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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 | ||
4ec1ca0f | 107 | //_____________________________________________________________________________ |
108 | void AliExternalTrackParam::CopyFromVTrack(const AliVTrack *vTrack) | |
109 | { | |
110 | // | |
111 | // Recreate TrackParams from VTrack | |
112 | // This is not a copy contructor ! | |
113 | // | |
114 | if (!vTrack) { | |
115 | AliError("Source VTrack is NULL"); | |
116 | return; | |
117 | } | |
118 | if (this==vTrack) { | |
119 | AliError("Copy of itself is requested"); | |
120 | return; | |
121 | } | |
122 | // | |
123 | if (vTrack->InheritsFrom(AliExternalTrackParam::Class())) { | |
124 | AliDebug(1,"Source itself is AliExternalTrackParam, using assignment operator"); | |
125 | *this = *(AliExternalTrackParam*)vTrack; | |
126 | return; | |
127 | } | |
128 | // | |
129 | AliVTrack::operator=( *vTrack ); | |
130 | // | |
131 | Double_t xyz[3],pxpypz[3],cv[21]; | |
132 | vTrack->GetXYZ(xyz); | |
133 | pxpypz[0]=vTrack->Px(); | |
134 | pxpypz[1]=vTrack->Py(); | |
135 | pxpypz[2]=vTrack->Pz(); | |
136 | vTrack->GetCovarianceXYZPxPyPz(cv); | |
137 | Short_t sign = (Short_t)vTrack->Charge(); | |
138 | Set(xyz,pxpypz,cv,sign); | |
139 | } | |
140 | ||
4f6e22bd | 141 | //_____________________________________________________________________________ |
142 | AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) : | |
143 | AliVTrack(), | |
144 | fX(0.), | |
145 | fAlpha(0.) | |
146 | { | |
147 | // | |
610e3088 | 148 | // Constructor from virtual track, |
149 | // This is not a copy contructor ! | |
4f6e22bd | 150 | // |
610e3088 | 151 | |
152 | if (vTrack->InheritsFrom("AliExternalTrackParam")) { | |
153 | AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !"); | |
154 | AliWarning("Calling the default constructor..."); | |
155 | AliExternalTrackParam(); | |
156 | return; | |
157 | } | |
158 | ||
892be05f | 159 | Double_t xyz[3],pxpypz[3],cv[21]; |
160 | vTrack->GetXYZ(xyz); | |
161 | pxpypz[0]=vTrack->Px(); | |
162 | pxpypz[1]=vTrack->Py(); | |
163 | pxpypz[2]=vTrack->Pz(); | |
4f6e22bd | 164 | vTrack->GetCovarianceXYZPxPyPz(cv); |
165 | Short_t sign = (Short_t)vTrack->Charge(); | |
166 | ||
167 | Set(xyz,pxpypz,cv,sign); | |
168 | } | |
169 | ||
90e48c0c | 170 | //_____________________________________________________________________________ |
da4e3deb | 171 | AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], |
172 | Double_t cv[21],Short_t sign) : | |
4f6e22bd | 173 | AliVTrack(), |
da4e3deb | 174 | fX(0.), |
175 | fAlpha(0.) | |
4f6e22bd | 176 | { |
177 | // | |
178 | // constructor from the global parameters | |
179 | // | |
180 | ||
181 | Set(xyz,pxpypz,cv,sign); | |
182 | } | |
183 | ||
d14ea120 | 184 | /* |
4f6e22bd | 185 | //_____________________________________________________________________________ |
186 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
187 | Double_t cv[21],Short_t sign) | |
da4e3deb | 188 | { |
189 | // | |
190 | // create external track parameters from the global parameters | |
191 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
192 | // A.Dainese 10.10.08 | |
193 | ||
aff56ff7 | 194 | // Calculate alpha: the rotation angle of the corresponding local system. |
195 | // | |
196 | // For global radial position inside the beam pipe, alpha is the | |
197 | // azimuthal angle of the momentum projected on (x,y). | |
198 | // | |
c99948ce | 199 | // For global radial position outside the ITS, alpha is the |
aff56ff7 | 200 | // azimuthal angle of the centre of the TPC sector in which the point |
201 | // xyz lies | |
202 | // | |
4349f5a4 | 203 | const double kSafe = 1e-5; |
aff56ff7 | 204 | Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1]; |
c99948ce | 205 | Double_t radMax = 45.; // approximately ITS outer radius |
4349f5a4 | 206 | if (radPos2 < radMax*radMax) { // inside the ITS |
aff56ff7 | 207 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); |
c99948ce | 208 | } else { // outside the ITS |
aff56ff7 | 209 | Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]); |
210 | fAlpha = | |
211 | TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10); | |
212 | } | |
4349f5a4 | 213 | // |
214 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
215 | // protection: avoid alpha being too close to 0 or +-pi/2 | |
5123be3b | 216 | if (TMath::Abs(sn)<2*kSafe) { |
217 | if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? 2*kSafe : -2*kSafe; | |
218 | else fAlpha += fAlpha>-TMath::Pi()/2. ? -2*kSafe : 2*kSafe; | |
4349f5a4 | 219 | cs=TMath::Cos(fAlpha); |
220 | sn=TMath::Sin(fAlpha); | |
221 | } | |
5123be3b | 222 | else if (TMath::Abs(cs)<2*kSafe) { |
223 | if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? 2*kSafe : -2*kSafe; | |
224 | else fAlpha += fAlpha>-TMath::Pi()/2. ? 2*kSafe : -2*kSafe; | |
4349f5a4 | 225 | cs=TMath::Cos(fAlpha); |
8defb4a0 | 226 | sn=TMath::Sin(fAlpha); |
4349f5a4 | 227 | } |
da4e3deb | 228 | // Get the vertex of origin and the momentum |
229 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
230 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
4349f5a4 | 231 | // |
232 | // avoid momenta along axis | |
233 | if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]); | |
234 | if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]); | |
da4e3deb | 235 | |
236 | // Rotate to the local coordinate system | |
237 | ver.RotateZ(-fAlpha); | |
238 | mom.RotateZ(-fAlpha); | |
239 | ||
d14ea120 | 240 | // |
da4e3deb | 241 | // x of the reference plane |
242 | fX = ver.X(); | |
243 | ||
244 | Double_t charge = (Double_t)sign; | |
245 | ||
246 | fP[0] = ver.Y(); | |
247 | fP[1] = ver.Z(); | |
248 | fP[2] = TMath::Sin(mom.Phi()); | |
249 | fP[3] = mom.Pz()/mom.Pt(); | |
250 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
d14ea120 | 251 | // |
252 | if (TMath::Abs( 1-fP[2]) < 3*kSafe) fP[2] = 1.- 3*kSafe; //Protection | |
253 | else if (TMath::Abs(-1-fP[2]) < 3*kSafe) fP[2] =-1.+ 3*kSafe; //Protection | |
254 | // | |
da4e3deb | 255 | // Covariance matrix (formulas to be simplified) |
da4e3deb | 256 | Double_t pt=1./TMath::Abs(fP[4]); |
d14ea120 | 257 | // avoid alpha+phi being to close to +-pi/2 in the cov.matrix evaluation |
258 | double fp2 = fP[2]; | |
259 | Double_t r=TMath::Sqrt((1.-fp2)*(1.+fp2)); | |
260 | // | |
da4e3deb | 261 | Double_t m00=-sn;// m10=cs; |
d14ea120 | 262 | Double_t m23=-pt*(sn + fp2*cs/r), m43=-pt*pt*(r*cs - fp2*sn); |
263 | Double_t m24= pt*(cs - fp2*sn/r), m44=-pt*pt*(r*sn + fp2*cs); | |
da4e3deb | 264 | Double_t m35=pt, m45=-pt*pt*fP[3]; |
265 | ||
266 | m43*=GetSign(); | |
267 | m44*=GetSign(); | |
268 | m45*=GetSign(); | |
269 | ||
270 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
271 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
272 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
273 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
d14ea120 | 274 | Double_t a4=cv[14]+2.*cv[9]; //cv[14]-2.*cv[9]*m24*m44/m23/m43; |
da4e3deb | 275 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; |
276 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
277 | ||
278 | fC[0 ] = cv[0 ]+cv[2 ]; | |
279 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
280 | fC[2 ] = cv[5 ]; | |
5123be3b | 281 | fC[3 ] = (cv[10]*m43-cv[6]*m44)/(m24*m43-m23*m44)/m00; |
da4e3deb | 282 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; |
283 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
5123be3b | 284 | fC[4 ] = (cv[12]*m43-cv[8]*m44)/(m24*m43-m23*m44); |
da4e3deb | 285 | fC[11] = (cv[8]-fC[4]*m23)/m43; |
286 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
5123be3b | 287 | fC[5 ] = TMath::Abs((a4*a3-a6*a1)/(a5*a3-a6*a2)); |
288 | fC[14] = TMath::Abs((a1-a2*fC[5])/a3); | |
da4e3deb | 289 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; |
290 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
291 | Double_t b2=m23*m35; | |
292 | Double_t b3=m43*m35; | |
293 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
294 | Double_t b5=m24*m35; | |
295 | Double_t b6=m44*m35; | |
296 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
297 | fC[13] = b1/b3-b2*fC[8]/b3; | |
298 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 299 | |
86be8934 | 300 | CheckCovariance(); |
301 | ||
4f6e22bd | 302 | return; |
da4e3deb | 303 | } |
d14ea120 | 304 | */ |
305 | ||
306 | //_____________________________________________________________________________ | |
307 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
308 | Double_t cv[21],Short_t sign) | |
309 | { | |
310 | // | |
311 | // create external track parameters from the global parameters | |
312 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
313 | // A.Dainese 10.10.08 | |
314 | ||
315 | // Calculate alpha: the rotation angle of the corresponding local system. | |
316 | // | |
317 | // For global radial position inside the beam pipe, alpha is the | |
318 | // azimuthal angle of the momentum projected on (x,y). | |
319 | // | |
320 | // For global radial position outside the ITS, alpha is the | |
321 | // azimuthal angle of the centre of the TPC sector in which the point | |
322 | // xyz lies | |
323 | // | |
324 | const double kSafe = 1e-5; | |
325 | Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1]; | |
326 | Double_t radMax = 45.; // approximately ITS outer radius | |
327 | if (radPos2 < radMax*radMax) { // inside the ITS | |
328 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); | |
329 | } else { // outside the ITS | |
330 | Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]); | |
331 | fAlpha = | |
332 | TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10); | |
333 | } | |
334 | // | |
335 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
336 | // protection: avoid alpha being too close to 0 or +-pi/2 | |
337 | if (TMath::Abs(sn)<2*kSafe) { | |
338 | if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? 2*kSafe : -2*kSafe; | |
339 | else fAlpha += fAlpha>-TMath::Pi()/2. ? -2*kSafe : 2*kSafe; | |
340 | cs=TMath::Cos(fAlpha); | |
341 | sn=TMath::Sin(fAlpha); | |
342 | } | |
343 | else if (TMath::Abs(cs)<2*kSafe) { | |
344 | if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? 2*kSafe : -2*kSafe; | |
345 | else fAlpha += fAlpha>-TMath::Pi()/2. ? 2*kSafe : -2*kSafe; | |
346 | cs=TMath::Cos(fAlpha); | |
347 | sn=TMath::Sin(fAlpha); | |
348 | } | |
349 | // Get the vertex of origin and the momentum | |
350 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
351 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
352 | // | |
353 | // Rotate to the local coordinate system | |
354 | ver.RotateZ(-fAlpha); | |
355 | mom.RotateZ(-fAlpha); | |
356 | ||
357 | // | |
358 | // x of the reference plane | |
359 | fX = ver.X(); | |
360 | ||
361 | Double_t charge = (Double_t)sign; | |
362 | ||
363 | fP[0] = ver.Y(); | |
364 | fP[1] = ver.Z(); | |
365 | fP[2] = TMath::Sin(mom.Phi()); | |
366 | fP[3] = mom.Pz()/mom.Pt(); | |
367 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
368 | // | |
369 | if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection | |
370 | else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection | |
371 | // | |
372 | // Covariance matrix (formulas to be simplified) | |
373 | Double_t pt=1./TMath::Abs(fP[4]); | |
374 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); | |
375 | // | |
376 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
377 | // | |
378 | Int_t special = 0; | |
379 | double sgcheck = r*sn + fP[2]*cs; | |
380 | if (TMath::Abs(sgcheck)>=1-kSafe) { // special case: lab phi is +-pi/2 | |
381 | special = 1; | |
382 | sgcheck = TMath::Sign(1.0,sgcheck); | |
383 | } | |
384 | else if (TMath::Abs(sgcheck)<kSafe) { | |
385 | sgcheck = TMath::Sign(1.0,cs); | |
386 | special = 2; // special case: lab phi is 0 | |
387 | } | |
388 | // | |
389 | fC[0 ] = cv[0 ]+cv[2 ]; | |
390 | fC[1 ] = TMath::Sign(cv34,-cv[3 ]*sn); | |
391 | fC[2 ] = cv[5 ]; | |
392 | // | |
393 | if (special==1) { | |
394 | double pti = 1./pt; | |
395 | double pti2 = pti*pti; | |
396 | int q = GetSign(); | |
397 | fC[3 ] = cv[6]*pti; | |
398 | fC[4 ] = -sgcheck*cv[8]*r*pti; | |
399 | fC[5 ] = TMath::Abs(cv[9]*r*r*pti2); | |
400 | fC[6 ] = (cv[10]*fP[3]-sgcheck*cv[15])*pti/r; | |
401 | fC[7 ] = (cv[17]-sgcheck*cv[12]*fP[3])*pti; | |
402 | fC[8 ] = (-sgcheck*cv[18]+cv[13]*fP[3])*r*pti2; | |
403 | fC[9 ] = TMath::Abs( cv[20]-2*sgcheck*cv[19]*fP[3]+cv[14]*fP[3]*fP[3])*pti2; | |
404 | fC[10] = cv[10]*pti2/r*q; | |
405 | fC[11] = -sgcheck*cv[12]*pti2*q; | |
406 | fC[12] = cv[13]*r*pti*pti2*q; | |
407 | fC[13] = (-sgcheck*cv[19]+cv[14]*fP[3])*r*pti2*pti; | |
408 | fC[14] = TMath::Abs(cv[14]*pti2*pti2); | |
409 | } else if (special==2) { | |
410 | double pti = 1./pt; | |
411 | double pti2 = pti*pti; | |
412 | int q = GetSign(); | |
413 | fC[3 ] = -cv[10]*pti*cs/sn; | |
414 | fC[4 ] = cv[12]*cs*pti; | |
415 | fC[5 ] = TMath::Abs(cv[14]*cs*cs*pti2); | |
416 | fC[6 ] = (sgcheck*cv[6]*fP[3]-cv[15])*pti/sn; | |
417 | fC[7 ] = (cv[17]-sgcheck*cv[8]*fP[3])*pti; | |
418 | fC[8 ] = (cv[19]-sgcheck*cv[13]*fP[3])*cs*pti2; | |
419 | fC[9 ] = TMath::Abs( cv[20]-2*sgcheck*cv[18]*fP[3]+cv[9]*fP[3]*fP[3])*pti2; | |
420 | fC[10] = sgcheck*cv[6]*pti2/sn*q; | |
421 | fC[11] = -sgcheck*cv[8]*pti2*q; | |
422 | fC[12] = -sgcheck*cv[13]*cs*pti*pti2*q; | |
423 | fC[13] = (-sgcheck*cv[18]+cv[9]*fP[3])*pti2*pti*q; | |
424 | fC[14] = TMath::Abs(cv[9]*pti2*pti2); | |
425 | } | |
426 | else { | |
427 | Double_t m00=-sn;// m10=cs; | |
428 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
429 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
430 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
431 | // | |
432 | m43*=GetSign(); | |
433 | m44*=GetSign(); | |
434 | m45*=GetSign(); | |
435 | // | |
436 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
437 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
438 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
439 | Double_t a4=cv[14]+2.*cv[9]; //cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
440 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
441 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
442 | // | |
443 | fC[3 ] = (cv[10]*m43-cv[6]*m44)/(m24*m43-m23*m44)/m00; | |
444 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
445 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
446 | fC[4 ] = (cv[12]*m43-cv[8]*m44)/(m24*m43-m23*m44); | |
447 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
448 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
449 | fC[5 ] = TMath::Abs((a4*a3-a6*a1)/(a5*a3-a6*a2)); | |
450 | fC[14] = TMath::Abs((a1-a2*fC[5])/a3); | |
451 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
452 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
453 | Double_t b2=m23*m35; | |
454 | Double_t b3=m43*m35; | |
455 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
456 | Double_t b5=m24*m35; | |
457 | Double_t b6=m44*m35; | |
458 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
459 | fC[13] = b1/b3-b2*fC[8]/b3; | |
460 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
461 | } | |
462 | CheckCovariance(); | |
463 | ||
464 | return; | |
465 | } | |
da4e3deb | 466 | |
51ad6848 | 467 | //_____________________________________________________________________________ |
c9ec41e8 | 468 | void AliExternalTrackParam::Reset() { |
1530f89c | 469 | // |
470 | // Resets all the parameters to 0 | |
471 | // | |
c9ec41e8 | 472 | fX=fAlpha=0.; |
473 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
474 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 475 | } |
476 | ||
3775b0ca | 477 | //_____________________________________________________________________________ |
478 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
479 | // | |
480 | // Add "something" to the track covarince matrix. | |
481 | // May be needed to account for unknown mis-calibration/mis-alignment | |
482 | // | |
483 | fC[0] +=c[0]; | |
484 | fC[1] +=c[1]; fC[2] +=c[2]; | |
485 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
486 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
487 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
86be8934 | 488 | CheckCovariance(); |
3775b0ca | 489 | } |
490 | ||
491 | ||
c9ec41e8 | 492 | Double_t AliExternalTrackParam::GetP() const { |
493 | //--------------------------------------------------------------------- | |
494 | // This function returns the track momentum | |
495 | // Results for (nearly) straight tracks are meaningless ! | |
496 | //--------------------------------------------------------------------- | |
06fb4a2f | 497 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 498 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 499 | } |
500 | ||
1d99986f | 501 | Double_t AliExternalTrackParam::Get1P() const { |
502 | //--------------------------------------------------------------------- | |
503 | // This function returns the 1/(track momentum) | |
504 | //--------------------------------------------------------------------- | |
505 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
506 | } | |
507 | ||
c9ec41e8 | 508 | //_______________________________________________________________________ |
c7bafca9 | 509 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 510 | //------------------------------------------------------------------ |
511 | // This function calculates the transverse impact parameter | |
512 | // with respect to a point with global coordinates (x,y) | |
513 | // in the magnetic field "b" (kG) | |
514 | //------------------------------------------------------------------ | |
5773defd | 515 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 516 | Double_t rp4=GetC(b); |
c9ec41e8 | 517 | |
518 | Double_t xt=fX, yt=fP[0]; | |
519 | ||
520 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
521 | Double_t a = x*cs + y*sn; | |
522 | y = -x*sn + y*cs; x=a; | |
523 | xt-=x; yt-=y; | |
524 | ||
bfd20868 | 525 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2])); |
526 | a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt); | |
1530f89c | 527 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
528 | } | |
529 | ||
530 | //_______________________________________________________________________ | |
531 | void AliExternalTrackParam:: | |
532 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
533 | //------------------------------------------------------------------ | |
534 | // This function calculates the transverse and longitudinal impact parameters | |
535 | // with respect to a point with global coordinates (x,y) | |
536 | // in the magnetic field "b" (kG) | |
537 | //------------------------------------------------------------------ | |
bfd20868 | 538 | Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1)); |
1530f89c | 539 | Double_t xt=fX, yt=fP[0]; |
540 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
541 | Double_t a = x*cs + y*sn; | |
542 | y = -x*sn + y*cs; x=a; | |
543 | xt-=x; yt-=y; | |
544 | ||
545 | Double_t rp4=GetC(b); | |
546 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
547 | dz[0] = -(xt*f1 - yt*r1); | |
548 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
549 | return; | |
550 | } | |
551 | ||
552 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
553 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
554 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
555 | dz[0] = -a/(1 + rr); | |
bfd20868 | 556 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2)); |
1530f89c | 557 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; |
51ad6848 | 558 | } |
559 | ||
49d13e89 | 560 | //_______________________________________________________________________ |
561 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
562 | //------------------------------------------------------------------ | |
563 | // This function calculates the transverse impact parameter | |
564 | // with respect to a point with global coordinates (xv,yv) | |
565 | // neglecting the track curvature. | |
566 | //------------------------------------------------------------------ | |
567 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
568 | Double_t x= xv*cs + yv*sn; | |
569 | Double_t y=-xv*sn + yv*cs; | |
570 | ||
bfd20868 | 571 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
49d13e89 | 572 | |
1530f89c | 573 | return -d; |
49d13e89 | 574 | } |
575 | ||
b8e07ed6 | 576 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx |
577 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
578 | Double_t dEdx, | |
579 | Bool_t anglecorr) { | |
116b445b | 580 | //------------------------------------------------------------------ |
581 | // This function corrects the track parameters for the crossed material. | |
582 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
2b99ff83 | 583 | // "xTimesRho" - is the product length*density (g/cm^2). |
584 | // It should be passed as negative when propagating tracks | |
585 | // from the intreaction point to the outside of the central barrel. | |
1d26da6d | 586 | // "mass" - the mass of this particle (GeV/c^2). Negative mass means charge=2 particle |
b8e07ed6 | 587 | // "dEdx" - mean enery loss (GeV/(g/cm^2) |
588 | // "anglecorr" - switch for the angular correction | |
116b445b | 589 | //------------------------------------------------------------------ |
590 | Double_t &fP2=fP[2]; | |
591 | Double_t &fP3=fP[3]; | |
592 | Double_t &fP4=fP[4]; | |
593 | ||
594 | Double_t &fC22=fC[5]; | |
595 | Double_t &fC33=fC[9]; | |
596 | Double_t &fC43=fC[13]; | |
597 | Double_t &fC44=fC[14]; | |
598 | ||
7dded1d5 | 599 | //Apply angle correction, if requested |
600 | if(anglecorr) { | |
bfd20868 | 601 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2))); |
7dded1d5 | 602 | xOverX0 *=angle; |
603 | xTimesRho *=angle; | |
604 | } | |
605 | ||
116b445b | 606 | Double_t p=GetP(); |
1d26da6d | 607 | if (mass<0) p += p; // q=2 particle |
116b445b | 608 | Double_t p2=p*p; |
609 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 610 | |
9f2bec63 | 611 | //Calculating the multiple scattering corrections****************** |
612 | Double_t cC22 = 0.; | |
613 | Double_t cC33 = 0.; | |
614 | Double_t cC43 = 0.; | |
615 | Double_t cC44 = 0.; | |
116b445b | 616 | if (xOverX0 != 0) { |
f2cef1b5 | 617 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
618 | Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0); | |
619 | if (GetUseLogTermMS()) { | |
620 | double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0)); | |
621 | if (lt>0) theta2 *= lt*lt; | |
622 | } | |
1d26da6d | 623 | if (mass<0) theta2 *= 4; // q=2 particle |
f2cef1b5 | 624 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
625 | cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3); | |
626 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
627 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
628 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
116b445b | 629 | } |
630 | ||
9f2bec63 | 631 | //Calculating the energy loss corrections************************ |
632 | Double_t cP4=1.; | |
116b445b | 633 | if ((xTimesRho != 0.) && (beta2 < 1.)) { |
b8e07ed6 | 634 | Double_t dE=dEdx*xTimesRho; |
116b445b | 635 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
636 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
76ece3d8 | 637 | if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE; |
c9038cae | 638 | cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben ! |
9f2bec63 | 639 | if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c |
4b2fa3ce | 640 | |
116b445b | 641 | |
642 | // Approximate energy loss fluctuation (M.Ivanov) | |
643 | const Double_t knst=0.07; // To be tuned. | |
644 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 645 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
116b445b | 646 | |
647 | } | |
648 | ||
9f2bec63 | 649 | //Applying the corrections***************************** |
650 | fC22 += cC22; | |
651 | fC33 += cC33; | |
652 | fC43 += cC43; | |
653 | fC44 += cC44; | |
654 | fP4 *= cP4; | |
655 | ||
86be8934 | 656 | CheckCovariance(); |
657 | ||
116b445b | 658 | return kTRUE; |
659 | } | |
660 | ||
b8e07ed6 | 661 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
662 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
663 | Bool_t anglecorr, | |
664 | Double_t (*Bethe)(Double_t)) { | |
665 | //------------------------------------------------------------------ | |
666 | // This function corrects the track parameters for the crossed material. | |
667 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
668 | // "xTimesRho" - is the product length*density (g/cm^2). | |
2b99ff83 | 669 | // It should be passed as negative when propagating tracks |
670 | // from the intreaction point to the outside of the central barrel. | |
1d26da6d | 671 | // "mass" - the mass of this particle (GeV/c^2). mass<0 means charge=2 |
b8e07ed6 | 672 | // "anglecorr" - switch for the angular correction |
673 | // "Bethe" - function calculating the energy loss (GeV/(g/cm^2)) | |
674 | //------------------------------------------------------------------ | |
37486ceb | 675 | |
b8e07ed6 | 676 | Double_t bg=GetP()/mass; |
1d26da6d | 677 | if (mass<0) { |
678 | if (mass<-990) { | |
d4da4017 | 679 | AliDebug(2,Form("Mass %f corresponds to unknown PID particle",mass)); |
1d26da6d | 680 | return kFALSE; |
681 | } | |
682 | bg = -2*bg; | |
937a4c16 | 683 | } |
b8e07ed6 | 684 | Double_t dEdx=Bethe(bg); |
1d26da6d | 685 | if (mass<0) dEdx *= 4; |
b8e07ed6 | 686 | |
687 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
688 | } | |
689 | ||
690 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA | |
691 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
692 | Double_t zOverA, | |
693 | Double_t density, | |
694 | Double_t exEnergy, | |
695 | Double_t jp1, | |
696 | Double_t jp2, | |
697 | Bool_t anglecorr) { | |
698 | //------------------------------------------------------------------ | |
699 | // This function corrects the track parameters for the crossed material | |
700 | // using the full Geant-like Bethe-Bloch formula parameterization | |
701 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
702 | // "xTimesRho" - is the product length*density (g/cm^2). | |
2b99ff83 | 703 | // It should be passed as negative when propagating tracks |
704 | // from the intreaction point to the outside of the central barrel. | |
1d26da6d | 705 | // "mass" - the mass of this particle (GeV/c^2). mass<0 means charge=2 particle |
b8e07ed6 | 706 | // "density" - mean density (g/cm^3) |
707 | // "zOverA" - mean Z/A | |
708 | // "exEnergy" - mean exitation energy (GeV) | |
709 | // "jp1" - density effect first junction point | |
710 | // "jp2" - density effect second junction point | |
711 | // "anglecorr" - switch for the angular correction | |
712 | // | |
713 | // The default values of the parameters are for silicon | |
714 | // | |
715 | //------------------------------------------------------------------ | |
716 | ||
717 | Double_t bg=GetP()/mass; | |
1d26da6d | 718 | if (mass<0) { |
719 | if (mass<-990) { | |
86a725e3 | 720 | AliDebug(2,Form("Mass %f corresponds to unknown PID particle",mass)); |
1d26da6d | 721 | return kFALSE; |
722 | } | |
723 | bg = -2*bg; | |
724 | } | |
b8e07ed6 | 725 | Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA); |
726 | ||
1d26da6d | 727 | if (mass<0) dEdx *= 4; |
b8e07ed6 | 728 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); |
729 | } | |
730 | ||
731 | ||
116b445b | 732 | |
ee5dba5e | 733 | Bool_t AliExternalTrackParam::CorrectForMaterial |
734 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 735 | //------------------------------------------------------------------ |
116b445b | 736 | // Deprecated function ! |
737 | // Better use CorrectForMeanMaterial instead of it. | |
738 | // | |
c7bafca9 | 739 | // This function corrects the track parameters for the crossed material |
740 | // "d" - the thickness (fraction of the radiation length) | |
2b99ff83 | 741 | // It should be passed as negative when propagating tracks |
742 | // from the intreaction point to the outside of the central barrel. | |
c7bafca9 | 743 | // "x0" - the radiation length (g/cm^2) |
744 | // "mass" - the mass of this particle (GeV/c^2) | |
745 | //------------------------------------------------------------------ | |
c7bafca9 | 746 | |
b8e07ed6 | 747 | return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe); |
c7bafca9 | 748 | |
c7bafca9 | 749 | } |
750 | ||
9c56b409 | 751 | Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg, |
752 | Double_t kp1, | |
753 | Double_t kp2, | |
754 | Double_t kp3, | |
755 | Double_t kp4, | |
756 | Double_t kp5) { | |
757 | // | |
758 | // This is the empirical ALEPH parameterization of the Bethe-Bloch formula. | |
759 | // It is normalized to 1 at the minimum. | |
760 | // | |
761 | // bg - beta*gamma | |
762 | // | |
763 | // The default values for the kp* parameters are for ALICE TPC. | |
764 | // The returned value is in MIP units | |
765 | // | |
766 | ||
767 | Double_t beta = bg/TMath::Sqrt(1.+ bg*bg); | |
768 | ||
769 | Double_t aa = TMath::Power(beta,kp4); | |
770 | Double_t bb = TMath::Power(1./bg,kp5); | |
771 | ||
772 | bb=TMath::Log(kp3+bb); | |
773 | ||
774 | return (kp2-aa-bb)*kp1/aa; | |
775 | } | |
776 | ||
777 | Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg, | |
778 | Double_t kp0, | |
779 | Double_t kp1, | |
780 | Double_t kp2, | |
781 | Double_t kp3, | |
782 | Double_t kp4) { | |
783 | // | |
784 | // This is the parameterization of the Bethe-Bloch formula inspired by Geant. | |
785 | // | |
786 | // bg - beta*gamma | |
787 | // kp0 - density [g/cm^3] | |
788 | // kp1 - density effect first junction point | |
789 | // kp2 - density effect second junction point | |
790 | // kp3 - mean excitation energy [GeV] | |
791 | // kp4 - mean Z/A | |
792 | // | |
793 | // The default values for the kp* parameters are for silicon. | |
794 | // The returned value is in [GeV/(g/cm^2)]. | |
795 | // | |
796 | ||
797 | const Double_t mK = 0.307075e-3; // [GeV*cm^2/g] | |
798 | const Double_t me = 0.511e-3; // [GeV/c^2] | |
799 | const Double_t rho = kp0; | |
800 | const Double_t x0 = kp1*2.303; | |
801 | const Double_t x1 = kp2*2.303; | |
802 | const Double_t mI = kp3; | |
803 | const Double_t mZA = kp4; | |
804 | const Double_t bg2 = bg*bg; | |
805 | const Double_t maxT= 2*me*bg2; // neglecting the electron mass | |
806 | ||
807 | //*** Density effect | |
808 | Double_t d2=0.; | |
809 | const Double_t x=TMath::Log(bg); | |
810 | const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI); | |
811 | if (x > x1) { | |
812 | d2 = lhwI + x - 0.5; | |
813 | } else if (x > x0) { | |
814 | const Double_t r=(x1-x)/(x1-x0); | |
815 | d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r; | |
816 | } | |
817 | ||
818 | return mK*mZA*(1+bg2)/bg2* | |
819 | (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2); | |
820 | } | |
821 | ||
d46683db | 822 | Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) { |
ee5dba5e | 823 | //------------------------------------------------------------------ |
d46683db | 824 | // This is an approximation of the Bethe-Bloch formula, |
825 | // reasonable for solid materials. | |
826 | // All the parameters are, in fact, for Si. | |
9b655cba | 827 | // The returned value is in [GeV/(g/cm^2)] |
ee5dba5e | 828 | //------------------------------------------------------------------ |
a821848c | 829 | |
9c56b409 | 830 | return BetheBlochGeant(bg); |
d46683db | 831 | } |
ee5dba5e | 832 | |
d46683db | 833 | Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) { |
834 | //------------------------------------------------------------------ | |
835 | // This is an approximation of the Bethe-Bloch formula, | |
836 | // reasonable for gas materials. | |
837 | // All the parameters are, in fact, for Ne. | |
9b655cba | 838 | // The returned value is in [GeV/(g/cm^2)] |
d46683db | 839 | //------------------------------------------------------------------ |
840 | ||
841 | const Double_t rho = 0.9e-3; | |
842 | const Double_t x0 = 2.; | |
843 | const Double_t x1 = 4.; | |
844 | const Double_t mI = 140.e-9; | |
845 | const Double_t mZA = 0.49555; | |
846 | ||
9c56b409 | 847 | return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); |
ee5dba5e | 848 | } |
849 | ||
49d13e89 | 850 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
851 | //------------------------------------------------------------------ | |
852 | // Transform this track to the local coord. system rotated | |
853 | // by angle "alpha" (rad) with respect to the global coord. system. | |
854 | //------------------------------------------------------------------ | |
dfcef74c | 855 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
856 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
857 | return kFALSE; | |
858 | } | |
859 | ||
49d13e89 | 860 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
861 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
862 | ||
863 | Double_t &fP0=fP[0]; | |
864 | Double_t &fP2=fP[2]; | |
865 | Double_t &fC00=fC[0]; | |
866 | Double_t &fC10=fC[1]; | |
867 | Double_t &fC20=fC[3]; | |
868 | Double_t &fC21=fC[4]; | |
869 | Double_t &fC22=fC[5]; | |
870 | Double_t &fC30=fC[6]; | |
871 | Double_t &fC32=fC[8]; | |
872 | Double_t &fC40=fC[10]; | |
873 | Double_t &fC42=fC[12]; | |
874 | ||
875 | Double_t x=fX; | |
876 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
bfd20868 | 877 | Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision |
07dfd570 | 878 | // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle |
879 | // direction in local frame is along the X axis | |
880 | if ((cf*ca+sf*sa)<0) { | |
1450dc8a | 881 | AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa)); |
07dfd570 | 882 | return kFALSE; |
883 | } | |
884 | // | |
dfcef74c | 885 | Double_t tmp=sf*ca - cf*sa; |
6e50abb1 | 886 | |
7248cf51 | 887 | if (TMath::Abs(tmp) >= kAlmost1) { |
888 | if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) | |
889 | AliWarning(Form("Rotation failed ! %.10e",tmp)); | |
0b69bbb2 | 890 | return kFALSE; |
891 | } | |
49d13e89 | 892 | fAlpha = alpha; |
893 | fX = x*ca + fP0*sa; | |
894 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 895 | fP2= tmp; |
49d13e89 | 896 | |
06fb4a2f | 897 | if (TMath::Abs(cf)<kAlmost0) { |
898 | AliError(Form("Too small cosine value %f",cf)); | |
899 | cf = kAlmost0; | |
900 | } | |
901 | ||
49d13e89 | 902 | Double_t rr=(ca+sf/cf*sa); |
903 | ||
904 | fC00 *= (ca*ca); | |
905 | fC10 *= ca; | |
906 | fC20 *= ca*rr; | |
907 | fC21 *= rr; | |
908 | fC22 *= rr*rr; | |
909 | fC30 *= ca; | |
910 | fC32 *= rr; | |
911 | fC40 *= ca; | |
912 | fC42 *= rr; | |
913 | ||
86be8934 | 914 | CheckCovariance(); |
915 | ||
49d13e89 | 916 | return kTRUE; |
917 | } | |
918 | ||
a251382e | 919 | //______________________________________________________ |
920 | Bool_t AliExternalTrackParam::RotateParamOnly(Double_t alpha) | |
921 | { | |
922 | // rotate to new frame, ignore covariance | |
923 | if (TMath::Abs(fP[2]) >= kAlmost1) { | |
924 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
925 | return kFALSE; | |
926 | } | |
927 | // | |
928 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); | |
929 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
930 | // | |
931 | Double_t &fP0=fP[0]; | |
932 | Double_t &fP2=fP[2]; | |
933 | // | |
934 | Double_t x=fX; | |
935 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
936 | Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision | |
937 | // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle | |
938 | // direction in local frame is along the X axis | |
939 | if ((cf*ca+sf*sa)<0) { | |
940 | AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa)); | |
941 | return kFALSE; | |
942 | } | |
943 | // | |
944 | Double_t tmp=sf*ca - cf*sa; | |
945 | ||
946 | if (TMath::Abs(tmp) >= kAlmost1) { | |
947 | if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) | |
948 | AliWarning(Form("Rotation failed ! %.10e",tmp)); | |
949 | return kFALSE; | |
950 | } | |
951 | fAlpha = alpha; | |
952 | fX = x*ca + fP0*sa; | |
953 | fP0= -x*sa + fP0*ca; | |
954 | fP2= tmp; | |
955 | return kTRUE; | |
956 | } | |
957 | ||
2d2fd909 | 958 | Bool_t AliExternalTrackParam::Invert() { |
959 | //------------------------------------------------------------------ | |
960 | // Transform this track to the local coord. system rotated by 180 deg. | |
961 | //------------------------------------------------------------------ | |
962 | fX = -fX; | |
963 | fAlpha += TMath::Pi(); | |
964 | while (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi(); | |
965 | while (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi(); | |
966 | // | |
967 | fP[0] = -fP[0]; | |
6e50abb1 | 968 | //fP[2] = -fP[2]; |
2d2fd909 | 969 | fP[3] = -fP[3]; |
970 | fP[4] = -fP[4]; | |
971 | // | |
6e50abb1 | 972 | fC[1] = -fC[1]; // since the fP1 and fP2 are not inverted, their covariances with others change sign |
973 | fC[3] = -fC[3]; | |
2d2fd909 | 974 | fC[7] = -fC[7]; |
6e50abb1 | 975 | fC[8] = -fC[8]; |
2d2fd909 | 976 | fC[11] = -fC[11]; |
6e50abb1 | 977 | fC[12] = -fC[12]; |
2d2fd909 | 978 | // |
979 | return kTRUE; | |
980 | } | |
981 | ||
49d13e89 | 982 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { |
983 | //---------------------------------------------------------------- | |
984 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
985 | //---------------------------------------------------------------- | |
49d13e89 | 986 | Double_t dx=xk-fX; |
e421f556 | 987 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 988 | |
1530f89c | 989 | Double_t crv=GetC(b); |
5773defd | 990 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
991 | ||
2de63fc5 | 992 | Double_t x2r = crv*dx; |
993 | Double_t f1=fP[2], f2=f1 + x2r; | |
bbefa4c4 | 994 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 995 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
4349f5a4 | 996 | if (TMath::Abs(fP[4])< kAlmost0) return kFALSE; |
49d13e89 | 997 | |
998 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
999 | Double_t | |
1000 | &fC00=fC[0], | |
1001 | &fC10=fC[1], &fC11=fC[2], | |
1002 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1003 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1004 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1005 | ||
bfd20868 | 1006 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
4349f5a4 | 1007 | if (TMath::Abs(r1)<kAlmost0) return kFALSE; |
1008 | if (TMath::Abs(r2)<kAlmost0) return kFALSE; | |
49d13e89 | 1009 | |
1010 | fX=xk; | |
2de63fc5 | 1011 | double dy2dx = (f1+f2)/(r1+r2); |
1012 | fP0 += dx*dy2dx; | |
0effb2c3 | 1013 | fP2 += x2r; |
1014 | if (TMath::Abs(x2r)<0.05) fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov ! | |
2de63fc5 | 1015 | else { |
1016 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
1017 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
1018 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
1019 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
0effb2c3 | 1020 | // double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one |
1021 | // double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
1022 | // fP1 += rot/crv*fP3; | |
1023 | // | |
1024 | fP1 += fP3/crv*TMath::ASin(r1*f2 - r2*f1); // more economic version from Yura. | |
2de63fc5 | 1025 | } |
49d13e89 | 1026 | |
1027 | //f = F - 1 | |
e804766b | 1028 | /* |
49d13e89 | 1029 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; |
1030 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
1031 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
1032 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
1033 | Double_t f13= dx/r1; | |
1034 | Double_t f24= dx; f24*=cc; | |
e804766b | 1035 | */ |
1036 | Double_t rinv = 1./r1; | |
1037 | Double_t r3inv = rinv*rinv*rinv; | |
1038 | Double_t f24= x2r/fP4; | |
1039 | Double_t f02= dx*r3inv; | |
1040 | Double_t f04=0.5*f24*f02; | |
1041 | Double_t f12= f02*fP3*f1; | |
1042 | Double_t f14=0.5*f24*f02*fP3*f1; | |
1043 | Double_t f13= dx*rinv; | |
1044 | ||
49d13e89 | 1045 | //b = C*ft |
1046 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
1047 | Double_t b02=f24*fC40; | |
1048 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
1049 | Double_t b12=f24*fC41; | |
1050 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
1051 | Double_t b22=f24*fC42; | |
1052 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
1053 | Double_t b42=f24*fC44; | |
1054 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
1055 | Double_t b32=f24*fC43; | |
1056 | ||
1057 | //a = f*b = f*C*ft | |
1058 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
1059 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
1060 | Double_t a22=f24*b42; | |
1061 | ||
1062 | //F*C*Ft = C + (b + bt + a) | |
1063 | fC00 += b00 + b00 + a00; | |
1064 | fC10 += b10 + b01 + a01; | |
1065 | fC20 += b20 + b02 + a02; | |
1066 | fC30 += b30; | |
1067 | fC40 += b40; | |
1068 | fC11 += b11 + b11 + a11; | |
1069 | fC21 += b21 + b12 + a12; | |
1070 | fC31 += b31; | |
1071 | fC41 += b41; | |
1072 | fC22 += b22 + b22 + a22; | |
1073 | fC32 += b32; | |
1074 | fC42 += b42; | |
1075 | ||
86be8934 | 1076 | CheckCovariance(); |
1077 | ||
49d13e89 | 1078 | return kTRUE; |
1079 | } | |
1080 | ||
599b440e | 1081 | Bool_t AliExternalTrackParam::PropagateParamOnlyTo(Double_t xk, Double_t b) { |
1082 | //---------------------------------------------------------------- | |
1083 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
1084 | // Only parameters are propagated, not the matrix. To be used for small | |
1085 | // distances only (<mm, i.e. misalignment) | |
1086 | //---------------------------------------------------------------- | |
1087 | Double_t dx=xk-fX; | |
1088 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
1089 | ||
1090 | Double_t crv=GetC(b); | |
1091 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1092 | ||
1093 | Double_t x2r = crv*dx; | |
1094 | Double_t f1=fP[2], f2=f1 + x2r; | |
1095 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1096 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1097 | if (TMath::Abs(fP[4])< kAlmost0) return kFALSE; | |
1098 | ||
1099 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); | |
1100 | if (TMath::Abs(r1)<kAlmost0) return kFALSE; | |
1101 | if (TMath::Abs(r2)<kAlmost0) return kFALSE; | |
1102 | ||
1103 | fX=xk; | |
1104 | double dy2dx = (f1+f2)/(r1+r2); | |
1105 | fP[0] += dx*dy2dx; | |
1106 | fP[1] += dx*(r2 + f2*dy2dx)*fP[3]; // Many thanks to P.Hristov ! | |
1107 | fP[2] += x2r; | |
1108 | ||
1109 | return kTRUE; | |
1110 | } | |
1111 | ||
9f2bec63 | 1112 | Bool_t |
1113 | AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) { | |
1114 | //------------------------------------------------------------------ | |
1115 | // Transform this track to the local coord. system rotated | |
1116 | // by angle "alpha" (rad) with respect to the global coord. system, | |
1117 | // and propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
1118 | //------------------------------------------------------------------ | |
1119 | ||
1120 | //Save the parameters | |
1121 | Double_t as=fAlpha; | |
1122 | Double_t xs=fX; | |
1123 | Double_t ps[5], cs[15]; | |
1124 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
1125 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
1126 | ||
1127 | if (Rotate(alpha)) | |
1128 | if (PropagateTo(x,b)) return kTRUE; | |
1129 | ||
1130 | //Restore the parameters, if the operation failed | |
1131 | fAlpha=as; | |
1132 | fX=xs; | |
1133 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
1134 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
1135 | return kFALSE; | |
1136 | } | |
1137 | ||
266a0f9b | 1138 | Bool_t AliExternalTrackParam::PropagateBxByBz |
1139 | (Double_t alpha, Double_t x, Double_t b[3]) { | |
1140 | //------------------------------------------------------------------ | |
1141 | // Transform this track to the local coord. system rotated | |
1142 | // by angle "alpha" (rad) with respect to the global coord. system, | |
1143 | // and propagate this track to the plane X=xk (cm), | |
1144 | // taking into account all three components of the B field, "b[3]" (kG) | |
1145 | //------------------------------------------------------------------ | |
1146 | ||
1147 | //Save the parameters | |
1148 | Double_t as=fAlpha; | |
1149 | Double_t xs=fX; | |
1150 | Double_t ps[5], cs[15]; | |
1151 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
1152 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
1153 | ||
1154 | if (Rotate(alpha)) | |
1155 | if (PropagateToBxByBz(x,b)) return kTRUE; | |
1156 | ||
1157 | //Restore the parameters, if the operation failed | |
1158 | fAlpha=as; | |
1159 | fX=xs; | |
1160 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
1161 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
1162 | return kFALSE; | |
1163 | } | |
1164 | ||
9f2bec63 | 1165 | |
052daaff | 1166 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
1167 | Double_t p[3], Double_t bz) const { | |
1168 | //+++++++++++++++++++++++++++++++++++++++++ | |
1169 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
1170 | // Extrapolate track along simple helix in magnetic field | |
1171 | // Arguments: len -distance alogn helix, [cm] | |
1172 | // bz - mag field, [kGaus] | |
1173 | // Returns: x and p contain extrapolated positon and momentum | |
1174 | // The momentum returned for straight-line tracks is meaningless ! | |
1175 | //+++++++++++++++++++++++++++++++++++++++++ | |
1176 | GetXYZ(x); | |
1177 | ||
2258e165 | 1178 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks |
052daaff | 1179 | Double_t unit[3]; GetDirection(unit); |
1180 | x[0]+=unit[0]*len; | |
1181 | x[1]+=unit[1]*len; | |
1182 | x[2]+=unit[2]*len; | |
1183 | ||
1184 | p[0]=unit[0]/kAlmost0; | |
1185 | p[1]=unit[1]/kAlmost0; | |
1186 | p[2]=unit[2]/kAlmost0; | |
1187 | } else { | |
1188 | GetPxPyPz(p); | |
1189 | Double_t pp=GetP(); | |
1190 | Double_t a = -kB2C*bz*GetSign(); | |
1191 | Double_t rho = a/pp; | |
1192 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
1193 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
1194 | x[2] += p[2]*len/pp; | |
1195 | ||
1196 | Double_t p0=p[0]; | |
1197 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
1198 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
1199 | } | |
1200 | } | |
1201 | ||
1202 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
1203 | Double_t bz) const { | |
1204 | //+++++++++++++++++++++++++++++++++++++++++ | |
1205 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
1206 | // Finds point of intersection (if exists) of the helix with the plane. | |
1207 | // Stores result in fX and fP. | |
1208 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
1209 | // and vector, normal to the plane | |
1210 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
1211 | //+++++++++++++++++++++++++++++++++++++++++ | |
1212 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
1213 | ||
1214 | //estimates initial helix length up to plane | |
1215 | Double_t s= | |
1216 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
1217 | Double_t dist=99999,distPrev=dist; | |
1218 | Double_t x[3],p[3]; | |
1219 | while(TMath::Abs(dist)>0.00001){ | |
1220 | //calculates helix at the distance s from x0 ALONG the helix | |
1221 | Propagate(s,x,p,bz); | |
1222 | ||
1223 | //distance between current helix position and plane | |
1224 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
1225 | ||
1226 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
1227 | distPrev=dist; | |
1228 | s-=dist; | |
1229 | } | |
1230 | //on exit pnt is intersection point,norm is track vector at that point, | |
1231 | //all in MARS | |
1232 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
1233 | return kTRUE; | |
1234 | } | |
1235 | ||
49d13e89 | 1236 | Double_t |
1237 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
1238 | //---------------------------------------------------------------- | |
1239 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
1240 | //---------------------------------------------------------------- | |
1241 | Double_t sdd = fC[0] + cov[0]; | |
1242 | Double_t sdz = fC[1] + cov[1]; | |
1243 | Double_t szz = fC[2] + cov[2]; | |
1244 | Double_t det = sdd*szz - sdz*sdz; | |
1245 | ||
1246 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
1247 | ||
1248 | Double_t d = fP[0] - p[0]; | |
1249 | Double_t z = fP[1] - p[1]; | |
1250 | ||
1251 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
1252 | } | |
1253 | ||
4b189f98 | 1254 | Double_t AliExternalTrackParam:: |
1255 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
1256 | //---------------------------------------------------------------- | |
1257 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 1258 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 1259 | // |
1260 | // Cov(x,x) ... : covxyz[0] | |
1261 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
1262 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
1263 | //---------------------------------------------------------------- | |
1264 | ||
1265 | Double_t res[3] = { | |
1266 | GetX() - p[0], | |
1267 | GetY() - p[1], | |
1268 | GetZ() - p[2] | |
1269 | }; | |
1270 | ||
1271 | Double_t f=GetSnp(); | |
1272 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
bfd20868 | 1273 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
4b189f98 | 1274 | Double_t a=f/r, b=GetTgl()/r; |
1275 | ||
1276 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
1277 | ||
1278 | TMatrixDSym v(3); | |
1279 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
1280 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
1281 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
1282 | ||
1283 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
1284 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
1285 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
1286 | ||
1287 | v.Invert(); | |
1288 | if (!v.IsValid()) return kVeryBig; | |
1289 | ||
1290 | Double_t chi2=0.; | |
1291 | for (Int_t i = 0; i < 3; i++) | |
1292 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
1293 | ||
1294 | return chi2; | |
acdfbc78 | 1295 | } |
1296 | ||
1297 | Double_t AliExternalTrackParam:: | |
1298 | GetPredictedChi2(const AliExternalTrackParam *t) const { | |
1299 | //---------------------------------------------------------------- | |
1300 | // Estimate the chi2 (5 dof) of this track with respect to the track | |
1301 | // given by the argument. | |
1302 | // The two tracks must be in the same reference system | |
1303 | // and estimated at the same reference plane. | |
1304 | //---------------------------------------------------------------- | |
1305 | ||
1306 | if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) { | |
1307 | AliError("The reference systems of the tracks differ !"); | |
1308 | return kVeryBig; | |
1309 | } | |
1310 | if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) { | |
1311 | AliError("The reference of the tracks planes differ !"); | |
1312 | return kVeryBig; | |
1313 | } | |
1314 | ||
1315 | TMatrixDSym c(5); | |
1316 | c(0,0)=GetSigmaY2(); | |
1317 | c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2(); | |
1318 | c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2(); | |
1319 | c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2(); | |
1320 | c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2(); | |
1321 | ||
1322 | c(0,0)+=t->GetSigmaY2(); | |
1323 | c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2(); | |
1324 | c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2(); | |
1325 | c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2(); | |
1326 | 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(); | |
1327 | c(0,1)=c(1,0); | |
1328 | c(0,2)=c(2,0); c(1,2)=c(2,1); | |
1329 | c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2); | |
1330 | c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3); | |
1331 | ||
1332 | c.Invert(); | |
1333 | if (!c.IsValid()) return kVeryBig; | |
1334 | ||
1335 | ||
1336 | Double_t res[5] = { | |
1337 | GetY() - t->GetY(), | |
1338 | GetZ() - t->GetZ(), | |
1339 | GetSnp() - t->GetSnp(), | |
1340 | GetTgl() - t->GetTgl(), | |
1341 | GetSigned1Pt() - t->GetSigned1Pt() | |
1342 | }; | |
4b189f98 | 1343 | |
acdfbc78 | 1344 | Double_t chi2=0.; |
1345 | for (Int_t i = 0; i < 5; i++) | |
1346 | for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j); | |
4b189f98 | 1347 | |
acdfbc78 | 1348 | return chi2; |
4b189f98 | 1349 | } |
1350 | ||
1e023a36 | 1351 | Bool_t AliExternalTrackParam:: |
1352 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
1353 | //---------------------------------------------------------------- | |
1354 | // Propagate this track to the plane | |
1355 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
1356 | // belongs to. | |
1357 | // The magnetic field is "bz" (kG) | |
1358 | // | |
1359 | // The track curvature and the change of the covariance matrix | |
1360 | // of the track parameters are negleted ! | |
1361 | // (So the "step" should be small compared with 1/curvature) | |
1362 | //---------------------------------------------------------------- | |
1363 | ||
1364 | Double_t f=GetSnp(); | |
1365 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
bfd20868 | 1366 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
1e023a36 | 1367 | Double_t a=f/r, b=GetTgl()/r; |
1368 | ||
1369 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
1370 | ||
1371 | TMatrixDSym tV(3); | |
1372 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
1373 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
1374 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
1375 | ||
1376 | TMatrixDSym pV(3); | |
1377 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
1378 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
1379 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
1380 | ||
1381 | TMatrixDSym tpV(tV); | |
1382 | tpV+=pV; | |
1383 | tpV.Invert(); | |
1384 | if (!tpV.IsValid()) return kFALSE; | |
1385 | ||
1386 | TMatrixDSym pW(3),tW(3); | |
1387 | for (Int_t i=0; i<3; i++) | |
1388 | for (Int_t j=0; j<3; j++) { | |
1389 | pW(i,j)=tW(i,j)=0.; | |
1390 | for (Int_t k=0; k<3; k++) { | |
1391 | pW(i,j) += tV(i,k)*tpV(k,j); | |
1392 | tW(i,j) += pV(i,k)*tpV(k,j); | |
1393 | } | |
1394 | } | |
1395 | ||
1396 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
1397 | ||
1398 | Double_t x=0.; | |
1399 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
1400 | Double_t crv=GetC(bz); | |
1401 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1402 | f += crv*(x-fX); | |
1403 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
1404 | fX=x; | |
1405 | ||
1406 | fP[0]=0.; | |
1407 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
1408 | fP[1]=0.; | |
1409 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
1410 | ||
1411 | return kTRUE; | |
1412 | } | |
1413 | ||
e23a38cb | 1414 | Double_t *AliExternalTrackParam::GetResiduals( |
1415 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
1416 | //------------------------------------------------------------------ | |
1417 | // Returns the track residuals with the space point "p" having | |
1418 | // the covariance matrix "cov". | |
1419 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
1420 | // otherwise they must be predicted. | |
1421 | //------------------------------------------------------------------ | |
1422 | static Double_t res[2]; | |
1423 | ||
1424 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1425 | if (updated) { | |
1426 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
1427 | } else { | |
1428 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
1429 | } | |
1430 | Double_t det=r00*r11 - r01*r01; | |
1431 | ||
1432 | if (TMath::Abs(det) < kAlmost0) return 0; | |
1433 | ||
1434 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 1435 | |
1436 | if (r00 < 0.) return 0; | |
1437 | if (r11 < 0.) return 0; | |
1438 | ||
e23a38cb | 1439 | Double_t dy = fP[0] - p[0]; |
1440 | Double_t dz = fP[1] - p[1]; | |
1441 | ||
1442 | res[0]=dy*TMath::Sqrt(r00); | |
1443 | res[1]=dz*TMath::Sqrt(r11); | |
1444 | ||
1445 | return res; | |
1446 | } | |
1447 | ||
49d13e89 | 1448 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
1449 | //------------------------------------------------------------------ | |
1450 | // Update the track parameters with the space point "p" having | |
1451 | // the covariance matrix "cov" | |
1452 | //------------------------------------------------------------------ | |
1453 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
1454 | Double_t | |
1455 | &fC00=fC[0], | |
1456 | &fC10=fC[1], &fC11=fC[2], | |
1457 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1458 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1459 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1460 | ||
1461 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1462 | r00+=fC00; r01+=fC10; r11+=fC11; | |
1463 | Double_t det=r00*r11 - r01*r01; | |
1464 | ||
1465 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
1466 | ||
1467 | ||
1468 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
1469 | ||
1470 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
1471 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
1472 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
1473 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
1474 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
1475 | ||
1476 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
1477 | Double_t sf=fP2 + k20*dy + k21*dz; | |
1478 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
1479 | ||
1480 | fP0 += k00*dy + k01*dz; | |
1481 | fP1 += k10*dy + k11*dz; | |
1482 | fP2 = sf; | |
1483 | fP3 += k30*dy + k31*dz; | |
1484 | fP4 += k40*dy + k41*dz; | |
1485 | ||
1486 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
1487 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
1488 | ||
1489 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
1490 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
1491 | fC40-=k00*c04+k01*c14; | |
1492 | ||
1493 | fC11-=k10*c01+k11*fC11; | |
1494 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
1495 | fC41-=k10*c04+k11*c14; | |
1496 | ||
1497 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
1498 | fC42-=k20*c04+k21*c14; | |
1499 | ||
1500 | fC33-=k30*c03+k31*c13; | |
1501 | fC43-=k30*c04+k31*c14; | |
599b440e | 1502 | |
49d13e89 | 1503 | fC44-=k40*c04+k41*c14; |
1504 | ||
86be8934 | 1505 | CheckCovariance(); |
1506 | ||
49d13e89 | 1507 | return kTRUE; |
1508 | } | |
1509 | ||
c7bafca9 | 1510 | void |
1511 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
1512 | //-------------------------------------------------------------------- | |
1513 | // External track parameters -> helix parameters | |
1514 | // "b" - magnetic field (kG) | |
1515 | //-------------------------------------------------------------------- | |
1516 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1517 | ||
1530f89c | 1518 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 1519 | |
1520 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
1521 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
1522 | //hlx[1]= // z0 | |
1523 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
1524 | //hlx[3]= // tgl | |
1530f89c | 1525 | hlx[4]=GetC(b); // C |
c7bafca9 | 1526 | } |
1527 | ||
1528 | ||
1529 | static void Evaluate(const Double_t *h, Double_t t, | |
1530 | Double_t r[3], //radius vector | |
1531 | Double_t g[3], //first defivatives | |
1532 | Double_t gg[3]) //second derivatives | |
1533 | { | |
1534 | //-------------------------------------------------------------------- | |
1535 | // Calculate position of a point on a track and some derivatives | |
1536 | //-------------------------------------------------------------------- | |
1537 | Double_t phase=h[4]*t+h[2]; | |
1538 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
1539 | ||
ba4550c4 | 1540 | r[0] = h[5]; |
1541 | r[1] = h[0]; | |
1542 | if (TMath::Abs(h[4])>kAlmost0) { | |
1543 | r[0] += (sn - h[6])/h[4]; | |
1544 | r[1] -= (cs - h[7])/h[4]; | |
1545 | } | |
c7bafca9 | 1546 | r[2] = h[1] + h[3]*t; |
1547 | ||
1548 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
1549 | ||
1550 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
1551 | } | |
1552 | ||
1553 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
1554 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
1555 | //------------------------------------------------------------ | |
1556 | // Returns the (weighed !) distance of closest approach between | |
1557 | // this track and the track "p". | |
1558 | // Other returned values: | |
1559 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
1560 | //----------------------------------------------------------- | |
1561 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
1562 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
1563 | Double_t dx2=dy2; | |
1564 | ||
c7bafca9 | 1565 | Double_t p1[8]; GetHelixParameters(p1,b); |
1566 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
1567 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
1568 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
1569 | ||
1570 | ||
1571 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
1572 | Evaluate(p1,t1,r1,g1,gg1); | |
1573 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
1574 | Evaluate(p2,t2,r2,g2,gg2); | |
1575 | ||
1576 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
1577 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1578 | ||
1579 | Int_t max=27; | |
1580 | while (max--) { | |
1581 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
1582 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
1583 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
1584 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
1585 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
1586 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
1587 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
1588 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
1589 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
1590 | ||
1591 | Double_t det=h11*h22-h12*h12; | |
1592 | ||
1593 | Double_t dt1,dt2; | |
1594 | if (TMath::Abs(det)<1.e-33) { | |
1595 | //(quasi)singular Hessian | |
1596 | dt1=-gt1; dt2=-gt2; | |
1597 | } else { | |
1598 | dt1=-(gt1*h22 - gt2*h12)/det; | |
1599 | dt2=-(h11*gt2 - h12*gt1)/det; | |
1600 | } | |
1601 | ||
1602 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
1603 | ||
1604 | //check delta(phase1) ? | |
1605 | //check delta(phase2) ? | |
1606 | ||
1607 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
1608 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
1609 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 1610 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 1611 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
1612 | if (lmb < 0.) | |
358f16ae | 1613 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 1614 | break; |
1615 | } | |
1616 | ||
1617 | Double_t dd=dm; | |
1618 | for (Int_t div=1 ; ; div*=2) { | |
1619 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
1620 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
1621 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
1622 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1623 | if (dd<dm) break; | |
1624 | dt1*=0.5; dt2*=0.5; | |
1625 | if (div>512) { | |
358f16ae | 1626 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 1627 | } |
1628 | } | |
1629 | dm=dd; | |
1630 | ||
1631 | t1+=dt1; | |
1632 | t2+=dt2; | |
1633 | ||
1634 | } | |
1635 | ||
358f16ae | 1636 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1637 | |
1638 | Double_t cs=TMath::Cos(GetAlpha()); | |
1639 | Double_t sn=TMath::Sin(GetAlpha()); | |
1640 | xthis=r1[0]*cs + r1[1]*sn; | |
1641 | ||
1642 | cs=TMath::Cos(p->GetAlpha()); | |
1643 | sn=TMath::Sin(p->GetAlpha()); | |
1644 | xp=r2[0]*cs + r2[1]*sn; | |
1645 | ||
1646 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1647 | } | |
1648 | ||
1649 | Double_t AliExternalTrackParam:: | |
1650 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1651 | //-------------------------------------------------------------- | |
1652 | // Propagates this track and the argument track to the position of the | |
1653 | // distance of closest approach. | |
1654 | // Returns the (weighed !) distance of closest approach. | |
1655 | //-------------------------------------------------------------- | |
1656 | Double_t xthis,xp; | |
1657 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1658 | ||
1659 | if (!PropagateTo(xthis,b)) { | |
1660 | //AliWarning(" propagation failed !"); | |
1661 | return 1e+33; | |
1662 | } | |
1663 | ||
1664 | if (!p->PropagateTo(xp,b)) { | |
1665 | //AliWarning(" propagation failed !"; | |
1666 | return 1e+33; | |
1667 | } | |
1668 | ||
1669 | return dca; | |
1670 | } | |
1671 | ||
1672 | ||
58e536c5 | 1673 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1674 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1675 | // |
e99a34df | 1676 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1677 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1678 | // Magnetic field is "b" (kG). | |
1679 | // | |
1680 | // a) The track gets extapolated to the DCA to the vertex. | |
1681 | // b) The impact parameters and their covariance matrix are calculated. | |
1682 | // | |
1683 | // In the case of success, the returned value is kTRUE | |
1684 | // (otherwise, it's kFALSE) | |
1685 | // | |
1686 | Double_t alpha=GetAlpha(); | |
1687 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1688 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1689 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1690 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1691 | x-=xv; y-=yv; |
1692 | ||
1693 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1694 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
f76701bf | 1695 | if (d > maxd) return kFALSE; |
1696 | ||
1697 | //Propagate to the DCA | |
2258e165 | 1698 | Double_t crv=GetC(b); |
e99a34df | 1699 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1700 | ||
bfd20868 | 1701 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1702 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
e99a34df | 1703 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1704 | else cs=1.; | |
f76701bf | 1705 | |
1706 | x = xv*cs + yv*sn; | |
1707 | yv=-xv*sn + yv*cs; xv=x; | |
1708 | ||
1709 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
266a0f9b | 1710 | |
1711 | if (dz==0) return kTRUE; | |
1712 | dz[0] = GetParameter()[0] - yv; | |
1713 | dz[1] = GetParameter()[1] - zv; | |
1714 | ||
1715 | if (covar==0) return kTRUE; | |
1716 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); | |
1717 | ||
1718 | //***** Improvements by A.Dainese | |
1719 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1720 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1721 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1722 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1723 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1724 | //***** | |
1725 | ||
1726 | return kTRUE; | |
1727 | } | |
1728 | ||
1729 | Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx, | |
1730 | Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) { | |
1731 | // | |
1732 | // Propagate this track to the DCA to vertex "vtx", | |
1733 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
1734 | // | |
1735 | // This function takes into account all three components of the magnetic | |
1736 | // field given by the b[3] arument (kG) | |
1737 | // | |
1738 | // a) The track gets extapolated to the DCA to the vertex. | |
1739 | // b) The impact parameters and their covariance matrix are calculated. | |
1740 | // | |
1741 | // In the case of success, the returned value is kTRUE | |
1742 | // (otherwise, it's kFALSE) | |
1743 | // | |
1744 | Double_t alpha=GetAlpha(); | |
1745 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1746 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
1747 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; | |
1748 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
1749 | x-=xv; y-=yv; | |
1750 | ||
1751 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1752 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
266a0f9b | 1753 | if (d > maxd) return kFALSE; |
1754 | ||
1755 | //Propagate to the DCA | |
8567bf39 | 1756 | Double_t crv=GetC(b[2]); |
1757 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
266a0f9b | 1758 | |
bfd20868 | 1759 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1760 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
266a0f9b | 1761 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1762 | else cs=1.; | |
1763 | ||
1764 | x = xv*cs + yv*sn; | |
1765 | yv=-xv*sn + yv*cs; xv=x; | |
1766 | ||
1767 | if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1768 | |
1769 | if (dz==0) return kTRUE; | |
1770 | dz[0] = GetParameter()[0] - yv; | |
1771 | dz[1] = GetParameter()[1] - zv; | |
1772 | ||
1773 | if (covar==0) return kTRUE; | |
58e536c5 | 1774 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1775 | |
1776 | //***** Improvements by A.Dainese | |
1777 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1778 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1779 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1780 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1781 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1782 | //***** | |
1783 | ||
29fbcc93 | 1784 | return kTRUE; |
f76701bf | 1785 | } |
1786 | ||
b1149664 | 1787 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1788 | //---------------------------------------------------------------- | |
1789 | // This function returns a unit vector along the track direction | |
1790 | // in the global coordinate system. | |
1791 | //---------------------------------------------------------------- | |
1792 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1793 | Double_t snp=fP[2]; | |
bfd20868 | 1794 | Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp)); |
b1149664 | 1795 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1796 | d[0]=(csp*cs - snp*sn)/norm; | |
1797 | d[1]=(snp*cs + csp*sn)/norm; | |
1798 | d[2]=fP[3]/norm; | |
1799 | } | |
1800 | ||
c683ddc2 | 1801 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1802 | //--------------------------------------------------------------------- |
1803 | // This function returns the global track momentum components | |
1804 | // Results for (nearly) straight tracks are meaningless ! | |
1805 | //--------------------------------------------------------------------- | |
1806 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1807 | return Local2GlobalMomentum(p,fAlpha); | |
1808 | } | |
a5e407e9 | 1809 | |
def9660e | 1810 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1811 | //--------------------------------------------------------------------- |
1812 | // Returns x-component of momentum | |
1813 | // Result for (nearly) straight tracks is meaningless ! | |
1814 | //--------------------------------------------------------------------- | |
def9660e | 1815 | |
957fb479 | 1816 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1817 | GetPxPyPz(p); |
1818 | ||
1819 | return p[0]; | |
1820 | } | |
1821 | ||
1822 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1823 | //--------------------------------------------------------------------- |
1824 | // Returns y-component of momentum | |
1825 | // Result for (nearly) straight tracks is meaningless ! | |
1826 | //--------------------------------------------------------------------- | |
def9660e | 1827 | |
957fb479 | 1828 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1829 | GetPxPyPz(p); |
1830 | ||
1831 | return p[1]; | |
1832 | } | |
1833 | ||
c683ddc2 | 1834 | Double_t AliExternalTrackParam::Xv() const { |
1835 | //--------------------------------------------------------------------- | |
1836 | // Returns x-component of first track point | |
1837 | //--------------------------------------------------------------------- | |
1838 | ||
1839 | Double_t r[3]={0.,0.,0.}; | |
1840 | GetXYZ(r); | |
1841 | ||
1842 | return r[0]; | |
1843 | } | |
1844 | ||
1845 | Double_t AliExternalTrackParam::Yv() const { | |
1846 | //--------------------------------------------------------------------- | |
1847 | // Returns y-component of first track point | |
1848 | //--------------------------------------------------------------------- | |
1849 | ||
1850 | Double_t r[3]={0.,0.,0.}; | |
1851 | GetXYZ(r); | |
1852 | ||
1853 | return r[1]; | |
1854 | } | |
1855 | ||
def9660e | 1856 | Double_t AliExternalTrackParam::Theta() const { |
1857 | // return theta angle of momentum | |
1858 | ||
7cdd0c20 | 1859 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1860 | } |
1861 | ||
1862 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1863 | //--------------------------------------------------------------------- |
1864 | // Returns the azimuthal angle of momentum | |
1865 | // 0 <= phi < 2*pi | |
1866 | //--------------------------------------------------------------------- | |
def9660e | 1867 | |
957fb479 | 1868 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1869 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1870 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1871 | ||
1872 | return phi; | |
def9660e | 1873 | } |
1874 | ||
1875 | Double_t AliExternalTrackParam::M() const { | |
1876 | // return particle mass | |
1877 | ||
1878 | // No mass information available so far. | |
1879 | // Redifine in derived class! | |
1880 | ||
1881 | return -999.; | |
1882 | } | |
1883 | ||
1884 | Double_t AliExternalTrackParam::E() const { | |
1885 | // return particle energy | |
1886 | ||
1887 | // No PID information available so far. | |
1888 | // Redifine in derived class! | |
1889 | ||
1890 | return -999.; | |
1891 | } | |
1892 | ||
1893 | Double_t AliExternalTrackParam::Eta() const { | |
1894 | // return pseudorapidity | |
1895 | ||
1896 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1897 | } | |
1898 | ||
1899 | Double_t AliExternalTrackParam::Y() const { | |
1900 | // return rapidity | |
1901 | ||
1902 | // No PID information available so far. | |
1903 | // Redifine in derived class! | |
1904 | ||
1905 | return -999.; | |
1906 | } | |
1907 | ||
c9ec41e8 | 1908 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1909 | //--------------------------------------------------------------------- | |
1910 | // This function returns the global track position | |
1911 | //--------------------------------------------------------------------- | |
1912 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1913 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1914 | } |
1915 | ||
c9ec41e8 | 1916 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1917 | //--------------------------------------------------------------------- | |
1918 | // This function returns the global covariance matrix of the track params | |
1919 | // | |
1920 | // Cov(x,x) ... : cv[0] | |
1921 | // Cov(y,x) ... : cv[1] cv[2] | |
1922 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1923 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1924 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1925 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1926 | // |
c9ec41e8 | 1927 | // Results for (nearly) straight tracks are meaningless ! |
1928 | //--------------------------------------------------------------------- | |
e421f556 | 1929 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1930 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1931 | return kFALSE; | |
a5e407e9 | 1932 | } |
49d13e89 | 1933 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1934 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1935 | return kFALSE; | |
1936 | } | |
1937 | Double_t pt=1./TMath::Abs(fP[4]); | |
1938 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1939 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1940 | |
1941 | Double_t m00=-sn, m10=cs; | |
1942 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1943 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1944 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1945 | ||
854d5d49 | 1946 | m43*=GetSign(); |
1947 | m44*=GetSign(); | |
1948 | m45*=GetSign(); | |
1949 | ||
c9ec41e8 | 1950 | cv[0 ] = fC[0]*m00*m00; |
1951 | cv[1 ] = fC[0]*m00*m10; | |
1952 | cv[2 ] = fC[0]*m10*m10; | |
1953 | cv[3 ] = fC[1]*m00; | |
1954 | cv[4 ] = fC[1]*m10; | |
1955 | cv[5 ] = fC[2]; | |
1956 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1957 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1958 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1959 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1960 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1961 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1962 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1963 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1964 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1965 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1966 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1967 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1968 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1969 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1970 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1971 | |
c9ec41e8 | 1972 | return kTRUE; |
51ad6848 | 1973 | } |
1974 | ||
51ad6848 | 1975 | |
c9ec41e8 | 1976 | Bool_t |
1977 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1978 | //--------------------------------------------------------------------- | |
1979 | // This function returns the global track momentum extrapolated to | |
1980 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1981 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1982 | p[0]=fP[4]; |
1530f89c | 1983 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1984 | p[2]=fP[3]; |
1985 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1986 | } |
1987 | ||
7cf7bb6c | 1988 | Bool_t |
1989 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1990 | //--------------------------------------------------------------------- | |
1991 | // This function returns the local Y-coordinate of the intersection | |
1992 | // point between this track and the reference plane "x" (cm). | |
1993 | // Magnetic field "b" (kG) | |
1994 | //--------------------------------------------------------------------- | |
1995 | Double_t dx=x-fX; | |
1996 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1997 | ||
1530f89c | 1998 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1999 | |
2000 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
2001 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
2002 | ||
60e55aee | 2003 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
7cf7bb6c | 2004 | y = fP[0] + dx*(f1+f2)/(r1+r2); |
2005 | return kTRUE; | |
2006 | } | |
2007 | ||
6c94f330 | 2008 | Bool_t |
2009 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
2010 | //--------------------------------------------------------------------- | |
2011 | // This function returns the local Z-coordinate of the intersection | |
2012 | // point between this track and the reference plane "x" (cm). | |
2013 | // Magnetic field "b" (kG) | |
2014 | //--------------------------------------------------------------------- | |
2015 | Double_t dx=x-fX; | |
2016 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
2017 | ||
71cec41f | 2018 | Double_t crv=GetC(b); |
2019 | Double_t x2r = crv*dx; | |
2020 | Double_t f1=fP[2], f2=f1 + x2r; | |
6c94f330 | 2021 | |
2022 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
2023 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
2024 | ||
60e55aee | 2025 | Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2)); |
71cec41f | 2026 | double dy2dx = (f1+f2)/(r1+r2); |
2027 | if (TMath::Abs(x2r)<0.05) { | |
2028 | z = fP[1] + dx*(r2 + f2*dy2dx)*fP[3]; // Many thanks to P.Hristov ! | |
2029 | } | |
2030 | else { | |
2031 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
2032 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
2033 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
2034 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
2035 | // Similarly, the rotation angle in linear in dx only for dx<<R | |
2036 | double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one | |
2037 | double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
2038 | z = fP[1] + rot/crv*fP[3]; | |
2039 | } | |
6c94f330 | 2040 | return kTRUE; |
2041 | } | |
2042 | ||
c9ec41e8 | 2043 | Bool_t |
2044 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
2045 | //--------------------------------------------------------------------- | |
2046 | // This function returns the global track position extrapolated to | |
2047 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
2048 | //--------------------------------------------------------------------- | |
c9ec41e8 | 2049 | Double_t dx=x-fX; |
e421f556 | 2050 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
2051 | ||
71cec41f | 2052 | Double_t crv=GetC(b); |
2053 | Double_t x2r = crv*dx; | |
2054 | Double_t f1=fP[2], f2=f1 + dx*crv; | |
c9ec41e8 | 2055 | |
e421f556 | 2056 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 2057 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 2058 | |
60e55aee | 2059 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
71cec41f | 2060 | double dy2dx = (f1+f2)/(r1+r2); |
c9ec41e8 | 2061 | r[0] = x; |
71cec41f | 2062 | r[1] = fP[0] + dx*dy2dx; |
2063 | if (TMath::Abs(x2r)<0.05) { | |
2064 | r[2] = fP[1] + dx*(r2 + f2*dy2dx)*fP[3];//Thanks to Andrea & Peter | |
2065 | } | |
2066 | else { | |
2067 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
2068 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
2069 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
2070 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
2071 | // Similarly, the rotation angle in linear in dx only for dx<<R | |
2072 | double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one | |
2073 | double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
2074 | r[2] = fP[1] + rot/crv*fP[3]; | |
2075 | } | |
f90a11c9 | 2076 | |
c9ec41e8 | 2077 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 2078 | } |
2079 | ||
51ad6848 | 2080 | //_____________________________________________________________________________ |
2081 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
2082 | { | |
2083 | // print the parameters and the covariance matrix | |
2084 | ||
2085 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
2086 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 2087 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
2088 | printf(" covariance: %12g\n", fC[0]); | |
2089 | printf(" %12g %12g\n", fC[1], fC[2]); | |
2090 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 2091 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 2092 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 2093 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 2094 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 2095 | } |
5b77d93c | 2096 | |
c194ba83 | 2097 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
2098 | // | |
2099 | // Get sinus at given x | |
2100 | // | |
1530f89c | 2101 | Double_t crv=GetC(b); |
c194ba83 | 2102 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
2103 | Double_t dx = x-fX; | |
2104 | Double_t res = fP[2]+dx*crv; | |
2105 | return res; | |
2106 | } | |
bf00ebb8 | 2107 | |
2108 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
2109 | //------------------------------------------------------------------------ | |
2110 | // Get the distance between two tracks at the local position x | |
2111 | // working in the local frame of this track. | |
2112 | // Origin : Marian.Ivanov@cern.ch | |
2113 | //----------------------------------------------------------------------- | |
2114 | Double_t xyz[3]; | |
2115 | Double_t xyz2[3]; | |
2116 | xyz[0]=x; | |
2117 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
2118 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
2119 | // | |
2120 | // | |
2121 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
2122 | xyz2[0]=x; | |
2123 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
2124 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
2125 | }else{ | |
2126 | // | |
2127 | Double_t xyz1[3]; | |
2128 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
2129 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
2130 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
2131 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
2132 | // | |
2133 | xyz1[0]=xyz2[0]; | |
2134 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
2135 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
2136 | // | |
2137 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
2138 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
2139 | xyz2[2] = xyz1[2]; | |
2140 | } | |
2141 | dist[0] = xyz[0]-xyz2[0]; | |
2142 | dist[1] = xyz[1]-xyz2[1]; | |
2143 | dist[2] = xyz[2]-xyz2[2]; | |
2144 | ||
2145 | return kTRUE; | |
2146 | } | |
0c19adf7 | 2147 | |
2148 | ||
2149 | // | |
2150 | // Draw functionality. | |
2151 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
2152 | // | |
2153 | ||
2154 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
2155 | // | |
2156 | // Draw track line | |
2157 | // | |
2158 | if (minR>maxR) return ; | |
2159 | if (stepR<=0) return ; | |
2160 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
2161 | if (npoints<1) return; | |
2162 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
2163 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
2164 | polymarker->Draw(); | |
2165 | } | |
2166 | ||
2167 | // | |
2168 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
2169 | // | |
2170 | // Fill points in the polymarker | |
2171 | // | |
2172 | Int_t counter=0; | |
2173 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
2174 | Double_t point[3]; | |
2175 | GetXYZAt(r,magF,point); | |
2176 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
047640da | 2177 | // printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); |
0c19adf7 | 2178 | counter++; |
2179 | } | |
2180 | } | |
0e8460af | 2181 | |
2182 | Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const { | |
2183 | // | |
2184 | Int_t min = TMath::Min(i,j); | |
2185 | Int_t max = TMath::Max(i,j); | |
2186 | ||
2187 | return min+(max+1)*max/2; | |
2188 | } | |
8b6e3369 | 2189 | |
2190 | ||
2191 | void AliExternalTrackParam::g3helx3(Double_t qfield, | |
2192 | Double_t step, | |
2193 | Double_t vect[7]) { | |
2194 | /****************************************************************** | |
2195 | * * | |
2196 | * GEANT3 tracking routine in a constant field oriented * | |
2197 | * along axis 3 * | |
2198 | * Tracking is performed with a conventional * | |
2199 | * helix step method * | |
2200 | * * | |
2201 | * Authors R.Brun, M.Hansroul ********* * | |
2202 | * Rewritten V.Perevoztchikov * | |
2203 | * * | |
2204 | * Rewritten in C++ by I.Belikov * | |
2205 | * * | |
2206 | * qfield (kG) - particle charge times magnetic field * | |
2207 | * step (cm) - step length along the helix * | |
2208 | * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p * | |
2209 | * * | |
2210 | ******************************************************************/ | |
2211 | const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6; | |
bfd20868 | 2212 | const Double_t kOvSqSix=TMath::Sqrt(1./6.); |
8b6e3369 | 2213 | |
2214 | Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz]; | |
2215 | ||
2216 | Double_t rho = qfield*kB2C/vect[ipp]; | |
2217 | Double_t tet = rho*step; | |
2218 | ||
2219 | Double_t tsint, sintt, sint, cos1t; | |
2de63fc5 | 2220 | if (TMath::Abs(tet) > 0.03) { |
8b6e3369 | 2221 | sint = TMath::Sin(tet); |
2222 | sintt = sint/tet; | |
2223 | tsint = (tet - sint)/tet; | |
2224 | Double_t t=TMath::Sin(0.5*tet); | |
2225 | cos1t = 2*t*t/tet; | |
2226 | } else { | |
2227 | tsint = tet*tet/6.; | |
bfd20868 | 2228 | sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint; |
8b6e3369 | 2229 | sint = tet*sintt; |
2230 | cos1t = 0.5*tet; | |
2231 | } | |
2232 | ||
2233 | Double_t f1 = step*sintt; | |
2234 | Double_t f2 = step*cos1t; | |
2235 | Double_t f3 = step*tsint*cosz; | |
2236 | Double_t f4 = -tet*cos1t; | |
2237 | Double_t f5 = sint; | |
2238 | ||
2239 | vect[ix] += f1*cosx - f2*cosy; | |
2240 | vect[iy] += f1*cosy + f2*cosx; | |
2241 | vect[iz] += f1*cosz + f3; | |
2242 | ||
2243 | vect[ipx] += f4*cosx - f5*cosy; | |
2244 | vect[ipy] += f4*cosy + f5*cosx; | |
2245 | ||
2246 | } | |
2247 | ||
2248 | Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) { | |
2249 | //---------------------------------------------------------------- | |
2250 | // Extrapolate this track to the plane X=xk in the field b[]. | |
2251 | // | |
2252 | // X [cm] is in the "tracking coordinate system" of this track. | |
2253 | // b[]={Bx,By,Bz} [kG] is in the Global coordidate system. | |
2254 | //---------------------------------------------------------------- | |
2255 | ||
2256 | Double_t dx=xk-fX; | |
2257 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
7e1b73dd | 2258 | if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE; |
ef3508c5 | 2259 | // Do not propagate tracks outside the ALICE detector |
2260 | if (TMath::Abs(dx)>1e5 || | |
2261 | TMath::Abs(GetY())>1e5 || | |
2262 | TMath::Abs(GetZ())>1e5) { | |
2263 | AliWarning(Form("Anomalous track, target X:%f",xk)); | |
2264 | Print(); | |
2265 | return kFALSE; | |
2266 | } | |
8b6e3369 | 2267 | |
2268 | Double_t crv=GetC(b[2]); | |
2269 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
2270 | ||
2de63fc5 | 2271 | Double_t x2r = crv*dx; |
2272 | Double_t f1=fP[2], f2=f1 + x2r; | |
8b6e3369 | 2273 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
2274 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
2275 | ||
2276 | ||
2277 | // Estimate the covariance matrix | |
2278 | Double_t &fP3=fP[3], &fP4=fP[4]; | |
2279 | Double_t | |
2280 | &fC00=fC[0], | |
2281 | &fC10=fC[1], &fC11=fC[2], | |
2282 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
2283 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
2284 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
2285 | ||
bfd20868 | 2286 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
8b6e3369 | 2287 | |
2288 | //f = F - 1 | |
e804766b | 2289 | /* |
8b6e3369 | 2290 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; |
2291 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
2292 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
2293 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
2294 | Double_t f13= dx/r1; | |
2295 | Double_t f24= dx; f24*=cc; | |
e804766b | 2296 | */ |
2297 | Double_t rinv = 1./r1; | |
2298 | Double_t r3inv = rinv*rinv*rinv; | |
2299 | Double_t f24= x2r/fP4; | |
2300 | Double_t f02= dx*r3inv; | |
2301 | Double_t f04=0.5*f24*f02; | |
2302 | Double_t f12= f02*fP3*f1; | |
2303 | Double_t f14=0.5*f24*f02*fP3*f1; | |
2304 | Double_t f13= dx*rinv; | |
2305 | ||
8b6e3369 | 2306 | //b = C*ft |
2307 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
2308 | Double_t b02=f24*fC40; | |
2309 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
2310 | Double_t b12=f24*fC41; | |
2311 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
2312 | Double_t b22=f24*fC42; | |
2313 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
2314 | Double_t b42=f24*fC44; | |
2315 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
2316 | Double_t b32=f24*fC43; | |
2317 | ||
2318 | //a = f*b = f*C*ft | |
2319 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
2320 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
2321 | Double_t a22=f24*b42; | |
2322 | ||
2323 | //F*C*Ft = C + (b + bt + a) | |
2324 | fC00 += b00 + b00 + a00; | |
2325 | fC10 += b10 + b01 + a01; | |
2326 | fC20 += b20 + b02 + a02; | |
2327 | fC30 += b30; | |
2328 | fC40 += b40; | |
2329 | fC11 += b11 + b11 + a11; | |
2330 | fC21 += b21 + b12 + a12; | |
2331 | fC31 += b31; | |
2332 | fC41 += b41; | |
2333 | fC22 += b22 + b22 + a22; | |
2334 | fC32 += b32; | |
2335 | fC42 += b42; | |
2336 | ||
86be8934 | 2337 | CheckCovariance(); |
8b6e3369 | 2338 | |
2339 | // Appoximate step length | |
2de63fc5 | 2340 | double dy2dx = (f1+f2)/(r1+r2); |
2341 | Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord | |
2342 | : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc | |
8b6e3369 | 2343 | step *= TMath::Sqrt(1.+ GetTgl()*GetTgl()); |
2344 | ||
8b6e3369 | 2345 | // Get the track's (x,y,z) and (px,py,pz) in the Global System |
2346 | Double_t r[3]; GetXYZ(r); | |
2347 | Double_t p[3]; GetPxPyPz(p); | |
2348 | Double_t pp=GetP(); | |
2349 | p[0] /= pp; | |
2350 | p[1] /= pp; | |
2351 | p[2] /= pp; | |
2352 | ||
2353 | ||
2354 | // Rotate to the system where Bx=By=0. | |
2355 | Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]); | |
2356 | Double_t cosphi=1., sinphi=0.; | |
2357 | if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;} | |
2358 | Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]); | |
2359 | Double_t costet=1., sintet=0.; | |
2360 | if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;} | |
2361 | Double_t vect[7]; | |
2362 | ||
2363 | vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2]; | |
2364 | vect[1] = -sinphi*r[0] + cosphi*r[1]; | |
2365 | vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2]; | |
2366 | ||
2367 | vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2]; | |
2368 | vect[4] = -sinphi*p[0] + cosphi*p[1]; | |
2369 | vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2]; | |
2370 | ||
2371 | vect[6] = pp; | |
2372 | ||
2373 | ||
2374 | // Do the helix step | |
2375 | g3helx3(GetSign()*bb,step,vect); | |
2376 | ||
2377 | ||
2378 | // Rotate back to the Global System | |
2379 | r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2]; | |
2380 | r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2]; | |
2381 | r[2] = -sintet*vect[0] + costet*vect[2]; | |
2382 | ||
2383 | p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5]; | |
2384 | p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5]; | |
2385 | p[2] = -sintet*vect[3] + costet*vect[5]; | |
2386 | ||
2387 | ||
2388 | // Rotate back to the Tracking System | |
2389 | Double_t cosalp = TMath::Cos(fAlpha); | |
2390 | Double_t sinalp =-TMath::Sin(fAlpha); | |
2391 | ||
2392 | Double_t | |
2393 | t = cosalp*r[0] - sinalp*r[1]; | |
2394 | r[1] = sinalp*r[0] + cosalp*r[1]; | |
2395 | r[0] = t; | |
2396 | ||
2397 | t = cosalp*p[0] - sinalp*p[1]; | |
2398 | p[1] = sinalp*p[0] + cosalp*p[1]; | |
2399 | p[0] = t; | |
2400 | ||
2401 | ||
2402 | // Do the final correcting step to the target plane (linear approximation) | |
2403 | Double_t x=r[0], y=r[1], z=r[2]; | |
2404 | if (TMath::Abs(dx) > kAlmost0) { | |
2405 | if (TMath::Abs(p[0]) < kAlmost0) return kFALSE; | |
2406 | dx = xk - r[0]; | |
2407 | x += dx; | |
2408 | y += p[1]/p[0]*dx; | |
2409 | z += p[2]/p[0]*dx; | |
2410 | } | |
2411 | ||
2412 | ||
2413 | // Calculate the track parameters | |
2414 | t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]); | |
2415 | fX = x; | |
2416 | fP[0] = y; | |
2417 | fP[1] = z; | |
2418 | fP[2] = p[1]/t; | |
2419 | fP[3] = p[2]/t; | |
2420 | fP[4] = GetSign()/(t*pp); | |
2421 | ||
2422 | return kTRUE; | |
2423 | } | |
2424 | ||
e0302afb | 2425 | Bool_t AliExternalTrackParam::PropagateParamOnlyBxByBzTo(Double_t xk, const Double_t b[3]) { |
2426 | //---------------------------------------------------------------- | |
2427 | // Extrapolate this track params (w/o cov matrix) to the plane X=xk in the field b[]. | |
2428 | // | |
2429 | // X [cm] is in the "tracking coordinate system" of this track. | |
2430 | // b[]={Bx,By,Bz} [kG] is in the Global coordidate system. | |
2431 | //---------------------------------------------------------------- | |
2432 | ||
2433 | Double_t dx=xk-fX; | |
2434 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
2435 | if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE; | |
2436 | // Do not propagate tracks outside the ALICE detector | |
2437 | if (TMath::Abs(dx)>1e5 || | |
2438 | TMath::Abs(GetY())>1e5 || | |
2439 | TMath::Abs(GetZ())>1e5) { | |
2440 | AliWarning(Form("Anomalous track, target X:%f",xk)); | |
2441 | Print(); | |
2442 | return kFALSE; | |
2443 | } | |
2444 | ||
2445 | Double_t crv=GetC(b[2]); | |
2446 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
2447 | ||
2448 | Double_t x2r = crv*dx; | |
2449 | Double_t f1=fP[2], f2=f1 + x2r; | |
2450 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
2451 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
2452 | // | |
2453 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); | |
2454 | // | |
2455 | // Appoximate step length | |
2456 | double dy2dx = (f1+f2)/(r1+r2); | |
2457 | Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord | |
2458 | : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc | |
2459 | step *= TMath::Sqrt(1.+ GetTgl()*GetTgl()); | |
2460 | ||
2461 | // Get the track's (x,y,z) and (px,py,pz) in the Global System | |
2462 | Double_t r[3]; GetXYZ(r); | |
2463 | Double_t p[3]; GetPxPyPz(p); | |
2464 | Double_t pp=GetP(); | |
2465 | p[0] /= pp; | |
2466 | p[1] /= pp; | |
2467 | p[2] /= pp; | |
2468 | ||
2469 | // Rotate to the system where Bx=By=0. | |
2470 | Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]); | |
2471 | Double_t cosphi=1., sinphi=0.; | |
2472 | if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;} | |
2473 | Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]); | |
2474 | Double_t costet=1., sintet=0.; | |
2475 | if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;} | |
2476 | Double_t vect[7]; | |
2477 | ||
2478 | vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2]; | |
2479 | vect[1] = -sinphi*r[0] + cosphi*r[1]; | |
2480 | vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2]; | |
2481 | ||
2482 | vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2]; | |
2483 | vect[4] = -sinphi*p[0] + cosphi*p[1]; | |
2484 | vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2]; | |
2485 | ||
2486 | vect[6] = pp; | |
2487 | ||
2488 | // Do the helix step | |
2489 | g3helx3(GetSign()*bb,step,vect); | |
2490 | ||
2491 | // Rotate back to the Global System | |
2492 | r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2]; | |
2493 | r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2]; | |
2494 | r[2] = -sintet*vect[0] + costet*vect[2]; | |
2495 | ||
2496 | p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5]; | |
2497 | p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5]; | |
2498 | p[2] = -sintet*vect[3] + costet*vect[5]; | |
2499 | ||
2500 | // Rotate back to the Tracking System | |
2501 | Double_t cosalp = TMath::Cos(fAlpha); | |
2502 | Double_t sinalp =-TMath::Sin(fAlpha); | |
2503 | ||
2504 | Double_t | |
2505 | t = cosalp*r[0] - sinalp*r[1]; | |
2506 | r[1] = sinalp*r[0] + cosalp*r[1]; | |
2507 | r[0] = t; | |
2508 | ||
2509 | t = cosalp*p[0] - sinalp*p[1]; | |
2510 | p[1] = sinalp*p[0] + cosalp*p[1]; | |
2511 | p[0] = t; | |
2512 | ||
2513 | // Do the final correcting step to the target plane (linear approximation) | |
2514 | Double_t x=r[0], y=r[1], z=r[2]; | |
2515 | if (TMath::Abs(dx) > kAlmost0) { | |
2516 | if (TMath::Abs(p[0]) < kAlmost0) return kFALSE; | |
2517 | dx = xk - r[0]; | |
2518 | x += dx; | |
2519 | y += p[1]/p[0]*dx; | |
2520 | z += p[2]/p[0]*dx; | |
2521 | } | |
2522 | ||
2523 | ||
2524 | // Calculate the track parameters | |
2525 | t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]); | |
2526 | fX = x; | |
2527 | fP[0] = y; | |
2528 | fP[1] = z; | |
2529 | fP[2] = p[1]/t; | |
2530 | fP[3] = p[2]/t; | |
2531 | fP[4] = GetSign()/(t*pp); | |
2532 | ||
2533 | return kTRUE; | |
2534 | } | |
2535 | ||
2536 | ||
cfdb62d4 | 2537 | Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){ |
2538 | // | |
2539 | //Translation: in the event mixing, the tracks can be shifted | |
2540 | //of the difference among primary vertices (vTrasl) and | |
2541 | //the covariance matrix is changed accordingly | |
2542 | //(covV = covariance of the primary vertex). | |
2543 | //Origin: "Romita, Rossella" <R.Romita@gsi.de> | |
2544 | // | |
2545 | TVector3 translation; | |
2546 | // vTrasl coordinates in the local system | |
2547 | translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]); | |
2548 | translation.RotateZ(-fAlpha); | |
2549 | translation.GetXYZ(vTrasl); | |
2550 | ||
2551 | //compute the new x,y,z of the track | |
5a87bb3d | 2552 | Double_t newX=fX-vTrasl[0]; |
2553 | Double_t newY=fP[0]-vTrasl[1]; | |
2554 | Double_t newZ=fP[1]-vTrasl[2]; | |
cfdb62d4 | 2555 | |
2556 | //define the new parameters | |
5a87bb3d | 2557 | Double_t newParam[5]; |
2558 | newParam[0]=newY; | |
2559 | newParam[1]=newZ; | |
2560 | newParam[2]=fP[2]; | |
2561 | newParam[3]=fP[3]; | |
2562 | newParam[4]=fP[4]; | |
cfdb62d4 | 2563 | |
2564 | // recompute the covariance matrix: | |
2565 | // 1. covV in the local system | |
2566 | Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha); | |
2567 | TMatrixD qQi(3,3); | |
2568 | qQi(0,0) = cosRot; | |
2569 | qQi(0,1) = sinRot; | |
2570 | qQi(0,2) = 0.; | |
2571 | qQi(1,0) = -sinRot; | |
2572 | qQi(1,1) = cosRot; | |
2573 | qQi(1,2) = 0.; | |
2574 | qQi(2,0) = 0.; | |
2575 | qQi(2,1) = 0.; | |
2576 | qQi(2,2) = 1.; | |
2577 | TMatrixD uUi(3,3); | |
2578 | uUi(0,0) = covV[0]; | |
2579 | uUi(0,0) = covV[0]; | |
2580 | uUi(1,0) = covV[1]; | |
2581 | uUi(0,1) = covV[1]; | |
2582 | uUi(2,0) = covV[3]; | |
2583 | uUi(0,2) = covV[3]; | |
2584 | uUi(1,1) = covV[2]; | |
2585 | uUi(2,2) = covV[5]; | |
2586 | uUi(1,2) = covV[4]; | |
2587 | if(uUi.Determinant() <= 0.) {return kFALSE;} | |
2588 | TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi); | |
2589 | TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi); | |
2590 | ||
2591 | //2. compute the new covariance matrix of the track | |
2592 | Double_t sigmaXX=m(0,0); | |
2593 | Double_t sigmaXZ=m(2,0); | |
2594 | Double_t sigmaXY=m(1,0); | |
2595 | Double_t sigmaYY=GetSigmaY2()+m(1,1); | |
2596 | Double_t sigmaYZ=fC[1]+m(1,2); | |
2597 | Double_t sigmaZZ=fC[2]+m(2,2); | |
2598 | Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX); | |
2599 | Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX); | |
2600 | Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX); | |
2601 | ||
2602 | Double_t newCov[15]; | |
2603 | newCov[0]=covarianceYY; | |
2604 | newCov[1]=covarianceYZ; | |
2605 | newCov[2]=covarianceZZ; | |
2606 | for(Int_t i=3;i<15;i++){ | |
2607 | newCov[i]=fC[i]; | |
2608 | } | |
2609 | ||
2610 | // set the new parameters | |
2611 | ||
5a87bb3d | 2612 | Set(newX,fAlpha,newParam,newCov); |
cfdb62d4 | 2613 | |
2614 | return kTRUE; | |
2615 | } | |
86be8934 | 2616 | |
2617 | void AliExternalTrackParam::CheckCovariance() { | |
2618 | ||
2619 | // This function forces the diagonal elements of the covariance matrix to be positive. | |
2620 | // In case the diagonal element is bigger than the maximal allowed value, it is set to | |
2621 | // the limit and the off-diagonal elements that correspond to it are set to zero. | |
2622 | ||
32e55f82 | 2623 | fC[0] = TMath::Abs(fC[0]); |
2624 | if (fC[0]>kC0max) { | |
2625 | double scl = TMath::Sqrt(kC0max/fC[0]); | |
2626 | fC[0] = kC0max; | |
2627 | fC[1] *= scl; | |
2628 | fC[3] *= scl; | |
2629 | fC[6] *= scl; | |
2630 | fC[10] *= scl; | |
2631 | } | |
2632 | fC[2] = TMath::Abs(fC[2]); | |
2633 | if (fC[2]>kC2max) { | |
2634 | double scl = TMath::Sqrt(kC2max/fC[2]); | |
2635 | fC[2] = kC2max; | |
2636 | fC[1] *= scl; | |
2637 | fC[4] *= scl; | |
2638 | fC[7] *= scl; | |
2639 | fC[11] *= scl; | |
2640 | } | |
2641 | fC[5] = TMath::Abs(fC[5]); | |
2642 | if (fC[5]>kC5max) { | |
2643 | double scl = TMath::Sqrt(kC5max/fC[5]); | |
2644 | fC[5] = kC5max; | |
2645 | fC[3] *= scl; | |
2646 | fC[4] *= scl; | |
2647 | fC[8] *= scl; | |
2648 | fC[12] *= scl; | |
2649 | } | |
2650 | fC[9] = TMath::Abs(fC[9]); | |
2651 | if (fC[9]>kC9max) { | |
2652 | double scl = TMath::Sqrt(kC9max/fC[9]); | |
2653 | fC[9] = kC9max; | |
2654 | fC[6] *= scl; | |
2655 | fC[7] *= scl; | |
2656 | fC[8] *= scl; | |
2657 | fC[13] *= scl; | |
2658 | } | |
2659 | fC[14] = TMath::Abs(fC[14]); | |
2660 | if (fC[14]>kC14max) { | |
2661 | double scl = TMath::Sqrt(kC14max/fC[14]); | |
2662 | fC[14] = kC14max; | |
2663 | fC[10] *= scl; | |
2664 | fC[11] *= scl; | |
2665 | fC[12] *= scl; | |
2666 | fC[13] *= scl; | |
2667 | } | |
2668 | ||
86be8934 | 2669 | // The part below is used for tests and normally is commented out |
2670 | // TMatrixDSym m(5); | |
2671 | // TVectorD eig(5); | |
2672 | ||
2673 | // m(0,0)=fC[0]; | |
2674 | // m(1,0)=fC[1]; m(1,1)=fC[2]; | |
2675 | // m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5]; | |
2676 | // m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9]; | |
2677 | // 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]; | |
2678 | ||
2679 | // m(0,1)=m(1,0); | |
2680 | // m(0,2)=m(2,0); m(1,2)=m(2,1); | |
2681 | // m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2); | |
2682 | // m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3); | |
2683 | // m.EigenVectors(eig); | |
2684 | ||
2685 | // // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0); | |
2686 | // if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) { | |
2687 | // AliWarning("Negative eigenvalues of the covariance matrix!"); | |
2688 | // this->Print(); | |
2689 | // eig.Print(); | |
2690 | // } | |
2691 | } | |
4c3dc2a0 | 2692 | |
2693 | Bool_t AliExternalTrackParam::ConstrainToVertex(const AliVVertex* vtx, Double_t b[3]) | |
2694 | { | |
2695 | // Constrain TPC inner params constrained | |
2696 | // | |
2697 | if (!vtx) | |
2698 | return kFALSE; | |
2699 | ||
2700 | Double_t dz[2], cov[3]; | |
2701 | if (!PropagateToDCABxByBz(vtx, b, 3, dz, cov)) | |
2702 | return kFALSE; | |
2703 | ||
2704 | Double_t covar[6]; | |
2705 | vtx->GetCovarianceMatrix(covar); | |
2706 | ||
2707 | Double_t p[2]= { fP[0] - dz[0], fP[1] - dz[1] }; | |
2708 | Double_t c[3]= { covar[2], 0., covar[5] }; | |
2709 | ||
2710 | Double_t chi2C = GetPredictedChi2(p,c); | |
2711 | if (chi2C>kVeryBig) | |
2712 | return kFALSE; | |
2713 | ||
2714 | if (!Update(p,c)) | |
2715 | return kFALSE; | |
2716 | ||
2717 | return kTRUE; | |
2718 | } | |
70580f26 | 2719 | |
2720 | //___________________________________________________________________________________________ | |
2721 | Bool_t AliExternalTrackParam::GetXatLabR(Double_t r,Double_t &x, Double_t bz, Int_t dir) const | |
2722 | { | |
2723 | // Get local X of the track position estimated at the radius lab radius r. | |
2724 | // The track curvature is accounted exactly | |
2725 | // | |
2726 | // The flag "dir" can be used to remove the ambiguity of which intersection to take (out of 2 possible) | |
2727 | // 0 - take the intersection closest to the current track position | |
2728 | // >0 - go along the track (increasing fX) | |
2729 | // <0 - go backward (decreasing fX) | |
2730 | // | |
2731 | const Double_t &fy=fP[0], &sn = fP[2]; | |
2732 | // | |
2733 | double crv = GetC(bz); | |
2734 | if (TMath::Abs(crv)<=kAlmost0) { // this is a straight track | |
2735 | if (TMath::Abs(sn)>=kAlmost1) { // || to Y axis | |
2736 | double det = (r-fX)*(r+fX); | |
2737 | if (det<0) return kFALSE; // does not reach raduis r | |
2738 | x = fX; | |
2739 | if (dir==0) return kTRUE; | |
2740 | det = TMath::Sqrt(det); | |
2741 | if (dir>0) { // along the track direction | |
2742 | if (sn>0) {if (fy>det) return kFALSE;} // track is along Y axis and above the circle | |
2743 | else {if (fy<-det) return kFALSE;} // track is against Y axis amd belo the circle | |
2744 | } | |
e804766b | 2745 | else { // agains track direction |
70580f26 | 2746 | if (sn>0) {if (fy<-det) return kFALSE;} // track is along Y axis |
2747 | else if (fy>det) return kFALSE; // track is against Y axis | |
2748 | } | |
2749 | } | |
2750 | else if (TMath::Abs(sn)<=kAlmost0) { // || to X axis | |
2751 | double det = (r-fy)*(r+fy); | |
2752 | if (det<0) return kFALSE; // does not reach raduis r | |
2753 | det = TMath::Sqrt(det); | |
2754 | if (!dir) { | |
2755 | x = fX>0 ? det : -det; // choose the solution requiring the smalest step | |
2756 | return kTRUE; | |
2757 | } | |
2758 | else if (dir>0) { // along the track direction | |
2759 | if (fX > det) return kFALSE; // current point is in on the right from the circle | |
2760 | else if (fX <-det) x = -det; // on the left | |
2761 | else x = det; // within the circle | |
2762 | } | |
2763 | else { // against the track direction | |
2764 | if (fX <-det) return kFALSE; | |
2765 | else if (fX > det) x = det; | |
2766 | else x = -det; | |
2767 | } | |
2768 | } | |
2769 | else { // general case of straight line | |
2770 | double cs = TMath::Sqrt((1-sn)*(1+sn)); | |
2771 | double xsyc = fX*sn-fy*cs; | |
2772 | double det = (r-xsyc)*(r+xsyc); | |
2773 | if (det<0) return kFALSE; // does not reach raduis r | |
2774 | det = TMath::Sqrt(det); | |
2775 | double xcys = fX*cs+fy*sn; | |
2776 | double t = -xcys; | |
2777 | if (dir==0) t += t>0 ? -det:det; // chose the solution requiring the smalest step | |
2778 | else if (dir>0) { // go in increasing fX direction. ( t+-det > 0) | |
2779 | if (t>=-det) t += -det; // take minimal step giving t>0 | |
2780 | else return kFALSE; // both solutions have negative t | |
2781 | } | |
2782 | else { // go in increasing fX direction. (t+-det < 0) | |
2783 | if (t<det) t -= det; // take minimal step giving t<0 | |
2784 | else return kFALSE; // both solutions have positive t | |
2785 | } | |
2786 | x = fX + cs*t; | |
2787 | } | |
2788 | } | |
2789 | else { // helix | |
2790 | // get center of the track circle | |
2791 | double tR = 1./crv; // track radius (for the moment signed) | |
2792 | double cs = TMath::Sqrt((1-sn)*(1+sn)); | |
2793 | double x0 = fX - sn*tR; | |
2794 | double y0 = fy + cs*tR; | |
2795 | double r0 = TMath::Sqrt(x0*x0+y0*y0); | |
2796 | // printf("Xc:%+e Yc:%+e\n",x0,y0); | |
2797 | // | |
2798 | if (r0<=kAlmost0) return kFALSE; // the track is concentric to circle | |
2799 | tR = TMath::Abs(tR); | |
2800 | double tR2r0 = tR/r0; | |
2801 | double g = 0.5*(r*r/(r0*tR) - tR2r0 - 1./tR2r0); | |
2802 | double det = (1.-g)*(1.+g); | |
2803 | if (det<0) return kFALSE; // does not reach raduis r | |
2804 | det = TMath::Sqrt(det); | |
2805 | // | |
2806 | // the intersection happens in 2 points: {x0+tR*C,y0+tR*S} | |
2807 | // with C=f*c0+-|s0|*det and S=f*s0-+c0 sign(s0)*det | |
2808 | // where s0 and c0 make direction for the circle center (=x0/r0 and y0/r0) | |
2809 | // | |
2810 | double tmp = 1.+g*tR2r0; | |
2811 | x = x0*tmp; | |
2812 | double y = y0*tmp; | |
2813 | if (TMath::Abs(y0)>kAlmost0) { // when y0==0 the x,y is unique | |
2814 | double dfx = tR2r0*TMath::Abs(y0)*det; | |
2815 | double dfy = tR2r0*x0*TMath::Sign(det,y0); | |
2816 | if (dir==0) { // chose the one which corresponds to smallest step | |
2817 | double delta = (x-fX)*dfx-(y-fy)*dfy; // the choice of + in C will lead to smaller step if delta<0 | |
2818 | if (delta<0) x += dfx; | |
2819 | else x -= dfx; | |
2820 | } | |
2821 | else if (dir>0) { // along track direction: x must be > fX | |
2822 | x -= dfx; // try the smallest step (dfx is positive) | |
2823 | if (x<fX && (x+=dfx+dfx)<fX) return kFALSE; | |
2824 | } | |
2825 | else { // backward: x must be < fX | |
2826 | x += dfx; // try the smallest step (dfx is positive) | |
2827 | if (x>fX && (x-=dfx+dfx)>fX) return kFALSE; | |
2828 | } | |
2829 | } | |
2830 | else { // special case: track touching the circle just in 1 point | |
2831 | if ( (dir>0&&x<fX) || (dir<0&&x>fX) ) return kFALSE; | |
2832 | } | |
2833 | } | |
2834 | // | |
2835 | return kTRUE; | |
2836 | } | |
7d2e151a | 2837 | //_________________________________________________________ |
2838 | Bool_t AliExternalTrackParam::GetXYZatR(Double_t xr,Double_t bz, Double_t *xyz, Double_t* alpSect) const | |
1445f03c | 2839 | { |
7d2e151a | 2840 | // This method has 3 modes of behaviour |
2841 | // 1) xyz[3] array is provided but alpSect pointer is 0: calculate the position of track intersection | |
2842 | // with circle of radius xr and fill it in xyz array | |
2843 | // 2) alpSect pointer is provided: find alpha of the sector where the track reaches local coordinate xr | |
2844 | // Note that in this case xr is NOT the radius but the local coordinate. | |
2845 | // If the xyz array is provided, it will be filled by track lab coordinates at local X in this sector | |
2846 | // 3) Neither alpSect nor xyz pointers are provided: just check if the track reaches radius xr | |
1445f03c | 2847 | // |
1445f03c | 2848 | // |
7d2e151a | 2849 | double crv = GetC(bz); |
2850 | if ( (TMath::Abs(bz))<kAlmost0Field ) crv=0.; | |
2851 | const double &fy = fP[0]; | |
2852 | const double &fz = fP[1]; | |
2853 | const double &sn = fP[2]; | |
2854 | const double &tgl = fP[3]; | |
2855 | // | |
2856 | // general circle parameterization: | |
2857 | // x = (r0+tR)cos(phi0) - tR cos(t+phi0) | |
2858 | // y = (r0+tR)sin(phi0) - tR sin(t+phi0) | |
2859 | // where qb is the sign of the curvature, tR is the track's signed radius and r0 | |
2860 | // is the DCA of helix to origin | |
2861 | // | |
2862 | double tR = 1./crv; // track radius signed | |
2863 | double cs = TMath::Sqrt((1-sn)*(1+sn)); | |
2864 | double x0 = fX - sn*tR; // helix center coordinates | |
2865 | double y0 = fy + cs*tR; | |
2866 | double phi0 = TMath::ATan2(y0,x0); // angle of PCA wrt to the origin | |
2867 | if (tR<0) phi0 += TMath::Pi(); | |
2868 | if (phi0 > TMath::Pi()) phi0 -= 2.*TMath::Pi(); | |
2869 | else if (phi0 <-TMath::Pi()) phi0 += 2.*TMath::Pi(); | |
2870 | double cs0 = TMath::Cos(phi0); | |
2871 | double sn0 = TMath::Sin(phi0); | |
2872 | double r0 = x0*cs0 + y0*sn0 - tR; // DCA to origin | |
2873 | double r2R = 1.+r0/tR; | |
2874 | // | |
2875 | // | |
2876 | if (r2R<kAlmost0) return kFALSE; // helix is centered at the origin, no specific intersection with other concetric circle | |
2877 | if (!xyz && !alpSect) return kTRUE; | |
2878 | double xr2R = xr/tR; | |
2879 | double r2Ri = 1./r2R; | |
2880 | // the intersection cos(t) = [1 + (r0/tR+1)^2 - (r0/tR)^2]/[2(1+r0/tR)] | |
2881 | double cosT = 0.5*(r2R + (1-xr2R*xr2R)*r2Ri); | |
2882 | if ( TMath::Abs(cosT)>kAlmost1 ) { | |
2883 | // printf("Does not reach : %f %f\n",r0,tR); | |
2884 | return kFALSE; // track does not reach the radius xr | |
1445f03c | 2885 | } |
2886 | // | |
7d2e151a | 2887 | double t = TMath::ACos(cosT); |
2888 | if (tR<0) t = -t; | |
2889 | // intersection point | |
2890 | double xyzi[3]; | |
2891 | xyzi[0] = x0 - tR*TMath::Cos(t+phi0); | |
2892 | xyzi[1] = y0 - tR*TMath::Sin(t+phi0); | |
2893 | if (xyz) { // if postition is requested, then z is needed: | |
2894 | double t0 = TMath::ATan2(cs,-sn) - phi0; | |
2895 | double z0 = fz - t0*tR*tgl; | |
2896 | xyzi[2] = z0 + tR*t*tgl; | |
1445f03c | 2897 | } |
7d2e151a | 2898 | else xyzi[2] = 0; |
2899 | // | |
2900 | Local2GlobalPosition(xyzi,fAlpha); | |
2901 | // | |
2902 | if (xyz) { | |
2903 | xyz[0] = xyzi[0]; | |
2904 | xyz[1] = xyzi[1]; | |
2905 | xyz[2] = xyzi[2]; | |
1445f03c | 2906 | } |
7d2e151a | 2907 | // |
2908 | if (alpSect) { | |
2909 | double &alp = *alpSect; | |
2910 | // determine the sector of crossing | |
2911 | double phiPos = TMath::Pi()+TMath::ATan2(-xyzi[1],-xyzi[0]); | |
2912 | int sect = ((Int_t)(phiPos*TMath::RadToDeg()))/20; | |
2913 | alp = TMath::DegToRad()*(20*sect+10); | |
2914 | double x2r,f1,f2,r1,r2,dx,dy2dx,yloc=0, ylocMax = xr*TMath::Tan(TMath::Pi()/18); // min max Y within sector at given X | |
2915 | // | |
2916 | while(1) { | |
2917 | Double_t ca=TMath::Cos(alp-fAlpha), sa=TMath::Sin(alp-fAlpha); | |
2918 | if ((cs*ca+sn*sa)<0) { | |
2919 | AliDebug(1,Form("Rotation to target sector impossible: local cos(phi) would become %.2f",cs*ca+sn*sa)); | |
2920 | return kFALSE; | |
2921 | } | |
2922 | // | |
2923 | f1 = sn*ca - cs*sa; | |
2924 | if (TMath::Abs(f1) >= kAlmost1) { | |
2925 | AliDebug(1,Form("Rotation to target sector impossible: local sin(phi) would become %.2f",f1)); | |
2926 | return kFALSE; | |
2927 | } | |
2928 | // | |
2929 | double tmpX = fX*ca + fy*sa; | |
2930 | double tmpY = -fX*sa + fy*ca; | |
2931 | // | |
2932 | // estimate Y at X=xr | |
2933 | dx=xr-tmpX; | |
2934 | x2r = crv*dx; | |
2935 | f2=f1 + x2r; | |
2936 | if (TMath::Abs(f2) >= kAlmost1) { | |
2937 | AliDebug(1,Form("Propagation in target sector failed ! %.10e",f2)); | |
2938 | return kFALSE; | |
2939 | } | |
2940 | r1 = TMath::Sqrt((1.-f1)*(1.+f1)); | |
2941 | r2 = TMath::Sqrt((1.-f2)*(1.+f2)); | |
2942 | dy2dx = (f1+f2)/(r1+r2); | |
2943 | yloc = tmpY + dx*dy2dx; | |
2944 | if (yloc>ylocMax) {alp += 2*TMath::Pi()/18; sect++;} | |
2945 | else if (yloc<-ylocMax) {alp -= 2*TMath::Pi()/18; sect--;} | |
2946 | else break; | |
2947 | if (alp >= TMath::Pi()) alp -= 2*TMath::Pi(); | |
2948 | else if (alp < -TMath::Pi()) alp += 2*TMath::Pi(); | |
2949 | // if (sect>=18) sect = 0; | |
2950 | // if (sect<=0) sect = 17; | |
2951 | } | |
2952 | // | |
2953 | // if alpha was requested, then recalculate the position at intersection in sector | |
2954 | if (xyz) { | |
2955 | xyz[0] = xr; | |
2956 | xyz[1] = yloc; | |
2957 | if (TMath::Abs(x2r)<0.05) xyz[2] = fz + dx*(r2 + f2*dy2dx)*tgl; | |
2958 | else { | |
2959 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
2960 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
2961 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
2962 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
2963 | // Similarly, the rotation angle in linear in dx only for dx<<R | |
2964 | double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one | |
2965 | double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
2966 | xyz[2] = fz + rot/crv*tgl; | |
2967 | } | |
2968 | Local2GlobalPosition(xyz,alp); | |
2969 | } | |
1445f03c | 2970 | } |
7d2e151a | 2971 | return kTRUE; |
2972 | // | |
1445f03c | 2973 | } |