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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; |
f2cef1b5 | 43 | Bool_t AliExternalTrackParam::fgUseLogTermMS = kFALSE;; |
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 | // | |
4349f5a4 | 168 | const double kSafe = 1e-5; |
aff56ff7 | 169 | Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1]; |
c99948ce | 170 | Double_t radMax = 45.; // approximately ITS outer radius |
4349f5a4 | 171 | if (radPos2 < radMax*radMax) { // inside the ITS |
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 | } | |
4349f5a4 | 178 | // |
179 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
180 | // protection: avoid alpha being too close to 0 or +-pi/2 | |
181 | if (TMath::Abs(sn)<kSafe) { | |
182 | fAlpha = kSafe; | |
183 | cs=TMath::Cos(fAlpha); | |
184 | sn=TMath::Sin(fAlpha); | |
185 | } | |
186 | else if (cs<kSafe) { | |
187 | fAlpha -= TMath::Sign(kSafe, fAlpha); | |
188 | cs=TMath::Cos(fAlpha); | |
189 | sn=TMath::Sin(fAlpha); | |
190 | } | |
da4e3deb | 191 | // Get the vertex of origin and the momentum |
192 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
193 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
4349f5a4 | 194 | // |
195 | // avoid momenta along axis | |
196 | if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]); | |
197 | if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]); | |
da4e3deb | 198 | |
199 | // Rotate to the local coordinate system | |
200 | ver.RotateZ(-fAlpha); | |
201 | mom.RotateZ(-fAlpha); | |
202 | ||
203 | // x of the reference plane | |
204 | fX = ver.X(); | |
205 | ||
206 | Double_t charge = (Double_t)sign; | |
207 | ||
208 | fP[0] = ver.Y(); | |
209 | fP[1] = ver.Z(); | |
210 | fP[2] = TMath::Sin(mom.Phi()); | |
211 | fP[3] = mom.Pz()/mom.Pt(); | |
212 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
213 | ||
214 | // Covariance matrix (formulas to be simplified) | |
215 | ||
752303df | 216 | if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection |
217 | else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection | |
218 | ||
da4e3deb | 219 | Double_t pt=1./TMath::Abs(fP[4]); |
da4e3deb | 220 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
221 | ||
222 | Double_t m00=-sn;// m10=cs; | |
223 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
224 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
225 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
226 | ||
227 | m43*=GetSign(); | |
228 | m44*=GetSign(); | |
229 | m45*=GetSign(); | |
230 | ||
231 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
232 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
233 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
234 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
235 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
236 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
237 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
238 | ||
239 | fC[0 ] = cv[0 ]+cv[2 ]; | |
240 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
241 | fC[2 ] = cv[5 ]; | |
242 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
243 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
244 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
245 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
246 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
247 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
248 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
249 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
250 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
251 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
252 | Double_t b2=m23*m35; | |
253 | Double_t b3=m43*m35; | |
254 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
255 | Double_t b5=m24*m35; | |
256 | Double_t b6=m44*m35; | |
257 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
258 | fC[13] = b1/b3-b2*fC[8]/b3; | |
259 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 260 | |
86be8934 | 261 | CheckCovariance(); |
262 | ||
4f6e22bd | 263 | return; |
da4e3deb | 264 | } |
265 | ||
51ad6848 | 266 | //_____________________________________________________________________________ |
c9ec41e8 | 267 | void AliExternalTrackParam::Reset() { |
1530f89c | 268 | // |
269 | // Resets all the parameters to 0 | |
270 | // | |
c9ec41e8 | 271 | fX=fAlpha=0.; |
272 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
273 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 274 | } |
275 | ||
3775b0ca | 276 | //_____________________________________________________________________________ |
277 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
278 | // | |
279 | // Add "something" to the track covarince matrix. | |
280 | // May be needed to account for unknown mis-calibration/mis-alignment | |
281 | // | |
282 | fC[0] +=c[0]; | |
283 | fC[1] +=c[1]; fC[2] +=c[2]; | |
284 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
285 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
286 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
86be8934 | 287 | CheckCovariance(); |
3775b0ca | 288 | } |
289 | ||
290 | ||
c9ec41e8 | 291 | Double_t AliExternalTrackParam::GetP() const { |
292 | //--------------------------------------------------------------------- | |
293 | // This function returns the track momentum | |
294 | // Results for (nearly) straight tracks are meaningless ! | |
295 | //--------------------------------------------------------------------- | |
06fb4a2f | 296 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 297 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 298 | } |
299 | ||
1d99986f | 300 | Double_t AliExternalTrackParam::Get1P() const { |
301 | //--------------------------------------------------------------------- | |
302 | // This function returns the 1/(track momentum) | |
303 | //--------------------------------------------------------------------- | |
304 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
305 | } | |
306 | ||
c9ec41e8 | 307 | //_______________________________________________________________________ |
c7bafca9 | 308 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 309 | //------------------------------------------------------------------ |
310 | // This function calculates the transverse impact parameter | |
311 | // with respect to a point with global coordinates (x,y) | |
312 | // in the magnetic field "b" (kG) | |
313 | //------------------------------------------------------------------ | |
5773defd | 314 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 315 | Double_t rp4=GetC(b); |
c9ec41e8 | 316 | |
317 | Double_t xt=fX, yt=fP[0]; | |
318 | ||
319 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
320 | Double_t a = x*cs + y*sn; | |
321 | y = -x*sn + y*cs; x=a; | |
322 | xt-=x; yt-=y; | |
323 | ||
bfd20868 | 324 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2])); |
325 | a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt); | |
1530f89c | 326 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
327 | } | |
328 | ||
329 | //_______________________________________________________________________ | |
330 | void AliExternalTrackParam:: | |
331 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
332 | //------------------------------------------------------------------ | |
333 | // This function calculates the transverse and longitudinal impact parameters | |
334 | // with respect to a point with global coordinates (x,y) | |
335 | // in the magnetic field "b" (kG) | |
336 | //------------------------------------------------------------------ | |
bfd20868 | 337 | Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1)); |
1530f89c | 338 | Double_t xt=fX, yt=fP[0]; |
339 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
340 | Double_t a = x*cs + y*sn; | |
341 | y = -x*sn + y*cs; x=a; | |
342 | xt-=x; yt-=y; | |
343 | ||
344 | Double_t rp4=GetC(b); | |
345 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
346 | dz[0] = -(xt*f1 - yt*r1); | |
347 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
348 | return; | |
349 | } | |
350 | ||
351 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
352 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
353 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
354 | dz[0] = -a/(1 + rr); | |
bfd20868 | 355 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2)); |
1530f89c | 356 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; |
51ad6848 | 357 | } |
358 | ||
49d13e89 | 359 | //_______________________________________________________________________ |
360 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
361 | //------------------------------------------------------------------ | |
362 | // This function calculates the transverse impact parameter | |
363 | // with respect to a point with global coordinates (xv,yv) | |
364 | // neglecting the track curvature. | |
365 | //------------------------------------------------------------------ | |
366 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
367 | Double_t x= xv*cs + yv*sn; | |
368 | Double_t y=-xv*sn + yv*cs; | |
369 | ||
bfd20868 | 370 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
49d13e89 | 371 | |
1530f89c | 372 | return -d; |
49d13e89 | 373 | } |
374 | ||
b8e07ed6 | 375 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx |
376 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
377 | Double_t dEdx, | |
378 | Bool_t anglecorr) { | |
116b445b | 379 | //------------------------------------------------------------------ |
380 | // This function corrects the track parameters for the crossed material. | |
381 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
2b99ff83 | 382 | // "xTimesRho" - is the product length*density (g/cm^2). |
383 | // It should be passed as negative when propagating tracks | |
384 | // from the intreaction point to the outside of the central barrel. | |
116b445b | 385 | // "mass" - the mass of this particle (GeV/c^2). |
b8e07ed6 | 386 | // "dEdx" - mean enery loss (GeV/(g/cm^2) |
387 | // "anglecorr" - switch for the angular correction | |
116b445b | 388 | //------------------------------------------------------------------ |
389 | Double_t &fP2=fP[2]; | |
390 | Double_t &fP3=fP[3]; | |
391 | Double_t &fP4=fP[4]; | |
392 | ||
393 | Double_t &fC22=fC[5]; | |
394 | Double_t &fC33=fC[9]; | |
395 | Double_t &fC43=fC[13]; | |
396 | Double_t &fC44=fC[14]; | |
397 | ||
7dded1d5 | 398 | //Apply angle correction, if requested |
399 | if(anglecorr) { | |
bfd20868 | 400 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2))); |
7dded1d5 | 401 | xOverX0 *=angle; |
402 | xTimesRho *=angle; | |
403 | } | |
404 | ||
116b445b | 405 | Double_t p=GetP(); |
406 | Double_t p2=p*p; | |
407 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 408 | |
9f2bec63 | 409 | //Calculating the multiple scattering corrections****************** |
410 | Double_t cC22 = 0.; | |
411 | Double_t cC33 = 0.; | |
412 | Double_t cC43 = 0.; | |
413 | Double_t cC44 = 0.; | |
116b445b | 414 | if (xOverX0 != 0) { |
f2cef1b5 | 415 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
416 | Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0); | |
417 | if (GetUseLogTermMS()) { | |
418 | double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0)); | |
419 | if (lt>0) theta2 *= lt*lt; | |
420 | } | |
421 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; | |
422 | cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3); | |
423 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
424 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
425 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
116b445b | 426 | } |
427 | ||
9f2bec63 | 428 | //Calculating the energy loss corrections************************ |
429 | Double_t cP4=1.; | |
116b445b | 430 | if ((xTimesRho != 0.) && (beta2 < 1.)) { |
b8e07ed6 | 431 | Double_t dE=dEdx*xTimesRho; |
116b445b | 432 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
433 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
c9038cae | 434 | //cP4 = (1.- e/p2*dE); |
76ece3d8 | 435 | if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE; |
c9038cae | 436 | cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben ! |
9f2bec63 | 437 | if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c |
4b2fa3ce | 438 | |
116b445b | 439 | |
440 | // Approximate energy loss fluctuation (M.Ivanov) | |
441 | const Double_t knst=0.07; // To be tuned. | |
442 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 443 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
116b445b | 444 | |
445 | } | |
446 | ||
9f2bec63 | 447 | //Applying the corrections***************************** |
448 | fC22 += cC22; | |
449 | fC33 += cC33; | |
450 | fC43 += cC43; | |
451 | fC44 += cC44; | |
452 | fP4 *= cP4; | |
453 | ||
86be8934 | 454 | CheckCovariance(); |
455 | ||
116b445b | 456 | return kTRUE; |
457 | } | |
458 | ||
b8e07ed6 | 459 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
460 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
461 | Bool_t anglecorr, | |
462 | Double_t (*Bethe)(Double_t)) { | |
463 | //------------------------------------------------------------------ | |
464 | // This function corrects the track parameters for the crossed material. | |
465 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
466 | // "xTimesRho" - is the product length*density (g/cm^2). | |
2b99ff83 | 467 | // It should be passed as negative when propagating tracks |
468 | // from the intreaction point to the outside of the central barrel. | |
b8e07ed6 | 469 | // "mass" - the mass of this particle (GeV/c^2). |
470 | // "anglecorr" - switch for the angular correction | |
471 | // "Bethe" - function calculating the energy loss (GeV/(g/cm^2)) | |
472 | //------------------------------------------------------------------ | |
473 | ||
474 | Double_t bg=GetP()/mass; | |
475 | Double_t dEdx=Bethe(bg); | |
476 | ||
477 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
478 | } | |
479 | ||
480 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA | |
481 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
482 | Double_t zOverA, | |
483 | Double_t density, | |
484 | Double_t exEnergy, | |
485 | Double_t jp1, | |
486 | Double_t jp2, | |
487 | Bool_t anglecorr) { | |
488 | //------------------------------------------------------------------ | |
489 | // This function corrects the track parameters for the crossed material | |
490 | // using the full Geant-like Bethe-Bloch formula parameterization | |
491 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
492 | // "xTimesRho" - is the product length*density (g/cm^2). | |
2b99ff83 | 493 | // It should be passed as negative when propagating tracks |
494 | // from the intreaction point to the outside of the central barrel. | |
b8e07ed6 | 495 | // "mass" - the mass of this particle (GeV/c^2). |
496 | // "density" - mean density (g/cm^3) | |
497 | // "zOverA" - mean Z/A | |
498 | // "exEnergy" - mean exitation energy (GeV) | |
499 | // "jp1" - density effect first junction point | |
500 | // "jp2" - density effect second junction point | |
501 | // "anglecorr" - switch for the angular correction | |
502 | // | |
503 | // The default values of the parameters are for silicon | |
504 | // | |
505 | //------------------------------------------------------------------ | |
506 | ||
507 | Double_t bg=GetP()/mass; | |
508 | Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA); | |
509 | ||
510 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
511 | } | |
512 | ||
513 | ||
116b445b | 514 | |
ee5dba5e | 515 | Bool_t AliExternalTrackParam::CorrectForMaterial |
516 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 517 | //------------------------------------------------------------------ |
116b445b | 518 | // Deprecated function ! |
519 | // Better use CorrectForMeanMaterial instead of it. | |
520 | // | |
c7bafca9 | 521 | // This function corrects the track parameters for the crossed material |
522 | // "d" - the thickness (fraction of the radiation length) | |
2b99ff83 | 523 | // It should be passed as negative when propagating tracks |
524 | // from the intreaction point to the outside of the central barrel. | |
c7bafca9 | 525 | // "x0" - the radiation length (g/cm^2) |
526 | // "mass" - the mass of this particle (GeV/c^2) | |
527 | //------------------------------------------------------------------ | |
c7bafca9 | 528 | |
b8e07ed6 | 529 | return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe); |
c7bafca9 | 530 | |
c7bafca9 | 531 | } |
532 | ||
9c56b409 | 533 | Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg, |
534 | Double_t kp1, | |
535 | Double_t kp2, | |
536 | Double_t kp3, | |
537 | Double_t kp4, | |
538 | Double_t kp5) { | |
539 | // | |
540 | // This is the empirical ALEPH parameterization of the Bethe-Bloch formula. | |
541 | // It is normalized to 1 at the minimum. | |
542 | // | |
543 | // bg - beta*gamma | |
544 | // | |
545 | // The default values for the kp* parameters are for ALICE TPC. | |
546 | // The returned value is in MIP units | |
547 | // | |
548 | ||
549 | Double_t beta = bg/TMath::Sqrt(1.+ bg*bg); | |
550 | ||
551 | Double_t aa = TMath::Power(beta,kp4); | |
552 | Double_t bb = TMath::Power(1./bg,kp5); | |
553 | ||
554 | bb=TMath::Log(kp3+bb); | |
555 | ||
556 | return (kp2-aa-bb)*kp1/aa; | |
557 | } | |
558 | ||
559 | Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg, | |
560 | Double_t kp0, | |
561 | Double_t kp1, | |
562 | Double_t kp2, | |
563 | Double_t kp3, | |
564 | Double_t kp4) { | |
565 | // | |
566 | // This is the parameterization of the Bethe-Bloch formula inspired by Geant. | |
567 | // | |
568 | // bg - beta*gamma | |
569 | // kp0 - density [g/cm^3] | |
570 | // kp1 - density effect first junction point | |
571 | // kp2 - density effect second junction point | |
572 | // kp3 - mean excitation energy [GeV] | |
573 | // kp4 - mean Z/A | |
574 | // | |
575 | // The default values for the kp* parameters are for silicon. | |
576 | // The returned value is in [GeV/(g/cm^2)]. | |
577 | // | |
578 | ||
579 | const Double_t mK = 0.307075e-3; // [GeV*cm^2/g] | |
580 | const Double_t me = 0.511e-3; // [GeV/c^2] | |
581 | const Double_t rho = kp0; | |
582 | const Double_t x0 = kp1*2.303; | |
583 | const Double_t x1 = kp2*2.303; | |
584 | const Double_t mI = kp3; | |
585 | const Double_t mZA = kp4; | |
586 | const Double_t bg2 = bg*bg; | |
587 | const Double_t maxT= 2*me*bg2; // neglecting the electron mass | |
588 | ||
589 | //*** Density effect | |
590 | Double_t d2=0.; | |
591 | const Double_t x=TMath::Log(bg); | |
592 | const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI); | |
593 | if (x > x1) { | |
594 | d2 = lhwI + x - 0.5; | |
595 | } else if (x > x0) { | |
596 | const Double_t r=(x1-x)/(x1-x0); | |
597 | d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r; | |
598 | } | |
599 | ||
600 | return mK*mZA*(1+bg2)/bg2* | |
601 | (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2); | |
602 | } | |
603 | ||
d46683db | 604 | Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) { |
ee5dba5e | 605 | //------------------------------------------------------------------ |
d46683db | 606 | // This is an approximation of the Bethe-Bloch formula, |
607 | // reasonable for solid materials. | |
608 | // All the parameters are, in fact, for Si. | |
9b655cba | 609 | // The returned value is in [GeV/(g/cm^2)] |
ee5dba5e | 610 | //------------------------------------------------------------------ |
a821848c | 611 | |
9c56b409 | 612 | return BetheBlochGeant(bg); |
d46683db | 613 | } |
ee5dba5e | 614 | |
d46683db | 615 | Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) { |
616 | //------------------------------------------------------------------ | |
617 | // This is an approximation of the Bethe-Bloch formula, | |
618 | // reasonable for gas materials. | |
619 | // All the parameters are, in fact, for Ne. | |
9b655cba | 620 | // The returned value is in [GeV/(g/cm^2)] |
d46683db | 621 | //------------------------------------------------------------------ |
622 | ||
623 | const Double_t rho = 0.9e-3; | |
624 | const Double_t x0 = 2.; | |
625 | const Double_t x1 = 4.; | |
626 | const Double_t mI = 140.e-9; | |
627 | const Double_t mZA = 0.49555; | |
628 | ||
9c56b409 | 629 | return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); |
ee5dba5e | 630 | } |
631 | ||
49d13e89 | 632 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
633 | //------------------------------------------------------------------ | |
634 | // Transform this track to the local coord. system rotated | |
635 | // by angle "alpha" (rad) with respect to the global coord. system. | |
636 | //------------------------------------------------------------------ | |
dfcef74c | 637 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
638 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
639 | return kFALSE; | |
640 | } | |
641 | ||
49d13e89 | 642 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
643 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
644 | ||
645 | Double_t &fP0=fP[0]; | |
646 | Double_t &fP2=fP[2]; | |
647 | Double_t &fC00=fC[0]; | |
648 | Double_t &fC10=fC[1]; | |
649 | Double_t &fC20=fC[3]; | |
650 | Double_t &fC21=fC[4]; | |
651 | Double_t &fC22=fC[5]; | |
652 | Double_t &fC30=fC[6]; | |
653 | Double_t &fC32=fC[8]; | |
654 | Double_t &fC40=fC[10]; | |
655 | Double_t &fC42=fC[12]; | |
656 | ||
657 | Double_t x=fX; | |
658 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
bfd20868 | 659 | Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision |
49d13e89 | 660 | |
07dfd570 | 661 | // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle |
662 | // direction in local frame is along the X axis | |
663 | if ((cf*ca+sf*sa)<0) { | |
664 | AliWarning(Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa)); | |
665 | return kFALSE; | |
666 | } | |
667 | // | |
dfcef74c | 668 | Double_t tmp=sf*ca - cf*sa; |
7248cf51 | 669 | if (TMath::Abs(tmp) >= kAlmost1) { |
670 | if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) | |
671 | AliWarning(Form("Rotation failed ! %.10e",tmp)); | |
0b69bbb2 | 672 | return kFALSE; |
673 | } | |
dfcef74c | 674 | |
49d13e89 | 675 | fAlpha = alpha; |
676 | fX = x*ca + fP0*sa; | |
677 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 678 | fP2= tmp; |
49d13e89 | 679 | |
06fb4a2f | 680 | if (TMath::Abs(cf)<kAlmost0) { |
681 | AliError(Form("Too small cosine value %f",cf)); | |
682 | cf = kAlmost0; | |
683 | } | |
684 | ||
49d13e89 | 685 | Double_t rr=(ca+sf/cf*sa); |
686 | ||
687 | fC00 *= (ca*ca); | |
688 | fC10 *= ca; | |
689 | fC20 *= ca*rr; | |
690 | fC21 *= rr; | |
691 | fC22 *= rr*rr; | |
692 | fC30 *= ca; | |
693 | fC32 *= rr; | |
694 | fC40 *= ca; | |
695 | fC42 *= rr; | |
696 | ||
86be8934 | 697 | CheckCovariance(); |
698 | ||
49d13e89 | 699 | return kTRUE; |
700 | } | |
701 | ||
702 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
703 | //---------------------------------------------------------------- | |
704 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
705 | //---------------------------------------------------------------- | |
49d13e89 | 706 | Double_t dx=xk-fX; |
e421f556 | 707 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 708 | |
1530f89c | 709 | Double_t crv=GetC(b); |
5773defd | 710 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
711 | ||
2de63fc5 | 712 | Double_t x2r = crv*dx; |
713 | Double_t f1=fP[2], f2=f1 + x2r; | |
bbefa4c4 | 714 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 715 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
4349f5a4 | 716 | if (TMath::Abs(fP[4])< kAlmost0) return kFALSE; |
49d13e89 | 717 | |
718 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
719 | Double_t | |
720 | &fC00=fC[0], | |
721 | &fC10=fC[1], &fC11=fC[2], | |
722 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
723 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
724 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
725 | ||
bfd20868 | 726 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
4349f5a4 | 727 | if (TMath::Abs(r1)<kAlmost0) return kFALSE; |
728 | if (TMath::Abs(r2)<kAlmost0) return kFALSE; | |
49d13e89 | 729 | |
730 | fX=xk; | |
2de63fc5 | 731 | double dy2dx = (f1+f2)/(r1+r2); |
732 | fP0 += dx*dy2dx; | |
733 | if (TMath::Abs(x2r)<0.05) { | |
734 | fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov ! | |
735 | fP2 += x2r; | |
736 | } | |
737 | else { | |
738 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
739 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
740 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
741 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
742 | // Similarly, the rotation angle in linear in dx only for dx<<R | |
743 | double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one | |
744 | double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
745 | fP1 += rot/crv*fP3; | |
746 | fP2 = TMath::Sin(rot + TMath::ASin(fP2)); | |
747 | } | |
49d13e89 | 748 | |
749 | //f = F - 1 | |
750 | ||
751 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
752 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
753 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
754 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
755 | Double_t f13= dx/r1; | |
756 | Double_t f24= dx; f24*=cc; | |
757 | ||
758 | //b = C*ft | |
759 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
760 | Double_t b02=f24*fC40; | |
761 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
762 | Double_t b12=f24*fC41; | |
763 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
764 | Double_t b22=f24*fC42; | |
765 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
766 | Double_t b42=f24*fC44; | |
767 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
768 | Double_t b32=f24*fC43; | |
769 | ||
770 | //a = f*b = f*C*ft | |
771 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
772 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
773 | Double_t a22=f24*b42; | |
774 | ||
775 | //F*C*Ft = C + (b + bt + a) | |
776 | fC00 += b00 + b00 + a00; | |
777 | fC10 += b10 + b01 + a01; | |
778 | fC20 += b20 + b02 + a02; | |
779 | fC30 += b30; | |
780 | fC40 += b40; | |
781 | fC11 += b11 + b11 + a11; | |
782 | fC21 += b21 + b12 + a12; | |
783 | fC31 += b31; | |
784 | fC41 += b41; | |
785 | fC22 += b22 + b22 + a22; | |
786 | fC32 += b32; | |
787 | fC42 += b42; | |
788 | ||
86be8934 | 789 | CheckCovariance(); |
790 | ||
49d13e89 | 791 | return kTRUE; |
792 | } | |
793 | ||
9f2bec63 | 794 | Bool_t |
795 | AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) { | |
796 | //------------------------------------------------------------------ | |
797 | // Transform this track to the local coord. system rotated | |
798 | // by angle "alpha" (rad) with respect to the global coord. system, | |
799 | // and propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
800 | //------------------------------------------------------------------ | |
801 | ||
802 | //Save the parameters | |
803 | Double_t as=fAlpha; | |
804 | Double_t xs=fX; | |
805 | Double_t ps[5], cs[15]; | |
806 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
807 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
808 | ||
809 | if (Rotate(alpha)) | |
810 | if (PropagateTo(x,b)) return kTRUE; | |
811 | ||
812 | //Restore the parameters, if the operation failed | |
813 | fAlpha=as; | |
814 | fX=xs; | |
815 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
816 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
817 | return kFALSE; | |
818 | } | |
819 | ||
266a0f9b | 820 | Bool_t AliExternalTrackParam::PropagateBxByBz |
821 | (Double_t alpha, Double_t x, Double_t b[3]) { | |
822 | //------------------------------------------------------------------ | |
823 | // Transform this track to the local coord. system rotated | |
824 | // by angle "alpha" (rad) with respect to the global coord. system, | |
825 | // and propagate this track to the plane X=xk (cm), | |
826 | // taking into account all three components of the B field, "b[3]" (kG) | |
827 | //------------------------------------------------------------------ | |
828 | ||
829 | //Save the parameters | |
830 | Double_t as=fAlpha; | |
831 | Double_t xs=fX; | |
832 | Double_t ps[5], cs[15]; | |
833 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
834 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
835 | ||
836 | if (Rotate(alpha)) | |
837 | if (PropagateToBxByBz(x,b)) return kTRUE; | |
838 | ||
839 | //Restore the parameters, if the operation failed | |
840 | fAlpha=as; | |
841 | fX=xs; | |
842 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
843 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
844 | return kFALSE; | |
845 | } | |
846 | ||
9f2bec63 | 847 | |
052daaff | 848 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
849 | Double_t p[3], Double_t bz) const { | |
850 | //+++++++++++++++++++++++++++++++++++++++++ | |
851 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
852 | // Extrapolate track along simple helix in magnetic field | |
853 | // Arguments: len -distance alogn helix, [cm] | |
854 | // bz - mag field, [kGaus] | |
855 | // Returns: x and p contain extrapolated positon and momentum | |
856 | // The momentum returned for straight-line tracks is meaningless ! | |
857 | //+++++++++++++++++++++++++++++++++++++++++ | |
858 | GetXYZ(x); | |
859 | ||
2258e165 | 860 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks |
052daaff | 861 | Double_t unit[3]; GetDirection(unit); |
862 | x[0]+=unit[0]*len; | |
863 | x[1]+=unit[1]*len; | |
864 | x[2]+=unit[2]*len; | |
865 | ||
866 | p[0]=unit[0]/kAlmost0; | |
867 | p[1]=unit[1]/kAlmost0; | |
868 | p[2]=unit[2]/kAlmost0; | |
869 | } else { | |
870 | GetPxPyPz(p); | |
871 | Double_t pp=GetP(); | |
872 | Double_t a = -kB2C*bz*GetSign(); | |
873 | Double_t rho = a/pp; | |
874 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
875 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
876 | x[2] += p[2]*len/pp; | |
877 | ||
878 | Double_t p0=p[0]; | |
879 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
880 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
881 | } | |
882 | } | |
883 | ||
884 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
885 | Double_t bz) const { | |
886 | //+++++++++++++++++++++++++++++++++++++++++ | |
887 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
888 | // Finds point of intersection (if exists) of the helix with the plane. | |
889 | // Stores result in fX and fP. | |
890 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
891 | // and vector, normal to the plane | |
892 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
893 | //+++++++++++++++++++++++++++++++++++++++++ | |
894 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
895 | ||
896 | //estimates initial helix length up to plane | |
897 | Double_t s= | |
898 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
899 | Double_t dist=99999,distPrev=dist; | |
900 | Double_t x[3],p[3]; | |
901 | while(TMath::Abs(dist)>0.00001){ | |
902 | //calculates helix at the distance s from x0 ALONG the helix | |
903 | Propagate(s,x,p,bz); | |
904 | ||
905 | //distance between current helix position and plane | |
906 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
907 | ||
908 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
909 | distPrev=dist; | |
910 | s-=dist; | |
911 | } | |
912 | //on exit pnt is intersection point,norm is track vector at that point, | |
913 | //all in MARS | |
914 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
915 | return kTRUE; | |
916 | } | |
917 | ||
49d13e89 | 918 | Double_t |
919 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
920 | //---------------------------------------------------------------- | |
921 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
922 | //---------------------------------------------------------------- | |
923 | Double_t sdd = fC[0] + cov[0]; | |
924 | Double_t sdz = fC[1] + cov[1]; | |
925 | Double_t szz = fC[2] + cov[2]; | |
926 | Double_t det = sdd*szz - sdz*sdz; | |
927 | ||
928 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
929 | ||
930 | Double_t d = fP[0] - p[0]; | |
931 | Double_t z = fP[1] - p[1]; | |
932 | ||
933 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
934 | } | |
935 | ||
4b189f98 | 936 | Double_t AliExternalTrackParam:: |
937 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
938 | //---------------------------------------------------------------- | |
939 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 940 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 941 | // |
942 | // Cov(x,x) ... : covxyz[0] | |
943 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
944 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
945 | //---------------------------------------------------------------- | |
946 | ||
947 | Double_t res[3] = { | |
948 | GetX() - p[0], | |
949 | GetY() - p[1], | |
950 | GetZ() - p[2] | |
951 | }; | |
952 | ||
953 | Double_t f=GetSnp(); | |
954 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
bfd20868 | 955 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
4b189f98 | 956 | Double_t a=f/r, b=GetTgl()/r; |
957 | ||
958 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
959 | ||
960 | TMatrixDSym v(3); | |
961 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
962 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
963 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
964 | ||
965 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
966 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
967 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
968 | ||
969 | v.Invert(); | |
970 | if (!v.IsValid()) return kVeryBig; | |
971 | ||
972 | Double_t chi2=0.; | |
973 | for (Int_t i = 0; i < 3; i++) | |
974 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
975 | ||
976 | return chi2; | |
acdfbc78 | 977 | } |
978 | ||
979 | Double_t AliExternalTrackParam:: | |
980 | GetPredictedChi2(const AliExternalTrackParam *t) const { | |
981 | //---------------------------------------------------------------- | |
982 | // Estimate the chi2 (5 dof) of this track with respect to the track | |
983 | // given by the argument. | |
984 | // The two tracks must be in the same reference system | |
985 | // and estimated at the same reference plane. | |
986 | //---------------------------------------------------------------- | |
987 | ||
988 | if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) { | |
989 | AliError("The reference systems of the tracks differ !"); | |
990 | return kVeryBig; | |
991 | } | |
992 | if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) { | |
993 | AliError("The reference of the tracks planes differ !"); | |
994 | return kVeryBig; | |
995 | } | |
996 | ||
997 | TMatrixDSym c(5); | |
998 | c(0,0)=GetSigmaY2(); | |
999 | c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2(); | |
1000 | c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2(); | |
1001 | c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2(); | |
1002 | c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2(); | |
1003 | ||
1004 | c(0,0)+=t->GetSigmaY2(); | |
1005 | c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2(); | |
1006 | c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2(); | |
1007 | c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2(); | |
1008 | 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(); | |
1009 | c(0,1)=c(1,0); | |
1010 | c(0,2)=c(2,0); c(1,2)=c(2,1); | |
1011 | c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2); | |
1012 | c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3); | |
1013 | ||
1014 | c.Invert(); | |
1015 | if (!c.IsValid()) return kVeryBig; | |
1016 | ||
1017 | ||
1018 | Double_t res[5] = { | |
1019 | GetY() - t->GetY(), | |
1020 | GetZ() - t->GetZ(), | |
1021 | GetSnp() - t->GetSnp(), | |
1022 | GetTgl() - t->GetTgl(), | |
1023 | GetSigned1Pt() - t->GetSigned1Pt() | |
1024 | }; | |
4b189f98 | 1025 | |
acdfbc78 | 1026 | Double_t chi2=0.; |
1027 | for (Int_t i = 0; i < 5; i++) | |
1028 | for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j); | |
4b189f98 | 1029 | |
acdfbc78 | 1030 | return chi2; |
4b189f98 | 1031 | } |
1032 | ||
1e023a36 | 1033 | Bool_t AliExternalTrackParam:: |
1034 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
1035 | //---------------------------------------------------------------- | |
1036 | // Propagate this track to the plane | |
1037 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
1038 | // belongs to. | |
1039 | // The magnetic field is "bz" (kG) | |
1040 | // | |
1041 | // The track curvature and the change of the covariance matrix | |
1042 | // of the track parameters are negleted ! | |
1043 | // (So the "step" should be small compared with 1/curvature) | |
1044 | //---------------------------------------------------------------- | |
1045 | ||
1046 | Double_t f=GetSnp(); | |
1047 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
bfd20868 | 1048 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
1e023a36 | 1049 | Double_t a=f/r, b=GetTgl()/r; |
1050 | ||
1051 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
1052 | ||
1053 | TMatrixDSym tV(3); | |
1054 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
1055 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
1056 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
1057 | ||
1058 | TMatrixDSym pV(3); | |
1059 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
1060 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
1061 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
1062 | ||
1063 | TMatrixDSym tpV(tV); | |
1064 | tpV+=pV; | |
1065 | tpV.Invert(); | |
1066 | if (!tpV.IsValid()) return kFALSE; | |
1067 | ||
1068 | TMatrixDSym pW(3),tW(3); | |
1069 | for (Int_t i=0; i<3; i++) | |
1070 | for (Int_t j=0; j<3; j++) { | |
1071 | pW(i,j)=tW(i,j)=0.; | |
1072 | for (Int_t k=0; k<3; k++) { | |
1073 | pW(i,j) += tV(i,k)*tpV(k,j); | |
1074 | tW(i,j) += pV(i,k)*tpV(k,j); | |
1075 | } | |
1076 | } | |
1077 | ||
1078 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
1079 | ||
1080 | Double_t x=0.; | |
1081 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
1082 | Double_t crv=GetC(bz); | |
1083 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1084 | f += crv*(x-fX); | |
1085 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
1086 | fX=x; | |
1087 | ||
1088 | fP[0]=0.; | |
1089 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
1090 | fP[1]=0.; | |
1091 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
1092 | ||
1093 | return kTRUE; | |
1094 | } | |
1095 | ||
e23a38cb | 1096 | Double_t *AliExternalTrackParam::GetResiduals( |
1097 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
1098 | //------------------------------------------------------------------ | |
1099 | // Returns the track residuals with the space point "p" having | |
1100 | // the covariance matrix "cov". | |
1101 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
1102 | // otherwise they must be predicted. | |
1103 | //------------------------------------------------------------------ | |
1104 | static Double_t res[2]; | |
1105 | ||
1106 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1107 | if (updated) { | |
1108 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
1109 | } else { | |
1110 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
1111 | } | |
1112 | Double_t det=r00*r11 - r01*r01; | |
1113 | ||
1114 | if (TMath::Abs(det) < kAlmost0) return 0; | |
1115 | ||
1116 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 1117 | |
1118 | if (r00 < 0.) return 0; | |
1119 | if (r11 < 0.) return 0; | |
1120 | ||
e23a38cb | 1121 | Double_t dy = fP[0] - p[0]; |
1122 | Double_t dz = fP[1] - p[1]; | |
1123 | ||
1124 | res[0]=dy*TMath::Sqrt(r00); | |
1125 | res[1]=dz*TMath::Sqrt(r11); | |
1126 | ||
1127 | return res; | |
1128 | } | |
1129 | ||
49d13e89 | 1130 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
1131 | //------------------------------------------------------------------ | |
1132 | // Update the track parameters with the space point "p" having | |
1133 | // the covariance matrix "cov" | |
1134 | //------------------------------------------------------------------ | |
1135 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
1136 | Double_t | |
1137 | &fC00=fC[0], | |
1138 | &fC10=fC[1], &fC11=fC[2], | |
1139 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1140 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1141 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1142 | ||
1143 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1144 | r00+=fC00; r01+=fC10; r11+=fC11; | |
1145 | Double_t det=r00*r11 - r01*r01; | |
1146 | ||
1147 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
1148 | ||
1149 | ||
1150 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
1151 | ||
1152 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
1153 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
1154 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
1155 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
1156 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
1157 | ||
1158 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
1159 | Double_t sf=fP2 + k20*dy + k21*dz; | |
1160 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
1161 | ||
1162 | fP0 += k00*dy + k01*dz; | |
1163 | fP1 += k10*dy + k11*dz; | |
1164 | fP2 = sf; | |
1165 | fP3 += k30*dy + k31*dz; | |
1166 | fP4 += k40*dy + k41*dz; | |
1167 | ||
1168 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
1169 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
1170 | ||
1171 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
1172 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
1173 | fC40-=k00*c04+k01*c14; | |
1174 | ||
1175 | fC11-=k10*c01+k11*fC11; | |
1176 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
1177 | fC41-=k10*c04+k11*c14; | |
1178 | ||
1179 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
1180 | fC42-=k20*c04+k21*c14; | |
1181 | ||
1182 | fC33-=k30*c03+k31*c13; | |
1183 | fC43-=k30*c04+k31*c14; | |
1184 | ||
1185 | fC44-=k40*c04+k41*c14; | |
1186 | ||
86be8934 | 1187 | CheckCovariance(); |
1188 | ||
49d13e89 | 1189 | return kTRUE; |
1190 | } | |
1191 | ||
c7bafca9 | 1192 | void |
1193 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
1194 | //-------------------------------------------------------------------- | |
1195 | // External track parameters -> helix parameters | |
1196 | // "b" - magnetic field (kG) | |
1197 | //-------------------------------------------------------------------- | |
1198 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1199 | ||
1530f89c | 1200 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 1201 | |
1202 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
1203 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
1204 | //hlx[1]= // z0 | |
1205 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
1206 | //hlx[3]= // tgl | |
1530f89c | 1207 | hlx[4]=GetC(b); // C |
c7bafca9 | 1208 | } |
1209 | ||
1210 | ||
1211 | static void Evaluate(const Double_t *h, Double_t t, | |
1212 | Double_t r[3], //radius vector | |
1213 | Double_t g[3], //first defivatives | |
1214 | Double_t gg[3]) //second derivatives | |
1215 | { | |
1216 | //-------------------------------------------------------------------- | |
1217 | // Calculate position of a point on a track and some derivatives | |
1218 | //-------------------------------------------------------------------- | |
1219 | Double_t phase=h[4]*t+h[2]; | |
1220 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
1221 | ||
ba4550c4 | 1222 | r[0] = h[5]; |
1223 | r[1] = h[0]; | |
1224 | if (TMath::Abs(h[4])>kAlmost0) { | |
1225 | r[0] += (sn - h[6])/h[4]; | |
1226 | r[1] -= (cs - h[7])/h[4]; | |
1227 | } | |
c7bafca9 | 1228 | r[2] = h[1] + h[3]*t; |
1229 | ||
1230 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
1231 | ||
1232 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
1233 | } | |
1234 | ||
1235 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
1236 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
1237 | //------------------------------------------------------------ | |
1238 | // Returns the (weighed !) distance of closest approach between | |
1239 | // this track and the track "p". | |
1240 | // Other returned values: | |
1241 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
1242 | //----------------------------------------------------------- | |
1243 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
1244 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
1245 | Double_t dx2=dy2; | |
1246 | ||
c7bafca9 | 1247 | Double_t p1[8]; GetHelixParameters(p1,b); |
1248 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
1249 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
1250 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
1251 | ||
1252 | ||
1253 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
1254 | Evaluate(p1,t1,r1,g1,gg1); | |
1255 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
1256 | Evaluate(p2,t2,r2,g2,gg2); | |
1257 | ||
1258 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
1259 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1260 | ||
1261 | Int_t max=27; | |
1262 | while (max--) { | |
1263 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
1264 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
1265 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
1266 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
1267 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
1268 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
1269 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
1270 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
1271 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
1272 | ||
1273 | Double_t det=h11*h22-h12*h12; | |
1274 | ||
1275 | Double_t dt1,dt2; | |
1276 | if (TMath::Abs(det)<1.e-33) { | |
1277 | //(quasi)singular Hessian | |
1278 | dt1=-gt1; dt2=-gt2; | |
1279 | } else { | |
1280 | dt1=-(gt1*h22 - gt2*h12)/det; | |
1281 | dt2=-(h11*gt2 - h12*gt1)/det; | |
1282 | } | |
1283 | ||
1284 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
1285 | ||
1286 | //check delta(phase1) ? | |
1287 | //check delta(phase2) ? | |
1288 | ||
1289 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
1290 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
1291 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 1292 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 1293 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
1294 | if (lmb < 0.) | |
358f16ae | 1295 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 1296 | break; |
1297 | } | |
1298 | ||
1299 | Double_t dd=dm; | |
1300 | for (Int_t div=1 ; ; div*=2) { | |
1301 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
1302 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
1303 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
1304 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1305 | if (dd<dm) break; | |
1306 | dt1*=0.5; dt2*=0.5; | |
1307 | if (div>512) { | |
358f16ae | 1308 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 1309 | } |
1310 | } | |
1311 | dm=dd; | |
1312 | ||
1313 | t1+=dt1; | |
1314 | t2+=dt2; | |
1315 | ||
1316 | } | |
1317 | ||
358f16ae | 1318 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1319 | |
1320 | Double_t cs=TMath::Cos(GetAlpha()); | |
1321 | Double_t sn=TMath::Sin(GetAlpha()); | |
1322 | xthis=r1[0]*cs + r1[1]*sn; | |
1323 | ||
1324 | cs=TMath::Cos(p->GetAlpha()); | |
1325 | sn=TMath::Sin(p->GetAlpha()); | |
1326 | xp=r2[0]*cs + r2[1]*sn; | |
1327 | ||
1328 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1329 | } | |
1330 | ||
1331 | Double_t AliExternalTrackParam:: | |
1332 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1333 | //-------------------------------------------------------------- | |
1334 | // Propagates this track and the argument track to the position of the | |
1335 | // distance of closest approach. | |
1336 | // Returns the (weighed !) distance of closest approach. | |
1337 | //-------------------------------------------------------------- | |
1338 | Double_t xthis,xp; | |
1339 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1340 | ||
1341 | if (!PropagateTo(xthis,b)) { | |
1342 | //AliWarning(" propagation failed !"); | |
1343 | return 1e+33; | |
1344 | } | |
1345 | ||
1346 | if (!p->PropagateTo(xp,b)) { | |
1347 | //AliWarning(" propagation failed !"; | |
1348 | return 1e+33; | |
1349 | } | |
1350 | ||
1351 | return dca; | |
1352 | } | |
1353 | ||
1354 | ||
58e536c5 | 1355 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1356 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1357 | // |
e99a34df | 1358 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1359 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1360 | // Magnetic field is "b" (kG). | |
1361 | // | |
1362 | // a) The track gets extapolated to the DCA to the vertex. | |
1363 | // b) The impact parameters and their covariance matrix are calculated. | |
1364 | // | |
1365 | // In the case of success, the returned value is kTRUE | |
1366 | // (otherwise, it's kFALSE) | |
1367 | // | |
1368 | Double_t alpha=GetAlpha(); | |
1369 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1370 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1371 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1372 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1373 | x-=xv; y-=yv; |
1374 | ||
1375 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1376 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
f76701bf | 1377 | if (d > maxd) return kFALSE; |
1378 | ||
1379 | //Propagate to the DCA | |
2258e165 | 1380 | Double_t crv=GetC(b); |
e99a34df | 1381 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1382 | ||
bfd20868 | 1383 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1384 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
e99a34df | 1385 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1386 | else cs=1.; | |
f76701bf | 1387 | |
1388 | x = xv*cs + yv*sn; | |
1389 | yv=-xv*sn + yv*cs; xv=x; | |
1390 | ||
1391 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
266a0f9b | 1392 | |
1393 | if (dz==0) return kTRUE; | |
1394 | dz[0] = GetParameter()[0] - yv; | |
1395 | dz[1] = GetParameter()[1] - zv; | |
1396 | ||
1397 | if (covar==0) return kTRUE; | |
1398 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); | |
1399 | ||
1400 | //***** Improvements by A.Dainese | |
1401 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1402 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1403 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1404 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1405 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1406 | //***** | |
1407 | ||
1408 | return kTRUE; | |
1409 | } | |
1410 | ||
1411 | Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx, | |
1412 | Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) { | |
1413 | // | |
1414 | // Propagate this track to the DCA to vertex "vtx", | |
1415 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
1416 | // | |
1417 | // This function takes into account all three components of the magnetic | |
1418 | // field given by the b[3] arument (kG) | |
1419 | // | |
1420 | // a) The track gets extapolated to the DCA to the vertex. | |
1421 | // b) The impact parameters and their covariance matrix are calculated. | |
1422 | // | |
1423 | // In the case of success, the returned value is kTRUE | |
1424 | // (otherwise, it's kFALSE) | |
1425 | // | |
1426 | Double_t alpha=GetAlpha(); | |
1427 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1428 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
1429 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; | |
1430 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
1431 | x-=xv; y-=yv; | |
1432 | ||
1433 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1434 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
266a0f9b | 1435 | if (d > maxd) return kFALSE; |
1436 | ||
1437 | //Propagate to the DCA | |
8567bf39 | 1438 | Double_t crv=GetC(b[2]); |
1439 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
266a0f9b | 1440 | |
bfd20868 | 1441 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1442 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
266a0f9b | 1443 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1444 | else cs=1.; | |
1445 | ||
1446 | x = xv*cs + yv*sn; | |
1447 | yv=-xv*sn + yv*cs; xv=x; | |
1448 | ||
1449 | if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1450 | |
1451 | if (dz==0) return kTRUE; | |
1452 | dz[0] = GetParameter()[0] - yv; | |
1453 | dz[1] = GetParameter()[1] - zv; | |
1454 | ||
1455 | if (covar==0) return kTRUE; | |
58e536c5 | 1456 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1457 | |
1458 | //***** Improvements by A.Dainese | |
1459 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1460 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1461 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1462 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1463 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1464 | //***** | |
1465 | ||
29fbcc93 | 1466 | return kTRUE; |
f76701bf | 1467 | } |
1468 | ||
b1149664 | 1469 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1470 | //---------------------------------------------------------------- | |
1471 | // This function returns a unit vector along the track direction | |
1472 | // in the global coordinate system. | |
1473 | //---------------------------------------------------------------- | |
1474 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1475 | Double_t snp=fP[2]; | |
bfd20868 | 1476 | Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp)); |
b1149664 | 1477 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1478 | d[0]=(csp*cs - snp*sn)/norm; | |
1479 | d[1]=(snp*cs + csp*sn)/norm; | |
1480 | d[2]=fP[3]/norm; | |
1481 | } | |
1482 | ||
c683ddc2 | 1483 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1484 | //--------------------------------------------------------------------- |
1485 | // This function returns the global track momentum components | |
1486 | // Results for (nearly) straight tracks are meaningless ! | |
1487 | //--------------------------------------------------------------------- | |
1488 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1489 | return Local2GlobalMomentum(p,fAlpha); | |
1490 | } | |
a5e407e9 | 1491 | |
def9660e | 1492 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1493 | //--------------------------------------------------------------------- |
1494 | // Returns x-component of momentum | |
1495 | // Result for (nearly) straight tracks is meaningless ! | |
1496 | //--------------------------------------------------------------------- | |
def9660e | 1497 | |
957fb479 | 1498 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1499 | GetPxPyPz(p); |
1500 | ||
1501 | return p[0]; | |
1502 | } | |
1503 | ||
1504 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1505 | //--------------------------------------------------------------------- |
1506 | // Returns y-component of momentum | |
1507 | // Result for (nearly) straight tracks is meaningless ! | |
1508 | //--------------------------------------------------------------------- | |
def9660e | 1509 | |
957fb479 | 1510 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1511 | GetPxPyPz(p); |
1512 | ||
1513 | return p[1]; | |
1514 | } | |
1515 | ||
c683ddc2 | 1516 | Double_t AliExternalTrackParam::Xv() const { |
1517 | //--------------------------------------------------------------------- | |
1518 | // Returns x-component of first track point | |
1519 | //--------------------------------------------------------------------- | |
1520 | ||
1521 | Double_t r[3]={0.,0.,0.}; | |
1522 | GetXYZ(r); | |
1523 | ||
1524 | return r[0]; | |
1525 | } | |
1526 | ||
1527 | Double_t AliExternalTrackParam::Yv() const { | |
1528 | //--------------------------------------------------------------------- | |
1529 | // Returns y-component of first track point | |
1530 | //--------------------------------------------------------------------- | |
1531 | ||
1532 | Double_t r[3]={0.,0.,0.}; | |
1533 | GetXYZ(r); | |
1534 | ||
1535 | return r[1]; | |
1536 | } | |
1537 | ||
def9660e | 1538 | Double_t AliExternalTrackParam::Theta() const { |
1539 | // return theta angle of momentum | |
1540 | ||
7cdd0c20 | 1541 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1542 | } |
1543 | ||
1544 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1545 | //--------------------------------------------------------------------- |
1546 | // Returns the azimuthal angle of momentum | |
1547 | // 0 <= phi < 2*pi | |
1548 | //--------------------------------------------------------------------- | |
def9660e | 1549 | |
957fb479 | 1550 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1551 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1552 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1553 | ||
1554 | return phi; | |
def9660e | 1555 | } |
1556 | ||
1557 | Double_t AliExternalTrackParam::M() const { | |
1558 | // return particle mass | |
1559 | ||
1560 | // No mass information available so far. | |
1561 | // Redifine in derived class! | |
1562 | ||
1563 | return -999.; | |
1564 | } | |
1565 | ||
1566 | Double_t AliExternalTrackParam::E() const { | |
1567 | // return particle energy | |
1568 | ||
1569 | // No PID information available so far. | |
1570 | // Redifine in derived class! | |
1571 | ||
1572 | return -999.; | |
1573 | } | |
1574 | ||
1575 | Double_t AliExternalTrackParam::Eta() const { | |
1576 | // return pseudorapidity | |
1577 | ||
1578 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1579 | } | |
1580 | ||
1581 | Double_t AliExternalTrackParam::Y() const { | |
1582 | // return rapidity | |
1583 | ||
1584 | // No PID information available so far. | |
1585 | // Redifine in derived class! | |
1586 | ||
1587 | return -999.; | |
1588 | } | |
1589 | ||
c9ec41e8 | 1590 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1591 | //--------------------------------------------------------------------- | |
1592 | // This function returns the global track position | |
1593 | //--------------------------------------------------------------------- | |
1594 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1595 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1596 | } |
1597 | ||
c9ec41e8 | 1598 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1599 | //--------------------------------------------------------------------- | |
1600 | // This function returns the global covariance matrix of the track params | |
1601 | // | |
1602 | // Cov(x,x) ... : cv[0] | |
1603 | // Cov(y,x) ... : cv[1] cv[2] | |
1604 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1605 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1606 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1607 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1608 | // |
c9ec41e8 | 1609 | // Results for (nearly) straight tracks are meaningless ! |
1610 | //--------------------------------------------------------------------- | |
e421f556 | 1611 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1612 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1613 | return kFALSE; | |
a5e407e9 | 1614 | } |
49d13e89 | 1615 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1616 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1617 | return kFALSE; | |
1618 | } | |
1619 | Double_t pt=1./TMath::Abs(fP[4]); | |
1620 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1621 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1622 | |
1623 | Double_t m00=-sn, m10=cs; | |
1624 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1625 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1626 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1627 | ||
854d5d49 | 1628 | m43*=GetSign(); |
1629 | m44*=GetSign(); | |
1630 | m45*=GetSign(); | |
1631 | ||
c9ec41e8 | 1632 | cv[0 ] = fC[0]*m00*m00; |
1633 | cv[1 ] = fC[0]*m00*m10; | |
1634 | cv[2 ] = fC[0]*m10*m10; | |
1635 | cv[3 ] = fC[1]*m00; | |
1636 | cv[4 ] = fC[1]*m10; | |
1637 | cv[5 ] = fC[2]; | |
1638 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1639 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1640 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1641 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1642 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1643 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1644 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1645 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1646 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1647 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1648 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1649 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1650 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1651 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1652 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1653 | |
c9ec41e8 | 1654 | return kTRUE; |
51ad6848 | 1655 | } |
1656 | ||
51ad6848 | 1657 | |
c9ec41e8 | 1658 | Bool_t |
1659 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1660 | //--------------------------------------------------------------------- | |
1661 | // This function returns the global track momentum extrapolated to | |
1662 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1663 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1664 | p[0]=fP[4]; |
1530f89c | 1665 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1666 | p[2]=fP[3]; |
1667 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1668 | } |
1669 | ||
7cf7bb6c | 1670 | Bool_t |
1671 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1672 | //--------------------------------------------------------------------- | |
1673 | // This function returns the local Y-coordinate of the intersection | |
1674 | // point between this track and the reference plane "x" (cm). | |
1675 | // Magnetic field "b" (kG) | |
1676 | //--------------------------------------------------------------------- | |
1677 | Double_t dx=x-fX; | |
1678 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1679 | ||
1530f89c | 1680 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1681 | |
1682 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1683 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1684 | ||
60e55aee | 1685 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
7cf7bb6c | 1686 | y = fP[0] + dx*(f1+f2)/(r1+r2); |
1687 | return kTRUE; | |
1688 | } | |
1689 | ||
6c94f330 | 1690 | Bool_t |
1691 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1692 | //--------------------------------------------------------------------- | |
1693 | // This function returns the local Z-coordinate of the intersection | |
1694 | // point between this track and the reference plane "x" (cm). | |
1695 | // Magnetic field "b" (kG) | |
1696 | //--------------------------------------------------------------------- | |
1697 | Double_t dx=x-fX; | |
1698 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1699 | ||
2258e165 | 1700 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
6c94f330 | 1701 | |
1702 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1703 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1704 | ||
60e55aee | 1705 | Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2)); |
6c94f330 | 1706 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! |
1707 | return kTRUE; | |
1708 | } | |
1709 | ||
c9ec41e8 | 1710 | Bool_t |
1711 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1712 | //--------------------------------------------------------------------- | |
1713 | // This function returns the global track position extrapolated to | |
1714 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1715 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1716 | Double_t dx=x-fX; |
e421f556 | 1717 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1718 | ||
1530f89c | 1719 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1720 | |
e421f556 | 1721 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1722 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1723 | |
60e55aee | 1724 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
c9ec41e8 | 1725 | r[0] = x; |
1726 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
f90a11c9 | 1727 | r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter |
1728 | ||
c9ec41e8 | 1729 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1730 | } |
1731 | ||
51ad6848 | 1732 | //_____________________________________________________________________________ |
1733 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1734 | { | |
1735 | // print the parameters and the covariance matrix | |
1736 | ||
1737 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1738 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1739 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1740 | printf(" covariance: %12g\n", fC[0]); | |
1741 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1742 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1743 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1744 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1745 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1746 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1747 | } |
5b77d93c | 1748 | |
c194ba83 | 1749 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1750 | // | |
1751 | // Get sinus at given x | |
1752 | // | |
1530f89c | 1753 | Double_t crv=GetC(b); |
c194ba83 | 1754 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1755 | Double_t dx = x-fX; | |
1756 | Double_t res = fP[2]+dx*crv; | |
1757 | return res; | |
1758 | } | |
bf00ebb8 | 1759 | |
1760 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1761 | //------------------------------------------------------------------------ | |
1762 | // Get the distance between two tracks at the local position x | |
1763 | // working in the local frame of this track. | |
1764 | // Origin : Marian.Ivanov@cern.ch | |
1765 | //----------------------------------------------------------------------- | |
1766 | Double_t xyz[3]; | |
1767 | Double_t xyz2[3]; | |
1768 | xyz[0]=x; | |
1769 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1770 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1771 | // | |
1772 | // | |
1773 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1774 | xyz2[0]=x; | |
1775 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1776 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1777 | }else{ | |
1778 | // | |
1779 | Double_t xyz1[3]; | |
1780 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1781 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1782 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1783 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1784 | // | |
1785 | xyz1[0]=xyz2[0]; | |
1786 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1787 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1788 | // | |
1789 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1790 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1791 | xyz2[2] = xyz1[2]; | |
1792 | } | |
1793 | dist[0] = xyz[0]-xyz2[0]; | |
1794 | dist[1] = xyz[1]-xyz2[1]; | |
1795 | dist[2] = xyz[2]-xyz2[2]; | |
1796 | ||
1797 | return kTRUE; | |
1798 | } | |
0c19adf7 | 1799 | |
1800 | ||
1801 | // | |
1802 | // Draw functionality. | |
1803 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1804 | // | |
1805 | ||
1806 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1807 | // | |
1808 | // Draw track line | |
1809 | // | |
1810 | if (minR>maxR) return ; | |
1811 | if (stepR<=0) return ; | |
1812 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1813 | if (npoints<1) return; | |
1814 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1815 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1816 | polymarker->Draw(); | |
1817 | } | |
1818 | ||
1819 | // | |
1820 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1821 | // | |
1822 | // Fill points in the polymarker | |
1823 | // | |
1824 | Int_t counter=0; | |
1825 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1826 | Double_t point[3]; | |
1827 | GetXYZAt(r,magF,point); | |
1828 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
047640da | 1829 | // printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); |
0c19adf7 | 1830 | counter++; |
1831 | } | |
1832 | } | |
0e8460af | 1833 | |
1834 | Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const { | |
1835 | // | |
1836 | Int_t min = TMath::Min(i,j); | |
1837 | Int_t max = TMath::Max(i,j); | |
1838 | ||
1839 | return min+(max+1)*max/2; | |
1840 | } | |
8b6e3369 | 1841 | |
1842 | ||
1843 | void AliExternalTrackParam::g3helx3(Double_t qfield, | |
1844 | Double_t step, | |
1845 | Double_t vect[7]) { | |
1846 | /****************************************************************** | |
1847 | * * | |
1848 | * GEANT3 tracking routine in a constant field oriented * | |
1849 | * along axis 3 * | |
1850 | * Tracking is performed with a conventional * | |
1851 | * helix step method * | |
1852 | * * | |
1853 | * Authors R.Brun, M.Hansroul ********* * | |
1854 | * Rewritten V.Perevoztchikov * | |
1855 | * * | |
1856 | * Rewritten in C++ by I.Belikov * | |
1857 | * * | |
1858 | * qfield (kG) - particle charge times magnetic field * | |
1859 | * step (cm) - step length along the helix * | |
1860 | * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p * | |
1861 | * * | |
1862 | ******************************************************************/ | |
1863 | const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6; | |
bfd20868 | 1864 | const Double_t kOvSqSix=TMath::Sqrt(1./6.); |
8b6e3369 | 1865 | |
1866 | Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz]; | |
1867 | ||
1868 | Double_t rho = qfield*kB2C/vect[ipp]; | |
1869 | Double_t tet = rho*step; | |
1870 | ||
1871 | Double_t tsint, sintt, sint, cos1t; | |
2de63fc5 | 1872 | if (TMath::Abs(tet) > 0.03) { |
8b6e3369 | 1873 | sint = TMath::Sin(tet); |
1874 | sintt = sint/tet; | |
1875 | tsint = (tet - sint)/tet; | |
1876 | Double_t t=TMath::Sin(0.5*tet); | |
1877 | cos1t = 2*t*t/tet; | |
1878 | } else { | |
1879 | tsint = tet*tet/6.; | |
bfd20868 | 1880 | sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint; |
8b6e3369 | 1881 | sint = tet*sintt; |
1882 | cos1t = 0.5*tet; | |
1883 | } | |
1884 | ||
1885 | Double_t f1 = step*sintt; | |
1886 | Double_t f2 = step*cos1t; | |
1887 | Double_t f3 = step*tsint*cosz; | |
1888 | Double_t f4 = -tet*cos1t; | |
1889 | Double_t f5 = sint; | |
1890 | ||
1891 | vect[ix] += f1*cosx - f2*cosy; | |
1892 | vect[iy] += f1*cosy + f2*cosx; | |
1893 | vect[iz] += f1*cosz + f3; | |
1894 | ||
1895 | vect[ipx] += f4*cosx - f5*cosy; | |
1896 | vect[ipy] += f4*cosy + f5*cosx; | |
1897 | ||
1898 | } | |
1899 | ||
1900 | Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) { | |
1901 | //---------------------------------------------------------------- | |
1902 | // Extrapolate this track to the plane X=xk in the field b[]. | |
1903 | // | |
1904 | // X [cm] is in the "tracking coordinate system" of this track. | |
1905 | // b[]={Bx,By,Bz} [kG] is in the Global coordidate system. | |
1906 | //---------------------------------------------------------------- | |
1907 | ||
1908 | Double_t dx=xk-fX; | |
1909 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
7e1b73dd | 1910 | if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE; |
ef3508c5 | 1911 | // Do not propagate tracks outside the ALICE detector |
1912 | if (TMath::Abs(dx)>1e5 || | |
1913 | TMath::Abs(GetY())>1e5 || | |
1914 | TMath::Abs(GetZ())>1e5) { | |
1915 | AliWarning(Form("Anomalous track, target X:%f",xk)); | |
1916 | Print(); | |
1917 | return kFALSE; | |
1918 | } | |
8b6e3369 | 1919 | |
1920 | Double_t crv=GetC(b[2]); | |
1921 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
1922 | ||
2de63fc5 | 1923 | Double_t x2r = crv*dx; |
1924 | Double_t f1=fP[2], f2=f1 + x2r; | |
8b6e3369 | 1925 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
1926 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1927 | ||
1928 | ||
1929 | // Estimate the covariance matrix | |
1930 | Double_t &fP3=fP[3], &fP4=fP[4]; | |
1931 | Double_t | |
1932 | &fC00=fC[0], | |
1933 | &fC10=fC[1], &fC11=fC[2], | |
1934 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1935 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1936 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1937 | ||
bfd20868 | 1938 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
8b6e3369 | 1939 | |
1940 | //f = F - 1 | |
1941 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
1942 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
1943 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
1944 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
1945 | Double_t f13= dx/r1; | |
1946 | Double_t f24= dx; f24*=cc; | |
1947 | ||
1948 | //b = C*ft | |
1949 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
1950 | Double_t b02=f24*fC40; | |
1951 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
1952 | Double_t b12=f24*fC41; | |
1953 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
1954 | Double_t b22=f24*fC42; | |
1955 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
1956 | Double_t b42=f24*fC44; | |
1957 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
1958 | Double_t b32=f24*fC43; | |
1959 | ||
1960 | //a = f*b = f*C*ft | |
1961 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
1962 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
1963 | Double_t a22=f24*b42; | |
1964 | ||
1965 | //F*C*Ft = C + (b + bt + a) | |
1966 | fC00 += b00 + b00 + a00; | |
1967 | fC10 += b10 + b01 + a01; | |
1968 | fC20 += b20 + b02 + a02; | |
1969 | fC30 += b30; | |
1970 | fC40 += b40; | |
1971 | fC11 += b11 + b11 + a11; | |
1972 | fC21 += b21 + b12 + a12; | |
1973 | fC31 += b31; | |
1974 | fC41 += b41; | |
1975 | fC22 += b22 + b22 + a22; | |
1976 | fC32 += b32; | |
1977 | fC42 += b42; | |
1978 | ||
86be8934 | 1979 | CheckCovariance(); |
8b6e3369 | 1980 | |
1981 | // Appoximate step length | |
2de63fc5 | 1982 | double dy2dx = (f1+f2)/(r1+r2); |
1983 | Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord | |
1984 | : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc | |
8b6e3369 | 1985 | step *= TMath::Sqrt(1.+ GetTgl()*GetTgl()); |
1986 | ||
8b6e3369 | 1987 | // Get the track's (x,y,z) and (px,py,pz) in the Global System |
1988 | Double_t r[3]; GetXYZ(r); | |
1989 | Double_t p[3]; GetPxPyPz(p); | |
1990 | Double_t pp=GetP(); | |
1991 | p[0] /= pp; | |
1992 | p[1] /= pp; | |
1993 | p[2] /= pp; | |
1994 | ||
1995 | ||
1996 | // Rotate to the system where Bx=By=0. | |
1997 | Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]); | |
1998 | Double_t cosphi=1., sinphi=0.; | |
1999 | if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;} | |
2000 | Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]); | |
2001 | Double_t costet=1., sintet=0.; | |
2002 | if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;} | |
2003 | Double_t vect[7]; | |
2004 | ||
2005 | vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2]; | |
2006 | vect[1] = -sinphi*r[0] + cosphi*r[1]; | |
2007 | vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2]; | |
2008 | ||
2009 | vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2]; | |
2010 | vect[4] = -sinphi*p[0] + cosphi*p[1]; | |
2011 | vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2]; | |
2012 | ||
2013 | vect[6] = pp; | |
2014 | ||
2015 | ||
2016 | // Do the helix step | |
2017 | g3helx3(GetSign()*bb,step,vect); | |
2018 | ||
2019 | ||
2020 | // Rotate back to the Global System | |
2021 | r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2]; | |
2022 | r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2]; | |
2023 | r[2] = -sintet*vect[0] + costet*vect[2]; | |
2024 | ||
2025 | p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5]; | |
2026 | p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5]; | |
2027 | p[2] = -sintet*vect[3] + costet*vect[5]; | |
2028 | ||
2029 | ||
2030 | // Rotate back to the Tracking System | |
2031 | Double_t cosalp = TMath::Cos(fAlpha); | |
2032 | Double_t sinalp =-TMath::Sin(fAlpha); | |
2033 | ||
2034 | Double_t | |
2035 | t = cosalp*r[0] - sinalp*r[1]; | |
2036 | r[1] = sinalp*r[0] + cosalp*r[1]; | |
2037 | r[0] = t; | |
2038 | ||
2039 | t = cosalp*p[0] - sinalp*p[1]; | |
2040 | p[1] = sinalp*p[0] + cosalp*p[1]; | |
2041 | p[0] = t; | |
2042 | ||
2043 | ||
2044 | // Do the final correcting step to the target plane (linear approximation) | |
2045 | Double_t x=r[0], y=r[1], z=r[2]; | |
2046 | if (TMath::Abs(dx) > kAlmost0) { | |
2047 | if (TMath::Abs(p[0]) < kAlmost0) return kFALSE; | |
2048 | dx = xk - r[0]; | |
2049 | x += dx; | |
2050 | y += p[1]/p[0]*dx; | |
2051 | z += p[2]/p[0]*dx; | |
2052 | } | |
2053 | ||
2054 | ||
2055 | // Calculate the track parameters | |
2056 | t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]); | |
2057 | fX = x; | |
2058 | fP[0] = y; | |
2059 | fP[1] = z; | |
2060 | fP[2] = p[1]/t; | |
2061 | fP[3] = p[2]/t; | |
2062 | fP[4] = GetSign()/(t*pp); | |
2063 | ||
2064 | return kTRUE; | |
2065 | } | |
2066 | ||
cfdb62d4 | 2067 | Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){ |
2068 | // | |
2069 | //Translation: in the event mixing, the tracks can be shifted | |
2070 | //of the difference among primary vertices (vTrasl) and | |
2071 | //the covariance matrix is changed accordingly | |
2072 | //(covV = covariance of the primary vertex). | |
2073 | //Origin: "Romita, Rossella" <R.Romita@gsi.de> | |
2074 | // | |
2075 | TVector3 translation; | |
2076 | // vTrasl coordinates in the local system | |
2077 | translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]); | |
2078 | translation.RotateZ(-fAlpha); | |
2079 | translation.GetXYZ(vTrasl); | |
2080 | ||
2081 | //compute the new x,y,z of the track | |
5a87bb3d | 2082 | Double_t newX=fX-vTrasl[0]; |
2083 | Double_t newY=fP[0]-vTrasl[1]; | |
2084 | Double_t newZ=fP[1]-vTrasl[2]; | |
cfdb62d4 | 2085 | |
2086 | //define the new parameters | |
5a87bb3d | 2087 | Double_t newParam[5]; |
2088 | newParam[0]=newY; | |
2089 | newParam[1]=newZ; | |
2090 | newParam[2]=fP[2]; | |
2091 | newParam[3]=fP[3]; | |
2092 | newParam[4]=fP[4]; | |
cfdb62d4 | 2093 | |
2094 | // recompute the covariance matrix: | |
2095 | // 1. covV in the local system | |
2096 | Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha); | |
2097 | TMatrixD qQi(3,3); | |
2098 | qQi(0,0) = cosRot; | |
2099 | qQi(0,1) = sinRot; | |
2100 | qQi(0,2) = 0.; | |
2101 | qQi(1,0) = -sinRot; | |
2102 | qQi(1,1) = cosRot; | |
2103 | qQi(1,2) = 0.; | |
2104 | qQi(2,0) = 0.; | |
2105 | qQi(2,1) = 0.; | |
2106 | qQi(2,2) = 1.; | |
2107 | TMatrixD uUi(3,3); | |
2108 | uUi(0,0) = covV[0]; | |
2109 | uUi(0,0) = covV[0]; | |
2110 | uUi(1,0) = covV[1]; | |
2111 | uUi(0,1) = covV[1]; | |
2112 | uUi(2,0) = covV[3]; | |
2113 | uUi(0,2) = covV[3]; | |
2114 | uUi(1,1) = covV[2]; | |
2115 | uUi(2,2) = covV[5]; | |
2116 | uUi(1,2) = covV[4]; | |
2117 | if(uUi.Determinant() <= 0.) {return kFALSE;} | |
2118 | TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi); | |
2119 | TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi); | |
2120 | ||
2121 | //2. compute the new covariance matrix of the track | |
2122 | Double_t sigmaXX=m(0,0); | |
2123 | Double_t sigmaXZ=m(2,0); | |
2124 | Double_t sigmaXY=m(1,0); | |
2125 | Double_t sigmaYY=GetSigmaY2()+m(1,1); | |
2126 | Double_t sigmaYZ=fC[1]+m(1,2); | |
2127 | Double_t sigmaZZ=fC[2]+m(2,2); | |
2128 | Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX); | |
2129 | Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX); | |
2130 | Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX); | |
2131 | ||
2132 | Double_t newCov[15]; | |
2133 | newCov[0]=covarianceYY; | |
2134 | newCov[1]=covarianceYZ; | |
2135 | newCov[2]=covarianceZZ; | |
2136 | for(Int_t i=3;i<15;i++){ | |
2137 | newCov[i]=fC[i]; | |
2138 | } | |
2139 | ||
2140 | // set the new parameters | |
2141 | ||
5a87bb3d | 2142 | Set(newX,fAlpha,newParam,newCov); |
cfdb62d4 | 2143 | |
2144 | return kTRUE; | |
2145 | } | |
86be8934 | 2146 | |
2147 | void AliExternalTrackParam::CheckCovariance() { | |
2148 | ||
2149 | // This function forces the diagonal elements of the covariance matrix to be positive. | |
2150 | // In case the diagonal element is bigger than the maximal allowed value, it is set to | |
2151 | // the limit and the off-diagonal elements that correspond to it are set to zero. | |
2152 | ||
2153 | fC[0] = TMath::Abs(fC[0]); | |
2154 | if (fC[0]>kC0max) { | |
2155 | fC[0] = kC0max; | |
2156 | fC[1] = 0; | |
2157 | fC[3] = 0; | |
2158 | fC[6] = 0; | |
2159 | fC[10] = 0; | |
2160 | } | |
2161 | fC[2] = TMath::Abs(fC[2]); | |
2162 | if (fC[2]>kC2max) { | |
2163 | fC[2] = kC2max; | |
2164 | fC[1] = 0; | |
2165 | fC[4] = 0; | |
2166 | fC[7] = 0; | |
2167 | fC[11] = 0; | |
2168 | } | |
2169 | fC[5] = TMath::Abs(fC[5]); | |
2170 | if (fC[5]>kC5max) { | |
2171 | fC[5] = kC5max; | |
2172 | fC[3] = 0; | |
2173 | fC[4] = 0; | |
2174 | fC[8] = 0; | |
2175 | fC[12] = 0; | |
2176 | } | |
2177 | fC[9] = TMath::Abs(fC[9]); | |
2178 | if (fC[9]>kC9max) { | |
2179 | fC[9] = kC9max; | |
2180 | fC[6] = 0; | |
2181 | fC[7] = 0; | |
2182 | fC[8] = 0; | |
2183 | fC[13] = 0; | |
2184 | } | |
2185 | fC[14] = TMath::Abs(fC[14]); | |
2186 | if (fC[14]>kC14max) { | |
2187 | fC[14] = kC14max; | |
2188 | fC[10] = 0; | |
2189 | fC[11] = 0; | |
2190 | fC[12] = 0; | |
2191 | fC[13] = 0; | |
2192 | } | |
2193 | ||
2194 | // The part below is used for tests and normally is commented out | |
2195 | // TMatrixDSym m(5); | |
2196 | // TVectorD eig(5); | |
2197 | ||
2198 | // m(0,0)=fC[0]; | |
2199 | // m(1,0)=fC[1]; m(1,1)=fC[2]; | |
2200 | // m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5]; | |
2201 | // m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9]; | |
2202 | // 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]; | |
2203 | ||
2204 | // m(0,1)=m(1,0); | |
2205 | // m(0,2)=m(2,0); m(1,2)=m(2,1); | |
2206 | // m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2); | |
2207 | // m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3); | |
2208 | // m.EigenVectors(eig); | |
2209 | ||
2210 | // // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0); | |
2211 | // if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) { | |
2212 | // AliWarning("Negative eigenvalues of the covariance matrix!"); | |
2213 | // this->Print(); | |
2214 | // eig.Print(); | |
2215 | // } | |
2216 | } |