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51ad6848 | 1 | /************************************************************************** |
2 | * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * | |
3 | * * | |
4 | * Author: The ALICE Off-line Project. * | |
5 | * Contributors are mentioned in the code where appropriate. * | |
6 | * * | |
7 | * Permission to use, copy, modify and distribute this software and its * | |
8 | * documentation strictly for non-commercial purposes is hereby granted * | |
9 | * without fee, provided that the above copyright notice appears in all * | |
10 | * copies and that both the copyright notice and this permission notice * | |
11 | * appear in the supporting documentation. The authors make no claims * | |
12 | * about the suitability of this software for any purpose. It is * | |
13 | * provided "as is" without express or implied warranty. * | |
14 | **************************************************************************/ | |
15 | ||
16 | /* $Id$ */ | |
17 | ||
18 | /////////////////////////////////////////////////////////////////////////////// | |
19 | // // | |
49d13e89 | 20 | // Implementation of the external track parameterisation class. // |
51ad6848 | 21 | // // |
49d13e89 | 22 | // This parameterisation is used to exchange tracks between the detectors. // |
23 | // A set of functions returning the position and the momentum of tracks // | |
24 | // in the global coordinate system as well as the track impact parameters // | |
25 | // are implemented. | |
26 | // Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch // | |
51ad6848 | 27 | /////////////////////////////////////////////////////////////////////////////// |
86be8934 | 28 | #include <cassert> |
29 | ||
30 | #include <TVectorD.h> | |
4b189f98 | 31 | #include <TMatrixDSym.h> |
d46683db | 32 | #include <TPolyMarker3D.h> |
33 | #include <TVector3.h> | |
cfdb62d4 | 34 | #include <TMatrixD.h> |
d46683db | 35 | |
51ad6848 | 36 | #include "AliExternalTrackParam.h" |
58e536c5 | 37 | #include "AliVVertex.h" |
6c94f330 | 38 | #include "AliLog.h" |
51ad6848 | 39 | |
40 | ClassImp(AliExternalTrackParam) | |
41 | ||
ed5f2849 | 42 | Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; |
43 | ||
51ad6848 | 44 | //_____________________________________________________________________________ |
90e48c0c | 45 | AliExternalTrackParam::AliExternalTrackParam() : |
4f6e22bd | 46 | AliVTrack(), |
90e48c0c | 47 | fX(0), |
c9ec41e8 | 48 | fAlpha(0) |
51ad6848 | 49 | { |
90e48c0c | 50 | // |
51 | // default constructor | |
52 | // | |
c9ec41e8 | 53 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
54 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 55 | } |
56 | ||
6c94f330 | 57 | //_____________________________________________________________________________ |
58 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
4f6e22bd | 59 | AliVTrack(track), |
6c94f330 | 60 | fX(track.fX), |
61 | fAlpha(track.fAlpha) | |
62 | { | |
63 | // | |
64 | // copy constructor | |
65 | // | |
66 | for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i]; | |
67 | for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i]; | |
86be8934 | 68 | CheckCovariance(); |
6c94f330 | 69 | } |
70 | ||
def9660e | 71 | //_____________________________________________________________________________ |
72 | AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar) | |
73 | { | |
74 | // | |
75 | // assignment operator | |
76 | // | |
77 | ||
78 | if (this!=&trkPar) { | |
4f6e22bd | 79 | AliVTrack::operator=(trkPar); |
def9660e | 80 | fX = trkPar.fX; |
81 | fAlpha = trkPar.fAlpha; | |
82 | ||
83 | for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i]; | |
84 | for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i]; | |
86be8934 | 85 | CheckCovariance(); |
def9660e | 86 | } |
87 | ||
88 | return *this; | |
89 | } | |
90 | ||
51ad6848 | 91 | //_____________________________________________________________________________ |
92 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
93 | const Double_t param[5], | |
90e48c0c | 94 | const Double_t covar[15]) : |
4f6e22bd | 95 | AliVTrack(), |
90e48c0c | 96 | fX(x), |
c9ec41e8 | 97 | fAlpha(alpha) |
51ad6848 | 98 | { |
90e48c0c | 99 | // |
100 | // create external track parameters from given arguments | |
101 | // | |
c9ec41e8 | 102 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
103 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
86be8934 | 104 | CheckCovariance(); |
51ad6848 | 105 | } |
106 | ||
4f6e22bd | 107 | //_____________________________________________________________________________ |
108 | AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) : | |
109 | AliVTrack(), | |
110 | fX(0.), | |
111 | fAlpha(0.) | |
112 | { | |
113 | // | |
610e3088 | 114 | // Constructor from virtual track, |
115 | // This is not a copy contructor ! | |
4f6e22bd | 116 | // |
610e3088 | 117 | |
118 | if (vTrack->InheritsFrom("AliExternalTrackParam")) { | |
119 | AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !"); | |
120 | AliWarning("Calling the default constructor..."); | |
121 | AliExternalTrackParam(); | |
122 | return; | |
123 | } | |
124 | ||
892be05f | 125 | Double_t xyz[3],pxpypz[3],cv[21]; |
126 | vTrack->GetXYZ(xyz); | |
127 | pxpypz[0]=vTrack->Px(); | |
128 | pxpypz[1]=vTrack->Py(); | |
129 | pxpypz[2]=vTrack->Pz(); | |
4f6e22bd | 130 | vTrack->GetCovarianceXYZPxPyPz(cv); |
131 | Short_t sign = (Short_t)vTrack->Charge(); | |
132 | ||
133 | Set(xyz,pxpypz,cv,sign); | |
134 | } | |
135 | ||
90e48c0c | 136 | //_____________________________________________________________________________ |
da4e3deb | 137 | AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], |
138 | Double_t cv[21],Short_t sign) : | |
4f6e22bd | 139 | AliVTrack(), |
da4e3deb | 140 | fX(0.), |
141 | fAlpha(0.) | |
4f6e22bd | 142 | { |
143 | // | |
144 | // constructor from the global parameters | |
145 | // | |
146 | ||
147 | Set(xyz,pxpypz,cv,sign); | |
148 | } | |
149 | ||
150 | //_____________________________________________________________________________ | |
151 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
152 | Double_t cv[21],Short_t sign) | |
da4e3deb | 153 | { |
154 | // | |
155 | // create external track parameters from the global parameters | |
156 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
157 | // A.Dainese 10.10.08 | |
158 | ||
aff56ff7 | 159 | // Calculate alpha: the rotation angle of the corresponding local system. |
160 | // | |
161 | // For global radial position inside the beam pipe, alpha is the | |
162 | // azimuthal angle of the momentum projected on (x,y). | |
163 | // | |
c99948ce | 164 | // For global radial position outside the ITS, alpha is the |
aff56ff7 | 165 | // azimuthal angle of the centre of the TPC sector in which the point |
166 | // xyz lies | |
167 | // | |
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 | ||
216 | Double_t pt=1./TMath::Abs(fP[4]); | |
da4e3deb | 217 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
218 | ||
219 | Double_t m00=-sn;// m10=cs; | |
220 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
221 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
222 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
223 | ||
224 | m43*=GetSign(); | |
225 | m44*=GetSign(); | |
226 | m45*=GetSign(); | |
227 | ||
228 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
229 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
230 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
231 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
232 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
233 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
234 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
235 | ||
236 | fC[0 ] = cv[0 ]+cv[2 ]; | |
237 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
238 | fC[2 ] = cv[5 ]; | |
239 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
240 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
241 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
242 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
243 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
244 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
245 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
246 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
247 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
248 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
249 | Double_t b2=m23*m35; | |
250 | Double_t b3=m43*m35; | |
251 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
252 | Double_t b5=m24*m35; | |
253 | Double_t b6=m44*m35; | |
254 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
255 | fC[13] = b1/b3-b2*fC[8]/b3; | |
256 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 257 | |
86be8934 | 258 | CheckCovariance(); |
259 | ||
4f6e22bd | 260 | return; |
da4e3deb | 261 | } |
262 | ||
51ad6848 | 263 | //_____________________________________________________________________________ |
c9ec41e8 | 264 | void AliExternalTrackParam::Reset() { |
1530f89c | 265 | // |
266 | // Resets all the parameters to 0 | |
267 | // | |
c9ec41e8 | 268 | fX=fAlpha=0.; |
269 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
270 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 271 | } |
272 | ||
3775b0ca | 273 | //_____________________________________________________________________________ |
274 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
275 | // | |
276 | // Add "something" to the track covarince matrix. | |
277 | // May be needed to account for unknown mis-calibration/mis-alignment | |
278 | // | |
279 | fC[0] +=c[0]; | |
280 | fC[1] +=c[1]; fC[2] +=c[2]; | |
281 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
282 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
283 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
86be8934 | 284 | CheckCovariance(); |
3775b0ca | 285 | } |
286 | ||
287 | ||
c9ec41e8 | 288 | Double_t AliExternalTrackParam::GetP() const { |
289 | //--------------------------------------------------------------------- | |
290 | // This function returns the track momentum | |
291 | // Results for (nearly) straight tracks are meaningless ! | |
292 | //--------------------------------------------------------------------- | |
06fb4a2f | 293 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 294 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 295 | } |
296 | ||
1d99986f | 297 | Double_t AliExternalTrackParam::Get1P() const { |
298 | //--------------------------------------------------------------------- | |
299 | // This function returns the 1/(track momentum) | |
300 | //--------------------------------------------------------------------- | |
301 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
302 | } | |
303 | ||
c9ec41e8 | 304 | //_______________________________________________________________________ |
c7bafca9 | 305 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 306 | //------------------------------------------------------------------ |
307 | // This function calculates the transverse impact parameter | |
308 | // with respect to a point with global coordinates (x,y) | |
309 | // in the magnetic field "b" (kG) | |
310 | //------------------------------------------------------------------ | |
5773defd | 311 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 312 | Double_t rp4=GetC(b); |
c9ec41e8 | 313 | |
314 | Double_t xt=fX, yt=fP[0]; | |
315 | ||
316 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
317 | Double_t a = x*cs + y*sn; | |
318 | y = -x*sn + y*cs; x=a; | |
319 | xt-=x; yt-=y; | |
320 | ||
bfd20868 | 321 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2])); |
322 | a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt); | |
1530f89c | 323 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
324 | } | |
325 | ||
326 | //_______________________________________________________________________ | |
327 | void AliExternalTrackParam:: | |
328 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
329 | //------------------------------------------------------------------ | |
330 | // This function calculates the transverse and longitudinal impact parameters | |
331 | // with respect to a point with global coordinates (x,y) | |
332 | // in the magnetic field "b" (kG) | |
333 | //------------------------------------------------------------------ | |
bfd20868 | 334 | Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1)); |
1530f89c | 335 | Double_t xt=fX, yt=fP[0]; |
336 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
337 | Double_t a = x*cs + y*sn; | |
338 | y = -x*sn + y*cs; x=a; | |
339 | xt-=x; yt-=y; | |
340 | ||
341 | Double_t rp4=GetC(b); | |
342 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
343 | dz[0] = -(xt*f1 - yt*r1); | |
344 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
345 | return; | |
346 | } | |
347 | ||
348 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
349 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
350 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
351 | dz[0] = -a/(1 + rr); | |
bfd20868 | 352 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2)); |
1530f89c | 353 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; |
51ad6848 | 354 | } |
355 | ||
49d13e89 | 356 | //_______________________________________________________________________ |
357 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
358 | //------------------------------------------------------------------ | |
359 | // This function calculates the transverse impact parameter | |
360 | // with respect to a point with global coordinates (xv,yv) | |
361 | // neglecting the track curvature. | |
362 | //------------------------------------------------------------------ | |
363 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
364 | Double_t x= xv*cs + yv*sn; | |
365 | Double_t y=-xv*sn + yv*cs; | |
366 | ||
bfd20868 | 367 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
49d13e89 | 368 | |
1530f89c | 369 | return -d; |
49d13e89 | 370 | } |
371 | ||
b8e07ed6 | 372 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx |
373 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
374 | Double_t dEdx, | |
375 | Bool_t anglecorr) { | |
116b445b | 376 | //------------------------------------------------------------------ |
377 | // This function corrects the track parameters for the crossed material. | |
378 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
379 | // "xTimesRho" - is the product length*density (g/cm^2). | |
380 | // "mass" - the mass of this particle (GeV/c^2). | |
b8e07ed6 | 381 | // "dEdx" - mean enery loss (GeV/(g/cm^2) |
382 | // "anglecorr" - switch for the angular correction | |
116b445b | 383 | //------------------------------------------------------------------ |
384 | Double_t &fP2=fP[2]; | |
385 | Double_t &fP3=fP[3]; | |
386 | Double_t &fP4=fP[4]; | |
387 | ||
388 | Double_t &fC22=fC[5]; | |
389 | Double_t &fC33=fC[9]; | |
390 | Double_t &fC43=fC[13]; | |
391 | Double_t &fC44=fC[14]; | |
392 | ||
7dded1d5 | 393 | //Apply angle correction, if requested |
394 | if(anglecorr) { | |
bfd20868 | 395 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2))); |
7dded1d5 | 396 | xOverX0 *=angle; |
397 | xTimesRho *=angle; | |
398 | } | |
399 | ||
116b445b | 400 | Double_t p=GetP(); |
401 | Double_t p2=p*p; | |
402 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 403 | |
9f2bec63 | 404 | //Calculating the multiple scattering corrections****************** |
405 | Double_t cC22 = 0.; | |
406 | Double_t cC33 = 0.; | |
407 | Double_t cC43 = 0.; | |
408 | Double_t cC44 = 0.; | |
116b445b | 409 | if (xOverX0 != 0) { |
410 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
411 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
9f2bec63 | 412 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
bfd20868 | 413 | cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3); |
9f2bec63 | 414 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); |
415 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
416 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
116b445b | 417 | } |
418 | ||
9f2bec63 | 419 | //Calculating the energy loss corrections************************ |
420 | Double_t cP4=1.; | |
116b445b | 421 | if ((xTimesRho != 0.) && (beta2 < 1.)) { |
b8e07ed6 | 422 | Double_t dE=dEdx*xTimesRho; |
116b445b | 423 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
424 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
c9038cae | 425 | //cP4 = (1.- e/p2*dE); |
76ece3d8 | 426 | if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE; |
c9038cae | 427 | cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben ! |
9f2bec63 | 428 | if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c |
4b2fa3ce | 429 | |
116b445b | 430 | |
431 | // Approximate energy loss fluctuation (M.Ivanov) | |
432 | const Double_t knst=0.07; // To be tuned. | |
433 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 434 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
116b445b | 435 | |
436 | } | |
437 | ||
9f2bec63 | 438 | //Applying the corrections***************************** |
439 | fC22 += cC22; | |
440 | fC33 += cC33; | |
441 | fC43 += cC43; | |
442 | fC44 += cC44; | |
443 | fP4 *= cP4; | |
444 | ||
86be8934 | 445 | CheckCovariance(); |
446 | ||
116b445b | 447 | return kTRUE; |
448 | } | |
449 | ||
b8e07ed6 | 450 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
451 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
452 | Bool_t anglecorr, | |
453 | Double_t (*Bethe)(Double_t)) { | |
454 | //------------------------------------------------------------------ | |
455 | // This function corrects the track parameters for the crossed material. | |
456 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
457 | // "xTimesRho" - is the product length*density (g/cm^2). | |
458 | // "mass" - the mass of this particle (GeV/c^2). | |
459 | // "anglecorr" - switch for the angular correction | |
460 | // "Bethe" - function calculating the energy loss (GeV/(g/cm^2)) | |
461 | //------------------------------------------------------------------ | |
462 | ||
463 | Double_t bg=GetP()/mass; | |
464 | Double_t dEdx=Bethe(bg); | |
465 | ||
466 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
467 | } | |
468 | ||
469 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA | |
470 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
471 | Double_t zOverA, | |
472 | Double_t density, | |
473 | Double_t exEnergy, | |
474 | Double_t jp1, | |
475 | Double_t jp2, | |
476 | Bool_t anglecorr) { | |
477 | //------------------------------------------------------------------ | |
478 | // This function corrects the track parameters for the crossed material | |
479 | // using the full Geant-like Bethe-Bloch formula parameterization | |
480 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
481 | // "xTimesRho" - is the product length*density (g/cm^2). | |
482 | // "mass" - the mass of this particle (GeV/c^2). | |
483 | // "density" - mean density (g/cm^3) | |
484 | // "zOverA" - mean Z/A | |
485 | // "exEnergy" - mean exitation energy (GeV) | |
486 | // "jp1" - density effect first junction point | |
487 | // "jp2" - density effect second junction point | |
488 | // "anglecorr" - switch for the angular correction | |
489 | // | |
490 | // The default values of the parameters are for silicon | |
491 | // | |
492 | //------------------------------------------------------------------ | |
493 | ||
494 | Double_t bg=GetP()/mass; | |
495 | Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA); | |
496 | ||
497 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
498 | } | |
499 | ||
500 | ||
116b445b | 501 | |
ee5dba5e | 502 | Bool_t AliExternalTrackParam::CorrectForMaterial |
503 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 504 | //------------------------------------------------------------------ |
116b445b | 505 | // Deprecated function ! |
506 | // Better use CorrectForMeanMaterial instead of it. | |
507 | // | |
c7bafca9 | 508 | // This function corrects the track parameters for the crossed material |
509 | // "d" - the thickness (fraction of the radiation length) | |
510 | // "x0" - the radiation length (g/cm^2) | |
511 | // "mass" - the mass of this particle (GeV/c^2) | |
512 | //------------------------------------------------------------------ | |
c7bafca9 | 513 | |
b8e07ed6 | 514 | return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe); |
c7bafca9 | 515 | |
c7bafca9 | 516 | } |
517 | ||
9c56b409 | 518 | Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg, |
519 | Double_t kp1, | |
520 | Double_t kp2, | |
521 | Double_t kp3, | |
522 | Double_t kp4, | |
523 | Double_t kp5) { | |
524 | // | |
525 | // This is the empirical ALEPH parameterization of the Bethe-Bloch formula. | |
526 | // It is normalized to 1 at the minimum. | |
527 | // | |
528 | // bg - beta*gamma | |
529 | // | |
530 | // The default values for the kp* parameters are for ALICE TPC. | |
531 | // The returned value is in MIP units | |
532 | // | |
533 | ||
534 | Double_t beta = bg/TMath::Sqrt(1.+ bg*bg); | |
535 | ||
536 | Double_t aa = TMath::Power(beta,kp4); | |
537 | Double_t bb = TMath::Power(1./bg,kp5); | |
538 | ||
539 | bb=TMath::Log(kp3+bb); | |
540 | ||
541 | return (kp2-aa-bb)*kp1/aa; | |
542 | } | |
543 | ||
544 | Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg, | |
545 | Double_t kp0, | |
546 | Double_t kp1, | |
547 | Double_t kp2, | |
548 | Double_t kp3, | |
549 | Double_t kp4) { | |
550 | // | |
551 | // This is the parameterization of the Bethe-Bloch formula inspired by Geant. | |
552 | // | |
553 | // bg - beta*gamma | |
554 | // kp0 - density [g/cm^3] | |
555 | // kp1 - density effect first junction point | |
556 | // kp2 - density effect second junction point | |
557 | // kp3 - mean excitation energy [GeV] | |
558 | // kp4 - mean Z/A | |
559 | // | |
560 | // The default values for the kp* parameters are for silicon. | |
561 | // The returned value is in [GeV/(g/cm^2)]. | |
562 | // | |
563 | ||
564 | const Double_t mK = 0.307075e-3; // [GeV*cm^2/g] | |
565 | const Double_t me = 0.511e-3; // [GeV/c^2] | |
566 | const Double_t rho = kp0; | |
567 | const Double_t x0 = kp1*2.303; | |
568 | const Double_t x1 = kp2*2.303; | |
569 | const Double_t mI = kp3; | |
570 | const Double_t mZA = kp4; | |
571 | const Double_t bg2 = bg*bg; | |
572 | const Double_t maxT= 2*me*bg2; // neglecting the electron mass | |
573 | ||
574 | //*** Density effect | |
575 | Double_t d2=0.; | |
576 | const Double_t x=TMath::Log(bg); | |
577 | const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI); | |
578 | if (x > x1) { | |
579 | d2 = lhwI + x - 0.5; | |
580 | } else if (x > x0) { | |
581 | const Double_t r=(x1-x)/(x1-x0); | |
582 | d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r; | |
583 | } | |
584 | ||
585 | return mK*mZA*(1+bg2)/bg2* | |
586 | (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2); | |
587 | } | |
588 | ||
d46683db | 589 | Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) { |
ee5dba5e | 590 | //------------------------------------------------------------------ |
d46683db | 591 | // This is an approximation of the Bethe-Bloch formula, |
592 | // reasonable for solid materials. | |
593 | // All the parameters are, in fact, for Si. | |
9b655cba | 594 | // The returned value is in [GeV/(g/cm^2)] |
ee5dba5e | 595 | //------------------------------------------------------------------ |
a821848c | 596 | |
9c56b409 | 597 | return BetheBlochGeant(bg); |
d46683db | 598 | } |
ee5dba5e | 599 | |
d46683db | 600 | Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) { |
601 | //------------------------------------------------------------------ | |
602 | // This is an approximation of the Bethe-Bloch formula, | |
603 | // reasonable for gas materials. | |
604 | // All the parameters are, in fact, for Ne. | |
9b655cba | 605 | // The returned value is in [GeV/(g/cm^2)] |
d46683db | 606 | //------------------------------------------------------------------ |
607 | ||
608 | const Double_t rho = 0.9e-3; | |
609 | const Double_t x0 = 2.; | |
610 | const Double_t x1 = 4.; | |
611 | const Double_t mI = 140.e-9; | |
612 | const Double_t mZA = 0.49555; | |
613 | ||
9c56b409 | 614 | return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); |
ee5dba5e | 615 | } |
616 | ||
49d13e89 | 617 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
618 | //------------------------------------------------------------------ | |
619 | // Transform this track to the local coord. system rotated | |
620 | // by angle "alpha" (rad) with respect to the global coord. system. | |
621 | //------------------------------------------------------------------ | |
dfcef74c | 622 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
623 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
624 | return kFALSE; | |
625 | } | |
626 | ||
49d13e89 | 627 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
628 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
629 | ||
630 | Double_t &fP0=fP[0]; | |
631 | Double_t &fP2=fP[2]; | |
632 | Double_t &fC00=fC[0]; | |
633 | Double_t &fC10=fC[1]; | |
634 | Double_t &fC20=fC[3]; | |
635 | Double_t &fC21=fC[4]; | |
636 | Double_t &fC22=fC[5]; | |
637 | Double_t &fC30=fC[6]; | |
638 | Double_t &fC32=fC[8]; | |
639 | Double_t &fC40=fC[10]; | |
640 | Double_t &fC42=fC[12]; | |
641 | ||
642 | Double_t x=fX; | |
643 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
bfd20868 | 644 | Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision |
49d13e89 | 645 | |
dfcef74c | 646 | Double_t tmp=sf*ca - cf*sa; |
7248cf51 | 647 | if (TMath::Abs(tmp) >= kAlmost1) { |
648 | if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) | |
649 | AliWarning(Form("Rotation failed ! %.10e",tmp)); | |
0b69bbb2 | 650 | return kFALSE; |
651 | } | |
dfcef74c | 652 | |
49d13e89 | 653 | fAlpha = alpha; |
654 | fX = x*ca + fP0*sa; | |
655 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 656 | fP2= tmp; |
49d13e89 | 657 | |
06fb4a2f | 658 | if (TMath::Abs(cf)<kAlmost0) { |
659 | AliError(Form("Too small cosine value %f",cf)); | |
660 | cf = kAlmost0; | |
661 | } | |
662 | ||
49d13e89 | 663 | Double_t rr=(ca+sf/cf*sa); |
664 | ||
665 | fC00 *= (ca*ca); | |
666 | fC10 *= ca; | |
667 | fC20 *= ca*rr; | |
668 | fC21 *= rr; | |
669 | fC22 *= rr*rr; | |
670 | fC30 *= ca; | |
671 | fC32 *= rr; | |
672 | fC40 *= ca; | |
673 | fC42 *= rr; | |
674 | ||
86be8934 | 675 | CheckCovariance(); |
676 | ||
49d13e89 | 677 | return kTRUE; |
678 | } | |
679 | ||
680 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
681 | //---------------------------------------------------------------- | |
682 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
683 | //---------------------------------------------------------------- | |
49d13e89 | 684 | Double_t dx=xk-fX; |
e421f556 | 685 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 686 | |
1530f89c | 687 | Double_t crv=GetC(b); |
5773defd | 688 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
689 | ||
2de63fc5 | 690 | Double_t x2r = crv*dx; |
691 | Double_t f1=fP[2], f2=f1 + x2r; | |
bbefa4c4 | 692 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 693 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
4349f5a4 | 694 | if (TMath::Abs(fP[4])< kAlmost0) return kFALSE; |
49d13e89 | 695 | |
696 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
697 | Double_t | |
698 | &fC00=fC[0], | |
699 | &fC10=fC[1], &fC11=fC[2], | |
700 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
701 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
702 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
703 | ||
bfd20868 | 704 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
4349f5a4 | 705 | if (TMath::Abs(r1)<kAlmost0) return kFALSE; |
706 | if (TMath::Abs(r2)<kAlmost0) return kFALSE; | |
49d13e89 | 707 | |
708 | fX=xk; | |
2de63fc5 | 709 | double dy2dx = (f1+f2)/(r1+r2); |
710 | fP0 += dx*dy2dx; | |
711 | if (TMath::Abs(x2r)<0.05) { | |
712 | fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov ! | |
713 | fP2 += x2r; | |
714 | } | |
715 | else { | |
716 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
717 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
718 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
719 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
720 | // Similarly, the rotation angle in linear in dx only for dx<<R | |
721 | double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one | |
722 | double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
723 | fP1 += rot/crv*fP3; | |
724 | fP2 = TMath::Sin(rot + TMath::ASin(fP2)); | |
725 | } | |
49d13e89 | 726 | |
727 | //f = F - 1 | |
728 | ||
729 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
730 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
731 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
732 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
733 | Double_t f13= dx/r1; | |
734 | Double_t f24= dx; f24*=cc; | |
735 | ||
736 | //b = C*ft | |
737 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
738 | Double_t b02=f24*fC40; | |
739 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
740 | Double_t b12=f24*fC41; | |
741 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
742 | Double_t b22=f24*fC42; | |
743 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
744 | Double_t b42=f24*fC44; | |
745 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
746 | Double_t b32=f24*fC43; | |
747 | ||
748 | //a = f*b = f*C*ft | |
749 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
750 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
751 | Double_t a22=f24*b42; | |
752 | ||
753 | //F*C*Ft = C + (b + bt + a) | |
754 | fC00 += b00 + b00 + a00; | |
755 | fC10 += b10 + b01 + a01; | |
756 | fC20 += b20 + b02 + a02; | |
757 | fC30 += b30; | |
758 | fC40 += b40; | |
759 | fC11 += b11 + b11 + a11; | |
760 | fC21 += b21 + b12 + a12; | |
761 | fC31 += b31; | |
762 | fC41 += b41; | |
763 | fC22 += b22 + b22 + a22; | |
764 | fC32 += b32; | |
765 | fC42 += b42; | |
766 | ||
86be8934 | 767 | CheckCovariance(); |
768 | ||
49d13e89 | 769 | return kTRUE; |
770 | } | |
771 | ||
9f2bec63 | 772 | Bool_t |
773 | AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) { | |
774 | //------------------------------------------------------------------ | |
775 | // Transform this track to the local coord. system rotated | |
776 | // by angle "alpha" (rad) with respect to the global coord. system, | |
777 | // and propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
778 | //------------------------------------------------------------------ | |
779 | ||
780 | //Save the parameters | |
781 | Double_t as=fAlpha; | |
782 | Double_t xs=fX; | |
783 | Double_t ps[5], cs[15]; | |
784 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
785 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
786 | ||
787 | if (Rotate(alpha)) | |
788 | if (PropagateTo(x,b)) return kTRUE; | |
789 | ||
790 | //Restore the parameters, if the operation failed | |
791 | fAlpha=as; | |
792 | fX=xs; | |
793 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
794 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
795 | return kFALSE; | |
796 | } | |
797 | ||
266a0f9b | 798 | Bool_t AliExternalTrackParam::PropagateBxByBz |
799 | (Double_t alpha, Double_t x, Double_t b[3]) { | |
800 | //------------------------------------------------------------------ | |
801 | // Transform this track to the local coord. system rotated | |
802 | // by angle "alpha" (rad) with respect to the global coord. system, | |
803 | // and propagate this track to the plane X=xk (cm), | |
804 | // taking into account all three components of the B field, "b[3]" (kG) | |
805 | //------------------------------------------------------------------ | |
806 | ||
807 | //Save the parameters | |
808 | Double_t as=fAlpha; | |
809 | Double_t xs=fX; | |
810 | Double_t ps[5], cs[15]; | |
811 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
812 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
813 | ||
814 | if (Rotate(alpha)) | |
815 | if (PropagateToBxByBz(x,b)) return kTRUE; | |
816 | ||
817 | //Restore the parameters, if the operation failed | |
818 | fAlpha=as; | |
819 | fX=xs; | |
820 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
821 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
822 | return kFALSE; | |
823 | } | |
824 | ||
9f2bec63 | 825 | |
052daaff | 826 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
827 | Double_t p[3], Double_t bz) const { | |
828 | //+++++++++++++++++++++++++++++++++++++++++ | |
829 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
830 | // Extrapolate track along simple helix in magnetic field | |
831 | // Arguments: len -distance alogn helix, [cm] | |
832 | // bz - mag field, [kGaus] | |
833 | // Returns: x and p contain extrapolated positon and momentum | |
834 | // The momentum returned for straight-line tracks is meaningless ! | |
835 | //+++++++++++++++++++++++++++++++++++++++++ | |
836 | GetXYZ(x); | |
837 | ||
2258e165 | 838 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks |
052daaff | 839 | Double_t unit[3]; GetDirection(unit); |
840 | x[0]+=unit[0]*len; | |
841 | x[1]+=unit[1]*len; | |
842 | x[2]+=unit[2]*len; | |
843 | ||
844 | p[0]=unit[0]/kAlmost0; | |
845 | p[1]=unit[1]/kAlmost0; | |
846 | p[2]=unit[2]/kAlmost0; | |
847 | } else { | |
848 | GetPxPyPz(p); | |
849 | Double_t pp=GetP(); | |
850 | Double_t a = -kB2C*bz*GetSign(); | |
851 | Double_t rho = a/pp; | |
852 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
853 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
854 | x[2] += p[2]*len/pp; | |
855 | ||
856 | Double_t p0=p[0]; | |
857 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
858 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
859 | } | |
860 | } | |
861 | ||
862 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
863 | Double_t bz) const { | |
864 | //+++++++++++++++++++++++++++++++++++++++++ | |
865 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
866 | // Finds point of intersection (if exists) of the helix with the plane. | |
867 | // Stores result in fX and fP. | |
868 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
869 | // and vector, normal to the plane | |
870 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
871 | //+++++++++++++++++++++++++++++++++++++++++ | |
872 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
873 | ||
874 | //estimates initial helix length up to plane | |
875 | Double_t s= | |
876 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
877 | Double_t dist=99999,distPrev=dist; | |
878 | Double_t x[3],p[3]; | |
879 | while(TMath::Abs(dist)>0.00001){ | |
880 | //calculates helix at the distance s from x0 ALONG the helix | |
881 | Propagate(s,x,p,bz); | |
882 | ||
883 | //distance between current helix position and plane | |
884 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
885 | ||
886 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
887 | distPrev=dist; | |
888 | s-=dist; | |
889 | } | |
890 | //on exit pnt is intersection point,norm is track vector at that point, | |
891 | //all in MARS | |
892 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
893 | return kTRUE; | |
894 | } | |
895 | ||
49d13e89 | 896 | Double_t |
897 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
898 | //---------------------------------------------------------------- | |
899 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
900 | //---------------------------------------------------------------- | |
901 | Double_t sdd = fC[0] + cov[0]; | |
902 | Double_t sdz = fC[1] + cov[1]; | |
903 | Double_t szz = fC[2] + cov[2]; | |
904 | Double_t det = sdd*szz - sdz*sdz; | |
905 | ||
906 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
907 | ||
908 | Double_t d = fP[0] - p[0]; | |
909 | Double_t z = fP[1] - p[1]; | |
910 | ||
911 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
912 | } | |
913 | ||
4b189f98 | 914 | Double_t AliExternalTrackParam:: |
915 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
916 | //---------------------------------------------------------------- | |
917 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 918 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 919 | // |
920 | // Cov(x,x) ... : covxyz[0] | |
921 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
922 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
923 | //---------------------------------------------------------------- | |
924 | ||
925 | Double_t res[3] = { | |
926 | GetX() - p[0], | |
927 | GetY() - p[1], | |
928 | GetZ() - p[2] | |
929 | }; | |
930 | ||
931 | Double_t f=GetSnp(); | |
932 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
bfd20868 | 933 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
4b189f98 | 934 | Double_t a=f/r, b=GetTgl()/r; |
935 | ||
936 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
937 | ||
938 | TMatrixDSym v(3); | |
939 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
940 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
941 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
942 | ||
943 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
944 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
945 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
946 | ||
947 | v.Invert(); | |
948 | if (!v.IsValid()) return kVeryBig; | |
949 | ||
950 | Double_t chi2=0.; | |
951 | for (Int_t i = 0; i < 3; i++) | |
952 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
953 | ||
954 | return chi2; | |
acdfbc78 | 955 | } |
956 | ||
957 | Double_t AliExternalTrackParam:: | |
958 | GetPredictedChi2(const AliExternalTrackParam *t) const { | |
959 | //---------------------------------------------------------------- | |
960 | // Estimate the chi2 (5 dof) of this track with respect to the track | |
961 | // given by the argument. | |
962 | // The two tracks must be in the same reference system | |
963 | // and estimated at the same reference plane. | |
964 | //---------------------------------------------------------------- | |
965 | ||
966 | if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) { | |
967 | AliError("The reference systems of the tracks differ !"); | |
968 | return kVeryBig; | |
969 | } | |
970 | if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) { | |
971 | AliError("The reference of the tracks planes differ !"); | |
972 | return kVeryBig; | |
973 | } | |
974 | ||
975 | TMatrixDSym c(5); | |
976 | c(0,0)=GetSigmaY2(); | |
977 | c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2(); | |
978 | c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2(); | |
979 | c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2(); | |
980 | c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2(); | |
981 | ||
982 | c(0,0)+=t->GetSigmaY2(); | |
983 | c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2(); | |
984 | c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2(); | |
985 | c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2(); | |
986 | 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(); | |
987 | c(0,1)=c(1,0); | |
988 | c(0,2)=c(2,0); c(1,2)=c(2,1); | |
989 | c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2); | |
990 | c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3); | |
991 | ||
992 | c.Invert(); | |
993 | if (!c.IsValid()) return kVeryBig; | |
994 | ||
995 | ||
996 | Double_t res[5] = { | |
997 | GetY() - t->GetY(), | |
998 | GetZ() - t->GetZ(), | |
999 | GetSnp() - t->GetSnp(), | |
1000 | GetTgl() - t->GetTgl(), | |
1001 | GetSigned1Pt() - t->GetSigned1Pt() | |
1002 | }; | |
4b189f98 | 1003 | |
acdfbc78 | 1004 | Double_t chi2=0.; |
1005 | for (Int_t i = 0; i < 5; i++) | |
1006 | for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j); | |
4b189f98 | 1007 | |
acdfbc78 | 1008 | return chi2; |
4b189f98 | 1009 | } |
1010 | ||
1e023a36 | 1011 | Bool_t AliExternalTrackParam:: |
1012 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
1013 | //---------------------------------------------------------------- | |
1014 | // Propagate this track to the plane | |
1015 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
1016 | // belongs to. | |
1017 | // The magnetic field is "bz" (kG) | |
1018 | // | |
1019 | // The track curvature and the change of the covariance matrix | |
1020 | // of the track parameters are negleted ! | |
1021 | // (So the "step" should be small compared with 1/curvature) | |
1022 | //---------------------------------------------------------------- | |
1023 | ||
1024 | Double_t f=GetSnp(); | |
1025 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
bfd20868 | 1026 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
1e023a36 | 1027 | Double_t a=f/r, b=GetTgl()/r; |
1028 | ||
1029 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
1030 | ||
1031 | TMatrixDSym tV(3); | |
1032 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
1033 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
1034 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
1035 | ||
1036 | TMatrixDSym pV(3); | |
1037 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
1038 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
1039 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
1040 | ||
1041 | TMatrixDSym tpV(tV); | |
1042 | tpV+=pV; | |
1043 | tpV.Invert(); | |
1044 | if (!tpV.IsValid()) return kFALSE; | |
1045 | ||
1046 | TMatrixDSym pW(3),tW(3); | |
1047 | for (Int_t i=0; i<3; i++) | |
1048 | for (Int_t j=0; j<3; j++) { | |
1049 | pW(i,j)=tW(i,j)=0.; | |
1050 | for (Int_t k=0; k<3; k++) { | |
1051 | pW(i,j) += tV(i,k)*tpV(k,j); | |
1052 | tW(i,j) += pV(i,k)*tpV(k,j); | |
1053 | } | |
1054 | } | |
1055 | ||
1056 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
1057 | ||
1058 | Double_t x=0.; | |
1059 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
1060 | Double_t crv=GetC(bz); | |
1061 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1062 | f += crv*(x-fX); | |
1063 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
1064 | fX=x; | |
1065 | ||
1066 | fP[0]=0.; | |
1067 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
1068 | fP[1]=0.; | |
1069 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
1070 | ||
1071 | return kTRUE; | |
1072 | } | |
1073 | ||
e23a38cb | 1074 | Double_t *AliExternalTrackParam::GetResiduals( |
1075 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
1076 | //------------------------------------------------------------------ | |
1077 | // Returns the track residuals with the space point "p" having | |
1078 | // the covariance matrix "cov". | |
1079 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
1080 | // otherwise they must be predicted. | |
1081 | //------------------------------------------------------------------ | |
1082 | static Double_t res[2]; | |
1083 | ||
1084 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1085 | if (updated) { | |
1086 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
1087 | } else { | |
1088 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
1089 | } | |
1090 | Double_t det=r00*r11 - r01*r01; | |
1091 | ||
1092 | if (TMath::Abs(det) < kAlmost0) return 0; | |
1093 | ||
1094 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 1095 | |
1096 | if (r00 < 0.) return 0; | |
1097 | if (r11 < 0.) return 0; | |
1098 | ||
e23a38cb | 1099 | Double_t dy = fP[0] - p[0]; |
1100 | Double_t dz = fP[1] - p[1]; | |
1101 | ||
1102 | res[0]=dy*TMath::Sqrt(r00); | |
1103 | res[1]=dz*TMath::Sqrt(r11); | |
1104 | ||
1105 | return res; | |
1106 | } | |
1107 | ||
49d13e89 | 1108 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
1109 | //------------------------------------------------------------------ | |
1110 | // Update the track parameters with the space point "p" having | |
1111 | // the covariance matrix "cov" | |
1112 | //------------------------------------------------------------------ | |
1113 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
1114 | Double_t | |
1115 | &fC00=fC[0], | |
1116 | &fC10=fC[1], &fC11=fC[2], | |
1117 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1118 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1119 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1120 | ||
1121 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1122 | r00+=fC00; r01+=fC10; r11+=fC11; | |
1123 | Double_t det=r00*r11 - r01*r01; | |
1124 | ||
1125 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
1126 | ||
1127 | ||
1128 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
1129 | ||
1130 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
1131 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
1132 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
1133 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
1134 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
1135 | ||
1136 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
1137 | Double_t sf=fP2 + k20*dy + k21*dz; | |
1138 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
1139 | ||
1140 | fP0 += k00*dy + k01*dz; | |
1141 | fP1 += k10*dy + k11*dz; | |
1142 | fP2 = sf; | |
1143 | fP3 += k30*dy + k31*dz; | |
1144 | fP4 += k40*dy + k41*dz; | |
1145 | ||
1146 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
1147 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
1148 | ||
1149 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
1150 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
1151 | fC40-=k00*c04+k01*c14; | |
1152 | ||
1153 | fC11-=k10*c01+k11*fC11; | |
1154 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
1155 | fC41-=k10*c04+k11*c14; | |
1156 | ||
1157 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
1158 | fC42-=k20*c04+k21*c14; | |
1159 | ||
1160 | fC33-=k30*c03+k31*c13; | |
1161 | fC43-=k30*c04+k31*c14; | |
1162 | ||
1163 | fC44-=k40*c04+k41*c14; | |
1164 | ||
86be8934 | 1165 | CheckCovariance(); |
1166 | ||
49d13e89 | 1167 | return kTRUE; |
1168 | } | |
1169 | ||
c7bafca9 | 1170 | void |
1171 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
1172 | //-------------------------------------------------------------------- | |
1173 | // External track parameters -> helix parameters | |
1174 | // "b" - magnetic field (kG) | |
1175 | //-------------------------------------------------------------------- | |
1176 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1177 | ||
1530f89c | 1178 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 1179 | |
1180 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
1181 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
1182 | //hlx[1]= // z0 | |
1183 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
1184 | //hlx[3]= // tgl | |
1530f89c | 1185 | hlx[4]=GetC(b); // C |
c7bafca9 | 1186 | } |
1187 | ||
1188 | ||
1189 | static void Evaluate(const Double_t *h, Double_t t, | |
1190 | Double_t r[3], //radius vector | |
1191 | Double_t g[3], //first defivatives | |
1192 | Double_t gg[3]) //second derivatives | |
1193 | { | |
1194 | //-------------------------------------------------------------------- | |
1195 | // Calculate position of a point on a track and some derivatives | |
1196 | //-------------------------------------------------------------------- | |
1197 | Double_t phase=h[4]*t+h[2]; | |
1198 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
1199 | ||
ba4550c4 | 1200 | r[0] = h[5]; |
1201 | r[1] = h[0]; | |
1202 | if (TMath::Abs(h[4])>kAlmost0) { | |
1203 | r[0] += (sn - h[6])/h[4]; | |
1204 | r[1] -= (cs - h[7])/h[4]; | |
1205 | } | |
c7bafca9 | 1206 | r[2] = h[1] + h[3]*t; |
1207 | ||
1208 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
1209 | ||
1210 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
1211 | } | |
1212 | ||
1213 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
1214 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
1215 | //------------------------------------------------------------ | |
1216 | // Returns the (weighed !) distance of closest approach between | |
1217 | // this track and the track "p". | |
1218 | // Other returned values: | |
1219 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
1220 | //----------------------------------------------------------- | |
1221 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
1222 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
1223 | Double_t dx2=dy2; | |
1224 | ||
c7bafca9 | 1225 | Double_t p1[8]; GetHelixParameters(p1,b); |
1226 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
1227 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
1228 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
1229 | ||
1230 | ||
1231 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
1232 | Evaluate(p1,t1,r1,g1,gg1); | |
1233 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
1234 | Evaluate(p2,t2,r2,g2,gg2); | |
1235 | ||
1236 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
1237 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1238 | ||
1239 | Int_t max=27; | |
1240 | while (max--) { | |
1241 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
1242 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
1243 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
1244 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
1245 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
1246 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
1247 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
1248 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
1249 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
1250 | ||
1251 | Double_t det=h11*h22-h12*h12; | |
1252 | ||
1253 | Double_t dt1,dt2; | |
1254 | if (TMath::Abs(det)<1.e-33) { | |
1255 | //(quasi)singular Hessian | |
1256 | dt1=-gt1; dt2=-gt2; | |
1257 | } else { | |
1258 | dt1=-(gt1*h22 - gt2*h12)/det; | |
1259 | dt2=-(h11*gt2 - h12*gt1)/det; | |
1260 | } | |
1261 | ||
1262 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
1263 | ||
1264 | //check delta(phase1) ? | |
1265 | //check delta(phase2) ? | |
1266 | ||
1267 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
1268 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
1269 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 1270 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 1271 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
1272 | if (lmb < 0.) | |
358f16ae | 1273 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 1274 | break; |
1275 | } | |
1276 | ||
1277 | Double_t dd=dm; | |
1278 | for (Int_t div=1 ; ; div*=2) { | |
1279 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
1280 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
1281 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
1282 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1283 | if (dd<dm) break; | |
1284 | dt1*=0.5; dt2*=0.5; | |
1285 | if (div>512) { | |
358f16ae | 1286 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 1287 | } |
1288 | } | |
1289 | dm=dd; | |
1290 | ||
1291 | t1+=dt1; | |
1292 | t2+=dt2; | |
1293 | ||
1294 | } | |
1295 | ||
358f16ae | 1296 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1297 | |
1298 | Double_t cs=TMath::Cos(GetAlpha()); | |
1299 | Double_t sn=TMath::Sin(GetAlpha()); | |
1300 | xthis=r1[0]*cs + r1[1]*sn; | |
1301 | ||
1302 | cs=TMath::Cos(p->GetAlpha()); | |
1303 | sn=TMath::Sin(p->GetAlpha()); | |
1304 | xp=r2[0]*cs + r2[1]*sn; | |
1305 | ||
1306 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1307 | } | |
1308 | ||
1309 | Double_t AliExternalTrackParam:: | |
1310 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1311 | //-------------------------------------------------------------- | |
1312 | // Propagates this track and the argument track to the position of the | |
1313 | // distance of closest approach. | |
1314 | // Returns the (weighed !) distance of closest approach. | |
1315 | //-------------------------------------------------------------- | |
1316 | Double_t xthis,xp; | |
1317 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1318 | ||
1319 | if (!PropagateTo(xthis,b)) { | |
1320 | //AliWarning(" propagation failed !"); | |
1321 | return 1e+33; | |
1322 | } | |
1323 | ||
1324 | if (!p->PropagateTo(xp,b)) { | |
1325 | //AliWarning(" propagation failed !"; | |
1326 | return 1e+33; | |
1327 | } | |
1328 | ||
1329 | return dca; | |
1330 | } | |
1331 | ||
1332 | ||
58e536c5 | 1333 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1334 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1335 | // |
e99a34df | 1336 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1337 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1338 | // Magnetic field is "b" (kG). | |
1339 | // | |
1340 | // a) The track gets extapolated to the DCA to the vertex. | |
1341 | // b) The impact parameters and their covariance matrix are calculated. | |
1342 | // | |
1343 | // In the case of success, the returned value is kTRUE | |
1344 | // (otherwise, it's kFALSE) | |
1345 | // | |
1346 | Double_t alpha=GetAlpha(); | |
1347 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1348 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1349 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1350 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1351 | x-=xv; y-=yv; |
1352 | ||
1353 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1354 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
f76701bf | 1355 | if (d > maxd) return kFALSE; |
1356 | ||
1357 | //Propagate to the DCA | |
2258e165 | 1358 | Double_t crv=GetC(b); |
e99a34df | 1359 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1360 | ||
bfd20868 | 1361 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1362 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
e99a34df | 1363 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1364 | else cs=1.; | |
f76701bf | 1365 | |
1366 | x = xv*cs + yv*sn; | |
1367 | yv=-xv*sn + yv*cs; xv=x; | |
1368 | ||
1369 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
266a0f9b | 1370 | |
1371 | if (dz==0) return kTRUE; | |
1372 | dz[0] = GetParameter()[0] - yv; | |
1373 | dz[1] = GetParameter()[1] - zv; | |
1374 | ||
1375 | if (covar==0) return kTRUE; | |
1376 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); | |
1377 | ||
1378 | //***** Improvements by A.Dainese | |
1379 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1380 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1381 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1382 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1383 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1384 | //***** | |
1385 | ||
1386 | return kTRUE; | |
1387 | } | |
1388 | ||
1389 | Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx, | |
1390 | Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) { | |
1391 | // | |
1392 | // Propagate this track to the DCA to vertex "vtx", | |
1393 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
1394 | // | |
1395 | // This function takes into account all three components of the magnetic | |
1396 | // field given by the b[3] arument (kG) | |
1397 | // | |
1398 | // a) The track gets extapolated to the DCA to the vertex. | |
1399 | // b) The impact parameters and their covariance matrix are calculated. | |
1400 | // | |
1401 | // In the case of success, the returned value is kTRUE | |
1402 | // (otherwise, it's kFALSE) | |
1403 | // | |
1404 | Double_t alpha=GetAlpha(); | |
1405 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1406 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
1407 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; | |
1408 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
1409 | x-=xv; y-=yv; | |
1410 | ||
1411 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1412 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
266a0f9b | 1413 | if (d > maxd) return kFALSE; |
1414 | ||
1415 | //Propagate to the DCA | |
8567bf39 | 1416 | Double_t crv=GetC(b[2]); |
1417 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
266a0f9b | 1418 | |
bfd20868 | 1419 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1420 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
266a0f9b | 1421 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1422 | else cs=1.; | |
1423 | ||
1424 | x = xv*cs + yv*sn; | |
1425 | yv=-xv*sn + yv*cs; xv=x; | |
1426 | ||
1427 | if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1428 | |
1429 | if (dz==0) return kTRUE; | |
1430 | dz[0] = GetParameter()[0] - yv; | |
1431 | dz[1] = GetParameter()[1] - zv; | |
1432 | ||
1433 | if (covar==0) return kTRUE; | |
58e536c5 | 1434 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1435 | |
1436 | //***** Improvements by A.Dainese | |
1437 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1438 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1439 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1440 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1441 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1442 | //***** | |
1443 | ||
29fbcc93 | 1444 | return kTRUE; |
f76701bf | 1445 | } |
1446 | ||
b1149664 | 1447 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1448 | //---------------------------------------------------------------- | |
1449 | // This function returns a unit vector along the track direction | |
1450 | // in the global coordinate system. | |
1451 | //---------------------------------------------------------------- | |
1452 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1453 | Double_t snp=fP[2]; | |
bfd20868 | 1454 | Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp)); |
b1149664 | 1455 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1456 | d[0]=(csp*cs - snp*sn)/norm; | |
1457 | d[1]=(snp*cs + csp*sn)/norm; | |
1458 | d[2]=fP[3]/norm; | |
1459 | } | |
1460 | ||
c683ddc2 | 1461 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1462 | //--------------------------------------------------------------------- |
1463 | // This function returns the global track momentum components | |
1464 | // Results for (nearly) straight tracks are meaningless ! | |
1465 | //--------------------------------------------------------------------- | |
1466 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1467 | return Local2GlobalMomentum(p,fAlpha); | |
1468 | } | |
a5e407e9 | 1469 | |
def9660e | 1470 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1471 | //--------------------------------------------------------------------- |
1472 | // Returns x-component of momentum | |
1473 | // Result for (nearly) straight tracks is meaningless ! | |
1474 | //--------------------------------------------------------------------- | |
def9660e | 1475 | |
957fb479 | 1476 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1477 | GetPxPyPz(p); |
1478 | ||
1479 | return p[0]; | |
1480 | } | |
1481 | ||
1482 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1483 | //--------------------------------------------------------------------- |
1484 | // Returns y-component of momentum | |
1485 | // Result for (nearly) straight tracks is meaningless ! | |
1486 | //--------------------------------------------------------------------- | |
def9660e | 1487 | |
957fb479 | 1488 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1489 | GetPxPyPz(p); |
1490 | ||
1491 | return p[1]; | |
1492 | } | |
1493 | ||
c683ddc2 | 1494 | Double_t AliExternalTrackParam::Xv() const { |
1495 | //--------------------------------------------------------------------- | |
1496 | // Returns x-component of first track point | |
1497 | //--------------------------------------------------------------------- | |
1498 | ||
1499 | Double_t r[3]={0.,0.,0.}; | |
1500 | GetXYZ(r); | |
1501 | ||
1502 | return r[0]; | |
1503 | } | |
1504 | ||
1505 | Double_t AliExternalTrackParam::Yv() const { | |
1506 | //--------------------------------------------------------------------- | |
1507 | // Returns y-component of first track point | |
1508 | //--------------------------------------------------------------------- | |
1509 | ||
1510 | Double_t r[3]={0.,0.,0.}; | |
1511 | GetXYZ(r); | |
1512 | ||
1513 | return r[1]; | |
1514 | } | |
1515 | ||
def9660e | 1516 | Double_t AliExternalTrackParam::Theta() const { |
1517 | // return theta angle of momentum | |
1518 | ||
7cdd0c20 | 1519 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1520 | } |
1521 | ||
1522 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1523 | //--------------------------------------------------------------------- |
1524 | // Returns the azimuthal angle of momentum | |
1525 | // 0 <= phi < 2*pi | |
1526 | //--------------------------------------------------------------------- | |
def9660e | 1527 | |
957fb479 | 1528 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1529 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1530 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1531 | ||
1532 | return phi; | |
def9660e | 1533 | } |
1534 | ||
1535 | Double_t AliExternalTrackParam::M() const { | |
1536 | // return particle mass | |
1537 | ||
1538 | // No mass information available so far. | |
1539 | // Redifine in derived class! | |
1540 | ||
1541 | return -999.; | |
1542 | } | |
1543 | ||
1544 | Double_t AliExternalTrackParam::E() const { | |
1545 | // return particle energy | |
1546 | ||
1547 | // No PID information available so far. | |
1548 | // Redifine in derived class! | |
1549 | ||
1550 | return -999.; | |
1551 | } | |
1552 | ||
1553 | Double_t AliExternalTrackParam::Eta() const { | |
1554 | // return pseudorapidity | |
1555 | ||
1556 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1557 | } | |
1558 | ||
1559 | Double_t AliExternalTrackParam::Y() const { | |
1560 | // return rapidity | |
1561 | ||
1562 | // No PID information available so far. | |
1563 | // Redifine in derived class! | |
1564 | ||
1565 | return -999.; | |
1566 | } | |
1567 | ||
c9ec41e8 | 1568 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1569 | //--------------------------------------------------------------------- | |
1570 | // This function returns the global track position | |
1571 | //--------------------------------------------------------------------- | |
1572 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1573 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1574 | } |
1575 | ||
c9ec41e8 | 1576 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1577 | //--------------------------------------------------------------------- | |
1578 | // This function returns the global covariance matrix of the track params | |
1579 | // | |
1580 | // Cov(x,x) ... : cv[0] | |
1581 | // Cov(y,x) ... : cv[1] cv[2] | |
1582 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1583 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1584 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1585 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1586 | // |
c9ec41e8 | 1587 | // Results for (nearly) straight tracks are meaningless ! |
1588 | //--------------------------------------------------------------------- | |
e421f556 | 1589 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1590 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1591 | return kFALSE; | |
a5e407e9 | 1592 | } |
49d13e89 | 1593 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1594 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1595 | return kFALSE; | |
1596 | } | |
1597 | Double_t pt=1./TMath::Abs(fP[4]); | |
1598 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1599 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1600 | |
1601 | Double_t m00=-sn, m10=cs; | |
1602 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1603 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1604 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1605 | ||
854d5d49 | 1606 | m43*=GetSign(); |
1607 | m44*=GetSign(); | |
1608 | m45*=GetSign(); | |
1609 | ||
c9ec41e8 | 1610 | cv[0 ] = fC[0]*m00*m00; |
1611 | cv[1 ] = fC[0]*m00*m10; | |
1612 | cv[2 ] = fC[0]*m10*m10; | |
1613 | cv[3 ] = fC[1]*m00; | |
1614 | cv[4 ] = fC[1]*m10; | |
1615 | cv[5 ] = fC[2]; | |
1616 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1617 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1618 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1619 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1620 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1621 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1622 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1623 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1624 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1625 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1626 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1627 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1628 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1629 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1630 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1631 | |
c9ec41e8 | 1632 | return kTRUE; |
51ad6848 | 1633 | } |
1634 | ||
51ad6848 | 1635 | |
c9ec41e8 | 1636 | Bool_t |
1637 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1638 | //--------------------------------------------------------------------- | |
1639 | // This function returns the global track momentum extrapolated to | |
1640 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1641 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1642 | p[0]=fP[4]; |
1530f89c | 1643 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1644 | p[2]=fP[3]; |
1645 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1646 | } |
1647 | ||
7cf7bb6c | 1648 | Bool_t |
1649 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1650 | //--------------------------------------------------------------------- | |
1651 | // This function returns the local Y-coordinate of the intersection | |
1652 | // point between this track and the reference plane "x" (cm). | |
1653 | // Magnetic field "b" (kG) | |
1654 | //--------------------------------------------------------------------- | |
1655 | Double_t dx=x-fX; | |
1656 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1657 | ||
1530f89c | 1658 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1659 | |
1660 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1661 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1662 | ||
60e55aee | 1663 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
7cf7bb6c | 1664 | y = fP[0] + dx*(f1+f2)/(r1+r2); |
1665 | return kTRUE; | |
1666 | } | |
1667 | ||
6c94f330 | 1668 | Bool_t |
1669 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1670 | //--------------------------------------------------------------------- | |
1671 | // This function returns the local Z-coordinate of the intersection | |
1672 | // point between this track and the reference plane "x" (cm). | |
1673 | // Magnetic field "b" (kG) | |
1674 | //--------------------------------------------------------------------- | |
1675 | Double_t dx=x-fX; | |
1676 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1677 | ||
2258e165 | 1678 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
6c94f330 | 1679 | |
1680 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1681 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1682 | ||
60e55aee | 1683 | Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2)); |
6c94f330 | 1684 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! |
1685 | return kTRUE; | |
1686 | } | |
1687 | ||
c9ec41e8 | 1688 | Bool_t |
1689 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1690 | //--------------------------------------------------------------------- | |
1691 | // This function returns the global track position extrapolated to | |
1692 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1693 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1694 | Double_t dx=x-fX; |
e421f556 | 1695 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1696 | ||
1530f89c | 1697 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1698 | |
e421f556 | 1699 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1700 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1701 | |
60e55aee | 1702 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
c9ec41e8 | 1703 | r[0] = x; |
1704 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
f90a11c9 | 1705 | r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter |
1706 | ||
c9ec41e8 | 1707 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1708 | } |
1709 | ||
51ad6848 | 1710 | //_____________________________________________________________________________ |
1711 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1712 | { | |
1713 | // print the parameters and the covariance matrix | |
1714 | ||
1715 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1716 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1717 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1718 | printf(" covariance: %12g\n", fC[0]); | |
1719 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1720 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1721 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1722 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1723 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1724 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1725 | } |
5b77d93c | 1726 | |
c194ba83 | 1727 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1728 | // | |
1729 | // Get sinus at given x | |
1730 | // | |
1530f89c | 1731 | Double_t crv=GetC(b); |
c194ba83 | 1732 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1733 | Double_t dx = x-fX; | |
1734 | Double_t res = fP[2]+dx*crv; | |
1735 | return res; | |
1736 | } | |
bf00ebb8 | 1737 | |
1738 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1739 | //------------------------------------------------------------------------ | |
1740 | // Get the distance between two tracks at the local position x | |
1741 | // working in the local frame of this track. | |
1742 | // Origin : Marian.Ivanov@cern.ch | |
1743 | //----------------------------------------------------------------------- | |
1744 | Double_t xyz[3]; | |
1745 | Double_t xyz2[3]; | |
1746 | xyz[0]=x; | |
1747 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1748 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1749 | // | |
1750 | // | |
1751 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1752 | xyz2[0]=x; | |
1753 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1754 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1755 | }else{ | |
1756 | // | |
1757 | Double_t xyz1[3]; | |
1758 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1759 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1760 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1761 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1762 | // | |
1763 | xyz1[0]=xyz2[0]; | |
1764 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1765 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1766 | // | |
1767 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1768 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1769 | xyz2[2] = xyz1[2]; | |
1770 | } | |
1771 | dist[0] = xyz[0]-xyz2[0]; | |
1772 | dist[1] = xyz[1]-xyz2[1]; | |
1773 | dist[2] = xyz[2]-xyz2[2]; | |
1774 | ||
1775 | return kTRUE; | |
1776 | } | |
0c19adf7 | 1777 | |
1778 | ||
1779 | // | |
1780 | // Draw functionality. | |
1781 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1782 | // | |
1783 | ||
1784 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1785 | // | |
1786 | // Draw track line | |
1787 | // | |
1788 | if (minR>maxR) return ; | |
1789 | if (stepR<=0) return ; | |
1790 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1791 | if (npoints<1) return; | |
1792 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1793 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1794 | polymarker->Draw(); | |
1795 | } | |
1796 | ||
1797 | // | |
1798 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1799 | // | |
1800 | // Fill points in the polymarker | |
1801 | // | |
1802 | Int_t counter=0; | |
1803 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1804 | Double_t point[3]; | |
1805 | GetXYZAt(r,magF,point); | |
1806 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
1807 | printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); | |
1808 | counter++; | |
1809 | } | |
1810 | } | |
0e8460af | 1811 | |
1812 | Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const { | |
1813 | // | |
1814 | Int_t min = TMath::Min(i,j); | |
1815 | Int_t max = TMath::Max(i,j); | |
1816 | ||
1817 | return min+(max+1)*max/2; | |
1818 | } | |
8b6e3369 | 1819 | |
1820 | ||
1821 | void AliExternalTrackParam::g3helx3(Double_t qfield, | |
1822 | Double_t step, | |
1823 | Double_t vect[7]) { | |
1824 | /****************************************************************** | |
1825 | * * | |
1826 | * GEANT3 tracking routine in a constant field oriented * | |
1827 | * along axis 3 * | |
1828 | * Tracking is performed with a conventional * | |
1829 | * helix step method * | |
1830 | * * | |
1831 | * Authors R.Brun, M.Hansroul ********* * | |
1832 | * Rewritten V.Perevoztchikov * | |
1833 | * * | |
1834 | * Rewritten in C++ by I.Belikov * | |
1835 | * * | |
1836 | * qfield (kG) - particle charge times magnetic field * | |
1837 | * step (cm) - step length along the helix * | |
1838 | * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p * | |
1839 | * * | |
1840 | ******************************************************************/ | |
1841 | const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6; | |
bfd20868 | 1842 | const Double_t kOvSqSix=TMath::Sqrt(1./6.); |
8b6e3369 | 1843 | |
1844 | Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz]; | |
1845 | ||
1846 | Double_t rho = qfield*kB2C/vect[ipp]; | |
1847 | Double_t tet = rho*step; | |
1848 | ||
1849 | Double_t tsint, sintt, sint, cos1t; | |
2de63fc5 | 1850 | if (TMath::Abs(tet) > 0.03) { |
8b6e3369 | 1851 | sint = TMath::Sin(tet); |
1852 | sintt = sint/tet; | |
1853 | tsint = (tet - sint)/tet; | |
1854 | Double_t t=TMath::Sin(0.5*tet); | |
1855 | cos1t = 2*t*t/tet; | |
1856 | } else { | |
1857 | tsint = tet*tet/6.; | |
bfd20868 | 1858 | sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint; |
8b6e3369 | 1859 | sint = tet*sintt; |
1860 | cos1t = 0.5*tet; | |
1861 | } | |
1862 | ||
1863 | Double_t f1 = step*sintt; | |
1864 | Double_t f2 = step*cos1t; | |
1865 | Double_t f3 = step*tsint*cosz; | |
1866 | Double_t f4 = -tet*cos1t; | |
1867 | Double_t f5 = sint; | |
1868 | ||
1869 | vect[ix] += f1*cosx - f2*cosy; | |
1870 | vect[iy] += f1*cosy + f2*cosx; | |
1871 | vect[iz] += f1*cosz + f3; | |
1872 | ||
1873 | vect[ipx] += f4*cosx - f5*cosy; | |
1874 | vect[ipy] += f4*cosy + f5*cosx; | |
1875 | ||
1876 | } | |
1877 | ||
1878 | Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) { | |
1879 | //---------------------------------------------------------------- | |
1880 | // Extrapolate this track to the plane X=xk in the field b[]. | |
1881 | // | |
1882 | // X [cm] is in the "tracking coordinate system" of this track. | |
1883 | // b[]={Bx,By,Bz} [kG] is in the Global coordidate system. | |
1884 | //---------------------------------------------------------------- | |
1885 | ||
1886 | Double_t dx=xk-fX; | |
1887 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
7e1b73dd | 1888 | if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE; |
ef3508c5 | 1889 | // Do not propagate tracks outside the ALICE detector |
1890 | if (TMath::Abs(dx)>1e5 || | |
1891 | TMath::Abs(GetY())>1e5 || | |
1892 | TMath::Abs(GetZ())>1e5) { | |
1893 | AliWarning(Form("Anomalous track, target X:%f",xk)); | |
1894 | Print(); | |
1895 | return kFALSE; | |
1896 | } | |
8b6e3369 | 1897 | |
1898 | Double_t crv=GetC(b[2]); | |
1899 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
1900 | ||
2de63fc5 | 1901 | Double_t x2r = crv*dx; |
1902 | Double_t f1=fP[2], f2=f1 + x2r; | |
8b6e3369 | 1903 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
1904 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1905 | ||
1906 | ||
1907 | // Estimate the covariance matrix | |
1908 | Double_t &fP3=fP[3], &fP4=fP[4]; | |
1909 | Double_t | |
1910 | &fC00=fC[0], | |
1911 | &fC10=fC[1], &fC11=fC[2], | |
1912 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1913 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1914 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1915 | ||
bfd20868 | 1916 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
8b6e3369 | 1917 | |
1918 | //f = F - 1 | |
1919 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
1920 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
1921 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
1922 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
1923 | Double_t f13= dx/r1; | |
1924 | Double_t f24= dx; f24*=cc; | |
1925 | ||
1926 | //b = C*ft | |
1927 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
1928 | Double_t b02=f24*fC40; | |
1929 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
1930 | Double_t b12=f24*fC41; | |
1931 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
1932 | Double_t b22=f24*fC42; | |
1933 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
1934 | Double_t b42=f24*fC44; | |
1935 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
1936 | Double_t b32=f24*fC43; | |
1937 | ||
1938 | //a = f*b = f*C*ft | |
1939 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
1940 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
1941 | Double_t a22=f24*b42; | |
1942 | ||
1943 | //F*C*Ft = C + (b + bt + a) | |
1944 | fC00 += b00 + b00 + a00; | |
1945 | fC10 += b10 + b01 + a01; | |
1946 | fC20 += b20 + b02 + a02; | |
1947 | fC30 += b30; | |
1948 | fC40 += b40; | |
1949 | fC11 += b11 + b11 + a11; | |
1950 | fC21 += b21 + b12 + a12; | |
1951 | fC31 += b31; | |
1952 | fC41 += b41; | |
1953 | fC22 += b22 + b22 + a22; | |
1954 | fC32 += b32; | |
1955 | fC42 += b42; | |
1956 | ||
86be8934 | 1957 | CheckCovariance(); |
8b6e3369 | 1958 | |
1959 | // Appoximate step length | |
2de63fc5 | 1960 | double dy2dx = (f1+f2)/(r1+r2); |
1961 | Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord | |
1962 | : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc | |
8b6e3369 | 1963 | step *= TMath::Sqrt(1.+ GetTgl()*GetTgl()); |
1964 | ||
8b6e3369 | 1965 | // Get the track's (x,y,z) and (px,py,pz) in the Global System |
1966 | Double_t r[3]; GetXYZ(r); | |
1967 | Double_t p[3]; GetPxPyPz(p); | |
1968 | Double_t pp=GetP(); | |
1969 | p[0] /= pp; | |
1970 | p[1] /= pp; | |
1971 | p[2] /= pp; | |
1972 | ||
1973 | ||
1974 | // Rotate to the system where Bx=By=0. | |
1975 | Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]); | |
1976 | Double_t cosphi=1., sinphi=0.; | |
1977 | if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;} | |
1978 | Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]); | |
1979 | Double_t costet=1., sintet=0.; | |
1980 | if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;} | |
1981 | Double_t vect[7]; | |
1982 | ||
1983 | vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2]; | |
1984 | vect[1] = -sinphi*r[0] + cosphi*r[1]; | |
1985 | vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2]; | |
1986 | ||
1987 | vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2]; | |
1988 | vect[4] = -sinphi*p[0] + cosphi*p[1]; | |
1989 | vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2]; | |
1990 | ||
1991 | vect[6] = pp; | |
1992 | ||
1993 | ||
1994 | // Do the helix step | |
1995 | g3helx3(GetSign()*bb,step,vect); | |
1996 | ||
1997 | ||
1998 | // Rotate back to the Global System | |
1999 | r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2]; | |
2000 | r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2]; | |
2001 | r[2] = -sintet*vect[0] + costet*vect[2]; | |
2002 | ||
2003 | p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5]; | |
2004 | p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5]; | |
2005 | p[2] = -sintet*vect[3] + costet*vect[5]; | |
2006 | ||
2007 | ||
2008 | // Rotate back to the Tracking System | |
2009 | Double_t cosalp = TMath::Cos(fAlpha); | |
2010 | Double_t sinalp =-TMath::Sin(fAlpha); | |
2011 | ||
2012 | Double_t | |
2013 | t = cosalp*r[0] - sinalp*r[1]; | |
2014 | r[1] = sinalp*r[0] + cosalp*r[1]; | |
2015 | r[0] = t; | |
2016 | ||
2017 | t = cosalp*p[0] - sinalp*p[1]; | |
2018 | p[1] = sinalp*p[0] + cosalp*p[1]; | |
2019 | p[0] = t; | |
2020 | ||
2021 | ||
2022 | // Do the final correcting step to the target plane (linear approximation) | |
2023 | Double_t x=r[0], y=r[1], z=r[2]; | |
2024 | if (TMath::Abs(dx) > kAlmost0) { | |
2025 | if (TMath::Abs(p[0]) < kAlmost0) return kFALSE; | |
2026 | dx = xk - r[0]; | |
2027 | x += dx; | |
2028 | y += p[1]/p[0]*dx; | |
2029 | z += p[2]/p[0]*dx; | |
2030 | } | |
2031 | ||
2032 | ||
2033 | // Calculate the track parameters | |
2034 | t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]); | |
2035 | fX = x; | |
2036 | fP[0] = y; | |
2037 | fP[1] = z; | |
2038 | fP[2] = p[1]/t; | |
2039 | fP[3] = p[2]/t; | |
2040 | fP[4] = GetSign()/(t*pp); | |
2041 | ||
2042 | return kTRUE; | |
2043 | } | |
2044 | ||
cfdb62d4 | 2045 | Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){ |
2046 | // | |
2047 | //Translation: in the event mixing, the tracks can be shifted | |
2048 | //of the difference among primary vertices (vTrasl) and | |
2049 | //the covariance matrix is changed accordingly | |
2050 | //(covV = covariance of the primary vertex). | |
2051 | //Origin: "Romita, Rossella" <R.Romita@gsi.de> | |
2052 | // | |
2053 | TVector3 translation; | |
2054 | // vTrasl coordinates in the local system | |
2055 | translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]); | |
2056 | translation.RotateZ(-fAlpha); | |
2057 | translation.GetXYZ(vTrasl); | |
2058 | ||
2059 | //compute the new x,y,z of the track | |
5a87bb3d | 2060 | Double_t newX=fX-vTrasl[0]; |
2061 | Double_t newY=fP[0]-vTrasl[1]; | |
2062 | Double_t newZ=fP[1]-vTrasl[2]; | |
cfdb62d4 | 2063 | |
2064 | //define the new parameters | |
5a87bb3d | 2065 | Double_t newParam[5]; |
2066 | newParam[0]=newY; | |
2067 | newParam[1]=newZ; | |
2068 | newParam[2]=fP[2]; | |
2069 | newParam[3]=fP[3]; | |
2070 | newParam[4]=fP[4]; | |
cfdb62d4 | 2071 | |
2072 | // recompute the covariance matrix: | |
2073 | // 1. covV in the local system | |
2074 | Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha); | |
2075 | TMatrixD qQi(3,3); | |
2076 | qQi(0,0) = cosRot; | |
2077 | qQi(0,1) = sinRot; | |
2078 | qQi(0,2) = 0.; | |
2079 | qQi(1,0) = -sinRot; | |
2080 | qQi(1,1) = cosRot; | |
2081 | qQi(1,2) = 0.; | |
2082 | qQi(2,0) = 0.; | |
2083 | qQi(2,1) = 0.; | |
2084 | qQi(2,2) = 1.; | |
2085 | TMatrixD uUi(3,3); | |
2086 | uUi(0,0) = covV[0]; | |
2087 | uUi(0,0) = covV[0]; | |
2088 | uUi(1,0) = covV[1]; | |
2089 | uUi(0,1) = covV[1]; | |
2090 | uUi(2,0) = covV[3]; | |
2091 | uUi(0,2) = covV[3]; | |
2092 | uUi(1,1) = covV[2]; | |
2093 | uUi(2,2) = covV[5]; | |
2094 | uUi(1,2) = covV[4]; | |
2095 | if(uUi.Determinant() <= 0.) {return kFALSE;} | |
2096 | TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi); | |
2097 | TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi); | |
2098 | ||
2099 | //2. compute the new covariance matrix of the track | |
2100 | Double_t sigmaXX=m(0,0); | |
2101 | Double_t sigmaXZ=m(2,0); | |
2102 | Double_t sigmaXY=m(1,0); | |
2103 | Double_t sigmaYY=GetSigmaY2()+m(1,1); | |
2104 | Double_t sigmaYZ=fC[1]+m(1,2); | |
2105 | Double_t sigmaZZ=fC[2]+m(2,2); | |
2106 | Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX); | |
2107 | Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX); | |
2108 | Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX); | |
2109 | ||
2110 | Double_t newCov[15]; | |
2111 | newCov[0]=covarianceYY; | |
2112 | newCov[1]=covarianceYZ; | |
2113 | newCov[2]=covarianceZZ; | |
2114 | for(Int_t i=3;i<15;i++){ | |
2115 | newCov[i]=fC[i]; | |
2116 | } | |
2117 | ||
2118 | // set the new parameters | |
2119 | ||
5a87bb3d | 2120 | Set(newX,fAlpha,newParam,newCov); |
cfdb62d4 | 2121 | |
2122 | return kTRUE; | |
2123 | } | |
86be8934 | 2124 | |
2125 | void AliExternalTrackParam::CheckCovariance() { | |
2126 | ||
2127 | // This function forces the diagonal elements of the covariance matrix to be positive. | |
2128 | // In case the diagonal element is bigger than the maximal allowed value, it is set to | |
2129 | // the limit and the off-diagonal elements that correspond to it are set to zero. | |
2130 | ||
2131 | fC[0] = TMath::Abs(fC[0]); | |
2132 | if (fC[0]>kC0max) { | |
2133 | fC[0] = kC0max; | |
2134 | fC[1] = 0; | |
2135 | fC[3] = 0; | |
2136 | fC[6] = 0; | |
2137 | fC[10] = 0; | |
2138 | } | |
2139 | fC[2] = TMath::Abs(fC[2]); | |
2140 | if (fC[2]>kC2max) { | |
2141 | fC[2] = kC2max; | |
2142 | fC[1] = 0; | |
2143 | fC[4] = 0; | |
2144 | fC[7] = 0; | |
2145 | fC[11] = 0; | |
2146 | } | |
2147 | fC[5] = TMath::Abs(fC[5]); | |
2148 | if (fC[5]>kC5max) { | |
2149 | fC[5] = kC5max; | |
2150 | fC[3] = 0; | |
2151 | fC[4] = 0; | |
2152 | fC[8] = 0; | |
2153 | fC[12] = 0; | |
2154 | } | |
2155 | fC[9] = TMath::Abs(fC[9]); | |
2156 | if (fC[9]>kC9max) { | |
2157 | fC[9] = kC9max; | |
2158 | fC[6] = 0; | |
2159 | fC[7] = 0; | |
2160 | fC[8] = 0; | |
2161 | fC[13] = 0; | |
2162 | } | |
2163 | fC[14] = TMath::Abs(fC[14]); | |
2164 | if (fC[14]>kC14max) { | |
2165 | fC[14] = kC14max; | |
2166 | fC[10] = 0; | |
2167 | fC[11] = 0; | |
2168 | fC[12] = 0; | |
2169 | fC[13] = 0; | |
2170 | } | |
2171 | ||
2172 | // The part below is used for tests and normally is commented out | |
2173 | // TMatrixDSym m(5); | |
2174 | // TVectorD eig(5); | |
2175 | ||
2176 | // m(0,0)=fC[0]; | |
2177 | // m(1,0)=fC[1]; m(1,1)=fC[2]; | |
2178 | // m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5]; | |
2179 | // m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9]; | |
2180 | // 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]; | |
2181 | ||
2182 | // m(0,1)=m(1,0); | |
2183 | // m(0,2)=m(2,0); m(1,2)=m(2,1); | |
2184 | // m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2); | |
2185 | // m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3); | |
2186 | // m.EigenVectors(eig); | |
2187 | ||
2188 | // // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0); | |
2189 | // if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) { | |
2190 | // AliWarning("Negative eigenvalues of the covariance matrix!"); | |
2191 | // this->Print(); | |
2192 | // eig.Print(); | |
2193 | // } | |
2194 | } |