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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 | /////////////////////////////////////////////////////////////////////////////// |
51ad6848 | 28 | #include "AliExternalTrackParam.h" |
29 | #include "AliKalmanTrack.h" | |
5b77d93c | 30 | #include "AliTracker.h" |
31 | ||
51ad6848 | 32 | |
33 | ClassImp(AliExternalTrackParam) | |
34 | ||
51ad6848 | 35 | //_____________________________________________________________________________ |
90e48c0c | 36 | AliExternalTrackParam::AliExternalTrackParam() : |
90e48c0c | 37 | fX(0), |
c9ec41e8 | 38 | fAlpha(0) |
51ad6848 | 39 | { |
90e48c0c | 40 | // |
41 | // default constructor | |
42 | // | |
c9ec41e8 | 43 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
44 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 45 | } |
46 | ||
47 | //_____________________________________________________________________________ | |
48 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
49 | const Double_t param[5], | |
90e48c0c | 50 | const Double_t covar[15]) : |
90e48c0c | 51 | fX(x), |
c9ec41e8 | 52 | fAlpha(alpha) |
51ad6848 | 53 | { |
90e48c0c | 54 | // |
55 | // create external track parameters from given arguments | |
56 | // | |
c9ec41e8 | 57 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
58 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 59 | } |
60 | ||
90e48c0c | 61 | //_____________________________________________________________________________ |
62 | AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) : | |
c9ec41e8 | 63 | fAlpha(track.GetAlpha()) |
51ad6848 | 64 | { |
65 | // | |
66 | // | |
c9ec41e8 | 67 | track.GetExternalParameters(fX,fP); |
68 | track.GetExternalCovariance(fC); | |
51ad6848 | 69 | } |
70 | ||
51ad6848 | 71 | //_____________________________________________________________________________ |
c9ec41e8 | 72 | void AliExternalTrackParam::Set(const AliKalmanTrack& track) { |
73 | // | |
74 | // | |
75 | fAlpha=track.GetAlpha(); | |
76 | track.GetExternalParameters(fX,fP); | |
77 | track.GetExternalCovariance(fC); | |
51ad6848 | 78 | } |
79 | ||
80 | //_____________________________________________________________________________ | |
c9ec41e8 | 81 | void AliExternalTrackParam::Reset() { |
82 | fX=fAlpha=0.; | |
83 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
84 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 85 | } |
86 | ||
c9ec41e8 | 87 | Double_t AliExternalTrackParam::GetP() const { |
88 | //--------------------------------------------------------------------- | |
89 | // This function returns the track momentum | |
90 | // Results for (nearly) straight tracks are meaningless ! | |
91 | //--------------------------------------------------------------------- | |
92 | if (TMath::Abs(fP[4])<=0) return 0; | |
93 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); | |
51ad6848 | 94 | } |
95 | ||
c9ec41e8 | 96 | //_______________________________________________________________________ |
97 | Double_t AliExternalTrackParam::GetD(Double_t b,Double_t x,Double_t y) const { | |
98 | //------------------------------------------------------------------ | |
99 | // This function calculates the transverse impact parameter | |
100 | // with respect to a point with global coordinates (x,y) | |
101 | // in the magnetic field "b" (kG) | |
102 | //------------------------------------------------------------------ | |
49d13e89 | 103 | Double_t rp4=kB2C*b*fP[4]; |
c9ec41e8 | 104 | |
105 | Double_t xt=fX, yt=fP[0]; | |
106 | ||
107 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
108 | Double_t a = x*cs + y*sn; | |
109 | y = -x*sn + y*cs; x=a; | |
110 | xt-=x; yt-=y; | |
111 | ||
112 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
113 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
114 | if (rp4<0) a=-a; | |
115 | return a/(1 + TMath::Sqrt(sn*sn + cs*cs)); | |
51ad6848 | 116 | } |
117 | ||
49d13e89 | 118 | //_______________________________________________________________________ |
119 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
120 | //------------------------------------------------------------------ | |
121 | // This function calculates the transverse impact parameter | |
122 | // with respect to a point with global coordinates (xv,yv) | |
123 | // neglecting the track curvature. | |
124 | //------------------------------------------------------------------ | |
125 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
126 | Double_t x= xv*cs + yv*sn; | |
127 | Double_t y=-xv*sn + yv*cs; | |
128 | ||
129 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
130 | ||
131 | return d; | |
132 | } | |
133 | ||
134 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { | |
135 | //------------------------------------------------------------------ | |
136 | // Transform this track to the local coord. system rotated | |
137 | // by angle "alpha" (rad) with respect to the global coord. system. | |
138 | //------------------------------------------------------------------ | |
139 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); | |
140 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
141 | ||
142 | Double_t &fP0=fP[0]; | |
143 | Double_t &fP2=fP[2]; | |
144 | Double_t &fC00=fC[0]; | |
145 | Double_t &fC10=fC[1]; | |
146 | Double_t &fC20=fC[3]; | |
147 | Double_t &fC21=fC[4]; | |
148 | Double_t &fC22=fC[5]; | |
149 | Double_t &fC30=fC[6]; | |
150 | Double_t &fC32=fC[8]; | |
151 | Double_t &fC40=fC[10]; | |
152 | Double_t &fC42=fC[12]; | |
153 | ||
154 | Double_t x=fX; | |
155 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
156 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
157 | ||
158 | fAlpha = alpha; | |
159 | fX = x*ca + fP0*sa; | |
160 | fP0= -x*sa + fP0*ca; | |
161 | fP2= sf*ca - cf*sa; | |
162 | ||
163 | Double_t rr=(ca+sf/cf*sa); | |
164 | ||
165 | fC00 *= (ca*ca); | |
166 | fC10 *= ca; | |
167 | fC20 *= ca*rr; | |
168 | fC21 *= rr; | |
169 | fC22 *= rr*rr; | |
170 | fC30 *= ca; | |
171 | fC32 *= rr; | |
172 | fC40 *= ca; | |
173 | fC42 *= rr; | |
174 | ||
175 | return kTRUE; | |
176 | } | |
177 | ||
178 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
179 | //---------------------------------------------------------------- | |
180 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
181 | //---------------------------------------------------------------- | |
182 | Double_t crv=kB2C*b*fP[4]; | |
183 | Double_t dx=xk-fX; | |
184 | Double_t f1=fP[2], f2=f1 + crv*dx; | |
bbefa4c4 | 185 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 186 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
187 | ||
188 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
189 | Double_t | |
190 | &fC00=fC[0], | |
191 | &fC10=fC[1], &fC11=fC[2], | |
192 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
193 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
194 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
195 | ||
196 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
197 | ||
198 | fX=xk; | |
199 | fP0 += dx*(f1+f2)/(r1+r2); | |
200 | fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3; | |
201 | fP2 += dx*crv; | |
202 | ||
203 | //f = F - 1 | |
204 | ||
205 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
206 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
207 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
208 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
209 | Double_t f13= dx/r1; | |
210 | Double_t f24= dx; f24*=cc; | |
211 | ||
212 | //b = C*ft | |
213 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
214 | Double_t b02=f24*fC40; | |
215 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
216 | Double_t b12=f24*fC41; | |
217 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
218 | Double_t b22=f24*fC42; | |
219 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
220 | Double_t b42=f24*fC44; | |
221 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
222 | Double_t b32=f24*fC43; | |
223 | ||
224 | //a = f*b = f*C*ft | |
225 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
226 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
227 | Double_t a22=f24*b42; | |
228 | ||
229 | //F*C*Ft = C + (b + bt + a) | |
230 | fC00 += b00 + b00 + a00; | |
231 | fC10 += b10 + b01 + a01; | |
232 | fC20 += b20 + b02 + a02; | |
233 | fC30 += b30; | |
234 | fC40 += b40; | |
235 | fC11 += b11 + b11 + a11; | |
236 | fC21 += b21 + b12 + a12; | |
237 | fC31 += b31; | |
238 | fC41 += b41; | |
239 | fC22 += b22 + b22 + a22; | |
240 | fC32 += b32; | |
241 | fC42 += b42; | |
242 | ||
243 | return kTRUE; | |
244 | } | |
245 | ||
246 | Double_t | |
247 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
248 | //---------------------------------------------------------------- | |
249 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
250 | //---------------------------------------------------------------- | |
251 | Double_t sdd = fC[0] + cov[0]; | |
252 | Double_t sdz = fC[1] + cov[1]; | |
253 | Double_t szz = fC[2] + cov[2]; | |
254 | Double_t det = sdd*szz - sdz*sdz; | |
255 | ||
256 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
257 | ||
258 | Double_t d = fP[0] - p[0]; | |
259 | Double_t z = fP[1] - p[1]; | |
260 | ||
261 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
262 | } | |
263 | ||
264 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { | |
265 | //------------------------------------------------------------------ | |
266 | // Update the track parameters with the space point "p" having | |
267 | // the covariance matrix "cov" | |
268 | //------------------------------------------------------------------ | |
269 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
270 | Double_t | |
271 | &fC00=fC[0], | |
272 | &fC10=fC[1], &fC11=fC[2], | |
273 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
274 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
275 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
276 | ||
277 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
278 | r00+=fC00; r01+=fC10; r11+=fC11; | |
279 | Double_t det=r00*r11 - r01*r01; | |
280 | ||
281 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
282 | ||
283 | ||
284 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
285 | ||
286 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
287 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
288 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
289 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
290 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
291 | ||
292 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
293 | Double_t sf=fP2 + k20*dy + k21*dz; | |
294 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
295 | ||
296 | fP0 += k00*dy + k01*dz; | |
297 | fP1 += k10*dy + k11*dz; | |
298 | fP2 = sf; | |
299 | fP3 += k30*dy + k31*dz; | |
300 | fP4 += k40*dy + k41*dz; | |
301 | ||
302 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
303 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
304 | ||
305 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
306 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
307 | fC40-=k00*c04+k01*c14; | |
308 | ||
309 | fC11-=k10*c01+k11*fC11; | |
310 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
311 | fC41-=k10*c04+k11*c14; | |
312 | ||
313 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
314 | fC42-=k20*c04+k21*c14; | |
315 | ||
316 | fC33-=k30*c03+k31*c13; | |
317 | fC43-=k30*c04+k31*c14; | |
318 | ||
319 | fC44-=k40*c04+k41*c14; | |
320 | ||
321 | return kTRUE; | |
322 | } | |
323 | ||
c9ec41e8 | 324 | Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) { |
325 | //---------------------------------------------------------------- | |
326 | // This function performs local->global transformation of the | |
327 | // track momentum. | |
328 | // When called, the arguments are: | |
329 | // p[0] = 1/pt of the track; | |
330 | // p[1] = sine of local azim. angle of the track momentum; | |
331 | // p[2] = tangent of the track momentum dip angle; | |
332 | // alpha - rotation angle. | |
333 | // The result is returned as: | |
334 | // p[0] = px | |
335 | // p[1] = py | |
336 | // p[2] = pz | |
337 | // Results for (nearly) straight tracks are meaningless ! | |
338 | //---------------------------------------------------------------- | |
339 | if (TMath::Abs(p[0])<=0) return kFALSE; | |
49d13e89 | 340 | if (TMath::Abs(p[1])> kAlmost1) return kFALSE; |
c9ec41e8 | 341 | |
342 | Double_t pt=1./TMath::Abs(p[0]); | |
343 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha); | |
344 | Double_t r=TMath::Sqrt(1 - p[1]*p[1]); | |
345 | p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2]; | |
a5e407e9 | 346 | |
347 | return kTRUE; | |
348 | } | |
349 | ||
c9ec41e8 | 350 | Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) { |
351 | //---------------------------------------------------------------- | |
352 | // This function performs local->global transformation of the | |
353 | // track position. | |
354 | // When called, the arguments are: | |
355 | // r[0] = local x | |
356 | // r[1] = local y | |
357 | // r[2] = local z | |
358 | // alpha - rotation angle. | |
359 | // The result is returned as: | |
360 | // r[0] = global x | |
361 | // r[1] = global y | |
362 | // r[2] = global z | |
363 | //---------------------------------------------------------------- | |
364 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0]; | |
365 | r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs; | |
a5e407e9 | 366 | |
a5e407e9 | 367 | return kTRUE; |
51ad6848 | 368 | } |
369 | ||
c9ec41e8 | 370 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const { |
371 | //--------------------------------------------------------------------- | |
372 | // This function returns the global track momentum components | |
373 | // Results for (nearly) straight tracks are meaningless ! | |
374 | //--------------------------------------------------------------------- | |
375 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
376 | return Local2GlobalMomentum(p,fAlpha); | |
377 | } | |
a5e407e9 | 378 | |
c9ec41e8 | 379 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
380 | //--------------------------------------------------------------------- | |
381 | // This function returns the global track position | |
382 | //--------------------------------------------------------------------- | |
383 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
384 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 385 | } |
386 | ||
c9ec41e8 | 387 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
388 | //--------------------------------------------------------------------- | |
389 | // This function returns the global covariance matrix of the track params | |
390 | // | |
391 | // Cov(x,x) ... : cv[0] | |
392 | // Cov(y,x) ... : cv[1] cv[2] | |
393 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
394 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
395 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
396 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 397 | // |
c9ec41e8 | 398 | // Results for (nearly) straight tracks are meaningless ! |
399 | //--------------------------------------------------------------------- | |
400 | if (TMath::Abs(fP[4])<=0) { | |
401 | for (Int_t i=0; i<21; i++) cv[i]=0.; | |
402 | return kFALSE; | |
a5e407e9 | 403 | } |
49d13e89 | 404 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 405 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
406 | return kFALSE; | |
407 | } | |
408 | Double_t pt=1./TMath::Abs(fP[4]); | |
409 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
410 | Double_t r=TMath::Sqrt(1-fP[2]*fP[2]); | |
411 | ||
412 | Double_t m00=-sn, m10=cs; | |
413 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
414 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
415 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
416 | ||
417 | cv[0 ] = fC[0]*m00*m00; | |
418 | cv[1 ] = fC[0]*m00*m10; | |
419 | cv[2 ] = fC[0]*m10*m10; | |
420 | cv[3 ] = fC[1]*m00; | |
421 | cv[4 ] = fC[1]*m10; | |
422 | cv[5 ] = fC[2]; | |
423 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
424 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
425 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
426 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
427 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
428 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
429 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
430 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
431 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
432 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
433 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
434 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
435 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
436 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
437 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 438 | |
c9ec41e8 | 439 | return kTRUE; |
51ad6848 | 440 | } |
441 | ||
51ad6848 | 442 | |
c9ec41e8 | 443 | Bool_t |
444 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
445 | //--------------------------------------------------------------------- | |
446 | // This function returns the global track momentum extrapolated to | |
447 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
448 | //--------------------------------------------------------------------- | |
c9ec41e8 | 449 | p[0]=fP[4]; |
49d13e89 | 450 | p[1]=fP[2]+(x-fX)*fP[4]*b*kB2C; |
c9ec41e8 | 451 | p[2]=fP[3]; |
452 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 453 | } |
454 | ||
c9ec41e8 | 455 | Bool_t |
456 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
457 | //--------------------------------------------------------------------- | |
458 | // This function returns the global track position extrapolated to | |
459 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
460 | //--------------------------------------------------------------------- | |
c9ec41e8 | 461 | Double_t dx=x-fX; |
49d13e89 | 462 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; |
c9ec41e8 | 463 | |
49d13e89 | 464 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 465 | |
466 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
467 | r[0] = x; | |
468 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
469 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; | |
470 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 471 | } |
472 | ||
473 | ||
474 | //_____________________________________________________________________________ | |
475 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
476 | { | |
477 | // print the parameters and the covariance matrix | |
478 | ||
479 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
480 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 481 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
482 | printf(" covariance: %12g\n", fC[0]); | |
483 | printf(" %12g %12g\n", fC[1], fC[2]); | |
484 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 485 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 486 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 487 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 488 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 489 | } |
5b77d93c | 490 | |
491 | ||
492 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t mass, Double_t maxStep, Bool_t rotateTo){ | |
493 | //---------------------------------------------------------------- | |
494 | // Propagate this track to the plane X=xk (cm) | |
495 | // correction for unhomogenity of the magnetic field and the | |
496 | // the correction for the material is included | |
497 | // | |
498 | // Require acces to magnetic field and geomanager | |
499 | // | |
500 | // mass - mass used in propagation - used for energy loss correction | |
501 | // maxStep - maximal step for propagation | |
502 | //---------------------------------------------------------------- | |
503 | const Double_t kEpsilon = 0.00001; | |
504 | Double_t xpos = GetX(); | |
505 | Double_t dir = (xpos<xToGo) ? 1.:-1.; | |
506 | // | |
507 | while ( (xToGo-xpos)*dir > kEpsilon){ | |
508 | Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep); | |
509 | Double_t x = xpos+step; | |
510 | Double_t xyz0[3],xyz1[3],param[7]; | |
511 | GetXYZ(xyz0); //starting global position | |
512 | Float_t pos0[3] = {xyz0[0],xyz0[1],xyz0[2]}; | |
513 | Double_t magZ = AliTracker::GetBz(pos0); | |
514 | if (!GetXYZAt(x,magZ,xyz1)) return kFALSE; // no prolongation | |
515 | AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param); | |
516 | if (!PropagateTo(x,magZ)) return kFALSE; | |
517 | Double_t distance = param[4]; | |
518 | if (!CorrectForMaterial(distance,param[1],param[0],mass)) return kFALSE; | |
519 | if (rotateTo){ | |
520 | GetXYZ(xyz0); // global position | |
521 | Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]); | |
522 | if (!Rotate(alphan)) return kFALSE; | |
523 | } | |
524 | xpos = GetX(); | |
525 | } | |
526 | return kTRUE; | |
527 | } | |
528 | ||
529 | //_____________________________________________________________________________ | |
530 | Bool_t AliExternalTrackParam::CorrectForMaterial(Double_t d, Double_t x0, Double_t rho, Double_t mass) | |
531 | { | |
532 | // | |
533 | // Take into account material effects assuming: | |
534 | // x0 - mean rad length | |
535 | // rho - mean density | |
536 | ||
537 | // | |
538 | // multiple scattering | |
539 | // | |
540 | if (mass<=0) { | |
541 | AliError("Non-positive mass"); | |
542 | return kFALSE; | |
543 | } | |
544 | Double_t p2=(1.+ fP[3]*fP[3])/(fP[4]*fP[4]); | |
545 | Double_t beta2=p2/(p2 + mass*mass); | |
546 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho; | |
547 | // | |
548 | fC[5] += theta2*(1.- fP[2]*fP[2])*(1. + fP[3]*fP[3]); | |
549 | fC[9] += theta2*(1. + fP[3]*fP[3])*(1. + fP[3]*fP[3]); | |
550 | fC[13] += theta2*fP[3]*fP[4]*(1. + fP[3]*fP[3]); | |
551 | fC[14] += theta2*fP[3]*fP[4]*fP[3]*fP[4]; | |
552 | // | |
553 | Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho; | |
554 | fP[4] *=(1.- TMath::Sqrt(p2+mass*mass)/p2*dE); | |
555 | // | |
556 | Double_t sigmade = 0.02*TMath::Sqrt(TMath::Abs(dE)); // energy loss fluctuation | |
557 | Double_t sigmac2 = sigmade*sigmade*fP[4]*fP[4]*(p2+mass*mass)/(p2*p2); | |
558 | fC[14] += sigmac2; | |
559 | return kTRUE; | |
560 | } | |
561 | ||
562 |