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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 | ||
184 | //_____________________________________________________________________________ | |
185 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
186 | Double_t cv[21],Short_t sign) | |
da4e3deb | 187 | { |
188 | // | |
189 | // create external track parameters from the global parameters | |
190 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
191 | // A.Dainese 10.10.08 | |
192 | ||
aff56ff7 | 193 | // Calculate alpha: the rotation angle of the corresponding local system. |
194 | // | |
195 | // For global radial position inside the beam pipe, alpha is the | |
196 | // azimuthal angle of the momentum projected on (x,y). | |
197 | // | |
c99948ce | 198 | // For global radial position outside the ITS, alpha is the |
aff56ff7 | 199 | // azimuthal angle of the centre of the TPC sector in which the point |
200 | // xyz lies | |
201 | // | |
4349f5a4 | 202 | const double kSafe = 1e-5; |
aff56ff7 | 203 | Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1]; |
c99948ce | 204 | Double_t radMax = 45.; // approximately ITS outer radius |
4349f5a4 | 205 | if (radPos2 < radMax*radMax) { // inside the ITS |
aff56ff7 | 206 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); |
c99948ce | 207 | } else { // outside the ITS |
aff56ff7 | 208 | Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]); |
209 | fAlpha = | |
210 | TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10); | |
211 | } | |
4349f5a4 | 212 | // |
213 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
214 | // protection: avoid alpha being too close to 0 or +-pi/2 | |
215 | if (TMath::Abs(sn)<kSafe) { | |
8defb4a0 | 216 | if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? kSafe : -kSafe; |
217 | else fAlpha += fAlpha>-TMath::Pi()/2. ? -kSafe : kSafe; | |
4349f5a4 | 218 | cs=TMath::Cos(fAlpha); |
219 | sn=TMath::Sin(fAlpha); | |
220 | } | |
8defb4a0 | 221 | else if (TMath::Abs(cs)<kSafe) { |
222 | if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? kSafe : -kSafe; | |
223 | else fAlpha += fAlpha>-TMath::Pi()/2. ? kSafe : -kSafe; | |
4349f5a4 | 224 | cs=TMath::Cos(fAlpha); |
8defb4a0 | 225 | sn=TMath::Sin(fAlpha); |
4349f5a4 | 226 | } |
da4e3deb | 227 | // Get the vertex of origin and the momentum |
228 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
229 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
4349f5a4 | 230 | // |
231 | // avoid momenta along axis | |
232 | if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]); | |
233 | if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]); | |
da4e3deb | 234 | |
235 | // Rotate to the local coordinate system | |
236 | ver.RotateZ(-fAlpha); | |
237 | mom.RotateZ(-fAlpha); | |
238 | ||
239 | // x of the reference plane | |
240 | fX = ver.X(); | |
241 | ||
242 | Double_t charge = (Double_t)sign; | |
243 | ||
244 | fP[0] = ver.Y(); | |
245 | fP[1] = ver.Z(); | |
246 | fP[2] = TMath::Sin(mom.Phi()); | |
247 | fP[3] = mom.Pz()/mom.Pt(); | |
248 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
249 | ||
250 | // Covariance matrix (formulas to be simplified) | |
251 | ||
752303df | 252 | if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection |
253 | else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection | |
254 | ||
da4e3deb | 255 | Double_t pt=1./TMath::Abs(fP[4]); |
da4e3deb | 256 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
257 | ||
258 | Double_t m00=-sn;// m10=cs; | |
259 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
260 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
261 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
262 | ||
263 | m43*=GetSign(); | |
264 | m44*=GetSign(); | |
265 | m45*=GetSign(); | |
266 | ||
267 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
268 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
269 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
270 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
271 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
272 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
273 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
274 | ||
275 | fC[0 ] = cv[0 ]+cv[2 ]; | |
276 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
277 | fC[2 ] = cv[5 ]; | |
278 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
279 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
280 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
281 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
282 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
283 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
284 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
285 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
286 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
287 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
288 | Double_t b2=m23*m35; | |
289 | Double_t b3=m43*m35; | |
290 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
291 | Double_t b5=m24*m35; | |
292 | Double_t b6=m44*m35; | |
293 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
294 | fC[13] = b1/b3-b2*fC[8]/b3; | |
295 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 296 | |
86be8934 | 297 | CheckCovariance(); |
298 | ||
4f6e22bd | 299 | return; |
da4e3deb | 300 | } |
301 | ||
51ad6848 | 302 | //_____________________________________________________________________________ |
c9ec41e8 | 303 | void AliExternalTrackParam::Reset() { |
1530f89c | 304 | // |
305 | // Resets all the parameters to 0 | |
306 | // | |
c9ec41e8 | 307 | fX=fAlpha=0.; |
308 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
309 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 310 | } |
311 | ||
3775b0ca | 312 | //_____________________________________________________________________________ |
313 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
314 | // | |
315 | // Add "something" to the track covarince matrix. | |
316 | // May be needed to account for unknown mis-calibration/mis-alignment | |
317 | // | |
318 | fC[0] +=c[0]; | |
319 | fC[1] +=c[1]; fC[2] +=c[2]; | |
320 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
321 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
322 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
86be8934 | 323 | CheckCovariance(); |
3775b0ca | 324 | } |
325 | ||
326 | ||
c9ec41e8 | 327 | Double_t AliExternalTrackParam::GetP() const { |
328 | //--------------------------------------------------------------------- | |
329 | // This function returns the track momentum | |
330 | // Results for (nearly) straight tracks are meaningless ! | |
331 | //--------------------------------------------------------------------- | |
06fb4a2f | 332 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 333 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 334 | } |
335 | ||
1d99986f | 336 | Double_t AliExternalTrackParam::Get1P() const { |
337 | //--------------------------------------------------------------------- | |
338 | // This function returns the 1/(track momentum) | |
339 | //--------------------------------------------------------------------- | |
340 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
341 | } | |
342 | ||
c9ec41e8 | 343 | //_______________________________________________________________________ |
c7bafca9 | 344 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 345 | //------------------------------------------------------------------ |
346 | // This function calculates the transverse impact parameter | |
347 | // with respect to a point with global coordinates (x,y) | |
348 | // in the magnetic field "b" (kG) | |
349 | //------------------------------------------------------------------ | |
5773defd | 350 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 351 | Double_t rp4=GetC(b); |
c9ec41e8 | 352 | |
353 | Double_t xt=fX, yt=fP[0]; | |
354 | ||
355 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
356 | Double_t a = x*cs + y*sn; | |
357 | y = -x*sn + y*cs; x=a; | |
358 | xt-=x; yt-=y; | |
359 | ||
bfd20868 | 360 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2])); |
361 | a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt); | |
1530f89c | 362 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
363 | } | |
364 | ||
365 | //_______________________________________________________________________ | |
366 | void AliExternalTrackParam:: | |
367 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
368 | //------------------------------------------------------------------ | |
369 | // This function calculates the transverse and longitudinal impact parameters | |
370 | // with respect to a point with global coordinates (x,y) | |
371 | // in the magnetic field "b" (kG) | |
372 | //------------------------------------------------------------------ | |
bfd20868 | 373 | Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1)); |
1530f89c | 374 | Double_t xt=fX, yt=fP[0]; |
375 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
376 | Double_t a = x*cs + y*sn; | |
377 | y = -x*sn + y*cs; x=a; | |
378 | xt-=x; yt-=y; | |
379 | ||
380 | Double_t rp4=GetC(b); | |
381 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
382 | dz[0] = -(xt*f1 - yt*r1); | |
383 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
384 | return; | |
385 | } | |
386 | ||
387 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
388 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
389 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
390 | dz[0] = -a/(1 + rr); | |
bfd20868 | 391 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2)); |
1530f89c | 392 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; |
51ad6848 | 393 | } |
394 | ||
49d13e89 | 395 | //_______________________________________________________________________ |
396 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
397 | //------------------------------------------------------------------ | |
398 | // This function calculates the transverse impact parameter | |
399 | // with respect to a point with global coordinates (xv,yv) | |
400 | // neglecting the track curvature. | |
401 | //------------------------------------------------------------------ | |
402 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
403 | Double_t x= xv*cs + yv*sn; | |
404 | Double_t y=-xv*sn + yv*cs; | |
405 | ||
bfd20868 | 406 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
49d13e89 | 407 | |
1530f89c | 408 | return -d; |
49d13e89 | 409 | } |
410 | ||
b8e07ed6 | 411 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx |
412 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
413 | Double_t dEdx, | |
414 | Bool_t anglecorr) { | |
116b445b | 415 | //------------------------------------------------------------------ |
416 | // This function corrects the track parameters for the crossed material. | |
417 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
2b99ff83 | 418 | // "xTimesRho" - is the product length*density (g/cm^2). |
419 | // It should be passed as negative when propagating tracks | |
420 | // from the intreaction point to the outside of the central barrel. | |
116b445b | 421 | // "mass" - the mass of this particle (GeV/c^2). |
b8e07ed6 | 422 | // "dEdx" - mean enery loss (GeV/(g/cm^2) |
423 | // "anglecorr" - switch for the angular correction | |
116b445b | 424 | //------------------------------------------------------------------ |
425 | Double_t &fP2=fP[2]; | |
426 | Double_t &fP3=fP[3]; | |
427 | Double_t &fP4=fP[4]; | |
428 | ||
429 | Double_t &fC22=fC[5]; | |
430 | Double_t &fC33=fC[9]; | |
431 | Double_t &fC43=fC[13]; | |
432 | Double_t &fC44=fC[14]; | |
433 | ||
7dded1d5 | 434 | //Apply angle correction, if requested |
435 | if(anglecorr) { | |
bfd20868 | 436 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2))); |
7dded1d5 | 437 | xOverX0 *=angle; |
438 | xTimesRho *=angle; | |
439 | } | |
440 | ||
116b445b | 441 | Double_t p=GetP(); |
442 | Double_t p2=p*p; | |
443 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 444 | |
9f2bec63 | 445 | //Calculating the multiple scattering corrections****************** |
446 | Double_t cC22 = 0.; | |
447 | Double_t cC33 = 0.; | |
448 | Double_t cC43 = 0.; | |
449 | Double_t cC44 = 0.; | |
116b445b | 450 | if (xOverX0 != 0) { |
f2cef1b5 | 451 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
452 | Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0); | |
453 | if (GetUseLogTermMS()) { | |
454 | double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0)); | |
455 | if (lt>0) theta2 *= lt*lt; | |
456 | } | |
457 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; | |
458 | cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3); | |
459 | cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
460 | cC43 = theta2*fP3*fP4*(1. + fP3*fP3); | |
461 | cC44 = theta2*fP3*fP4*fP3*fP4; | |
116b445b | 462 | } |
463 | ||
9f2bec63 | 464 | //Calculating the energy loss corrections************************ |
465 | Double_t cP4=1.; | |
116b445b | 466 | if ((xTimesRho != 0.) && (beta2 < 1.)) { |
b8e07ed6 | 467 | Double_t dE=dEdx*xTimesRho; |
116b445b | 468 | Double_t e=TMath::Sqrt(p2 + mass*mass); |
469 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
c9038cae | 470 | //cP4 = (1.- e/p2*dE); |
76ece3d8 | 471 | if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE; |
c9038cae | 472 | cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben ! |
9f2bec63 | 473 | if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c |
4b2fa3ce | 474 | |
116b445b | 475 | |
476 | // Approximate energy loss fluctuation (M.Ivanov) | |
477 | const Double_t knst=0.07; // To be tuned. | |
478 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
9f2bec63 | 479 | cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
116b445b | 480 | |
481 | } | |
482 | ||
9f2bec63 | 483 | //Applying the corrections***************************** |
484 | fC22 += cC22; | |
485 | fC33 += cC33; | |
486 | fC43 += cC43; | |
487 | fC44 += cC44; | |
488 | fP4 *= cP4; | |
489 | ||
86be8934 | 490 | CheckCovariance(); |
491 | ||
116b445b | 492 | return kTRUE; |
493 | } | |
494 | ||
b8e07ed6 | 495 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
496 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
497 | Bool_t anglecorr, | |
498 | Double_t (*Bethe)(Double_t)) { | |
499 | //------------------------------------------------------------------ | |
500 | // This function corrects the track parameters for the crossed material. | |
501 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
502 | // "xTimesRho" - is the product length*density (g/cm^2). | |
2b99ff83 | 503 | // It should be passed as negative when propagating tracks |
504 | // from the intreaction point to the outside of the central barrel. | |
b8e07ed6 | 505 | // "mass" - the mass of this particle (GeV/c^2). |
506 | // "anglecorr" - switch for the angular correction | |
507 | // "Bethe" - function calculating the energy loss (GeV/(g/cm^2)) | |
508 | //------------------------------------------------------------------ | |
509 | ||
510 | Double_t bg=GetP()/mass; | |
511 | Double_t dEdx=Bethe(bg); | |
512 | ||
513 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
514 | } | |
515 | ||
516 | Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA | |
517 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, | |
518 | Double_t zOverA, | |
519 | Double_t density, | |
520 | Double_t exEnergy, | |
521 | Double_t jp1, | |
522 | Double_t jp2, | |
523 | Bool_t anglecorr) { | |
524 | //------------------------------------------------------------------ | |
525 | // This function corrects the track parameters for the crossed material | |
526 | // using the full Geant-like Bethe-Bloch formula parameterization | |
527 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
528 | // "xTimesRho" - is the product length*density (g/cm^2). | |
2b99ff83 | 529 | // It should be passed as negative when propagating tracks |
530 | // from the intreaction point to the outside of the central barrel. | |
b8e07ed6 | 531 | // "mass" - the mass of this particle (GeV/c^2). |
532 | // "density" - mean density (g/cm^3) | |
533 | // "zOverA" - mean Z/A | |
534 | // "exEnergy" - mean exitation energy (GeV) | |
535 | // "jp1" - density effect first junction point | |
536 | // "jp2" - density effect second junction point | |
537 | // "anglecorr" - switch for the angular correction | |
538 | // | |
539 | // The default values of the parameters are for silicon | |
540 | // | |
541 | //------------------------------------------------------------------ | |
542 | ||
543 | Double_t bg=GetP()/mass; | |
544 | Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA); | |
545 | ||
546 | return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr); | |
547 | } | |
548 | ||
549 | ||
116b445b | 550 | |
ee5dba5e | 551 | Bool_t AliExternalTrackParam::CorrectForMaterial |
552 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 553 | //------------------------------------------------------------------ |
116b445b | 554 | // Deprecated function ! |
555 | // Better use CorrectForMeanMaterial instead of it. | |
556 | // | |
c7bafca9 | 557 | // This function corrects the track parameters for the crossed material |
558 | // "d" - the thickness (fraction of the radiation length) | |
2b99ff83 | 559 | // It should be passed as negative when propagating tracks |
560 | // from the intreaction point to the outside of the central barrel. | |
c7bafca9 | 561 | // "x0" - the radiation length (g/cm^2) |
562 | // "mass" - the mass of this particle (GeV/c^2) | |
563 | //------------------------------------------------------------------ | |
c7bafca9 | 564 | |
b8e07ed6 | 565 | return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe); |
c7bafca9 | 566 | |
c7bafca9 | 567 | } |
568 | ||
9c56b409 | 569 | Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg, |
570 | Double_t kp1, | |
571 | Double_t kp2, | |
572 | Double_t kp3, | |
573 | Double_t kp4, | |
574 | Double_t kp5) { | |
575 | // | |
576 | // This is the empirical ALEPH parameterization of the Bethe-Bloch formula. | |
577 | // It is normalized to 1 at the minimum. | |
578 | // | |
579 | // bg - beta*gamma | |
580 | // | |
581 | // The default values for the kp* parameters are for ALICE TPC. | |
582 | // The returned value is in MIP units | |
583 | // | |
584 | ||
585 | Double_t beta = bg/TMath::Sqrt(1.+ bg*bg); | |
586 | ||
587 | Double_t aa = TMath::Power(beta,kp4); | |
588 | Double_t bb = TMath::Power(1./bg,kp5); | |
589 | ||
590 | bb=TMath::Log(kp3+bb); | |
591 | ||
592 | return (kp2-aa-bb)*kp1/aa; | |
593 | } | |
594 | ||
595 | Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg, | |
596 | Double_t kp0, | |
597 | Double_t kp1, | |
598 | Double_t kp2, | |
599 | Double_t kp3, | |
600 | Double_t kp4) { | |
601 | // | |
602 | // This is the parameterization of the Bethe-Bloch formula inspired by Geant. | |
603 | // | |
604 | // bg - beta*gamma | |
605 | // kp0 - density [g/cm^3] | |
606 | // kp1 - density effect first junction point | |
607 | // kp2 - density effect second junction point | |
608 | // kp3 - mean excitation energy [GeV] | |
609 | // kp4 - mean Z/A | |
610 | // | |
611 | // The default values for the kp* parameters are for silicon. | |
612 | // The returned value is in [GeV/(g/cm^2)]. | |
613 | // | |
614 | ||
615 | const Double_t mK = 0.307075e-3; // [GeV*cm^2/g] | |
616 | const Double_t me = 0.511e-3; // [GeV/c^2] | |
617 | const Double_t rho = kp0; | |
618 | const Double_t x0 = kp1*2.303; | |
619 | const Double_t x1 = kp2*2.303; | |
620 | const Double_t mI = kp3; | |
621 | const Double_t mZA = kp4; | |
622 | const Double_t bg2 = bg*bg; | |
623 | const Double_t maxT= 2*me*bg2; // neglecting the electron mass | |
624 | ||
625 | //*** Density effect | |
626 | Double_t d2=0.; | |
627 | const Double_t x=TMath::Log(bg); | |
628 | const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI); | |
629 | if (x > x1) { | |
630 | d2 = lhwI + x - 0.5; | |
631 | } else if (x > x0) { | |
632 | const Double_t r=(x1-x)/(x1-x0); | |
633 | d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r; | |
634 | } | |
635 | ||
636 | return mK*mZA*(1+bg2)/bg2* | |
637 | (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2); | |
638 | } | |
639 | ||
d46683db | 640 | Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) { |
ee5dba5e | 641 | //------------------------------------------------------------------ |
d46683db | 642 | // This is an approximation of the Bethe-Bloch formula, |
643 | // reasonable for solid materials. | |
644 | // All the parameters are, in fact, for Si. | |
9b655cba | 645 | // The returned value is in [GeV/(g/cm^2)] |
ee5dba5e | 646 | //------------------------------------------------------------------ |
a821848c | 647 | |
9c56b409 | 648 | return BetheBlochGeant(bg); |
d46683db | 649 | } |
ee5dba5e | 650 | |
d46683db | 651 | Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) { |
652 | //------------------------------------------------------------------ | |
653 | // This is an approximation of the Bethe-Bloch formula, | |
654 | // reasonable for gas materials. | |
655 | // All the parameters are, in fact, for Ne. | |
9b655cba | 656 | // The returned value is in [GeV/(g/cm^2)] |
d46683db | 657 | //------------------------------------------------------------------ |
658 | ||
659 | const Double_t rho = 0.9e-3; | |
660 | const Double_t x0 = 2.; | |
661 | const Double_t x1 = 4.; | |
662 | const Double_t mI = 140.e-9; | |
663 | const Double_t mZA = 0.49555; | |
664 | ||
9c56b409 | 665 | return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); |
ee5dba5e | 666 | } |
667 | ||
49d13e89 | 668 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
669 | //------------------------------------------------------------------ | |
670 | // Transform this track to the local coord. system rotated | |
671 | // by angle "alpha" (rad) with respect to the global coord. system. | |
672 | //------------------------------------------------------------------ | |
dfcef74c | 673 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
674 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
675 | return kFALSE; | |
676 | } | |
677 | ||
49d13e89 | 678 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
679 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
680 | ||
681 | Double_t &fP0=fP[0]; | |
682 | Double_t &fP2=fP[2]; | |
683 | Double_t &fC00=fC[0]; | |
684 | Double_t &fC10=fC[1]; | |
685 | Double_t &fC20=fC[3]; | |
686 | Double_t &fC21=fC[4]; | |
687 | Double_t &fC22=fC[5]; | |
688 | Double_t &fC30=fC[6]; | |
689 | Double_t &fC32=fC[8]; | |
690 | Double_t &fC40=fC[10]; | |
691 | Double_t &fC42=fC[12]; | |
692 | ||
693 | Double_t x=fX; | |
694 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
bfd20868 | 695 | Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision |
07dfd570 | 696 | // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle |
697 | // direction in local frame is along the X axis | |
698 | if ((cf*ca+sf*sa)<0) { | |
1450dc8a | 699 | AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa)); |
07dfd570 | 700 | return kFALSE; |
701 | } | |
702 | // | |
dfcef74c | 703 | Double_t tmp=sf*ca - cf*sa; |
6e50abb1 | 704 | |
7248cf51 | 705 | if (TMath::Abs(tmp) >= kAlmost1) { |
706 | if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) | |
707 | AliWarning(Form("Rotation failed ! %.10e",tmp)); | |
0b69bbb2 | 708 | return kFALSE; |
709 | } | |
49d13e89 | 710 | fAlpha = alpha; |
711 | fX = x*ca + fP0*sa; | |
712 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 713 | fP2= tmp; |
49d13e89 | 714 | |
06fb4a2f | 715 | if (TMath::Abs(cf)<kAlmost0) { |
716 | AliError(Form("Too small cosine value %f",cf)); | |
717 | cf = kAlmost0; | |
718 | } | |
719 | ||
49d13e89 | 720 | Double_t rr=(ca+sf/cf*sa); |
721 | ||
722 | fC00 *= (ca*ca); | |
723 | fC10 *= ca; | |
724 | fC20 *= ca*rr; | |
725 | fC21 *= rr; | |
726 | fC22 *= rr*rr; | |
727 | fC30 *= ca; | |
728 | fC32 *= rr; | |
729 | fC40 *= ca; | |
730 | fC42 *= rr; | |
731 | ||
86be8934 | 732 | CheckCovariance(); |
733 | ||
49d13e89 | 734 | return kTRUE; |
735 | } | |
736 | ||
2d2fd909 | 737 | Bool_t AliExternalTrackParam::Invert() { |
738 | //------------------------------------------------------------------ | |
739 | // Transform this track to the local coord. system rotated by 180 deg. | |
740 | //------------------------------------------------------------------ | |
741 | fX = -fX; | |
742 | fAlpha += TMath::Pi(); | |
743 | while (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi(); | |
744 | while (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi(); | |
745 | // | |
746 | fP[0] = -fP[0]; | |
6e50abb1 | 747 | //fP[2] = -fP[2]; |
2d2fd909 | 748 | fP[3] = -fP[3]; |
749 | fP[4] = -fP[4]; | |
750 | // | |
6e50abb1 | 751 | fC[1] = -fC[1]; // since the fP1 and fP2 are not inverted, their covariances with others change sign |
752 | fC[3] = -fC[3]; | |
2d2fd909 | 753 | fC[7] = -fC[7]; |
6e50abb1 | 754 | fC[8] = -fC[8]; |
2d2fd909 | 755 | fC[11] = -fC[11]; |
6e50abb1 | 756 | fC[12] = -fC[12]; |
2d2fd909 | 757 | // |
758 | return kTRUE; | |
759 | } | |
760 | ||
49d13e89 | 761 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { |
762 | //---------------------------------------------------------------- | |
763 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
764 | //---------------------------------------------------------------- | |
49d13e89 | 765 | Double_t dx=xk-fX; |
e421f556 | 766 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 767 | |
1530f89c | 768 | Double_t crv=GetC(b); |
5773defd | 769 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
770 | ||
2de63fc5 | 771 | Double_t x2r = crv*dx; |
772 | Double_t f1=fP[2], f2=f1 + x2r; | |
bbefa4c4 | 773 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 774 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
4349f5a4 | 775 | if (TMath::Abs(fP[4])< kAlmost0) return kFALSE; |
49d13e89 | 776 | |
777 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
778 | Double_t | |
779 | &fC00=fC[0], | |
780 | &fC10=fC[1], &fC11=fC[2], | |
781 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
782 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
783 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
784 | ||
bfd20868 | 785 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
4349f5a4 | 786 | if (TMath::Abs(r1)<kAlmost0) return kFALSE; |
787 | if (TMath::Abs(r2)<kAlmost0) return kFALSE; | |
49d13e89 | 788 | |
789 | fX=xk; | |
2de63fc5 | 790 | double dy2dx = (f1+f2)/(r1+r2); |
791 | fP0 += dx*dy2dx; | |
792 | if (TMath::Abs(x2r)<0.05) { | |
793 | fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov ! | |
794 | fP2 += x2r; | |
795 | } | |
796 | else { | |
797 | // for small dx/R the linear apporximation of the arc by the segment is OK, | |
798 | // but at large dx/R the error is very large and leads to incorrect Z propagation | |
799 | // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi | |
800 | // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2) | |
801 | // Similarly, the rotation angle in linear in dx only for dx<<R | |
802 | double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one | |
803 | double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center | |
804 | fP1 += rot/crv*fP3; | |
805 | fP2 = TMath::Sin(rot + TMath::ASin(fP2)); | |
806 | } | |
49d13e89 | 807 | |
808 | //f = F - 1 | |
e804766b | 809 | /* |
49d13e89 | 810 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; |
811 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
812 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
813 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
814 | Double_t f13= dx/r1; | |
815 | Double_t f24= dx; f24*=cc; | |
e804766b | 816 | */ |
817 | Double_t rinv = 1./r1; | |
818 | Double_t r3inv = rinv*rinv*rinv; | |
819 | Double_t f24= x2r/fP4; | |
820 | Double_t f02= dx*r3inv; | |
821 | Double_t f04=0.5*f24*f02; | |
822 | Double_t f12= f02*fP3*f1; | |
823 | Double_t f14=0.5*f24*f02*fP3*f1; | |
824 | Double_t f13= dx*rinv; | |
825 | ||
49d13e89 | 826 | //b = C*ft |
827 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
828 | Double_t b02=f24*fC40; | |
829 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
830 | Double_t b12=f24*fC41; | |
831 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
832 | Double_t b22=f24*fC42; | |
833 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
834 | Double_t b42=f24*fC44; | |
835 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
836 | Double_t b32=f24*fC43; | |
837 | ||
838 | //a = f*b = f*C*ft | |
839 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
840 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
841 | Double_t a22=f24*b42; | |
842 | ||
843 | //F*C*Ft = C + (b + bt + a) | |
844 | fC00 += b00 + b00 + a00; | |
845 | fC10 += b10 + b01 + a01; | |
846 | fC20 += b20 + b02 + a02; | |
847 | fC30 += b30; | |
848 | fC40 += b40; | |
849 | fC11 += b11 + b11 + a11; | |
850 | fC21 += b21 + b12 + a12; | |
851 | fC31 += b31; | |
852 | fC41 += b41; | |
853 | fC22 += b22 + b22 + a22; | |
854 | fC32 += b32; | |
855 | fC42 += b42; | |
856 | ||
86be8934 | 857 | CheckCovariance(); |
858 | ||
49d13e89 | 859 | return kTRUE; |
860 | } | |
861 | ||
599b440e | 862 | Bool_t AliExternalTrackParam::PropagateParamOnlyTo(Double_t xk, Double_t b) { |
863 | //---------------------------------------------------------------- | |
864 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
865 | // Only parameters are propagated, not the matrix. To be used for small | |
866 | // distances only (<mm, i.e. misalignment) | |
867 | //---------------------------------------------------------------- | |
868 | Double_t dx=xk-fX; | |
869 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
870 | ||
871 | Double_t crv=GetC(b); | |
872 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
873 | ||
874 | Double_t x2r = crv*dx; | |
875 | Double_t f1=fP[2], f2=f1 + x2r; | |
876 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
877 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
878 | if (TMath::Abs(fP[4])< kAlmost0) return kFALSE; | |
879 | ||
880 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); | |
881 | if (TMath::Abs(r1)<kAlmost0) return kFALSE; | |
882 | if (TMath::Abs(r2)<kAlmost0) return kFALSE; | |
883 | ||
884 | fX=xk; | |
885 | double dy2dx = (f1+f2)/(r1+r2); | |
886 | fP[0] += dx*dy2dx; | |
887 | fP[1] += dx*(r2 + f2*dy2dx)*fP[3]; // Many thanks to P.Hristov ! | |
888 | fP[2] += x2r; | |
889 | ||
890 | return kTRUE; | |
891 | } | |
892 | ||
9f2bec63 | 893 | Bool_t |
894 | AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) { | |
895 | //------------------------------------------------------------------ | |
896 | // Transform this track to the local coord. system rotated | |
897 | // by angle "alpha" (rad) with respect to the global coord. system, | |
898 | // and propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
899 | //------------------------------------------------------------------ | |
900 | ||
901 | //Save the parameters | |
902 | Double_t as=fAlpha; | |
903 | Double_t xs=fX; | |
904 | Double_t ps[5], cs[15]; | |
905 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
906 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
907 | ||
908 | if (Rotate(alpha)) | |
909 | if (PropagateTo(x,b)) return kTRUE; | |
910 | ||
911 | //Restore the parameters, if the operation failed | |
912 | fAlpha=as; | |
913 | fX=xs; | |
914 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
915 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
916 | return kFALSE; | |
917 | } | |
918 | ||
266a0f9b | 919 | Bool_t AliExternalTrackParam::PropagateBxByBz |
920 | (Double_t alpha, Double_t x, Double_t b[3]) { | |
921 | //------------------------------------------------------------------ | |
922 | // Transform this track to the local coord. system rotated | |
923 | // by angle "alpha" (rad) with respect to the global coord. system, | |
924 | // and propagate this track to the plane X=xk (cm), | |
925 | // taking into account all three components of the B field, "b[3]" (kG) | |
926 | //------------------------------------------------------------------ | |
927 | ||
928 | //Save the parameters | |
929 | Double_t as=fAlpha; | |
930 | Double_t xs=fX; | |
931 | Double_t ps[5], cs[15]; | |
932 | for (Int_t i=0; i<5; i++) ps[i]=fP[i]; | |
933 | for (Int_t i=0; i<15; i++) cs[i]=fC[i]; | |
934 | ||
935 | if (Rotate(alpha)) | |
936 | if (PropagateToBxByBz(x,b)) return kTRUE; | |
937 | ||
938 | //Restore the parameters, if the operation failed | |
939 | fAlpha=as; | |
940 | fX=xs; | |
941 | for (Int_t i=0; i<5; i++) fP[i]=ps[i]; | |
942 | for (Int_t i=0; i<15; i++) fC[i]=cs[i]; | |
943 | return kFALSE; | |
944 | } | |
945 | ||
9f2bec63 | 946 | |
052daaff | 947 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
948 | Double_t p[3], Double_t bz) const { | |
949 | //+++++++++++++++++++++++++++++++++++++++++ | |
950 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
951 | // Extrapolate track along simple helix in magnetic field | |
952 | // Arguments: len -distance alogn helix, [cm] | |
953 | // bz - mag field, [kGaus] | |
954 | // Returns: x and p contain extrapolated positon and momentum | |
955 | // The momentum returned for straight-line tracks is meaningless ! | |
956 | //+++++++++++++++++++++++++++++++++++++++++ | |
957 | GetXYZ(x); | |
958 | ||
2258e165 | 959 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks |
052daaff | 960 | Double_t unit[3]; GetDirection(unit); |
961 | x[0]+=unit[0]*len; | |
962 | x[1]+=unit[1]*len; | |
963 | x[2]+=unit[2]*len; | |
964 | ||
965 | p[0]=unit[0]/kAlmost0; | |
966 | p[1]=unit[1]/kAlmost0; | |
967 | p[2]=unit[2]/kAlmost0; | |
968 | } else { | |
969 | GetPxPyPz(p); | |
970 | Double_t pp=GetP(); | |
971 | Double_t a = -kB2C*bz*GetSign(); | |
972 | Double_t rho = a/pp; | |
973 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
974 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
975 | x[2] += p[2]*len/pp; | |
976 | ||
977 | Double_t p0=p[0]; | |
978 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
979 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
980 | } | |
981 | } | |
982 | ||
983 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
984 | Double_t bz) const { | |
985 | //+++++++++++++++++++++++++++++++++++++++++ | |
986 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
987 | // Finds point of intersection (if exists) of the helix with the plane. | |
988 | // Stores result in fX and fP. | |
989 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
990 | // and vector, normal to the plane | |
991 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
992 | //+++++++++++++++++++++++++++++++++++++++++ | |
993 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
994 | ||
995 | //estimates initial helix length up to plane | |
996 | Double_t s= | |
997 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
998 | Double_t dist=99999,distPrev=dist; | |
999 | Double_t x[3],p[3]; | |
1000 | while(TMath::Abs(dist)>0.00001){ | |
1001 | //calculates helix at the distance s from x0 ALONG the helix | |
1002 | Propagate(s,x,p,bz); | |
1003 | ||
1004 | //distance between current helix position and plane | |
1005 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
1006 | ||
1007 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
1008 | distPrev=dist; | |
1009 | s-=dist; | |
1010 | } | |
1011 | //on exit pnt is intersection point,norm is track vector at that point, | |
1012 | //all in MARS | |
1013 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
1014 | return kTRUE; | |
1015 | } | |
1016 | ||
49d13e89 | 1017 | Double_t |
1018 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
1019 | //---------------------------------------------------------------- | |
1020 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
1021 | //---------------------------------------------------------------- | |
1022 | Double_t sdd = fC[0] + cov[0]; | |
1023 | Double_t sdz = fC[1] + cov[1]; | |
1024 | Double_t szz = fC[2] + cov[2]; | |
1025 | Double_t det = sdd*szz - sdz*sdz; | |
1026 | ||
1027 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
1028 | ||
1029 | Double_t d = fP[0] - p[0]; | |
1030 | Double_t z = fP[1] - p[1]; | |
1031 | ||
1032 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
1033 | } | |
1034 | ||
4b189f98 | 1035 | Double_t AliExternalTrackParam:: |
1036 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
1037 | //---------------------------------------------------------------- | |
1038 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 1039 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 1040 | // |
1041 | // Cov(x,x) ... : covxyz[0] | |
1042 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
1043 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
1044 | //---------------------------------------------------------------- | |
1045 | ||
1046 | Double_t res[3] = { | |
1047 | GetX() - p[0], | |
1048 | GetY() - p[1], | |
1049 | GetZ() - p[2] | |
1050 | }; | |
1051 | ||
1052 | Double_t f=GetSnp(); | |
1053 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
bfd20868 | 1054 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
4b189f98 | 1055 | Double_t a=f/r, b=GetTgl()/r; |
1056 | ||
1057 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
1058 | ||
1059 | TMatrixDSym v(3); | |
1060 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
1061 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
1062 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
1063 | ||
1064 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
1065 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
1066 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
1067 | ||
1068 | v.Invert(); | |
1069 | if (!v.IsValid()) return kVeryBig; | |
1070 | ||
1071 | Double_t chi2=0.; | |
1072 | for (Int_t i = 0; i < 3; i++) | |
1073 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
1074 | ||
1075 | return chi2; | |
acdfbc78 | 1076 | } |
1077 | ||
1078 | Double_t AliExternalTrackParam:: | |
1079 | GetPredictedChi2(const AliExternalTrackParam *t) const { | |
1080 | //---------------------------------------------------------------- | |
1081 | // Estimate the chi2 (5 dof) of this track with respect to the track | |
1082 | // given by the argument. | |
1083 | // The two tracks must be in the same reference system | |
1084 | // and estimated at the same reference plane. | |
1085 | //---------------------------------------------------------------- | |
1086 | ||
1087 | if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) { | |
1088 | AliError("The reference systems of the tracks differ !"); | |
1089 | return kVeryBig; | |
1090 | } | |
1091 | if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) { | |
1092 | AliError("The reference of the tracks planes differ !"); | |
1093 | return kVeryBig; | |
1094 | } | |
1095 | ||
1096 | TMatrixDSym c(5); | |
1097 | c(0,0)=GetSigmaY2(); | |
1098 | c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2(); | |
1099 | c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2(); | |
1100 | c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2(); | |
1101 | c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2(); | |
1102 | ||
1103 | c(0,0)+=t->GetSigmaY2(); | |
1104 | c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2(); | |
1105 | c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2(); | |
1106 | c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2(); | |
1107 | 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(); | |
1108 | c(0,1)=c(1,0); | |
1109 | c(0,2)=c(2,0); c(1,2)=c(2,1); | |
1110 | c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2); | |
1111 | c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3); | |
1112 | ||
1113 | c.Invert(); | |
1114 | if (!c.IsValid()) return kVeryBig; | |
1115 | ||
1116 | ||
1117 | Double_t res[5] = { | |
1118 | GetY() - t->GetY(), | |
1119 | GetZ() - t->GetZ(), | |
1120 | GetSnp() - t->GetSnp(), | |
1121 | GetTgl() - t->GetTgl(), | |
1122 | GetSigned1Pt() - t->GetSigned1Pt() | |
1123 | }; | |
4b189f98 | 1124 | |
acdfbc78 | 1125 | Double_t chi2=0.; |
1126 | for (Int_t i = 0; i < 5; i++) | |
1127 | for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j); | |
4b189f98 | 1128 | |
acdfbc78 | 1129 | return chi2; |
4b189f98 | 1130 | } |
1131 | ||
1e023a36 | 1132 | Bool_t AliExternalTrackParam:: |
1133 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
1134 | //---------------------------------------------------------------- | |
1135 | // Propagate this track to the plane | |
1136 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
1137 | // belongs to. | |
1138 | // The magnetic field is "bz" (kG) | |
1139 | // | |
1140 | // The track curvature and the change of the covariance matrix | |
1141 | // of the track parameters are negleted ! | |
1142 | // (So the "step" should be small compared with 1/curvature) | |
1143 | //---------------------------------------------------------------- | |
1144 | ||
1145 | Double_t f=GetSnp(); | |
1146 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
bfd20868 | 1147 | Double_t r=TMath::Sqrt((1.-f)*(1.+f)); |
1e023a36 | 1148 | Double_t a=f/r, b=GetTgl()/r; |
1149 | ||
1150 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
1151 | ||
1152 | TMatrixDSym tV(3); | |
1153 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
1154 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
1155 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
1156 | ||
1157 | TMatrixDSym pV(3); | |
1158 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
1159 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
1160 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
1161 | ||
1162 | TMatrixDSym tpV(tV); | |
1163 | tpV+=pV; | |
1164 | tpV.Invert(); | |
1165 | if (!tpV.IsValid()) return kFALSE; | |
1166 | ||
1167 | TMatrixDSym pW(3),tW(3); | |
1168 | for (Int_t i=0; i<3; i++) | |
1169 | for (Int_t j=0; j<3; j++) { | |
1170 | pW(i,j)=tW(i,j)=0.; | |
1171 | for (Int_t k=0; k<3; k++) { | |
1172 | pW(i,j) += tV(i,k)*tpV(k,j); | |
1173 | tW(i,j) += pV(i,k)*tpV(k,j); | |
1174 | } | |
1175 | } | |
1176 | ||
1177 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
1178 | ||
1179 | Double_t x=0.; | |
1180 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
1181 | Double_t crv=GetC(bz); | |
1182 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1183 | f += crv*(x-fX); | |
1184 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
1185 | fX=x; | |
1186 | ||
1187 | fP[0]=0.; | |
1188 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
1189 | fP[1]=0.; | |
1190 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
1191 | ||
1192 | return kTRUE; | |
1193 | } | |
1194 | ||
e23a38cb | 1195 | Double_t *AliExternalTrackParam::GetResiduals( |
1196 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
1197 | //------------------------------------------------------------------ | |
1198 | // Returns the track residuals with the space point "p" having | |
1199 | // the covariance matrix "cov". | |
1200 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
1201 | // otherwise they must be predicted. | |
1202 | //------------------------------------------------------------------ | |
1203 | static Double_t res[2]; | |
1204 | ||
1205 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1206 | if (updated) { | |
1207 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
1208 | } else { | |
1209 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
1210 | } | |
1211 | Double_t det=r00*r11 - r01*r01; | |
1212 | ||
1213 | if (TMath::Abs(det) < kAlmost0) return 0; | |
1214 | ||
1215 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 1216 | |
1217 | if (r00 < 0.) return 0; | |
1218 | if (r11 < 0.) return 0; | |
1219 | ||
e23a38cb | 1220 | Double_t dy = fP[0] - p[0]; |
1221 | Double_t dz = fP[1] - p[1]; | |
1222 | ||
1223 | res[0]=dy*TMath::Sqrt(r00); | |
1224 | res[1]=dz*TMath::Sqrt(r11); | |
1225 | ||
1226 | return res; | |
1227 | } | |
1228 | ||
49d13e89 | 1229 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
1230 | //------------------------------------------------------------------ | |
1231 | // Update the track parameters with the space point "p" having | |
1232 | // the covariance matrix "cov" | |
1233 | //------------------------------------------------------------------ | |
1234 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
1235 | Double_t | |
1236 | &fC00=fC[0], | |
1237 | &fC10=fC[1], &fC11=fC[2], | |
1238 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
1239 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
1240 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
1241 | ||
1242 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
1243 | r00+=fC00; r01+=fC10; r11+=fC11; | |
1244 | Double_t det=r00*r11 - r01*r01; | |
1245 | ||
1246 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
1247 | ||
1248 | ||
1249 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
1250 | ||
1251 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
1252 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
1253 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
1254 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
1255 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
1256 | ||
1257 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
1258 | Double_t sf=fP2 + k20*dy + k21*dz; | |
1259 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
1260 | ||
1261 | fP0 += k00*dy + k01*dz; | |
1262 | fP1 += k10*dy + k11*dz; | |
1263 | fP2 = sf; | |
1264 | fP3 += k30*dy + k31*dz; | |
1265 | fP4 += k40*dy + k41*dz; | |
1266 | ||
1267 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
1268 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
1269 | ||
1270 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
1271 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
1272 | fC40-=k00*c04+k01*c14; | |
1273 | ||
1274 | fC11-=k10*c01+k11*fC11; | |
1275 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
1276 | fC41-=k10*c04+k11*c14; | |
1277 | ||
1278 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
1279 | fC42-=k20*c04+k21*c14; | |
1280 | ||
1281 | fC33-=k30*c03+k31*c13; | |
1282 | fC43-=k30*c04+k31*c14; | |
599b440e | 1283 | |
49d13e89 | 1284 | fC44-=k40*c04+k41*c14; |
1285 | ||
86be8934 | 1286 | CheckCovariance(); |
1287 | ||
49d13e89 | 1288 | return kTRUE; |
1289 | } | |
1290 | ||
c7bafca9 | 1291 | void |
1292 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
1293 | //-------------------------------------------------------------------- | |
1294 | // External track parameters -> helix parameters | |
1295 | // "b" - magnetic field (kG) | |
1296 | //-------------------------------------------------------------------- | |
1297 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1298 | ||
1530f89c | 1299 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 1300 | |
1301 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
1302 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
1303 | //hlx[1]= // z0 | |
1304 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
1305 | //hlx[3]= // tgl | |
1530f89c | 1306 | hlx[4]=GetC(b); // C |
c7bafca9 | 1307 | } |
1308 | ||
1309 | ||
1310 | static void Evaluate(const Double_t *h, Double_t t, | |
1311 | Double_t r[3], //radius vector | |
1312 | Double_t g[3], //first defivatives | |
1313 | Double_t gg[3]) //second derivatives | |
1314 | { | |
1315 | //-------------------------------------------------------------------- | |
1316 | // Calculate position of a point on a track and some derivatives | |
1317 | //-------------------------------------------------------------------- | |
1318 | Double_t phase=h[4]*t+h[2]; | |
1319 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
1320 | ||
ba4550c4 | 1321 | r[0] = h[5]; |
1322 | r[1] = h[0]; | |
1323 | if (TMath::Abs(h[4])>kAlmost0) { | |
1324 | r[0] += (sn - h[6])/h[4]; | |
1325 | r[1] -= (cs - h[7])/h[4]; | |
1326 | } | |
c7bafca9 | 1327 | r[2] = h[1] + h[3]*t; |
1328 | ||
1329 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
1330 | ||
1331 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
1332 | } | |
1333 | ||
1334 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
1335 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
1336 | //------------------------------------------------------------ | |
1337 | // Returns the (weighed !) distance of closest approach between | |
1338 | // this track and the track "p". | |
1339 | // Other returned values: | |
1340 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
1341 | //----------------------------------------------------------- | |
1342 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
1343 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
1344 | Double_t dx2=dy2; | |
1345 | ||
c7bafca9 | 1346 | Double_t p1[8]; GetHelixParameters(p1,b); |
1347 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
1348 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
1349 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
1350 | ||
1351 | ||
1352 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
1353 | Evaluate(p1,t1,r1,g1,gg1); | |
1354 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
1355 | Evaluate(p2,t2,r2,g2,gg2); | |
1356 | ||
1357 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
1358 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1359 | ||
1360 | Int_t max=27; | |
1361 | while (max--) { | |
1362 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
1363 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
1364 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
1365 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
1366 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
1367 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
1368 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
1369 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
1370 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
1371 | ||
1372 | Double_t det=h11*h22-h12*h12; | |
1373 | ||
1374 | Double_t dt1,dt2; | |
1375 | if (TMath::Abs(det)<1.e-33) { | |
1376 | //(quasi)singular Hessian | |
1377 | dt1=-gt1; dt2=-gt2; | |
1378 | } else { | |
1379 | dt1=-(gt1*h22 - gt2*h12)/det; | |
1380 | dt2=-(h11*gt2 - h12*gt1)/det; | |
1381 | } | |
1382 | ||
1383 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
1384 | ||
1385 | //check delta(phase1) ? | |
1386 | //check delta(phase2) ? | |
1387 | ||
1388 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
1389 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
1390 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 1391 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 1392 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
1393 | if (lmb < 0.) | |
358f16ae | 1394 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 1395 | break; |
1396 | } | |
1397 | ||
1398 | Double_t dd=dm; | |
1399 | for (Int_t div=1 ; ; div*=2) { | |
1400 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
1401 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
1402 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
1403 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
1404 | if (dd<dm) break; | |
1405 | dt1*=0.5; dt2*=0.5; | |
1406 | if (div>512) { | |
358f16ae | 1407 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 1408 | } |
1409 | } | |
1410 | dm=dd; | |
1411 | ||
1412 | t1+=dt1; | |
1413 | t2+=dt2; | |
1414 | ||
1415 | } | |
1416 | ||
358f16ae | 1417 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1418 | |
1419 | Double_t cs=TMath::Cos(GetAlpha()); | |
1420 | Double_t sn=TMath::Sin(GetAlpha()); | |
1421 | xthis=r1[0]*cs + r1[1]*sn; | |
1422 | ||
1423 | cs=TMath::Cos(p->GetAlpha()); | |
1424 | sn=TMath::Sin(p->GetAlpha()); | |
1425 | xp=r2[0]*cs + r2[1]*sn; | |
1426 | ||
1427 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1428 | } | |
1429 | ||
1430 | Double_t AliExternalTrackParam:: | |
1431 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1432 | //-------------------------------------------------------------- | |
1433 | // Propagates this track and the argument track to the position of the | |
1434 | // distance of closest approach. | |
1435 | // Returns the (weighed !) distance of closest approach. | |
1436 | //-------------------------------------------------------------- | |
1437 | Double_t xthis,xp; | |
1438 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1439 | ||
1440 | if (!PropagateTo(xthis,b)) { | |
1441 | //AliWarning(" propagation failed !"); | |
1442 | return 1e+33; | |
1443 | } | |
1444 | ||
1445 | if (!p->PropagateTo(xp,b)) { | |
1446 | //AliWarning(" propagation failed !"; | |
1447 | return 1e+33; | |
1448 | } | |
1449 | ||
1450 | return dca; | |
1451 | } | |
1452 | ||
1453 | ||
58e536c5 | 1454 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1455 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1456 | // |
e99a34df | 1457 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1458 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1459 | // Magnetic field is "b" (kG). | |
1460 | // | |
1461 | // a) The track gets extapolated to the DCA to the vertex. | |
1462 | // b) The impact parameters and their covariance matrix are calculated. | |
1463 | // | |
1464 | // In the case of success, the returned value is kTRUE | |
1465 | // (otherwise, it's kFALSE) | |
1466 | // | |
1467 | Double_t alpha=GetAlpha(); | |
1468 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1469 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1470 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1471 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1472 | x-=xv; y-=yv; |
1473 | ||
1474 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1475 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
f76701bf | 1476 | if (d > maxd) return kFALSE; |
1477 | ||
1478 | //Propagate to the DCA | |
2258e165 | 1479 | Double_t crv=GetC(b); |
e99a34df | 1480 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1481 | ||
bfd20868 | 1482 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1483 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
e99a34df | 1484 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1485 | else cs=1.; | |
f76701bf | 1486 | |
1487 | x = xv*cs + yv*sn; | |
1488 | yv=-xv*sn + yv*cs; xv=x; | |
1489 | ||
1490 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
266a0f9b | 1491 | |
1492 | if (dz==0) return kTRUE; | |
1493 | dz[0] = GetParameter()[0] - yv; | |
1494 | dz[1] = GetParameter()[1] - zv; | |
1495 | ||
1496 | if (covar==0) return kTRUE; | |
1497 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); | |
1498 | ||
1499 | //***** Improvements by A.Dainese | |
1500 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1501 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1502 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1503 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1504 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1505 | //***** | |
1506 | ||
1507 | return kTRUE; | |
1508 | } | |
1509 | ||
1510 | Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx, | |
1511 | Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) { | |
1512 | // | |
1513 | // Propagate this track to the DCA to vertex "vtx", | |
1514 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
1515 | // | |
1516 | // This function takes into account all three components of the magnetic | |
1517 | // field given by the b[3] arument (kG) | |
1518 | // | |
1519 | // a) The track gets extapolated to the DCA to the vertex. | |
1520 | // b) The impact parameters and their covariance matrix are calculated. | |
1521 | // | |
1522 | // In the case of success, the returned value is kTRUE | |
1523 | // (otherwise, it's kFALSE) | |
1524 | // | |
1525 | Double_t alpha=GetAlpha(); | |
1526 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1527 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
1528 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; | |
1529 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
1530 | x-=xv; y-=yv; | |
1531 | ||
1532 | //Estimate the impact parameter neglecting the track curvature | |
bfd20868 | 1533 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp))); |
266a0f9b | 1534 | if (d > maxd) return kFALSE; |
1535 | ||
1536 | //Propagate to the DCA | |
8567bf39 | 1537 | Double_t crv=GetC(b[2]); |
1538 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
266a0f9b | 1539 | |
bfd20868 | 1540 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp))); |
1541 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn)); | |
266a0f9b | 1542 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1543 | else cs=1.; | |
1544 | ||
1545 | x = xv*cs + yv*sn; | |
1546 | yv=-xv*sn + yv*cs; xv=x; | |
1547 | ||
1548 | if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1549 | |
1550 | if (dz==0) return kTRUE; | |
1551 | dz[0] = GetParameter()[0] - yv; | |
1552 | dz[1] = GetParameter()[1] - zv; | |
1553 | ||
1554 | if (covar==0) return kTRUE; | |
58e536c5 | 1555 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1556 | |
1557 | //***** Improvements by A.Dainese | |
1558 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1559 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1560 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1561 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1562 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1563 | //***** | |
1564 | ||
29fbcc93 | 1565 | return kTRUE; |
f76701bf | 1566 | } |
1567 | ||
b1149664 | 1568 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1569 | //---------------------------------------------------------------- | |
1570 | // This function returns a unit vector along the track direction | |
1571 | // in the global coordinate system. | |
1572 | //---------------------------------------------------------------- | |
1573 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1574 | Double_t snp=fP[2]; | |
bfd20868 | 1575 | Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp)); |
b1149664 | 1576 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1577 | d[0]=(csp*cs - snp*sn)/norm; | |
1578 | d[1]=(snp*cs + csp*sn)/norm; | |
1579 | d[2]=fP[3]/norm; | |
1580 | } | |
1581 | ||
c683ddc2 | 1582 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1583 | //--------------------------------------------------------------------- |
1584 | // This function returns the global track momentum components | |
1585 | // Results for (nearly) straight tracks are meaningless ! | |
1586 | //--------------------------------------------------------------------- | |
1587 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1588 | return Local2GlobalMomentum(p,fAlpha); | |
1589 | } | |
a5e407e9 | 1590 | |
def9660e | 1591 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1592 | //--------------------------------------------------------------------- |
1593 | // Returns x-component of momentum | |
1594 | // Result for (nearly) straight tracks is meaningless ! | |
1595 | //--------------------------------------------------------------------- | |
def9660e | 1596 | |
957fb479 | 1597 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1598 | GetPxPyPz(p); |
1599 | ||
1600 | return p[0]; | |
1601 | } | |
1602 | ||
1603 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1604 | //--------------------------------------------------------------------- |
1605 | // Returns y-component of momentum | |
1606 | // Result for (nearly) straight tracks is meaningless ! | |
1607 | //--------------------------------------------------------------------- | |
def9660e | 1608 | |
957fb479 | 1609 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1610 | GetPxPyPz(p); |
1611 | ||
1612 | return p[1]; | |
1613 | } | |
1614 | ||
c683ddc2 | 1615 | Double_t AliExternalTrackParam::Xv() const { |
1616 | //--------------------------------------------------------------------- | |
1617 | // Returns x-component of first track point | |
1618 | //--------------------------------------------------------------------- | |
1619 | ||
1620 | Double_t r[3]={0.,0.,0.}; | |
1621 | GetXYZ(r); | |
1622 | ||
1623 | return r[0]; | |
1624 | } | |
1625 | ||
1626 | Double_t AliExternalTrackParam::Yv() const { | |
1627 | //--------------------------------------------------------------------- | |
1628 | // Returns y-component of first track point | |
1629 | //--------------------------------------------------------------------- | |
1630 | ||
1631 | Double_t r[3]={0.,0.,0.}; | |
1632 | GetXYZ(r); | |
1633 | ||
1634 | return r[1]; | |
1635 | } | |
1636 | ||
def9660e | 1637 | Double_t AliExternalTrackParam::Theta() const { |
1638 | // return theta angle of momentum | |
1639 | ||
7cdd0c20 | 1640 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1641 | } |
1642 | ||
1643 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1644 | //--------------------------------------------------------------------- |
1645 | // Returns the azimuthal angle of momentum | |
1646 | // 0 <= phi < 2*pi | |
1647 | //--------------------------------------------------------------------- | |
def9660e | 1648 | |
957fb479 | 1649 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1650 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1651 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1652 | ||
1653 | return phi; | |
def9660e | 1654 | } |
1655 | ||
1656 | Double_t AliExternalTrackParam::M() const { | |
1657 | // return particle mass | |
1658 | ||
1659 | // No mass information available so far. | |
1660 | // Redifine in derived class! | |
1661 | ||
1662 | return -999.; | |
1663 | } | |
1664 | ||
1665 | Double_t AliExternalTrackParam::E() const { | |
1666 | // return particle energy | |
1667 | ||
1668 | // No PID information available so far. | |
1669 | // Redifine in derived class! | |
1670 | ||
1671 | return -999.; | |
1672 | } | |
1673 | ||
1674 | Double_t AliExternalTrackParam::Eta() const { | |
1675 | // return pseudorapidity | |
1676 | ||
1677 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1678 | } | |
1679 | ||
1680 | Double_t AliExternalTrackParam::Y() const { | |
1681 | // return rapidity | |
1682 | ||
1683 | // No PID information available so far. | |
1684 | // Redifine in derived class! | |
1685 | ||
1686 | return -999.; | |
1687 | } | |
1688 | ||
c9ec41e8 | 1689 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1690 | //--------------------------------------------------------------------- | |
1691 | // This function returns the global track position | |
1692 | //--------------------------------------------------------------------- | |
1693 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1694 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1695 | } |
1696 | ||
c9ec41e8 | 1697 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1698 | //--------------------------------------------------------------------- | |
1699 | // This function returns the global covariance matrix of the track params | |
1700 | // | |
1701 | // Cov(x,x) ... : cv[0] | |
1702 | // Cov(y,x) ... : cv[1] cv[2] | |
1703 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1704 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1705 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1706 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1707 | // |
c9ec41e8 | 1708 | // Results for (nearly) straight tracks are meaningless ! |
1709 | //--------------------------------------------------------------------- | |
e421f556 | 1710 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1711 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1712 | return kFALSE; | |
a5e407e9 | 1713 | } |
49d13e89 | 1714 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1715 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1716 | return kFALSE; | |
1717 | } | |
1718 | Double_t pt=1./TMath::Abs(fP[4]); | |
1719 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1720 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1721 | |
1722 | Double_t m00=-sn, m10=cs; | |
1723 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1724 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1725 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1726 | ||
854d5d49 | 1727 | m43*=GetSign(); |
1728 | m44*=GetSign(); | |
1729 | m45*=GetSign(); | |
1730 | ||
c9ec41e8 | 1731 | cv[0 ] = fC[0]*m00*m00; |
1732 | cv[1 ] = fC[0]*m00*m10; | |
1733 | cv[2 ] = fC[0]*m10*m10; | |
1734 | cv[3 ] = fC[1]*m00; | |
1735 | cv[4 ] = fC[1]*m10; | |
1736 | cv[5 ] = fC[2]; | |
1737 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1738 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1739 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1740 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1741 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1742 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1743 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1744 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1745 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1746 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1747 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1748 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1749 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1750 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1751 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1752 | |
c9ec41e8 | 1753 | return kTRUE; |
51ad6848 | 1754 | } |
1755 | ||
51ad6848 | 1756 | |
c9ec41e8 | 1757 | Bool_t |
1758 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1759 | //--------------------------------------------------------------------- | |
1760 | // This function returns the global track momentum extrapolated to | |
1761 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1762 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1763 | p[0]=fP[4]; |
1530f89c | 1764 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1765 | p[2]=fP[3]; |
1766 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1767 | } |
1768 | ||
7cf7bb6c | 1769 | Bool_t |
1770 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1771 | //--------------------------------------------------------------------- | |
1772 | // This function returns the local Y-coordinate of the intersection | |
1773 | // point between this track and the reference plane "x" (cm). | |
1774 | // Magnetic field "b" (kG) | |
1775 | //--------------------------------------------------------------------- | |
1776 | Double_t dx=x-fX; | |
1777 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1778 | ||
1530f89c | 1779 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1780 | |
1781 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1782 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1783 | ||
60e55aee | 1784 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
7cf7bb6c | 1785 | y = fP[0] + dx*(f1+f2)/(r1+r2); |
1786 | return kTRUE; | |
1787 | } | |
1788 | ||
6c94f330 | 1789 | Bool_t |
1790 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1791 | //--------------------------------------------------------------------- | |
1792 | // This function returns the local Z-coordinate of the intersection | |
1793 | // point between this track and the reference plane "x" (cm). | |
1794 | // Magnetic field "b" (kG) | |
1795 | //--------------------------------------------------------------------- | |
1796 | Double_t dx=x-fX; | |
1797 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1798 | ||
2258e165 | 1799 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
6c94f330 | 1800 | |
1801 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1802 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1803 | ||
60e55aee | 1804 | Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2)); |
6c94f330 | 1805 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! |
1806 | return kTRUE; | |
1807 | } | |
1808 | ||
c9ec41e8 | 1809 | Bool_t |
1810 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1811 | //--------------------------------------------------------------------- | |
1812 | // This function returns the global track position extrapolated to | |
1813 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1814 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1815 | Double_t dx=x-fX; |
e421f556 | 1816 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1817 | ||
1530f89c | 1818 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1819 | |
e421f556 | 1820 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1821 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1822 | |
60e55aee | 1823 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
c9ec41e8 | 1824 | r[0] = x; |
1825 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
f90a11c9 | 1826 | r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter |
1827 | ||
c9ec41e8 | 1828 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1829 | } |
1830 | ||
51ad6848 | 1831 | //_____________________________________________________________________________ |
1832 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1833 | { | |
1834 | // print the parameters and the covariance matrix | |
1835 | ||
1836 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1837 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1838 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1839 | printf(" covariance: %12g\n", fC[0]); | |
1840 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1841 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1842 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1843 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1844 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1845 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1846 | } |
5b77d93c | 1847 | |
c194ba83 | 1848 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1849 | // | |
1850 | // Get sinus at given x | |
1851 | // | |
1530f89c | 1852 | Double_t crv=GetC(b); |
c194ba83 | 1853 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1854 | Double_t dx = x-fX; | |
1855 | Double_t res = fP[2]+dx*crv; | |
1856 | return res; | |
1857 | } | |
bf00ebb8 | 1858 | |
1859 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1860 | //------------------------------------------------------------------------ | |
1861 | // Get the distance between two tracks at the local position x | |
1862 | // working in the local frame of this track. | |
1863 | // Origin : Marian.Ivanov@cern.ch | |
1864 | //----------------------------------------------------------------------- | |
1865 | Double_t xyz[3]; | |
1866 | Double_t xyz2[3]; | |
1867 | xyz[0]=x; | |
1868 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1869 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1870 | // | |
1871 | // | |
1872 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1873 | xyz2[0]=x; | |
1874 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1875 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1876 | }else{ | |
1877 | // | |
1878 | Double_t xyz1[3]; | |
1879 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1880 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1881 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1882 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1883 | // | |
1884 | xyz1[0]=xyz2[0]; | |
1885 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1886 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1887 | // | |
1888 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1889 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1890 | xyz2[2] = xyz1[2]; | |
1891 | } | |
1892 | dist[0] = xyz[0]-xyz2[0]; | |
1893 | dist[1] = xyz[1]-xyz2[1]; | |
1894 | dist[2] = xyz[2]-xyz2[2]; | |
1895 | ||
1896 | return kTRUE; | |
1897 | } | |
0c19adf7 | 1898 | |
1899 | ||
1900 | // | |
1901 | // Draw functionality. | |
1902 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1903 | // | |
1904 | ||
1905 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1906 | // | |
1907 | // Draw track line | |
1908 | // | |
1909 | if (minR>maxR) return ; | |
1910 | if (stepR<=0) return ; | |
1911 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1912 | if (npoints<1) return; | |
1913 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1914 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1915 | polymarker->Draw(); | |
1916 | } | |
1917 | ||
1918 | // | |
1919 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1920 | // | |
1921 | // Fill points in the polymarker | |
1922 | // | |
1923 | Int_t counter=0; | |
1924 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1925 | Double_t point[3]; | |
1926 | GetXYZAt(r,magF,point); | |
1927 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
047640da | 1928 | // printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); |
0c19adf7 | 1929 | counter++; |
1930 | } | |
1931 | } | |
0e8460af | 1932 | |
1933 | Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const { | |
1934 | // | |
1935 | Int_t min = TMath::Min(i,j); | |
1936 | Int_t max = TMath::Max(i,j); | |
1937 | ||
1938 | return min+(max+1)*max/2; | |
1939 | } | |
8b6e3369 | 1940 | |
1941 | ||
1942 | void AliExternalTrackParam::g3helx3(Double_t qfield, | |
1943 | Double_t step, | |
1944 | Double_t vect[7]) { | |
1945 | /****************************************************************** | |
1946 | * * | |
1947 | * GEANT3 tracking routine in a constant field oriented * | |
1948 | * along axis 3 * | |
1949 | * Tracking is performed with a conventional * | |
1950 | * helix step method * | |
1951 | * * | |
1952 | * Authors R.Brun, M.Hansroul ********* * | |
1953 | * Rewritten V.Perevoztchikov * | |
1954 | * * | |
1955 | * Rewritten in C++ by I.Belikov * | |
1956 | * * | |
1957 | * qfield (kG) - particle charge times magnetic field * | |
1958 | * step (cm) - step length along the helix * | |
1959 | * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p * | |
1960 | * * | |
1961 | ******************************************************************/ | |
1962 | const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6; | |
bfd20868 | 1963 | const Double_t kOvSqSix=TMath::Sqrt(1./6.); |
8b6e3369 | 1964 | |
1965 | Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz]; | |
1966 | ||
1967 | Double_t rho = qfield*kB2C/vect[ipp]; | |
1968 | Double_t tet = rho*step; | |
1969 | ||
1970 | Double_t tsint, sintt, sint, cos1t; | |
2de63fc5 | 1971 | if (TMath::Abs(tet) > 0.03) { |
8b6e3369 | 1972 | sint = TMath::Sin(tet); |
1973 | sintt = sint/tet; | |
1974 | tsint = (tet - sint)/tet; | |
1975 | Double_t t=TMath::Sin(0.5*tet); | |
1976 | cos1t = 2*t*t/tet; | |
1977 | } else { | |
1978 | tsint = tet*tet/6.; | |
bfd20868 | 1979 | sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 1.- tsint; |
8b6e3369 | 1980 | sint = tet*sintt; |
1981 | cos1t = 0.5*tet; | |
1982 | } | |
1983 | ||
1984 | Double_t f1 = step*sintt; | |
1985 | Double_t f2 = step*cos1t; | |
1986 | Double_t f3 = step*tsint*cosz; | |
1987 | Double_t f4 = -tet*cos1t; | |
1988 | Double_t f5 = sint; | |
1989 | ||
1990 | vect[ix] += f1*cosx - f2*cosy; | |
1991 | vect[iy] += f1*cosy + f2*cosx; | |
1992 | vect[iz] += f1*cosz + f3; | |
1993 | ||
1994 | vect[ipx] += f4*cosx - f5*cosy; | |
1995 | vect[ipy] += f4*cosy + f5*cosx; | |
1996 | ||
1997 | } | |
1998 | ||
1999 | Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) { | |
2000 | //---------------------------------------------------------------- | |
2001 | // Extrapolate this track to the plane X=xk in the field b[]. | |
2002 | // | |
2003 | // X [cm] is in the "tracking coordinate system" of this track. | |
2004 | // b[]={Bx,By,Bz} [kG] is in the Global coordidate system. | |
2005 | //---------------------------------------------------------------- | |
2006 | ||
2007 | Double_t dx=xk-fX; | |
2008 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; | |
7e1b73dd | 2009 | if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE; |
ef3508c5 | 2010 | // Do not propagate tracks outside the ALICE detector |
2011 | if (TMath::Abs(dx)>1e5 || | |
2012 | TMath::Abs(GetY())>1e5 || | |
2013 | TMath::Abs(GetZ())>1e5) { | |
2014 | AliWarning(Form("Anomalous track, target X:%f",xk)); | |
2015 | Print(); | |
2016 | return kFALSE; | |
2017 | } | |
8b6e3369 | 2018 | |
2019 | Double_t crv=GetC(b[2]); | |
2020 | if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.; | |
2021 | ||
2de63fc5 | 2022 | Double_t x2r = crv*dx; |
2023 | Double_t f1=fP[2], f2=f1 + x2r; | |
8b6e3369 | 2024 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
2025 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
2026 | ||
2027 | ||
2028 | // Estimate the covariance matrix | |
2029 | Double_t &fP3=fP[3], &fP4=fP[4]; | |
2030 | Double_t | |
2031 | &fC00=fC[0], | |
2032 | &fC10=fC[1], &fC11=fC[2], | |
2033 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
2034 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
2035 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
2036 | ||
bfd20868 | 2037 | Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)); |
8b6e3369 | 2038 | |
2039 | //f = F - 1 | |
e804766b | 2040 | /* |
8b6e3369 | 2041 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; |
2042 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
2043 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
2044 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
2045 | Double_t f13= dx/r1; | |
2046 | Double_t f24= dx; f24*=cc; | |
e804766b | 2047 | */ |
2048 | Double_t rinv = 1./r1; | |
2049 | Double_t r3inv = rinv*rinv*rinv; | |
2050 | Double_t f24= x2r/fP4; | |
2051 | Double_t f02= dx*r3inv; | |
2052 | Double_t f04=0.5*f24*f02; | |
2053 | Double_t f12= f02*fP3*f1; | |
2054 | Double_t f14=0.5*f24*f02*fP3*f1; | |
2055 | Double_t f13= dx*rinv; | |
2056 | ||
8b6e3369 | 2057 | //b = C*ft |
2058 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
2059 | Double_t b02=f24*fC40; | |
2060 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
2061 | Double_t b12=f24*fC41; | |
2062 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
2063 | Double_t b22=f24*fC42; | |
2064 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
2065 | Double_t b42=f24*fC44; | |
2066 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
2067 | Double_t b32=f24*fC43; | |
2068 | ||
2069 | //a = f*b = f*C*ft | |
2070 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
2071 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
2072 | Double_t a22=f24*b42; | |
2073 | ||
2074 | //F*C*Ft = C + (b + bt + a) | |
2075 | fC00 += b00 + b00 + a00; | |
2076 | fC10 += b10 + b01 + a01; | |
2077 | fC20 += b20 + b02 + a02; | |
2078 | fC30 += b30; | |
2079 | fC40 += b40; | |
2080 | fC11 += b11 + b11 + a11; | |
2081 | fC21 += b21 + b12 + a12; | |
2082 | fC31 += b31; | |
2083 | fC41 += b41; | |
2084 | fC22 += b22 + b22 + a22; | |
2085 | fC32 += b32; | |
2086 | fC42 += b42; | |
2087 | ||
86be8934 | 2088 | CheckCovariance(); |
8b6e3369 | 2089 | |
2090 | // Appoximate step length | |
2de63fc5 | 2091 | double dy2dx = (f1+f2)/(r1+r2); |
2092 | Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord | |
2093 | : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc | |
8b6e3369 | 2094 | step *= TMath::Sqrt(1.+ GetTgl()*GetTgl()); |
2095 | ||
8b6e3369 | 2096 | // Get the track's (x,y,z) and (px,py,pz) in the Global System |
2097 | Double_t r[3]; GetXYZ(r); | |
2098 | Double_t p[3]; GetPxPyPz(p); | |
2099 | Double_t pp=GetP(); | |
2100 | p[0] /= pp; | |
2101 | p[1] /= pp; | |
2102 | p[2] /= pp; | |
2103 | ||
2104 | ||
2105 | // Rotate to the system where Bx=By=0. | |
2106 | Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]); | |
2107 | Double_t cosphi=1., sinphi=0.; | |
2108 | if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;} | |
2109 | Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]); | |
2110 | Double_t costet=1., sintet=0.; | |
2111 | if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;} | |
2112 | Double_t vect[7]; | |
2113 | ||
2114 | vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2]; | |
2115 | vect[1] = -sinphi*r[0] + cosphi*r[1]; | |
2116 | vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2]; | |
2117 | ||
2118 | vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2]; | |
2119 | vect[4] = -sinphi*p[0] + cosphi*p[1]; | |
2120 | vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2]; | |
2121 | ||
2122 | vect[6] = pp; | |
2123 | ||
2124 | ||
2125 | // Do the helix step | |
2126 | g3helx3(GetSign()*bb,step,vect); | |
2127 | ||
2128 | ||
2129 | // Rotate back to the Global System | |
2130 | r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2]; | |
2131 | r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2]; | |
2132 | r[2] = -sintet*vect[0] + costet*vect[2]; | |
2133 | ||
2134 | p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5]; | |
2135 | p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5]; | |
2136 | p[2] = -sintet*vect[3] + costet*vect[5]; | |
2137 | ||
2138 | ||
2139 | // Rotate back to the Tracking System | |
2140 | Double_t cosalp = TMath::Cos(fAlpha); | |
2141 | Double_t sinalp =-TMath::Sin(fAlpha); | |
2142 | ||
2143 | Double_t | |
2144 | t = cosalp*r[0] - sinalp*r[1]; | |
2145 | r[1] = sinalp*r[0] + cosalp*r[1]; | |
2146 | r[0] = t; | |
2147 | ||
2148 | t = cosalp*p[0] - sinalp*p[1]; | |
2149 | p[1] = sinalp*p[0] + cosalp*p[1]; | |
2150 | p[0] = t; | |
2151 | ||
2152 | ||
2153 | // Do the final correcting step to the target plane (linear approximation) | |
2154 | Double_t x=r[0], y=r[1], z=r[2]; | |
2155 | if (TMath::Abs(dx) > kAlmost0) { | |
2156 | if (TMath::Abs(p[0]) < kAlmost0) return kFALSE; | |
2157 | dx = xk - r[0]; | |
2158 | x += dx; | |
2159 | y += p[1]/p[0]*dx; | |
2160 | z += p[2]/p[0]*dx; | |
2161 | } | |
2162 | ||
2163 | ||
2164 | // Calculate the track parameters | |
2165 | t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]); | |
2166 | fX = x; | |
2167 | fP[0] = y; | |
2168 | fP[1] = z; | |
2169 | fP[2] = p[1]/t; | |
2170 | fP[3] = p[2]/t; | |
2171 | fP[4] = GetSign()/(t*pp); | |
2172 | ||
2173 | return kTRUE; | |
2174 | } | |
2175 | ||
cfdb62d4 | 2176 | Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){ |
2177 | // | |
2178 | //Translation: in the event mixing, the tracks can be shifted | |
2179 | //of the difference among primary vertices (vTrasl) and | |
2180 | //the covariance matrix is changed accordingly | |
2181 | //(covV = covariance of the primary vertex). | |
2182 | //Origin: "Romita, Rossella" <R.Romita@gsi.de> | |
2183 | // | |
2184 | TVector3 translation; | |
2185 | // vTrasl coordinates in the local system | |
2186 | translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]); | |
2187 | translation.RotateZ(-fAlpha); | |
2188 | translation.GetXYZ(vTrasl); | |
2189 | ||
2190 | //compute the new x,y,z of the track | |
5a87bb3d | 2191 | Double_t newX=fX-vTrasl[0]; |
2192 | Double_t newY=fP[0]-vTrasl[1]; | |
2193 | Double_t newZ=fP[1]-vTrasl[2]; | |
cfdb62d4 | 2194 | |
2195 | //define the new parameters | |
5a87bb3d | 2196 | Double_t newParam[5]; |
2197 | newParam[0]=newY; | |
2198 | newParam[1]=newZ; | |
2199 | newParam[2]=fP[2]; | |
2200 | newParam[3]=fP[3]; | |
2201 | newParam[4]=fP[4]; | |
cfdb62d4 | 2202 | |
2203 | // recompute the covariance matrix: | |
2204 | // 1. covV in the local system | |
2205 | Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha); | |
2206 | TMatrixD qQi(3,3); | |
2207 | qQi(0,0) = cosRot; | |
2208 | qQi(0,1) = sinRot; | |
2209 | qQi(0,2) = 0.; | |
2210 | qQi(1,0) = -sinRot; | |
2211 | qQi(1,1) = cosRot; | |
2212 | qQi(1,2) = 0.; | |
2213 | qQi(2,0) = 0.; | |
2214 | qQi(2,1) = 0.; | |
2215 | qQi(2,2) = 1.; | |
2216 | TMatrixD uUi(3,3); | |
2217 | uUi(0,0) = covV[0]; | |
2218 | uUi(0,0) = covV[0]; | |
2219 | uUi(1,0) = covV[1]; | |
2220 | uUi(0,1) = covV[1]; | |
2221 | uUi(2,0) = covV[3]; | |
2222 | uUi(0,2) = covV[3]; | |
2223 | uUi(1,1) = covV[2]; | |
2224 | uUi(2,2) = covV[5]; | |
2225 | uUi(1,2) = covV[4]; | |
2226 | if(uUi.Determinant() <= 0.) {return kFALSE;} | |
2227 | TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi); | |
2228 | TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi); | |
2229 | ||
2230 | //2. compute the new covariance matrix of the track | |
2231 | Double_t sigmaXX=m(0,0); | |
2232 | Double_t sigmaXZ=m(2,0); | |
2233 | Double_t sigmaXY=m(1,0); | |
2234 | Double_t sigmaYY=GetSigmaY2()+m(1,1); | |
2235 | Double_t sigmaYZ=fC[1]+m(1,2); | |
2236 | Double_t sigmaZZ=fC[2]+m(2,2); | |
2237 | Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX); | |
2238 | Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX); | |
2239 | Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX); | |
2240 | ||
2241 | Double_t newCov[15]; | |
2242 | newCov[0]=covarianceYY; | |
2243 | newCov[1]=covarianceYZ; | |
2244 | newCov[2]=covarianceZZ; | |
2245 | for(Int_t i=3;i<15;i++){ | |
2246 | newCov[i]=fC[i]; | |
2247 | } | |
2248 | ||
2249 | // set the new parameters | |
2250 | ||
5a87bb3d | 2251 | Set(newX,fAlpha,newParam,newCov); |
cfdb62d4 | 2252 | |
2253 | return kTRUE; | |
2254 | } | |
86be8934 | 2255 | |
2256 | void AliExternalTrackParam::CheckCovariance() { | |
2257 | ||
2258 | // This function forces the diagonal elements of the covariance matrix to be positive. | |
2259 | // In case the diagonal element is bigger than the maximal allowed value, it is set to | |
2260 | // the limit and the off-diagonal elements that correspond to it are set to zero. | |
2261 | ||
2262 | fC[0] = TMath::Abs(fC[0]); | |
2263 | if (fC[0]>kC0max) { | |
2264 | fC[0] = kC0max; | |
2265 | fC[1] = 0; | |
2266 | fC[3] = 0; | |
2267 | fC[6] = 0; | |
2268 | fC[10] = 0; | |
2269 | } | |
2270 | fC[2] = TMath::Abs(fC[2]); | |
2271 | if (fC[2]>kC2max) { | |
2272 | fC[2] = kC2max; | |
2273 | fC[1] = 0; | |
2274 | fC[4] = 0; | |
2275 | fC[7] = 0; | |
2276 | fC[11] = 0; | |
2277 | } | |
2278 | fC[5] = TMath::Abs(fC[5]); | |
2279 | if (fC[5]>kC5max) { | |
2280 | fC[5] = kC5max; | |
2281 | fC[3] = 0; | |
2282 | fC[4] = 0; | |
2283 | fC[8] = 0; | |
2284 | fC[12] = 0; | |
2285 | } | |
2286 | fC[9] = TMath::Abs(fC[9]); | |
2287 | if (fC[9]>kC9max) { | |
2288 | fC[9] = kC9max; | |
2289 | fC[6] = 0; | |
2290 | fC[7] = 0; | |
2291 | fC[8] = 0; | |
2292 | fC[13] = 0; | |
2293 | } | |
2294 | fC[14] = TMath::Abs(fC[14]); | |
2295 | if (fC[14]>kC14max) { | |
2296 | fC[14] = kC14max; | |
2297 | fC[10] = 0; | |
2298 | fC[11] = 0; | |
2299 | fC[12] = 0; | |
2300 | fC[13] = 0; | |
2301 | } | |
2302 | ||
2303 | // The part below is used for tests and normally is commented out | |
2304 | // TMatrixDSym m(5); | |
2305 | // TVectorD eig(5); | |
2306 | ||
2307 | // m(0,0)=fC[0]; | |
2308 | // m(1,0)=fC[1]; m(1,1)=fC[2]; | |
2309 | // m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5]; | |
2310 | // m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9]; | |
2311 | // 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]; | |
2312 | ||
2313 | // m(0,1)=m(1,0); | |
2314 | // m(0,2)=m(2,0); m(1,2)=m(2,1); | |
2315 | // m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2); | |
2316 | // m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3); | |
2317 | // m.EigenVectors(eig); | |
2318 | ||
2319 | // // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0); | |
2320 | // if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) { | |
2321 | // AliWarning("Negative eigenvalues of the covariance matrix!"); | |
2322 | // this->Print(); | |
2323 | // eig.Print(); | |
2324 | // } | |
2325 | } | |
4c3dc2a0 | 2326 | |
2327 | Bool_t AliExternalTrackParam::ConstrainToVertex(const AliVVertex* vtx, Double_t b[3]) | |
2328 | { | |
2329 | // Constrain TPC inner params constrained | |
2330 | // | |
2331 | if (!vtx) | |
2332 | return kFALSE; | |
2333 | ||
2334 | Double_t dz[2], cov[3]; | |
2335 | if (!PropagateToDCABxByBz(vtx, b, 3, dz, cov)) | |
2336 | return kFALSE; | |
2337 | ||
2338 | Double_t covar[6]; | |
2339 | vtx->GetCovarianceMatrix(covar); | |
2340 | ||
2341 | Double_t p[2]= { fP[0] - dz[0], fP[1] - dz[1] }; | |
2342 | Double_t c[3]= { covar[2], 0., covar[5] }; | |
2343 | ||
2344 | Double_t chi2C = GetPredictedChi2(p,c); | |
2345 | if (chi2C>kVeryBig) | |
2346 | return kFALSE; | |
2347 | ||
2348 | if (!Update(p,c)) | |
2349 | return kFALSE; | |
2350 | ||
2351 | return kTRUE; | |
2352 | } | |
70580f26 | 2353 | |
2354 | //___________________________________________________________________________________________ | |
2355 | Bool_t AliExternalTrackParam::GetXatLabR(Double_t r,Double_t &x, Double_t bz, Int_t dir) const | |
2356 | { | |
2357 | // Get local X of the track position estimated at the radius lab radius r. | |
2358 | // The track curvature is accounted exactly | |
2359 | // | |
2360 | // The flag "dir" can be used to remove the ambiguity of which intersection to take (out of 2 possible) | |
2361 | // 0 - take the intersection closest to the current track position | |
2362 | // >0 - go along the track (increasing fX) | |
2363 | // <0 - go backward (decreasing fX) | |
2364 | // | |
2365 | const Double_t &fy=fP[0], &sn = fP[2]; | |
2366 | // | |
2367 | double crv = GetC(bz); | |
2368 | if (TMath::Abs(crv)<=kAlmost0) { // this is a straight track | |
2369 | if (TMath::Abs(sn)>=kAlmost1) { // || to Y axis | |
2370 | double det = (r-fX)*(r+fX); | |
2371 | if (det<0) return kFALSE; // does not reach raduis r | |
2372 | x = fX; | |
2373 | if (dir==0) return kTRUE; | |
2374 | det = TMath::Sqrt(det); | |
2375 | if (dir>0) { // along the track direction | |
2376 | if (sn>0) {if (fy>det) return kFALSE;} // track is along Y axis and above the circle | |
2377 | else {if (fy<-det) return kFALSE;} // track is against Y axis amd belo the circle | |
2378 | } | |
e804766b | 2379 | else { // agains track direction |
70580f26 | 2380 | if (sn>0) {if (fy<-det) return kFALSE;} // track is along Y axis |
2381 | else if (fy>det) return kFALSE; // track is against Y axis | |
2382 | } | |
2383 | } | |
2384 | else if (TMath::Abs(sn)<=kAlmost0) { // || to X axis | |
2385 | double det = (r-fy)*(r+fy); | |
2386 | if (det<0) return kFALSE; // does not reach raduis r | |
2387 | det = TMath::Sqrt(det); | |
2388 | if (!dir) { | |
2389 | x = fX>0 ? det : -det; // choose the solution requiring the smalest step | |
2390 | return kTRUE; | |
2391 | } | |
2392 | else if (dir>0) { // along the track direction | |
2393 | if (fX > det) return kFALSE; // current point is in on the right from the circle | |
2394 | else if (fX <-det) x = -det; // on the left | |
2395 | else x = det; // within the circle | |
2396 | } | |
2397 | else { // against the track direction | |
2398 | if (fX <-det) return kFALSE; | |
2399 | else if (fX > det) x = det; | |
2400 | else x = -det; | |
2401 | } | |
2402 | } | |
2403 | else { // general case of straight line | |
2404 | double cs = TMath::Sqrt((1-sn)*(1+sn)); | |
2405 | double xsyc = fX*sn-fy*cs; | |
2406 | double det = (r-xsyc)*(r+xsyc); | |
2407 | if (det<0) return kFALSE; // does not reach raduis r | |
2408 | det = TMath::Sqrt(det); | |
2409 | double xcys = fX*cs+fy*sn; | |
2410 | double t = -xcys; | |
2411 | if (dir==0) t += t>0 ? -det:det; // chose the solution requiring the smalest step | |
2412 | else if (dir>0) { // go in increasing fX direction. ( t+-det > 0) | |
2413 | if (t>=-det) t += -det; // take minimal step giving t>0 | |
2414 | else return kFALSE; // both solutions have negative t | |
2415 | } | |
2416 | else { // go in increasing fX direction. (t+-det < 0) | |
2417 | if (t<det) t -= det; // take minimal step giving t<0 | |
2418 | else return kFALSE; // both solutions have positive t | |
2419 | } | |
2420 | x = fX + cs*t; | |
2421 | } | |
2422 | } | |
2423 | else { // helix | |
2424 | // get center of the track circle | |
2425 | double tR = 1./crv; // track radius (for the moment signed) | |
2426 | double cs = TMath::Sqrt((1-sn)*(1+sn)); | |
2427 | double x0 = fX - sn*tR; | |
2428 | double y0 = fy + cs*tR; | |
2429 | double r0 = TMath::Sqrt(x0*x0+y0*y0); | |
2430 | // printf("Xc:%+e Yc:%+e\n",x0,y0); | |
2431 | // | |
2432 | if (r0<=kAlmost0) return kFALSE; // the track is concentric to circle | |
2433 | tR = TMath::Abs(tR); | |
2434 | double tR2r0 = tR/r0; | |
2435 | double g = 0.5*(r*r/(r0*tR) - tR2r0 - 1./tR2r0); | |
2436 | double det = (1.-g)*(1.+g); | |
2437 | if (det<0) return kFALSE; // does not reach raduis r | |
2438 | det = TMath::Sqrt(det); | |
2439 | // | |
2440 | // the intersection happens in 2 points: {x0+tR*C,y0+tR*S} | |
2441 | // with C=f*c0+-|s0|*det and S=f*s0-+c0 sign(s0)*det | |
2442 | // where s0 and c0 make direction for the circle center (=x0/r0 and y0/r0) | |
2443 | // | |
2444 | double tmp = 1.+g*tR2r0; | |
2445 | x = x0*tmp; | |
2446 | double y = y0*tmp; | |
2447 | if (TMath::Abs(y0)>kAlmost0) { // when y0==0 the x,y is unique | |
2448 | double dfx = tR2r0*TMath::Abs(y0)*det; | |
2449 | double dfy = tR2r0*x0*TMath::Sign(det,y0); | |
2450 | if (dir==0) { // chose the one which corresponds to smallest step | |
2451 | double delta = (x-fX)*dfx-(y-fy)*dfy; // the choice of + in C will lead to smaller step if delta<0 | |
2452 | if (delta<0) x += dfx; | |
2453 | else x -= dfx; | |
2454 | } | |
2455 | else if (dir>0) { // along track direction: x must be > fX | |
2456 | x -= dfx; // try the smallest step (dfx is positive) | |
2457 | if (x<fX && (x+=dfx+dfx)<fX) return kFALSE; | |
2458 | } | |
2459 | else { // backward: x must be < fX | |
2460 | x += dfx; // try the smallest step (dfx is positive) | |
2461 | if (x>fX && (x-=dfx+dfx)>fX) return kFALSE; | |
2462 | } | |
2463 | } | |
2464 | else { // special case: track touching the circle just in 1 point | |
2465 | if ( (dir>0&&x<fX) || (dir<0&&x>fX) ) return kFALSE; | |
2466 | } | |
2467 | } | |
2468 | // | |
2469 | return kTRUE; | |
2470 | } |