1194 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
1195 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
1196 | ||
1197 | ||
1198 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
1199 | Evaluate(p1,t1,r1,g1,gg1); | |
1200 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
1201 | Evaluate(p2,t2,r2,g2,gg2); | |
1202 | ||
1203 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
1204 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1205 | ||
1206 | Int_t max=27; | |
1207 | while (max--) { | |
1208 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
1209 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
1210 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
1211 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
1212 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
1213 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
1214 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
1215 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
1216 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
1217 | ||
1218 | Double_t det=h11*h22-h12*h12; | |
1219 | ||
1220 | Double_t dt1,dt2; | |
1221 | if (TMath::Abs(det)<1.e-33) { | |
1222 | //(quasi)singular Hessian | |
1223 | dt1=-gt1; dt2=-gt2; | |
1224 | } else { | |
1225 | dt1=-(gt1*h22 - gt2*h12)/det; | |
1226 | dt2=-(h11*gt2 - h12*gt1)/det; | |
1227 | } | |
1228 | ||
1229 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
1230 | ||
1231 | //check delta(phase1) ? | |
1232 | //check delta(phase2) ? | |
1233 | ||
1234 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
1235 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
1236 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 1237 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 1238 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
1239 | if (lmb < 0.) | |
358f16ae | 1240 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 1241 | break; |
1242 | } | |
1243 | ||
1244 | Double_t dd=dm; | |
1245 | for (Int_t div=1 ; ; div*=2) { | |
1246 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
1247 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
1248 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
1249 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1250 | if (dd<dm) break; | |
1251 | dt1*=0.5; dt2*=0.5; | |
1252 | if (div>512) { | |
358f16ae | 1253 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 1254 | } |
1255 | } | |
1256 | dm=dd; | |
1257 | ||
1258 | t1+=dt1; | |
1259 | t2+=dt2; | |
1260 | ||
1261 | } | |
1262 | ||
358f16ae | 1263 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1264 | |
1265 | Double_t cs=TMath::Cos(GetAlpha()); | |
1266 | Double_t sn=TMath::Sin(GetAlpha()); | |
1267 | xthis=r1[0]*cs + r1[1]*sn; | |
1268 | ||
1269 | cs=TMath::Cos(p->GetAlpha()); | |
1270 | sn=TMath::Sin(p->GetAlpha()); | |
1271 | xp=r2[0]*cs + r2[1]*sn; | |
1272 | ||
1273 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1274 | } | |
1275 | ||
1276 | Double_t AliExternalTrackParam:: | |
1277 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1278 | //-------------------------------------------------------------- | |
1279 | // Propagates this track and the argument track to the position of the | |
1280 | // distance of closest approach. | |
1281 | // Returns the (weighed !) distance of closest approach. | |
1282 | //-------------------------------------------------------------- | |
1283 | Double_t xthis,xp; | |
1284 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1285 | ||
1286 | if (!PropagateTo(xthis,b)) { | |
1287 | //AliWarning(" propagation failed !"); | |
1288 | return 1e+33; | |
1289 | } | |
1290 | ||
1291 | if (!p->PropagateTo(xp,b)) { | |
1292 | //AliWarning(" propagation failed !"; | |
1293 | return 1e+33; | |
1294 | } | |
1295 | ||
1296 | return dca; | |
1297 | } | |
1298 | ||
1299 | ||
58e536c5 | 1300 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1301 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1302 | // |
e99a34df | 1303 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1304 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1305 | // Magnetic field is "b" (kG). | |
1306 | // | |
1307 | // a) The track gets extapolated to the DCA to the vertex. | |
1308 | // b) The impact parameters and their covariance matrix are calculated. | |
1309 | // | |
1310 | // In the case of success, the returned value is kTRUE | |
1311 | // (otherwise, it's kFALSE) | |
1312 | // | |
1313 | Double_t alpha=GetAlpha(); | |
1314 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1315 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1316 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1317 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1318 | x-=xv; y-=yv; |
1319 | ||
1320 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1321 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
f76701bf | 1322 | if (d > maxd) return kFALSE; |
1323 | ||
1324 | //Propagate to the DCA | |
2258e165 | 1325 | Double_t crv=GetC(b); |
e99a34df | 1326 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1327 | ||
bfd20868 | 1328 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1329 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
e99a34df | 1330 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1331 | else cs=1.; | |
f76701bf | 1332 | |
1333 | x = xv*cs + yv*sn; | |
1334 | yv=-xv*sn + yv*cs; xv=x; | |
1335 | ||
1336 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
266a0f9b | 1337 | |
1338 | if (dz==0) return kTRUE; | |
1339 | dz[0] = GetParameter()[0] - yv; | |
1340 | dz[1] = GetParameter()[1] - zv; | |
1341 | ||
1342 | if (covar==0) return kTRUE; | |
1343 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); | |
1344 | ||
1345 | //***** Improvements by A.Dainese | |
1346 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1347 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1348 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1349 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1350 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1351 | //***** | |
1352 | ||
1353 | return kTRUE; | |
1354 | } | |
1355 | ||
1356 | Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx, | |
1357 | Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) { | |
1358 | // | |
1359 | // Propagate this track to the DCA to vertex "vtx", | |
1360 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
1361 | // | |
1362 | // This function takes into account all three components of the magnetic | |
1363 | // field given by the b[3] arument (kG) | |
1364 | // | |
1365 | // a) The track gets extapolated to the DCA to the vertex. | |
1366 | // b) The impact parameters and their covariance matrix are calculated. | |
1367 | // | |
1368 | // In the case of success, the returned value is kTRUE | |
1369 | // (otherwise, it's kFALSE) | |
1370 | // | |
1371 | Double_t alpha=GetAlpha(); | |
1372 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1373 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
1374 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; | |
1375 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
1376 | x-=xv; y-=yv; | |
1377 | ||
1378 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1379 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
266a0f9b | 1380 | if (d > maxd) return kFALSE; |
1381 | ||
1382 | //Propagate to the DCA | |
8567bf39 | 1383 | Double_t crv=GetC(b[2]); |
1384 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
266a0f9b | 1385 | |
bfd20868 | 1386 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1387 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
266a0f9b | 1388 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1389 | else cs=1.; | |
1390 | ||
1391 | x = xv*cs + yv*sn; | |
1392 | yv=-xv*sn + yv*cs; xv=x; | |
1393 | ||
1394 | if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1395 | |
1396 | if (dz==0) return kTRUE; | |
1397 | dz[0] = GetParameter()[0] - yv; | |
1398 | dz[1] = GetParameter()[1] - zv; | |
1399 | ||
1400 | if (covar==0) return kTRUE; | |
58e536c5 | 1401 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1402 | |
1403 | //***** Improvements by A.Dainese | |
1404 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1405 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1406 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1407 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1408 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1409 | //***** | |
1410 | ||
29fbcc93 | 1411 | return kTRUE; |
f76701bf | 1412 | } |
1413 | ||
b1149664 | 1414 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1415 | //---------------------------------------------------------------- | |
1416 | // This function returns a unit vector along the track direction | |
1417 | // in the global coordinate system. | |
1418 | //---------------------------------------------------------------- | |
1419 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1420 | Double_t snp=fP[2]; | |
bfd20868 | 1421 | Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp)); |
b1149664 | 1422 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1423 | d[0]=(csp*cs - snp*sn)/norm; | |
1424 | d[1]=(snp*cs + csp*sn)/norm; | |
1425 | d[2]=fP[3]/norm; | |
1426 | } | |
1427 | ||
c683ddc2 | 1428 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1429 | //--------------------------------------------------------------------- |
1430 | // This function returns the global track momentum components | |
1431 | // Results for (nearly) straight tracks are meaningless ! | |
1432 | //--------------------------------------------------------------------- | |
1433 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1434 | return Local2GlobalMomentum(p,fAlpha); | |
1435 | } | |
a5e407e9 | 1436 | |
def9660e | 1437 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1438 | //--------------------------------------------------------------------- |
1439 | // Returns x-component of momentum | |
1440 | // Result for (nearly) straight tracks is meaningless ! | |
1441 | //--------------------------------------------------------------------- | |
def9660e | 1442 | |
957fb479 | 1443 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1444 | GetPxPyPz(p); |
1445 | ||
1446 | return p[0]; | |
1447 | } | |
1448 | ||
1449 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1450 | //--------------------------------------------------------------------- |
1451 | // Returns y-component of momentum | |
1452 | // Result for (nearly) straight tracks is meaningless ! | |
1453 | //--------------------------------------------------------------------- | |
def9660e | 1454 | |
957fb479 | 1455 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1456 | GetPxPyPz(p); |
1457 | ||
1458 | return p[1]; | |
1459 | } | |
1460 | ||
c683ddc2 | 1461 | Double_t AliExternalTrackParam::Xv() const { |
1462 | //--------------------------------------------------------------------- | |
1463 | // Returns x-component of first track point | |
1464 | //--------------------------------------------------------------------- | |
1465 | ||
1466 | Double_t r[3]={0.,0.,0.}; | |
1467 | GetXYZ(r); | |
1468 | ||
1469 | return r[0]; | |
1470 | } | |
1471 | ||
1472 | Double_t AliExternalTrackParam::Yv() const { | |
1473 | //--------------------------------------------------------------------- | |
1474 | // Returns y-component of first track point | |
1475 | //--------------------------------------------------------------------- | |
1476 | ||
1477 | Double_t r[3]={0.,0.,0.}; | |
1478 | GetXYZ(r); | |
1479 | ||
1480 | return r[1]; | |
1481 | } | |
1482 | ||
def9660e | 1483 | Double_t AliExternalTrackParam::Theta() const { |
1484 | // return theta angle of momentum | |
1485 | ||
7cdd0c20 | 1486 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1487 | } |
1488 | ||
1489 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1490 | //--------------------------------------------------------------------- |
1491 | // Returns the azimuthal angle of momentum | |
1492 | // 0 <= phi < 2*pi | |
1493 | //--------------------------------------------------------------------- | |
def9660e | 1494 | |
957fb479 | 1495 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1496 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1497 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1498 | ||
1499 | return phi; | |
def9660e | 1500 | } |
1501 | ||
1502 | Double_t AliExternalTrackParam::M() const { | |
1503 | // return particle mass | |
1504 | ||
1505 | // No mass information available so far. | |
1506 | // Redifine in derived class! | |
1507 | ||
1508 | return -999.; | |
1509 | } | |
1510 | ||
1511 | Double_t AliExternalTrackParam::E() const { | |
1512 | // return particle energy | |
1513 | ||
1514 | // No PID information available so far. | |
1515 | // Redifine in derived class! | |
1516 | ||
1517 | return -999.; | |
1518 | } | |
1519 | ||
1520 | Double_t AliExternalTrackParam::Eta() const { | |
1521 | // return pseudorapidity | |
1522 | ||
1523 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1524 | } | |
1525 | ||
1526 | Double_t AliExternalTrackParam::Y() const { | |
1527 | // return rapidity | |
1528 | ||
1529 | // No PID information available so far. | |
1530 | // Redifine in derived class! | |
1531 | ||
1532 | return -999.; | |
1533 | } | |
1534 | ||
c9ec41e8 | 1535 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1536 | //--------------------------------------------------------------------- | |
1537 | // This function returns the global track position | |
1538 | //--------------------------------------------------------------------- | |
1539 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1540 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1541 | } |
1542 | ||
c9ec41e8 | 1543 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1544 | //--------------------------------------------------------------------- | |
1545 | // This function returns the global covariance matrix of the track params | |
1546 | // | |
1547 | // Cov(x,x) ... : cv[0] | |
1548 | // Cov(y,x) ... : cv[1] cv[2] | |
1549 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1550 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1551 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1552 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1553 | // |
c9ec41e8 | 1554 | // Results for (nearly) straight tracks are meaningless ! |
1555 | //--------------------------------------------------------------------- | |
e421f556 | 1556 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1557 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1558 | return kFALSE; | |
a5e407e9 | 1559 | } |
49d13e89 | 1560 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1561 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1562 | return kFALSE; | |
1563 | } | |
1564 | Double_t pt=1./TMath::Abs(fP[4]); | |
1565 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1566 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1567 | |
1568 | Double_t m00=-sn, m10=cs; | |
1569 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1570 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1571 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1572 | ||
854d5d49 | 1573 | m43*=GetSign(); |
1574 | m44*=GetSign(); | |
1575 | m45*=GetSign(); | |
1576 | ||
c9ec41e8 | 1577 | cv[0 ] = fC[0]*m00*m00; |
1578 | cv[1 ] = fC[0]*m00*m10; | |
1579 | cv[2 ] = fC[0]*m10*m10; | |
1580 | cv[3 ] = fC[1]*m00; | |
1581 | cv[4 ] = fC[1]*m10; | |
1582 | cv[5 ] = fC[2]; | |
1583 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1584 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1585 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1586 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1587 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1588 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1589 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1590 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1591 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1592 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1593 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1594 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1595 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1596 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1597 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1598 | |
c9ec41e8 | 1599 | return kTRUE; |
51ad6848 | 1600 | } |
1601 | ||
51ad6848 | 1602 | |
c9ec41e8 | 1603 | Bool_t |
1604 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1605 | //--------------------------------------------------------------------- | |
1606 | // This function returns the global track momentum extrapolated to | |
1607 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1608 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1609 | p[0]=fP[4]; |
1530f89c | 1610 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1611 | p[2]=fP[3]; |
1612 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1613 | } |
1614 | ||
7cf7bb6c | 1615 | Bool_t |
1616 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1617 | //--------------------------------------------------------------------- | |
1618 | // This function returns the local Y-coordinate of the intersection | |
1619 | // point between this track and the reference plane "x" (cm). | |
1620 | // Magnetic field "b" (kG) | |
1621 | //--------------------------------------------------------------------- | |
1622 | Double_t dx=x-fX; | |
1623 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1624 | ||
1530f89c | 1625 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1626 | |
1627 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1628 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1629 | ||
60e55aee | 1630 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
7cf7bb6c | 1631 | y = fP[0] + dx*(f1+f2)/(r1+r2); |
1632 | return kTRUE; | |
1633 | } | |
1634 | ||
6c94f330 | 1635 | Bool_t |
1636 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1637 | //--------------------------------------------------------------------- | |
1638 | // This function returns the local Z-coordinate of the intersection | |
1639 | // point between this track and the reference plane "x" (cm). | |
1640 | // Magnetic field "b" (kG) | |
1641 | //--------------------------------------------------------------------- | |
1642 | Double_t dx=x-fX; | |
1643 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1644 | ||
2258e165 | 1645 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
6c94f330 | 1646 | |
1647 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1648 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1649 | ||
60e55aee | 1650 | Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2)); |
6c94f330 | 1651 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! |
1652 | return kTRUE; | |
1653 | } | |
1654 | ||
c9ec41e8 | 1655 | Bool_t |
1656 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1657 | //--------------------------------------------------------------------- | |
1658 | // This function returns the global track position extrapolated to | |
1659 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1660 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1661 | Double_t dx=x-fX; |
e421f556 | 1662 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1663 | ||
1530f89c | 1664 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1665 | |
e421f556 | 1666 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1667 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1668 | |
60e55aee | 1669 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
c9ec41e8 | 1670 | r[0] = x; |
1671 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
f90a11c9 | 1672 | r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter |
1673 | ||
c9ec41e8 | 1674 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1675 | } |
1676 | ||
51ad6848 | 1677 | //_____________________________________________________________________________ |
1678 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1679 | { | |
1680 | // print the parameters and the covariance matrix | |
1681 | ||
1682 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1683 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1684 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1685 | printf(" covariance: %12g\n", fC[0]); | |
1686 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1687 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1688 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1689 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1690 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1691 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1692 | } |
5b77d93c | 1693 | |
c194ba83 | 1694 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1695 | // | |
1696 | // Get sinus at given x | |
1697 | // | |
1530f89c | 1698 | Double_t crv=GetC(b); |
c194ba83 | 1699 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1700 | Double_t dx = x-fX; | |
1701 | Double_t res = fP[2]+dx*crv; | |
1702 | return res; | |
1703 | } | |
bf00ebb8 | 1704 | |
1705 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1706 | //------------------------------------------------------------------------ | |
1707 | // Get the distance between two tracks at the local position x | |
1708 | // working in the local frame of this track. | |
1709 | // Origin : Marian.Ivanov@cern.ch | |
1710 | //----------------------------------------------------------------------- | |
1711 | Double_t xyz[3]; | |
1712 | Double_t xyz2[3]; | |
1713 | xyz[0]=x; | |
1714 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1715 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1716 | // | |
1717 | // | |
1718 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1719 | xyz2[0]=x; | |
1720 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1721 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1722 | }else{ | |
1723 | // | |
1724 | Double_t xyz1[3]; | |
1725 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1726 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1727 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1728 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1729 | // | |
1730 | xyz1[0]=xyz2[0]; | |
1731 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1732 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1733 | // | |
1734 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1735 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1736 | xyz2[2] = xyz1[2]; | |
1737 | } | |
1738 | dist[0] = xyz[0]-xyz2[0]; | |
1739 | dist[1] = xyz[1]-xyz2[1]; | |
1740 | dist[2] = xyz[2]-xyz2[2]; | |
1741 | ||
1742 | return kTRUE; | |
1743 | } | |
0c19adf7 | 1744 | |
1745 | ||
1746 | // | |
1747 | // Draw functionality. | |
1748 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1749 | // | |
1750 | ||
1751 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1752 | // | |
1753 | // Draw track line | |
1754 | // | |
1755 | if (minR>maxR) return ; | |
1756 | if (stepR<=0) return ; | |
1757 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1758 | if (npoints<1) return; | |
1759 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1760 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1761 | polymarker->Draw(); | |
1762 | } | |
1763 | ||
1764 | // | |
1765 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1766 | // | |
1767 | // Fill points in the polymarker | |
1768 | // | |
1769 | Int_t counter=0; | |
1770 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1771 | Double_t point[3]; | |
1772 | GetXYZAt(r,magF,point); | |
1773 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
1774 | printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); | |
1775 | counter++; | |
1776 | } | |
1777 | } | |
0e8460af | 1778 | |
1779 | Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const { | |
1780 | // | |
1781 | Int_t min = TMath::Min(i,j); | |
1782 | Int_t max = TMath::Max(i,j); | |
1783 | ||
1784 | return min+(max+1)*max/2; | |
1785 | } | |
8b6e3369 | 1786 | |
1787 | ||
1788 | void AliExternalTrackParam::g3helx3(Double_t qfield, | |
1789 | Double_t step, | |
1790 | Double_t vect[7]) { | |
1791 | /****************************************************************** | |
1792 | * * | |
1793 | * GEANT3 tracking routine in a constant field oriented * | |
1794 | * along axis 3 * | |
1795 | * Tracking is performed with a conventional * | |
1796 | * helix step method * | |
1797 | * * | |
1798 | * Authors R.Brun, M.Hansroul ********* * | |
1799 | * Rewritten V.Perevoztchikov * | |
1800 | * * | |
1801 | * Rewritten in C++ by I.Belikov * | |
1802 | * * | |
1803 | * qfield (kG) - particle charge times magnetic field * | |
1804 | * step (cm) - step length along the helix * | |
1805 | * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p * | |
1806 | * * | |
1807 | ******************************************************************/ | |
1808 | const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6; | |
bfd20868 | 1809 | const Double_t kOvSqSix=TMath::Sqrt(1./6.); |
8b6e3369 | 1810 | |
1811 | Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz]; | |
1812 | ||
1813 | Double_t rho = qfield*kB2C/vect[ipp]; | |
1814 | Double_t tet = rho*step; | |
1815 | ||
1816 | Double_t tsint, sintt, sint, cos1t; | |
1817 | if (TMath::Abs(tet) > 0.15) { | |
1818 | sint = TMath::Sin(tet); | |
1819 | sintt = sint/tet; | |
1820 | tsint = (tet - sint)/tet; | |
1821 | Double_t t=TMath::Sin(0.5*tet); | |
1822 | cos1t = 2*t*t/tet; | |
1823 | } else { | |
1824 | tsint = tet*tet/6.; | |
bfd20868 | 1825 | sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint; |
8b6e3369 | 1826 | sint = tet*sintt; |
1827 | cos1t = 0.5*tet; | |
1828 | } | |
1829 | ||
1830 | Double_t f1 = step*sintt; | |
1831 | Double_t f2 = step*cos1t; | |
1832 | Double_t f3 = step*tsint*cosz; | |
1833 | Double_t f4 = -tet*cos1t; | |
1834 | Double_t f5 = sint; | |
1835 | ||
1836 | vect[ix] += f1*cosx - f2*cosy; | |
1837 | vect[iy] += f1*cosy + f2*cosx; | |
1838 | vect[iz] += f1*cosz + f3; | |
1839 | ||
1840 | vect[ipx] += f4*cosx - f5*cosy; | |
1841 | vect[ipy] += f4*cosy + f5*cosx; | |
1842 | ||
1843 | } | |
1844 | ||
1845 | Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) { | |
1846 | //---------------------------------------------------------------- | |
1847 | // Extrapolate this track to the plane X=xk in the field b[]. | |
1848 | // | |
1849 | // X [cm] is in the "tracking coordinate system" of this track. | |
1850 | // b[]={Bx,By,Bz} [kG] is in the Global coordidate system. | |
1851 | //---------------------------------------------------------------- | |
1852 | ||
1853 | Double_t dx=xk-fX; | |
1854 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
1855 | ||
1856 | Double_t crv=GetC(b[2]); | |
1857 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
1858 | ||
1859 | Double_t f1=fP[2], f2=f1 + crv*dx; | |
1860 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1861 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1862 | ||
1863 | ||
1864 | // Estimate the covariance matrix | |
1865 | Double_t &fP3=fP[3], &fP4=fP[4]; | |
1866 | Double_t | |
1867 | &fC00=fC[0], | |
1868 | &fC10=fC[1], &fC11=fC[2], | |
1869 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1870 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1871 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1872 | ||
bfd20868 | 1873 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
8b6e3369 | 1874 | |
1875 | //f = F - 1 | |
1876 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
1877 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
1878 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
1879 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
1880 | Double_t f13= dx/r1; | |
1881 | Double_t f24= dx; f24*=cc; | |
1882 | ||
1883 | //b = C*ft | |
1884 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
1885 | Double_t b02=f24*fC40; | |
1886 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
1887 | Double_t b12=f24*fC41; | |
1888 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
1889 | Double_t b22=f24*fC42; | |
1890 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
1891 | Double_t b42=f24*fC44; | |
1892 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
1893 | Double_t b32=f24*fC43; | |
1894 | ||
1895 | //a = f*b = f*C*ft | |
1896 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
1897 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
1898 | Double_t a22=f24*b42; | |
1899 | ||
1900 | //F*C*Ft = C + (b + bt + a) | |
1901 | fC00 += b00 + b00 + a00; | |
1902 | fC10 += b10 + b01 + a01; | |
1903 | fC20 += b20 + b02 + a02; | |
1904 | fC30 += b30; | |
1905 | fC40 += b40; | |
1906 | fC11 += b11 + b11 + a11; | |
1907 | fC21 += b21 + b12 + a12; | |
1908 | fC31 += b31; | |
1909 | fC41 += b41; | |
1910 | fC22 += b22 + b22 + a22; | |
1911 | fC32 += b32; | |
1912 | fC42 += b42; | |
1913 | ||
86be8934 | 1914 | CheckCovariance(); |
8b6e3369 | 1915 | |
1916 | // Appoximate step length | |
1917 | Double_t step=dx*TMath::Abs(r2 + f2*(f1+f2)/(r1+r2)); | |
1918 | step *= TMath::Sqrt(1.+ GetTgl()*GetTgl()); | |
1919 | ||
1920 | ||
1921 | // Get the track's (x,y,z) and (px,py,pz) in the Global System | |
1922 | Double_t r[3]; GetXYZ(r); | |
1923 | Double_t p[3]; GetPxPyPz(p); | |
1924 | Double_t pp=GetP(); | |
1925 | p[0] /= pp; | |
1926 | p[1] /= pp; | |
1927 | p[2] /= pp; | |
1928 | ||
1929 | ||
1930 | // Rotate to the system where Bx=By=0. | |
1931 | Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]); | |
1932 | Double_t cosphi=1., sinphi=0.; | |
1933 | if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;} | |
1934 | Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]); | |
1935 | Double_t costet=1., sintet=0.; | |
1936 | if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;} | |
1937 | Double_t vect[7]; | |
1938 | ||
1939 | vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2]; | |
1940 | vect[1] = -sinphi*r[0] + cosphi*r[1]; | |
1941 | vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2]; | |
1942 | ||
1943 | vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2]; | |
1944 | vect[4] = -sinphi*p[0] + cosphi*p[1]; | |
1945 | vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2]; | |
1946 | ||
1947 | vect[6] = pp; | |
1948 | ||
1949 | ||
1950 | // Do the helix step | |
1951 | g3helx3(GetSign()*bb,step,vect); | |
1952 | ||
1953 | ||
1954 | // Rotate back to the Global System | |
1955 | r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2]; | |
1956 | r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2]; | |
1957 | r[2] = -sintet*vect[0] + costet*vect[2]; | |
1958 | ||
1959 | p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5]; | |
1960 | p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5]; | |
1961 | p[2] = -sintet*vect[3] + costet*vect[5]; | |
1962 | ||
1963 | ||
1964 | // Rotate back to the Tracking System | |
1965 | Double_t cosalp = TMath::Cos(fAlpha); | |
1966 | Double_t sinalp =-TMath::Sin(fAlpha); | |
1967 | ||
1968 | Double_t | |
1969 | t = cosalp*r[0] - sinalp*r[1]; | |
1970 | r[1] = sinalp*r[0] + cosalp*r[1]; | |
1971 | r[0] = t; | |
1972 | ||
1973 | t = cosalp*p[0] - sinalp*p[1]; | |
1974 | p[1] = sinalp*p[0] + cosalp*p[1]; | |
1975 | p[0] = t; | |
1976 | ||
1977 | ||
1978 | // Do the final correcting step to the target plane (linear approximation) | |
1979 | Double_t x=r[0], y=r[1], z=r[2]; | |
1980 | if (TMath::Abs(dx) > kAlmost0) { | |
1981 | if (TMath::Abs(p[0]) < kAlmost0) return kFALSE; | |
1982 | dx = xk - r[0]; | |
1983 | x += dx; | |
1984 | y += p[1]/p[0]*dx; | |
1985 | z += p[2]/p[0]*dx; | |
1986 | } | |
1987 | ||
1988 | ||
1989 | // Calculate the track parameters | |
1990 | t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]); | |
1991 | fX = x; | |
1992 | fP[0] = y; | |
1993 | fP[1] = z; | |
1994 | fP[2] = p[1]/t; | |
1995 | fP[3] = p[2]/t; | |
1996 | fP[4] = GetSign()/(t*pp); | |
1997 | ||
1998 | return kTRUE; | |
1999 | } | |
2000 | ||
cfdb62d4 | 2001 | Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){ |
2002 | // | |
2003 | //Translation: in the event mixing, the tracks can be shifted | |
2004 | //of the difference among primary vertices (vTrasl) and | |
2005 | //the covariance matrix is changed accordingly | |
2006 | //(covV = covariance of the primary vertex). | |
2007 | //Origin: "Romita, Rossella" <R.Romita@gsi.de> | |
2008 | // | |
2009 | TVector3 translation; | |
2010 | // vTrasl coordinates in the local system | |
2011 | translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]); | |
2012 | translation.RotateZ(-fAlpha); | |
2013 | translation.GetXYZ(vTrasl); | |
2014 | ||
2015 | //compute the new x,y,z of the track | |
5a87bb3d | 2016 | Double_t newX=fX-vTrasl[0]; |
2017 | Double_t newY=fP[0]-vTrasl[1]; | |
2018 | Double_t newZ=fP[1]-vTrasl[2]; | |
cfdb62d4 | 2019 | |
2020 | //define the new parameters | |
5a87bb3d | 2021 | Double_t newParam[5]; |
2022 | newParam[0]=newY; | |
2023 | newParam[1]=newZ; | |
2024 | newParam[2]=fP[2]; | |
2025 | newParam[3]=fP[3]; | |
2026 | newParam[4]=fP[4]; | |
cfdb62d4 | 2027 | |
2028 | // recompute the covariance matrix: | |
2029 | // 1. covV in the local system | |
2030 | Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha); | |
2031 | TMatrixD qQi(3,3); | |
2032 | qQi(0,0) = cosRot; | |
2033 | qQi(0,1) = sinRot; | |
2034 | qQi(0,2) = 0.; | |
2035 | qQi(1,0) = -sinRot; | |
2036 | qQi(1,1) = cosRot; | |
2037 | qQi(1,2) = 0.; | |
2038 | qQi(2,0) = 0.; | |
2039 | qQi(2,1) = 0.; | |
2040 | qQi(2,2) = 1.; | |
2041 | TMatrixD uUi(3,3); | |
2042 | uUi(0,0) = covV[0]; | |
2043 | uUi(0,0) = covV[0]; | |
2044 | uUi(1,0) = covV[1]; | |
2045 | uUi(0,1) = covV[1]; | |
2046 | uUi(2,0) = covV[3]; | |
2047 | uUi(0,2) = covV[3]; | |
2048 | uUi(1,1) = covV[2]; | |
2049 | uUi(2,2) = covV[5]; | |
2050 | uUi(1,2) = covV[4]; | |
2051 | if(uUi.Determinant() <= 0.) {return kFALSE;} | |
2052 | TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi); | |
2053 | TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi); | |
2054 | ||
2055 | //2. compute the new covariance matrix of the track | |
2056 | Double_t sigmaXX=m(0,0); | |
2057 | Double_t sigmaXZ=m(2,0); | |
2058 | Double_t sigmaXY=m(1,0); | |
2059 | Double_t sigmaYY=GetSigmaY2()+m(1,1); | |
2060 | Double_t sigmaYZ=fC[1]+m(1,2); | |
2061 | Double_t sigmaZZ=fC[2]+m(2,2); | |
2062 | Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX); | |
2063 | Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX); | |
2064 | Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX); | |
2065 | ||
2066 | Double_t newCov[15]; | |
2067 | newCov[0]=covarianceYY; | |
2068 | newCov[1]=covarianceYZ; | |
2069 | newCov[2]=covarianceZZ; | |
2070 | for(Int_t i=3;i<15;i++){ | |
2071 | newCov[i]=fC[i]; | |
2072 | } | |
2073 | ||
2074 | // set the new parameters | |
2075 | ||
5a87bb3d | 2076 | Set(newX,fAlpha,newParam,newCov); |
cfdb62d4 | 2077 | |
2078 | return kTRUE; | |
2079 | } | |
86be8934 | 2080 | |
2081 | void AliExternalTrackParam::CheckCovariance() { | |
2082 | ||
2083 | // This function forces the diagonal elements of the covariance matrix to be positive. | |
2084 | // In case the diagonal element is bigger than the maximal allowed value, it is set to | |
2085 | // the limit and the off-diagonal elements that correspond to it are set to zero. | |
2086 | ||
2087 | fC[0] = TMath::Abs(fC[0]); | |
2088 | if (fC[0]>kC0max) { | |
2089 | fC[0] = kC0max; | |
2090 | fC[1] = 0; | |
2091 | fC[3] = 0; | |
2092 | fC[6] = 0; | |
2093 | fC[10] = 0; | |
2094 | } | |
2095 | fC[2] = TMath::Abs(fC[2]); | |
2096 | if (fC[2]>kC2max) { | |
2097 | fC[2] = kC2max; | |
2098 | fC[1] = 0; | |
2099 | fC[4] = 0; | |
2100 | fC[7] = 0; | |
2101 | fC[11] = 0; | |
2102 | } | |
2103 | fC[5] = TMath::Abs(fC[5]); | |
2104 | if (fC[5]>kC5max) { | |
2105 | fC[5] = kC5max; | |
2106 | fC[3] = 0; | |
2107 | fC[4] = 0; | |
2108 | fC[8] = 0; | |
2109 | fC[12] = 0; | |
2110 | } | |
2111 | fC[9] = TMath::Abs(fC[9]); | |
2112 | if (fC[9]>kC9max) { | |
2113 | fC[9] = kC9max; | |
2114 | fC[6] = 0; | |
2115 | fC[7] = 0; | |
2116 | fC[8] = 0; | |
2117 | fC[13] = 0; | |
2118 | } | |
2119 | fC[14] = TMath::Abs(fC[14]); | |
2120 | if (fC[14]>kC14max) { | |
2121 | fC[14] = kC14max; | |
2122 | fC[10] = 0; | |
2123 | fC[11] = 0; | |
2124 | fC[12] = 0; | |
2125 | fC[13] = 0; | |
2126 | } | |
2127 | ||
2128 | // The part below is used for tests and normally is commented out | |
2129 | // TMatrixDSym m(5); | |
2130 | // TVectorD eig(5); | |
2131 | ||
2132 | // m(0,0)=fC[0]; | |
2133 | // m(1,0)=fC[1]; m(1,1)=fC[2]; | |
2134 | // m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5]; | |
2135 | // m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9]; | |
2136 | // m(4,0)=fC[10]; m(4,1)=fC[11]; m(4,2)=fC[12]; m(4,3)=fC[13]; m(4,4)=fC[14]; | |
2137 | ||
2138 | // m(0,1)=m(1,0); | |
2139 | // m(0,2)=m(2,0); m(1,2)=m(2,1); | |
2140 | // m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2); | |
2141 | // m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3); | |
2142 | // m.EigenVectors(eig); | |
2143 | ||
2144 | // // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0); | |
2145 | // if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) { | |
2146 | // AliWarning("Negative eigenvalues of the covariance matrix!"); | |
2147 | // this->Print(); | |
2148 | // eig.Print(); | |
2149 | // } | |
2150 | } |