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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 | /////////////////////////////////////////////////////////////////////////////// |
4b189f98 | 28 | #include <TMatrixDSym.h> |
51ad6848 | 29 | #include "AliExternalTrackParam.h" |
58e536c5 | 30 | #include "AliVVertex.h" |
0c19adf7 | 31 | #include "TPolyMarker3D.h" |
da4e3deb | 32 | #include "TVector3.h" |
6c94f330 | 33 | #include "AliLog.h" |
51ad6848 | 34 | |
35 | ClassImp(AliExternalTrackParam) | |
36 | ||
ed5f2849 | 37 | Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; |
38 | ||
51ad6848 | 39 | //_____________________________________________________________________________ |
90e48c0c | 40 | AliExternalTrackParam::AliExternalTrackParam() : |
4f6e22bd | 41 | AliVTrack(), |
90e48c0c | 42 | fX(0), |
c9ec41e8 | 43 | fAlpha(0) |
51ad6848 | 44 | { |
90e48c0c | 45 | // |
46 | // default constructor | |
47 | // | |
c9ec41e8 | 48 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
49 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 50 | } |
51 | ||
6c94f330 | 52 | //_____________________________________________________________________________ |
53 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
4f6e22bd | 54 | AliVTrack(track), |
6c94f330 | 55 | fX(track.fX), |
56 | fAlpha(track.fAlpha) | |
57 | { | |
58 | // | |
59 | // copy constructor | |
60 | // | |
61 | for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i]; | |
62 | for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i]; | |
63 | } | |
64 | ||
def9660e | 65 | //_____________________________________________________________________________ |
66 | AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar) | |
67 | { | |
68 | // | |
69 | // assignment operator | |
70 | // | |
71 | ||
72 | if (this!=&trkPar) { | |
4f6e22bd | 73 | AliVTrack::operator=(trkPar); |
def9660e | 74 | fX = trkPar.fX; |
75 | fAlpha = trkPar.fAlpha; | |
76 | ||
77 | for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i]; | |
78 | for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i]; | |
79 | } | |
80 | ||
81 | return *this; | |
82 | } | |
83 | ||
51ad6848 | 84 | //_____________________________________________________________________________ |
85 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
86 | const Double_t param[5], | |
90e48c0c | 87 | const Double_t covar[15]) : |
4f6e22bd | 88 | AliVTrack(), |
90e48c0c | 89 | fX(x), |
c9ec41e8 | 90 | fAlpha(alpha) |
51ad6848 | 91 | { |
90e48c0c | 92 | // |
93 | // create external track parameters from given arguments | |
94 | // | |
c9ec41e8 | 95 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
96 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 97 | } |
98 | ||
4f6e22bd | 99 | //_____________________________________________________________________________ |
100 | AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) : | |
101 | AliVTrack(), | |
102 | fX(0.), | |
103 | fAlpha(0.) | |
104 | { | |
105 | // | |
106 | // constructor from virtual track | |
107 | // | |
108 | Double_t xyz[3]={vTrack->Xv(),vTrack->Yv(),vTrack->Zv()}; | |
109 | Double_t pxpypz[3]={vTrack->Px(),vTrack->Py(),vTrack->Pz()}; | |
110 | Double_t cv[21]; | |
111 | vTrack->GetCovarianceXYZPxPyPz(cv); | |
112 | Short_t sign = (Short_t)vTrack->Charge(); | |
113 | ||
114 | Set(xyz,pxpypz,cv,sign); | |
115 | } | |
116 | ||
90e48c0c | 117 | //_____________________________________________________________________________ |
da4e3deb | 118 | AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], |
119 | Double_t cv[21],Short_t sign) : | |
4f6e22bd | 120 | AliVTrack(), |
da4e3deb | 121 | fX(0.), |
122 | fAlpha(0.) | |
4f6e22bd | 123 | { |
124 | // | |
125 | // constructor from the global parameters | |
126 | // | |
127 | ||
128 | Set(xyz,pxpypz,cv,sign); | |
129 | } | |
130 | ||
131 | //_____________________________________________________________________________ | |
132 | void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], | |
133 | Double_t cv[21],Short_t sign) | |
da4e3deb | 134 | { |
135 | // | |
136 | // create external track parameters from the global parameters | |
137 | // x,y,z,px,py,pz and their 6x6 covariance matrix | |
138 | // A.Dainese 10.10.08 | |
139 | ||
140 | // Calculate alpha: the rotation angle of the corresponding local system | |
141 | fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]); | |
142 | ||
143 | // Get the vertex of origin and the momentum | |
144 | TVector3 ver(xyz[0],xyz[1],xyz[2]); | |
145 | TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]); | |
146 | ||
147 | // Rotate to the local coordinate system | |
148 | ver.RotateZ(-fAlpha); | |
149 | mom.RotateZ(-fAlpha); | |
150 | ||
151 | // x of the reference plane | |
152 | fX = ver.X(); | |
153 | ||
154 | Double_t charge = (Double_t)sign; | |
155 | ||
156 | fP[0] = ver.Y(); | |
157 | fP[1] = ver.Z(); | |
158 | fP[2] = TMath::Sin(mom.Phi()); | |
159 | fP[3] = mom.Pz()/mom.Pt(); | |
160 | fP[4] = TMath::Sign(1/mom.Pt(),charge); | |
161 | ||
162 | // Covariance matrix (formulas to be simplified) | |
163 | ||
164 | Double_t pt=1./TMath::Abs(fP[4]); | |
165 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
166 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); | |
167 | ||
168 | Double_t m00=-sn;// m10=cs; | |
169 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
170 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
171 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
172 | ||
173 | m43*=GetSign(); | |
174 | m44*=GetSign(); | |
175 | m45*=GetSign(); | |
176 | ||
177 | Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]); | |
178 | Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43; | |
179 | Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43; | |
180 | Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23; | |
181 | Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43; | |
182 | Double_t a5=m24*m24-2.*m24*m44*m23/m43; | |
183 | Double_t a6=m44*m44-2.*m24*m44*m43/m23; | |
184 | ||
185 | fC[0 ] = cv[0 ]+cv[2 ]; | |
186 | fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00); | |
187 | fC[2 ] = cv[5 ]; | |
188 | fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00; | |
189 | fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43; | |
190 | fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35; | |
191 | fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43); | |
192 | fC[11] = (cv[8]-fC[4]*m23)/m43; | |
193 | fC[7 ] = cv[17]/m35-fC[11]*m45/m35; | |
194 | fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3)); | |
195 | fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3); | |
196 | fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43; | |
197 | Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45; | |
198 | Double_t b2=m23*m35; | |
199 | Double_t b3=m43*m35; | |
200 | Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45; | |
201 | Double_t b5=m24*m35; | |
202 | Double_t b6=m44*m35; | |
203 | fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3); | |
204 | fC[13] = b1/b3-b2*fC[8]/b3; | |
205 | fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35)); | |
4f6e22bd | 206 | |
207 | return; | |
da4e3deb | 208 | } |
209 | ||
210 | //_____________________________________________________________________________ | |
6c94f330 | 211 | void AliExternalTrackParam::Set(Double_t x, Double_t alpha, |
212 | const Double_t p[5], const Double_t cov[15]) { | |
c9ec41e8 | 213 | // |
6c94f330 | 214 | // Sets the parameters |
c9ec41e8 | 215 | // |
6c94f330 | 216 | fX=x; |
217 | fAlpha=alpha; | |
218 | for (Int_t i = 0; i < 5; i++) fP[i] = p[i]; | |
219 | for (Int_t i = 0; i < 15; i++) fC[i] = cov[i]; | |
51ad6848 | 220 | } |
221 | ||
222 | //_____________________________________________________________________________ | |
c9ec41e8 | 223 | void AliExternalTrackParam::Reset() { |
1530f89c | 224 | // |
225 | // Resets all the parameters to 0 | |
226 | // | |
c9ec41e8 | 227 | fX=fAlpha=0.; |
228 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
229 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 230 | } |
231 | ||
3775b0ca | 232 | //_____________________________________________________________________________ |
233 | void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { | |
234 | // | |
235 | // Add "something" to the track covarince matrix. | |
236 | // May be needed to account for unknown mis-calibration/mis-alignment | |
237 | // | |
238 | fC[0] +=c[0]; | |
239 | fC[1] +=c[1]; fC[2] +=c[2]; | |
240 | fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5]; | |
241 | fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9]; | |
242 | fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14]; | |
243 | } | |
244 | ||
245 | ||
c9ec41e8 | 246 | Double_t AliExternalTrackParam::GetP() const { |
247 | //--------------------------------------------------------------------- | |
248 | // This function returns the track momentum | |
249 | // Results for (nearly) straight tracks are meaningless ! | |
250 | //--------------------------------------------------------------------- | |
06fb4a2f | 251 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 252 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 253 | } |
254 | ||
1d99986f | 255 | Double_t AliExternalTrackParam::Get1P() const { |
256 | //--------------------------------------------------------------------- | |
257 | // This function returns the 1/(track momentum) | |
258 | //--------------------------------------------------------------------- | |
259 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
260 | } | |
261 | ||
c9ec41e8 | 262 | //_______________________________________________________________________ |
c7bafca9 | 263 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 264 | //------------------------------------------------------------------ |
265 | // This function calculates the transverse impact parameter | |
266 | // with respect to a point with global coordinates (x,y) | |
267 | // in the magnetic field "b" (kG) | |
268 | //------------------------------------------------------------------ | |
5773defd | 269 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 270 | Double_t rp4=GetC(b); |
c9ec41e8 | 271 | |
272 | Double_t xt=fX, yt=fP[0]; | |
273 | ||
274 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
275 | Double_t a = x*cs + y*sn; | |
276 | y = -x*sn + y*cs; x=a; | |
277 | xt-=x; yt-=y; | |
278 | ||
279 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
280 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
1530f89c | 281 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
282 | } | |
283 | ||
284 | //_______________________________________________________________________ | |
285 | void AliExternalTrackParam:: | |
286 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
287 | //------------------------------------------------------------------ | |
288 | // This function calculates the transverse and longitudinal impact parameters | |
289 | // with respect to a point with global coordinates (x,y) | |
290 | // in the magnetic field "b" (kG) | |
291 | //------------------------------------------------------------------ | |
292 | Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1); | |
293 | Double_t xt=fX, yt=fP[0]; | |
294 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
295 | Double_t a = x*cs + y*sn; | |
296 | y = -x*sn + y*cs; x=a; | |
297 | xt-=x; yt-=y; | |
298 | ||
299 | Double_t rp4=GetC(b); | |
300 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
301 | dz[0] = -(xt*f1 - yt*r1); | |
302 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
303 | return; | |
304 | } | |
305 | ||
306 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
307 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
308 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
309 | dz[0] = -a/(1 + rr); | |
310 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2); | |
311 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; | |
51ad6848 | 312 | } |
313 | ||
49d13e89 | 314 | //_______________________________________________________________________ |
315 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
316 | //------------------------------------------------------------------ | |
317 | // This function calculates the transverse impact parameter | |
318 | // with respect to a point with global coordinates (xv,yv) | |
319 | // neglecting the track curvature. | |
320 | //------------------------------------------------------------------ | |
321 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
322 | Double_t x= xv*cs + yv*sn; | |
323 | Double_t y=-xv*sn + yv*cs; | |
324 | ||
325 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
326 | ||
1530f89c | 327 | return -d; |
49d13e89 | 328 | } |
329 | ||
116b445b | 330 | Bool_t AliExternalTrackParam::CorrectForMeanMaterial |
7dded1d5 | 331 | (Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr, |
332 | Double_t (*Bethe)(Double_t)) { | |
116b445b | 333 | //------------------------------------------------------------------ |
334 | // This function corrects the track parameters for the crossed material. | |
335 | // "xOverX0" - X/X0, the thickness in units of the radiation length. | |
336 | // "xTimesRho" - is the product length*density (g/cm^2). | |
337 | // "mass" - the mass of this particle (GeV/c^2). | |
338 | //------------------------------------------------------------------ | |
339 | Double_t &fP2=fP[2]; | |
340 | Double_t &fP3=fP[3]; | |
341 | Double_t &fP4=fP[4]; | |
342 | ||
343 | Double_t &fC22=fC[5]; | |
344 | Double_t &fC33=fC[9]; | |
345 | Double_t &fC43=fC[13]; | |
346 | Double_t &fC44=fC[14]; | |
347 | ||
7dded1d5 | 348 | //Apply angle correction, if requested |
349 | if(anglecorr) { | |
350 | Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
351 | xOverX0 *=angle; | |
352 | xTimesRho *=angle; | |
353 | } | |
354 | ||
116b445b | 355 | Double_t p=GetP(); |
356 | Double_t p2=p*p; | |
357 | Double_t beta2=p2/(p2 + mass*mass); | |
116b445b | 358 | |
359 | //Multiple scattering****************** | |
360 | if (xOverX0 != 0) { | |
361 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0); | |
9a53dcc6 | 362 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
116b445b | 363 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
364 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
365 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
366 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
367 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
368 | } | |
369 | ||
370 | //Energy losses************************ | |
371 | if ((xTimesRho != 0.) && (beta2 < 1.)) { | |
372 | Double_t dE=Bethe(beta2)*xTimesRho; | |
373 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
374 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! | |
375 | fP4*=(1.- e/p2*dE); | |
4b2fa3ce | 376 | if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c |
377 | ||
116b445b | 378 | |
379 | // Approximate energy loss fluctuation (M.Ivanov) | |
380 | const Double_t knst=0.07; // To be tuned. | |
381 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
382 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); | |
383 | ||
384 | } | |
385 | ||
386 | return kTRUE; | |
387 | } | |
388 | ||
389 | ||
ee5dba5e | 390 | Bool_t AliExternalTrackParam::CorrectForMaterial |
391 | (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) { | |
c7bafca9 | 392 | //------------------------------------------------------------------ |
116b445b | 393 | // Deprecated function ! |
394 | // Better use CorrectForMeanMaterial instead of it. | |
395 | // | |
c7bafca9 | 396 | // This function corrects the track parameters for the crossed material |
397 | // "d" - the thickness (fraction of the radiation length) | |
398 | // "x0" - the radiation length (g/cm^2) | |
399 | // "mass" - the mass of this particle (GeV/c^2) | |
400 | //------------------------------------------------------------------ | |
401 | Double_t &fP2=fP[2]; | |
402 | Double_t &fP3=fP[3]; | |
403 | Double_t &fP4=fP[4]; | |
404 | ||
405 | Double_t &fC22=fC[5]; | |
406 | Double_t &fC33=fC[9]; | |
407 | Double_t &fC43=fC[13]; | |
408 | Double_t &fC44=fC[14]; | |
409 | ||
7b5ef2e6 | 410 | Double_t p=GetP(); |
411 | Double_t p2=p*p; | |
c7bafca9 | 412 | Double_t beta2=p2/(p2 + mass*mass); |
413 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
414 | ||
415 | //Multiple scattering****************** | |
416 | if (d!=0) { | |
417 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
9a53dcc6 | 418 | if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; |
c7bafca9 | 419 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; |
420 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
421 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
422 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
423 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
424 | } | |
425 | ||
426 | //Energy losses************************ | |
8fc1985d | 427 | if (x0!=0. && beta2<1) { |
c7bafca9 | 428 | d*=x0; |
ee5dba5e | 429 | Double_t dE=Bethe(beta2)*d; |
430 | Double_t e=TMath::Sqrt(p2 + mass*mass); | |
ae666100 | 431 | if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much! |
ee5dba5e | 432 | fP4*=(1.- e/p2*dE); |
433 | ||
434 | // Approximate energy loss fluctuation (M.Ivanov) | |
ed5f2849 | 435 | const Double_t knst=0.07; // To be tuned. |
436 | Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE)); | |
ee5dba5e | 437 | fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); |
438 | ||
c7bafca9 | 439 | } |
440 | ||
441 | return kTRUE; | |
442 | } | |
443 | ||
ee5dba5e | 444 | Double_t ApproximateBetheBloch(Double_t beta2) { |
445 | //------------------------------------------------------------------ | |
446 | // This is an approximation of the Bethe-Bloch formula with | |
447 | // the density effect taken into account at beta*gamma > 3.5 | |
448 | // (the approximation is reasonable only for solid materials) | |
449 | //------------------------------------------------------------------ | |
a821848c | 450 | if (beta2 >= 1) return kVeryBig; |
451 | ||
ee5dba5e | 452 | if (beta2/(1-beta2)>3.5*3.5) |
453 | return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); | |
454 | ||
455 | return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); | |
456 | } | |
457 | ||
49d13e89 | 458 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
459 | //------------------------------------------------------------------ | |
460 | // Transform this track to the local coord. system rotated | |
461 | // by angle "alpha" (rad) with respect to the global coord. system. | |
462 | //------------------------------------------------------------------ | |
dfcef74c | 463 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
464 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
465 | return kFALSE; | |
466 | } | |
467 | ||
49d13e89 | 468 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
469 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
470 | ||
471 | Double_t &fP0=fP[0]; | |
472 | Double_t &fP2=fP[2]; | |
473 | Double_t &fC00=fC[0]; | |
474 | Double_t &fC10=fC[1]; | |
475 | Double_t &fC20=fC[3]; | |
476 | Double_t &fC21=fC[4]; | |
477 | Double_t &fC22=fC[5]; | |
478 | Double_t &fC30=fC[6]; | |
479 | Double_t &fC32=fC[8]; | |
480 | Double_t &fC40=fC[10]; | |
481 | Double_t &fC42=fC[12]; | |
482 | ||
483 | Double_t x=fX; | |
484 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
485 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
486 | ||
dfcef74c | 487 | Double_t tmp=sf*ca - cf*sa; |
488 | if (TMath::Abs(tmp) >= kAlmost1) return kFALSE; | |
489 | ||
49d13e89 | 490 | fAlpha = alpha; |
491 | fX = x*ca + fP0*sa; | |
492 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 493 | fP2= tmp; |
49d13e89 | 494 | |
06fb4a2f | 495 | if (TMath::Abs(cf)<kAlmost0) { |
496 | AliError(Form("Too small cosine value %f",cf)); | |
497 | cf = kAlmost0; | |
498 | } | |
499 | ||
49d13e89 | 500 | Double_t rr=(ca+sf/cf*sa); |
501 | ||
502 | fC00 *= (ca*ca); | |
503 | fC10 *= ca; | |
504 | fC20 *= ca*rr; | |
505 | fC21 *= rr; | |
506 | fC22 *= rr*rr; | |
507 | fC30 *= ca; | |
508 | fC32 *= rr; | |
509 | fC40 *= ca; | |
510 | fC42 *= rr; | |
511 | ||
512 | return kTRUE; | |
513 | } | |
514 | ||
515 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
516 | //---------------------------------------------------------------- | |
517 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
518 | //---------------------------------------------------------------- | |
49d13e89 | 519 | Double_t dx=xk-fX; |
e421f556 | 520 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 521 | |
1530f89c | 522 | Double_t crv=GetC(b); |
5773defd | 523 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
524 | ||
49d13e89 | 525 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 526 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 527 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
528 | ||
529 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
530 | Double_t | |
531 | &fC00=fC[0], | |
532 | &fC10=fC[1], &fC11=fC[2], | |
533 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
534 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
535 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
536 | ||
537 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
538 | ||
539 | fX=xk; | |
540 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 541 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 542 | fP2 += dx*crv; |
543 | ||
544 | //f = F - 1 | |
545 | ||
546 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
547 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
548 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
549 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
550 | Double_t f13= dx/r1; | |
551 | Double_t f24= dx; f24*=cc; | |
552 | ||
553 | //b = C*ft | |
554 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
555 | Double_t b02=f24*fC40; | |
556 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
557 | Double_t b12=f24*fC41; | |
558 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
559 | Double_t b22=f24*fC42; | |
560 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
561 | Double_t b42=f24*fC44; | |
562 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
563 | Double_t b32=f24*fC43; | |
564 | ||
565 | //a = f*b = f*C*ft | |
566 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
567 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
568 | Double_t a22=f24*b42; | |
569 | ||
570 | //F*C*Ft = C + (b + bt + a) | |
571 | fC00 += b00 + b00 + a00; | |
572 | fC10 += b10 + b01 + a01; | |
573 | fC20 += b20 + b02 + a02; | |
574 | fC30 += b30; | |
575 | fC40 += b40; | |
576 | fC11 += b11 + b11 + a11; | |
577 | fC21 += b21 + b12 + a12; | |
578 | fC31 += b31; | |
579 | fC41 += b41; | |
580 | fC22 += b22 + b22 + a22; | |
581 | fC32 += b32; | |
582 | fC42 += b42; | |
583 | ||
584 | return kTRUE; | |
585 | } | |
586 | ||
052daaff | 587 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
588 | Double_t p[3], Double_t bz) const { | |
589 | //+++++++++++++++++++++++++++++++++++++++++ | |
590 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
591 | // Extrapolate track along simple helix in magnetic field | |
592 | // Arguments: len -distance alogn helix, [cm] | |
593 | // bz - mag field, [kGaus] | |
594 | // Returns: x and p contain extrapolated positon and momentum | |
595 | // The momentum returned for straight-line tracks is meaningless ! | |
596 | //+++++++++++++++++++++++++++++++++++++++++ | |
597 | GetXYZ(x); | |
598 | ||
def9660e | 599 | if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks |
052daaff | 600 | Double_t unit[3]; GetDirection(unit); |
601 | x[0]+=unit[0]*len; | |
602 | x[1]+=unit[1]*len; | |
603 | x[2]+=unit[2]*len; | |
604 | ||
605 | p[0]=unit[0]/kAlmost0; | |
606 | p[1]=unit[1]/kAlmost0; | |
607 | p[2]=unit[2]/kAlmost0; | |
608 | } else { | |
609 | GetPxPyPz(p); | |
610 | Double_t pp=GetP(); | |
611 | Double_t a = -kB2C*bz*GetSign(); | |
612 | Double_t rho = a/pp; | |
613 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
614 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
615 | x[2] += p[2]*len/pp; | |
616 | ||
617 | Double_t p0=p[0]; | |
618 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
619 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
620 | } | |
621 | } | |
622 | ||
623 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
624 | Double_t bz) const { | |
625 | //+++++++++++++++++++++++++++++++++++++++++ | |
626 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
627 | // Finds point of intersection (if exists) of the helix with the plane. | |
628 | // Stores result in fX and fP. | |
629 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
630 | // and vector, normal to the plane | |
631 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
632 | //+++++++++++++++++++++++++++++++++++++++++ | |
633 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
634 | ||
635 | //estimates initial helix length up to plane | |
636 | Double_t s= | |
637 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
638 | Double_t dist=99999,distPrev=dist; | |
639 | Double_t x[3],p[3]; | |
640 | while(TMath::Abs(dist)>0.00001){ | |
641 | //calculates helix at the distance s from x0 ALONG the helix | |
642 | Propagate(s,x,p,bz); | |
643 | ||
644 | //distance between current helix position and plane | |
645 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
646 | ||
647 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
648 | distPrev=dist; | |
649 | s-=dist; | |
650 | } | |
651 | //on exit pnt is intersection point,norm is track vector at that point, | |
652 | //all in MARS | |
653 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
654 | return kTRUE; | |
655 | } | |
656 | ||
49d13e89 | 657 | Double_t |
658 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
659 | //---------------------------------------------------------------- | |
660 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
661 | //---------------------------------------------------------------- | |
662 | Double_t sdd = fC[0] + cov[0]; | |
663 | Double_t sdz = fC[1] + cov[1]; | |
664 | Double_t szz = fC[2] + cov[2]; | |
665 | Double_t det = sdd*szz - sdz*sdz; | |
666 | ||
667 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
668 | ||
669 | Double_t d = fP[0] - p[0]; | |
670 | Double_t z = fP[1] - p[1]; | |
671 | ||
672 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
673 | } | |
674 | ||
4b189f98 | 675 | Double_t AliExternalTrackParam:: |
676 | GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { | |
677 | //---------------------------------------------------------------- | |
678 | // Estimate the chi2 of the 3D space point "p" and | |
1e023a36 | 679 | // the full covariance matrix "covyz" and "covxyz" |
4b189f98 | 680 | // |
681 | // Cov(x,x) ... : covxyz[0] | |
682 | // Cov(y,x) ... : covxyz[1] covyz[0] | |
683 | // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2] | |
684 | //---------------------------------------------------------------- | |
685 | ||
686 | Double_t res[3] = { | |
687 | GetX() - p[0], | |
688 | GetY() - p[1], | |
689 | GetZ() - p[2] | |
690 | }; | |
691 | ||
692 | Double_t f=GetSnp(); | |
693 | if (TMath::Abs(f) >= kAlmost1) return kVeryBig; | |
694 | Double_t r=TMath::Sqrt(1.- f*f); | |
695 | Double_t a=f/r, b=GetTgl()/r; | |
696 | ||
697 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
698 | ||
699 | TMatrixDSym v(3); | |
700 | v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;; | |
701 | v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY(); | |
702 | v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2(); | |
703 | ||
704 | v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2]; | |
705 | v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1]; | |
706 | v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2]; | |
707 | ||
708 | v.Invert(); | |
709 | if (!v.IsValid()) return kVeryBig; | |
710 | ||
711 | Double_t chi2=0.; | |
712 | for (Int_t i = 0; i < 3; i++) | |
713 | for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j); | |
714 | ||
715 | return chi2; | |
716 | ||
717 | ||
718 | } | |
719 | ||
1e023a36 | 720 | Bool_t AliExternalTrackParam:: |
721 | PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { | |
722 | //---------------------------------------------------------------- | |
723 | // Propagate this track to the plane | |
724 | // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz") | |
725 | // belongs to. | |
726 | // The magnetic field is "bz" (kG) | |
727 | // | |
728 | // The track curvature and the change of the covariance matrix | |
729 | // of the track parameters are negleted ! | |
730 | // (So the "step" should be small compared with 1/curvature) | |
731 | //---------------------------------------------------------------- | |
732 | ||
733 | Double_t f=GetSnp(); | |
734 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
735 | Double_t r=TMath::Sqrt(1.- f*f); | |
736 | Double_t a=f/r, b=GetTgl()/r; | |
737 | ||
738 | Double_t s2=333.*333.; //something reasonably big (cm^2) | |
739 | ||
740 | TMatrixDSym tV(3); | |
741 | tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2; | |
742 | tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2; | |
743 | tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2; | |
744 | ||
745 | TMatrixDSym pV(3); | |
746 | pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2]; | |
747 | pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1]; | |
748 | pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2]; | |
749 | ||
750 | TMatrixDSym tpV(tV); | |
751 | tpV+=pV; | |
752 | tpV.Invert(); | |
753 | if (!tpV.IsValid()) return kFALSE; | |
754 | ||
755 | TMatrixDSym pW(3),tW(3); | |
756 | for (Int_t i=0; i<3; i++) | |
757 | for (Int_t j=0; j<3; j++) { | |
758 | pW(i,j)=tW(i,j)=0.; | |
759 | for (Int_t k=0; k<3; k++) { | |
760 | pW(i,j) += tV(i,k)*tpV(k,j); | |
761 | tW(i,j) += pV(i,k)*tpV(k,j); | |
762 | } | |
763 | } | |
764 | ||
765 | Double_t t[3] = {GetX(), GetY(), GetZ()}; | |
766 | ||
767 | Double_t x=0.; | |
768 | for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]); | |
769 | Double_t crv=GetC(bz); | |
770 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
771 | f += crv*(x-fX); | |
772 | if (TMath::Abs(f) >= kAlmost1) return kFALSE; | |
773 | fX=x; | |
774 | ||
775 | fP[0]=0.; | |
776 | for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]); | |
777 | fP[1]=0.; | |
778 | for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]); | |
779 | ||
780 | return kTRUE; | |
781 | } | |
782 | ||
e23a38cb | 783 | Double_t *AliExternalTrackParam::GetResiduals( |
784 | Double_t *p,Double_t *cov,Bool_t updated) const { | |
785 | //------------------------------------------------------------------ | |
786 | // Returns the track residuals with the space point "p" having | |
787 | // the covariance matrix "cov". | |
788 | // If "updated" is kTRUE, the track parameters expected to be updated, | |
789 | // otherwise they must be predicted. | |
790 | //------------------------------------------------------------------ | |
791 | static Double_t res[2]; | |
792 | ||
793 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
794 | if (updated) { | |
795 | r00-=fC[0]; r01-=fC[1]; r11-=fC[2]; | |
796 | } else { | |
797 | r00+=fC[0]; r01+=fC[1]; r11+=fC[2]; | |
798 | } | |
799 | Double_t det=r00*r11 - r01*r01; | |
800 | ||
801 | if (TMath::Abs(det) < kAlmost0) return 0; | |
802 | ||
803 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; | |
f0fbf964 | 804 | |
805 | if (r00 < 0.) return 0; | |
806 | if (r11 < 0.) return 0; | |
807 | ||
e23a38cb | 808 | Double_t dy = fP[0] - p[0]; |
809 | Double_t dz = fP[1] - p[1]; | |
810 | ||
811 | res[0]=dy*TMath::Sqrt(r00); | |
812 | res[1]=dz*TMath::Sqrt(r11); | |
813 | ||
814 | return res; | |
815 | } | |
816 | ||
49d13e89 | 817 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { |
818 | //------------------------------------------------------------------ | |
819 | // Update the track parameters with the space point "p" having | |
820 | // the covariance matrix "cov" | |
821 | //------------------------------------------------------------------ | |
822 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
823 | Double_t | |
824 | &fC00=fC[0], | |
825 | &fC10=fC[1], &fC11=fC[2], | |
826 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
827 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
828 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
829 | ||
830 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
831 | r00+=fC00; r01+=fC10; r11+=fC11; | |
832 | Double_t det=r00*r11 - r01*r01; | |
833 | ||
834 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
835 | ||
836 | ||
837 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
838 | ||
839 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
840 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
841 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
842 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
843 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
844 | ||
845 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
846 | Double_t sf=fP2 + k20*dy + k21*dz; | |
847 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
848 | ||
849 | fP0 += k00*dy + k01*dz; | |
850 | fP1 += k10*dy + k11*dz; | |
851 | fP2 = sf; | |
852 | fP3 += k30*dy + k31*dz; | |
853 | fP4 += k40*dy + k41*dz; | |
854 | ||
855 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
856 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
857 | ||
858 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
859 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
860 | fC40-=k00*c04+k01*c14; | |
861 | ||
862 | fC11-=k10*c01+k11*fC11; | |
863 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
864 | fC41-=k10*c04+k11*c14; | |
865 | ||
866 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
867 | fC42-=k20*c04+k21*c14; | |
868 | ||
869 | fC33-=k30*c03+k31*c13; | |
870 | fC43-=k30*c04+k31*c14; | |
871 | ||
872 | fC44-=k40*c04+k41*c14; | |
873 | ||
874 | return kTRUE; | |
875 | } | |
876 | ||
c7bafca9 | 877 | void |
878 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
879 | //-------------------------------------------------------------------- | |
880 | // External track parameters -> helix parameters | |
881 | // "b" - magnetic field (kG) | |
882 | //-------------------------------------------------------------------- | |
883 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
884 | ||
1530f89c | 885 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 886 | |
887 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
888 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
889 | //hlx[1]= // z0 | |
890 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
891 | //hlx[3]= // tgl | |
1530f89c | 892 | hlx[4]=GetC(b); // C |
c7bafca9 | 893 | } |
894 | ||
895 | ||
896 | static void Evaluate(const Double_t *h, Double_t t, | |
897 | Double_t r[3], //radius vector | |
898 | Double_t g[3], //first defivatives | |
899 | Double_t gg[3]) //second derivatives | |
900 | { | |
901 | //-------------------------------------------------------------------- | |
902 | // Calculate position of a point on a track and some derivatives | |
903 | //-------------------------------------------------------------------- | |
904 | Double_t phase=h[4]*t+h[2]; | |
905 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
906 | ||
907 | r[0] = h[5] + (sn - h[6])/h[4]; | |
908 | r[1] = h[0] - (cs - h[7])/h[4]; | |
909 | r[2] = h[1] + h[3]*t; | |
910 | ||
911 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
912 | ||
913 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
914 | } | |
915 | ||
916 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
917 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
918 | //------------------------------------------------------------ | |
919 | // Returns the (weighed !) distance of closest approach between | |
920 | // this track and the track "p". | |
921 | // Other returned values: | |
922 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
923 | //----------------------------------------------------------- | |
924 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
925 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
926 | Double_t dx2=dy2; | |
927 | ||
928 | //dx2=dy2=dz2=1.; | |
929 | ||
930 | Double_t p1[8]; GetHelixParameters(p1,b); | |
931 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
932 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
933 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
934 | ||
935 | ||
936 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
937 | Evaluate(p1,t1,r1,g1,gg1); | |
938 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
939 | Evaluate(p2,t2,r2,g2,gg2); | |
940 | ||
941 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
942 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
943 | ||
944 | Int_t max=27; | |
945 | while (max--) { | |
946 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
947 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
948 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
949 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
950 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
951 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
952 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
953 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
954 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
955 | ||
956 | Double_t det=h11*h22-h12*h12; | |
957 | ||
958 | Double_t dt1,dt2; | |
959 | if (TMath::Abs(det)<1.e-33) { | |
960 | //(quasi)singular Hessian | |
961 | dt1=-gt1; dt2=-gt2; | |
962 | } else { | |
963 | dt1=-(gt1*h22 - gt2*h12)/det; | |
964 | dt2=-(h11*gt2 - h12*gt1)/det; | |
965 | } | |
966 | ||
967 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
968 | ||
969 | //check delta(phase1) ? | |
970 | //check delta(phase2) ? | |
971 | ||
972 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
973 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
974 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
358f16ae | 975 | AliDebug(1," stopped at not a stationary point !"); |
c7bafca9 | 976 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); |
977 | if (lmb < 0.) | |
358f16ae | 978 | AliDebug(1," stopped at not a minimum !"); |
c7bafca9 | 979 | break; |
980 | } | |
981 | ||
982 | Double_t dd=dm; | |
983 | for (Int_t div=1 ; ; div*=2) { | |
984 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
985 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
986 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
987 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
988 | if (dd<dm) break; | |
989 | dt1*=0.5; dt2*=0.5; | |
990 | if (div>512) { | |
358f16ae | 991 | AliDebug(1," overshoot !"); break; |
c7bafca9 | 992 | } |
993 | } | |
994 | dm=dd; | |
995 | ||
996 | t1+=dt1; | |
997 | t2+=dt2; | |
998 | ||
999 | } | |
1000 | ||
358f16ae | 1001 | if (max<=0) AliDebug(1," too many iterations !"); |
c7bafca9 | 1002 | |
1003 | Double_t cs=TMath::Cos(GetAlpha()); | |
1004 | Double_t sn=TMath::Sin(GetAlpha()); | |
1005 | xthis=r1[0]*cs + r1[1]*sn; | |
1006 | ||
1007 | cs=TMath::Cos(p->GetAlpha()); | |
1008 | sn=TMath::Sin(p->GetAlpha()); | |
1009 | xp=r2[0]*cs + r2[1]*sn; | |
1010 | ||
1011 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
1012 | } | |
1013 | ||
1014 | Double_t AliExternalTrackParam:: | |
1015 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
1016 | //-------------------------------------------------------------- | |
1017 | // Propagates this track and the argument track to the position of the | |
1018 | // distance of closest approach. | |
1019 | // Returns the (weighed !) distance of closest approach. | |
1020 | //-------------------------------------------------------------- | |
1021 | Double_t xthis,xp; | |
1022 | Double_t dca=GetDCA(p,b,xthis,xp); | |
1023 | ||
1024 | if (!PropagateTo(xthis,b)) { | |
1025 | //AliWarning(" propagation failed !"); | |
1026 | return 1e+33; | |
1027 | } | |
1028 | ||
1029 | if (!p->PropagateTo(xp,b)) { | |
1030 | //AliWarning(" propagation failed !"; | |
1031 | return 1e+33; | |
1032 | } | |
1033 | ||
1034 | return dca; | |
1035 | } | |
1036 | ||
1037 | ||
58e536c5 | 1038 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx, |
e99a34df | 1039 | Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { |
f76701bf | 1040 | // |
e99a34df | 1041 | // Propagate this track to the DCA to vertex "vtx", |
f76701bf | 1042 | // if the (rough) transverse impact parameter is not bigger then "maxd". |
1043 | // Magnetic field is "b" (kG). | |
1044 | // | |
1045 | // a) The track gets extapolated to the DCA to the vertex. | |
1046 | // b) The impact parameters and their covariance matrix are calculated. | |
1047 | // | |
1048 | // In the case of success, the returned value is kTRUE | |
1049 | // (otherwise, it's kFALSE) | |
1050 | // | |
1051 | Double_t alpha=GetAlpha(); | |
1052 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
1053 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
58e536c5 | 1054 | Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn; |
1055 | Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ(); | |
f76701bf | 1056 | x-=xv; y-=yv; |
1057 | ||
1058 | //Estimate the impact parameter neglecting the track curvature | |
1059 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
1060 | if (d > maxd) return kFALSE; | |
1061 | ||
1062 | //Propagate to the DCA | |
e99a34df | 1063 | Double_t crv=kB2C*b*GetParameter()[4]; |
1064 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; | |
1065 | ||
f76701bf | 1066 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); |
1067 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
e99a34df | 1068 | if (TMath::Abs(tgfv)>0.) cs = sn/tgfv; |
1069 | else cs=1.; | |
f76701bf | 1070 | |
1071 | x = xv*cs + yv*sn; | |
1072 | yv=-xv*sn + yv*cs; xv=x; | |
1073 | ||
1074 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
e99a34df | 1075 | |
1076 | if (dz==0) return kTRUE; | |
1077 | dz[0] = GetParameter()[0] - yv; | |
1078 | dz[1] = GetParameter()[1] - zv; | |
1079 | ||
1080 | if (covar==0) return kTRUE; | |
58e536c5 | 1081 | Double_t cov[6]; vtx->GetCovarianceMatrix(cov); |
e99a34df | 1082 | |
1083 | //***** Improvements by A.Dainese | |
1084 | alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); | |
1085 | Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn; | |
1086 | covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations | |
1087 | covar[1] = GetCovariance()[1]; // between (x,y) and z | |
1088 | covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix | |
1089 | //***** | |
1090 | ||
29fbcc93 | 1091 | return kTRUE; |
f76701bf | 1092 | } |
1093 | ||
1094 | ||
b1149664 | 1095 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
1096 | //---------------------------------------------------------------- | |
1097 | // This function returns a unit vector along the track direction | |
1098 | // in the global coordinate system. | |
1099 | //---------------------------------------------------------------- | |
1100 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
1101 | Double_t snp=fP[2]; | |
92934324 | 1102 | Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp)); |
b1149664 | 1103 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); |
1104 | d[0]=(csp*cs - snp*sn)/norm; | |
1105 | d[1]=(snp*cs + csp*sn)/norm; | |
1106 | d[2]=fP[3]/norm; | |
1107 | } | |
1108 | ||
c683ddc2 | 1109 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const { |
c9ec41e8 | 1110 | //--------------------------------------------------------------------- |
1111 | // This function returns the global track momentum components | |
1112 | // Results for (nearly) straight tracks are meaningless ! | |
1113 | //--------------------------------------------------------------------- | |
1114 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
1115 | return Local2GlobalMomentum(p,fAlpha); | |
1116 | } | |
a5e407e9 | 1117 | |
def9660e | 1118 | Double_t AliExternalTrackParam::Px() const { |
957fb479 | 1119 | //--------------------------------------------------------------------- |
1120 | // Returns x-component of momentum | |
1121 | // Result for (nearly) straight tracks is meaningless ! | |
1122 | //--------------------------------------------------------------------- | |
def9660e | 1123 | |
957fb479 | 1124 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1125 | GetPxPyPz(p); |
1126 | ||
1127 | return p[0]; | |
1128 | } | |
1129 | ||
1130 | Double_t AliExternalTrackParam::Py() const { | |
957fb479 | 1131 | //--------------------------------------------------------------------- |
1132 | // Returns y-component of momentum | |
1133 | // Result for (nearly) straight tracks is meaningless ! | |
1134 | //--------------------------------------------------------------------- | |
def9660e | 1135 | |
957fb479 | 1136 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1137 | GetPxPyPz(p); |
1138 | ||
1139 | return p[1]; | |
1140 | } | |
1141 | ||
1142 | Double_t AliExternalTrackParam::Pz() const { | |
957fb479 | 1143 | //--------------------------------------------------------------------- |
1144 | // Returns z-component of momentum | |
1145 | // Result for (nearly) straight tracks is meaningless ! | |
1146 | //--------------------------------------------------------------------- | |
def9660e | 1147 | |
957fb479 | 1148 | Double_t p[3]={kVeryBig,kVeryBig,kVeryBig}; |
def9660e | 1149 | GetPxPyPz(p); |
1150 | ||
1151 | return p[2]; | |
1152 | } | |
1153 | ||
c683ddc2 | 1154 | Double_t AliExternalTrackParam::Xv() const { |
1155 | //--------------------------------------------------------------------- | |
1156 | // Returns x-component of first track point | |
1157 | //--------------------------------------------------------------------- | |
1158 | ||
1159 | Double_t r[3]={0.,0.,0.}; | |
1160 | GetXYZ(r); | |
1161 | ||
1162 | return r[0]; | |
1163 | } | |
1164 | ||
1165 | Double_t AliExternalTrackParam::Yv() const { | |
1166 | //--------------------------------------------------------------------- | |
1167 | // Returns y-component of first track point | |
1168 | //--------------------------------------------------------------------- | |
1169 | ||
1170 | Double_t r[3]={0.,0.,0.}; | |
1171 | GetXYZ(r); | |
1172 | ||
1173 | return r[1]; | |
1174 | } | |
1175 | ||
1176 | Double_t AliExternalTrackParam::Zv() const { | |
1177 | //--------------------------------------------------------------------- | |
1178 | // Returns z-component of first track point | |
1179 | //--------------------------------------------------------------------- | |
1180 | ||
1181 | Double_t r[3]={0.,0.,0.}; | |
1182 | GetXYZ(r); | |
1183 | ||
1184 | return r[2]; | |
1185 | } | |
1186 | ||
def9660e | 1187 | Double_t AliExternalTrackParam::Theta() const { |
1188 | // return theta angle of momentum | |
1189 | ||
7cdd0c20 | 1190 | return 0.5*TMath::Pi() - TMath::ATan(fP[3]); |
def9660e | 1191 | } |
1192 | ||
1193 | Double_t AliExternalTrackParam::Phi() const { | |
957fb479 | 1194 | //--------------------------------------------------------------------- |
1195 | // Returns the azimuthal angle of momentum | |
1196 | // 0 <= phi < 2*pi | |
1197 | //--------------------------------------------------------------------- | |
def9660e | 1198 | |
957fb479 | 1199 | Double_t phi=TMath::ASin(fP[2]) + fAlpha; |
1200 | if (phi<0.) phi+=2.*TMath::Pi(); | |
1201 | else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi(); | |
1202 | ||
1203 | return phi; | |
def9660e | 1204 | } |
1205 | ||
1206 | Double_t AliExternalTrackParam::M() const { | |
1207 | // return particle mass | |
1208 | ||
1209 | // No mass information available so far. | |
1210 | // Redifine in derived class! | |
1211 | ||
1212 | return -999.; | |
1213 | } | |
1214 | ||
1215 | Double_t AliExternalTrackParam::E() const { | |
1216 | // return particle energy | |
1217 | ||
1218 | // No PID information available so far. | |
1219 | // Redifine in derived class! | |
1220 | ||
1221 | return -999.; | |
1222 | } | |
1223 | ||
1224 | Double_t AliExternalTrackParam::Eta() const { | |
1225 | // return pseudorapidity | |
1226 | ||
1227 | return -TMath::Log(TMath::Tan(0.5 * Theta())); | |
1228 | } | |
1229 | ||
1230 | Double_t AliExternalTrackParam::Y() const { | |
1231 | // return rapidity | |
1232 | ||
1233 | // No PID information available so far. | |
1234 | // Redifine in derived class! | |
1235 | ||
1236 | return -999.; | |
1237 | } | |
1238 | ||
c9ec41e8 | 1239 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
1240 | //--------------------------------------------------------------------- | |
1241 | // This function returns the global track position | |
1242 | //--------------------------------------------------------------------- | |
1243 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
1244 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 1245 | } |
1246 | ||
c9ec41e8 | 1247 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
1248 | //--------------------------------------------------------------------- | |
1249 | // This function returns the global covariance matrix of the track params | |
1250 | // | |
1251 | // Cov(x,x) ... : cv[0] | |
1252 | // Cov(y,x) ... : cv[1] cv[2] | |
1253 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
1254 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
1255 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
1256 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 1257 | // |
c9ec41e8 | 1258 | // Results for (nearly) straight tracks are meaningless ! |
1259 | //--------------------------------------------------------------------- | |
e421f556 | 1260 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 1261 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1262 | return kFALSE; | |
a5e407e9 | 1263 | } |
49d13e89 | 1264 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 1265 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
1266 | return kFALSE; | |
1267 | } | |
1268 | Double_t pt=1./TMath::Abs(fP[4]); | |
1269 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
92934324 | 1270 | Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2])); |
c9ec41e8 | 1271 | |
1272 | Double_t m00=-sn, m10=cs; | |
1273 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
1274 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
1275 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
1276 | ||
854d5d49 | 1277 | m43*=GetSign(); |
1278 | m44*=GetSign(); | |
1279 | m45*=GetSign(); | |
1280 | ||
c9ec41e8 | 1281 | cv[0 ] = fC[0]*m00*m00; |
1282 | cv[1 ] = fC[0]*m00*m10; | |
1283 | cv[2 ] = fC[0]*m10*m10; | |
1284 | cv[3 ] = fC[1]*m00; | |
1285 | cv[4 ] = fC[1]*m10; | |
1286 | cv[5 ] = fC[2]; | |
1287 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
1288 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
1289 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
1290 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
1291 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
1292 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
1293 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
1294 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
1295 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
1296 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
1297 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
1298 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
1299 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
1300 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
1301 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 1302 | |
c9ec41e8 | 1303 | return kTRUE; |
51ad6848 | 1304 | } |
1305 | ||
51ad6848 | 1306 | |
c9ec41e8 | 1307 | Bool_t |
1308 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
1309 | //--------------------------------------------------------------------- | |
1310 | // This function returns the global track momentum extrapolated to | |
1311 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1312 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1313 | p[0]=fP[4]; |
1530f89c | 1314 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 1315 | p[2]=fP[3]; |
1316 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 1317 | } |
1318 | ||
7cf7bb6c | 1319 | Bool_t |
1320 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
1321 | //--------------------------------------------------------------------- | |
1322 | // This function returns the local Y-coordinate of the intersection | |
1323 | // point between this track and the reference plane "x" (cm). | |
1324 | // Magnetic field "b" (kG) | |
1325 | //--------------------------------------------------------------------- | |
1326 | Double_t dx=x-fX; | |
1327 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
1328 | ||
1530f89c | 1329 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 1330 | |
1331 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1332 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1333 | ||
1334 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1335 | y = fP[0] + dx*(f1+f2)/(r1+r2); | |
1336 | return kTRUE; | |
1337 | } | |
1338 | ||
6c94f330 | 1339 | Bool_t |
1340 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
1341 | //--------------------------------------------------------------------- | |
1342 | // This function returns the local Z-coordinate of the intersection | |
1343 | // point between this track and the reference plane "x" (cm). | |
1344 | // Magnetic field "b" (kG) | |
1345 | //--------------------------------------------------------------------- | |
1346 | Double_t dx=x-fX; | |
1347 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
1348 | ||
1349 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; | |
1350 | ||
1351 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
1352 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
1353 | ||
1354 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); | |
1355 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! | |
1356 | return kTRUE; | |
1357 | } | |
1358 | ||
c9ec41e8 | 1359 | Bool_t |
1360 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
1361 | //--------------------------------------------------------------------- | |
1362 | // This function returns the global track position extrapolated to | |
1363 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
1364 | //--------------------------------------------------------------------- | |
c9ec41e8 | 1365 | Double_t dx=x-fX; |
e421f556 | 1366 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
1367 | ||
1530f89c | 1368 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 1369 | |
e421f556 | 1370 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 1371 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 1372 | |
1373 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
1374 | r[0] = x; | |
1375 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
6c94f330 | 1376 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; |
c9ec41e8 | 1377 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 1378 | } |
1379 | ||
51ad6848 | 1380 | //_____________________________________________________________________________ |
1381 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
1382 | { | |
1383 | // print the parameters and the covariance matrix | |
1384 | ||
1385 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
1386 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 1387 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
1388 | printf(" covariance: %12g\n", fC[0]); | |
1389 | printf(" %12g %12g\n", fC[1], fC[2]); | |
1390 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 1391 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 1392 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 1393 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 1394 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 1395 | } |
5b77d93c | 1396 | |
c194ba83 | 1397 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
1398 | // | |
1399 | // Get sinus at given x | |
1400 | // | |
1530f89c | 1401 | Double_t crv=GetC(b); |
c194ba83 | 1402 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
1403 | Double_t dx = x-fX; | |
1404 | Double_t res = fP[2]+dx*crv; | |
1405 | return res; | |
1406 | } | |
bf00ebb8 | 1407 | |
1408 | Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){ | |
1409 | //------------------------------------------------------------------------ | |
1410 | // Get the distance between two tracks at the local position x | |
1411 | // working in the local frame of this track. | |
1412 | // Origin : Marian.Ivanov@cern.ch | |
1413 | //----------------------------------------------------------------------- | |
1414 | Double_t xyz[3]; | |
1415 | Double_t xyz2[3]; | |
1416 | xyz[0]=x; | |
1417 | if (!GetYAt(x,bz,xyz[1])) return kFALSE; | |
1418 | if (!GetZAt(x,bz,xyz[2])) return kFALSE; | |
1419 | // | |
1420 | // | |
1421 | if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){ | |
1422 | xyz2[0]=x; | |
1423 | if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE; | |
1424 | if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE; | |
1425 | }else{ | |
1426 | // | |
1427 | Double_t xyz1[3]; | |
1428 | Double_t dfi = param2->GetAlpha()-GetAlpha(); | |
1429 | Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi); | |
1430 | xyz2[0] = xyz[0]*ca+xyz[1]*sa; | |
1431 | xyz2[1] = -xyz[0]*sa+xyz[1]*ca; | |
1432 | // | |
1433 | xyz1[0]=xyz2[0]; | |
1434 | if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE; | |
1435 | if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE; | |
1436 | // | |
1437 | xyz2[0] = xyz1[0]*ca-xyz1[1]*sa; | |
1438 | xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca; | |
1439 | xyz2[2] = xyz1[2]; | |
1440 | } | |
1441 | dist[0] = xyz[0]-xyz2[0]; | |
1442 | dist[1] = xyz[1]-xyz2[1]; | |
1443 | dist[2] = xyz[2]-xyz2[2]; | |
1444 | ||
1445 | return kTRUE; | |
1446 | } | |
0c19adf7 | 1447 | |
1448 | ||
1449 | // | |
1450 | // Draw functionality. | |
1451 | // Origin: Marian Ivanov, Marian.Ivanov@cern.ch | |
1452 | // | |
1453 | ||
1454 | void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){ | |
1455 | // | |
1456 | // Draw track line | |
1457 | // | |
1458 | if (minR>maxR) return ; | |
1459 | if (stepR<=0) return ; | |
1460 | Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1; | |
1461 | if (npoints<1) return; | |
1462 | TPolyMarker3D *polymarker = new TPolyMarker3D(npoints); | |
1463 | FillPolymarker(polymarker, magf,minR,maxR,stepR); | |
1464 | polymarker->Draw(); | |
1465 | } | |
1466 | ||
1467 | // | |
1468 | void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){ | |
1469 | // | |
1470 | // Fill points in the polymarker | |
1471 | // | |
1472 | Int_t counter=0; | |
1473 | for (Double_t r=minR; r<maxR; r+=stepR){ | |
1474 | Double_t point[3]; | |
1475 | GetXYZAt(r,magF,point); | |
1476 | pol->SetPoint(counter,point[0],point[1], point[2]); | |
1477 | printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]); | |
1478 | counter++; | |
1479 | } | |
1480 | } |