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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" |
edc97986 | 31 | #include "AliStrLine.h" |
f76701bf | 32 | #include "AliESDVertex.h" |
5b77d93c | 33 | |
51ad6848 | 34 | |
35 | ClassImp(AliExternalTrackParam) | |
36 | ||
51ad6848 | 37 | //_____________________________________________________________________________ |
90e48c0c | 38 | AliExternalTrackParam::AliExternalTrackParam() : |
90e48c0c | 39 | fX(0), |
c9ec41e8 | 40 | fAlpha(0) |
51ad6848 | 41 | { |
90e48c0c | 42 | // |
43 | // default constructor | |
44 | // | |
c9ec41e8 | 45 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; |
46 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 47 | } |
48 | ||
49 | //_____________________________________________________________________________ | |
50 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
51 | const Double_t param[5], | |
90e48c0c | 52 | const Double_t covar[15]) : |
90e48c0c | 53 | fX(x), |
c9ec41e8 | 54 | fAlpha(alpha) |
51ad6848 | 55 | { |
90e48c0c | 56 | // |
57 | // create external track parameters from given arguments | |
58 | // | |
c9ec41e8 | 59 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
60 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 61 | } |
62 | ||
90e48c0c | 63 | //_____________________________________________________________________________ |
64 | AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) : | |
c9ec41e8 | 65 | fAlpha(track.GetAlpha()) |
51ad6848 | 66 | { |
67 | // | |
68 | // | |
c9ec41e8 | 69 | track.GetExternalParameters(fX,fP); |
70 | track.GetExternalCovariance(fC); | |
51ad6848 | 71 | } |
72 | ||
51ad6848 | 73 | //_____________________________________________________________________________ |
c9ec41e8 | 74 | void AliExternalTrackParam::Set(const AliKalmanTrack& track) { |
75 | // | |
76 | // | |
77 | fAlpha=track.GetAlpha(); | |
78 | track.GetExternalParameters(fX,fP); | |
79 | track.GetExternalCovariance(fC); | |
51ad6848 | 80 | } |
81 | ||
82 | //_____________________________________________________________________________ | |
c9ec41e8 | 83 | void AliExternalTrackParam::Reset() { |
84 | fX=fAlpha=0.; | |
85 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
86 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 87 | } |
88 | ||
c9ec41e8 | 89 | Double_t AliExternalTrackParam::GetP() const { |
90 | //--------------------------------------------------------------------- | |
91 | // This function returns the track momentum | |
92 | // Results for (nearly) straight tracks are meaningless ! | |
93 | //--------------------------------------------------------------------- | |
06fb4a2f | 94 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 95 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 96 | } |
97 | ||
1d99986f | 98 | Double_t AliExternalTrackParam::Get1P() const { |
99 | //--------------------------------------------------------------------- | |
100 | // This function returns the 1/(track momentum) | |
101 | //--------------------------------------------------------------------- | |
102 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
103 | } | |
104 | ||
c9ec41e8 | 105 | //_______________________________________________________________________ |
c7bafca9 | 106 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 107 | //------------------------------------------------------------------ |
108 | // This function calculates the transverse impact parameter | |
109 | // with respect to a point with global coordinates (x,y) | |
110 | // in the magnetic field "b" (kG) | |
111 | //------------------------------------------------------------------ | |
5773defd | 112 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
49d13e89 | 113 | Double_t rp4=kB2C*b*fP[4]; |
c9ec41e8 | 114 | |
115 | Double_t xt=fX, yt=fP[0]; | |
116 | ||
117 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
118 | Double_t a = x*cs + y*sn; | |
119 | y = -x*sn + y*cs; x=a; | |
120 | xt-=x; yt-=y; | |
121 | ||
122 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
123 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
124 | if (rp4<0) a=-a; | |
125 | return a/(1 + TMath::Sqrt(sn*sn + cs*cs)); | |
51ad6848 | 126 | } |
127 | ||
49d13e89 | 128 | //_______________________________________________________________________ |
129 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
130 | //------------------------------------------------------------------ | |
131 | // This function calculates the transverse impact parameter | |
132 | // with respect to a point with global coordinates (xv,yv) | |
133 | // neglecting the track curvature. | |
134 | //------------------------------------------------------------------ | |
135 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
136 | Double_t x= xv*cs + yv*sn; | |
137 | Double_t y=-xv*sn + yv*cs; | |
138 | ||
139 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
140 | ||
141 | return d; | |
142 | } | |
143 | ||
c7bafca9 | 144 | Bool_t AliExternalTrackParam:: |
145 | CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) { | |
146 | //------------------------------------------------------------------ | |
147 | // This function corrects the track parameters for the crossed material | |
148 | // "d" - the thickness (fraction of the radiation length) | |
149 | // "x0" - the radiation length (g/cm^2) | |
150 | // "mass" - the mass of this particle (GeV/c^2) | |
151 | //------------------------------------------------------------------ | |
152 | Double_t &fP2=fP[2]; | |
153 | Double_t &fP3=fP[3]; | |
154 | Double_t &fP4=fP[4]; | |
155 | ||
156 | Double_t &fC22=fC[5]; | |
157 | Double_t &fC33=fC[9]; | |
158 | Double_t &fC43=fC[13]; | |
159 | Double_t &fC44=fC[14]; | |
160 | ||
161 | Double_t p2=(1.+ fP3*fP3)/(fP4*fP4); | |
162 | Double_t beta2=p2/(p2 + mass*mass); | |
163 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
164 | ||
165 | //Multiple scattering****************** | |
166 | if (d!=0) { | |
167 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
168 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
169 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
170 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
171 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
172 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
173 | } | |
174 | ||
175 | //Energy losses************************ | |
176 | if (x0!=0.) { | |
177 | d*=x0; | |
178 | Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d; | |
179 | if (beta2/(1-beta2)>3.5*3.5) | |
180 | dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d; | |
181 | ||
182 | fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE); | |
183 | } | |
184 | ||
185 | return kTRUE; | |
186 | } | |
187 | ||
49d13e89 | 188 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
189 | //------------------------------------------------------------------ | |
190 | // Transform this track to the local coord. system rotated | |
191 | // by angle "alpha" (rad) with respect to the global coord. system. | |
192 | //------------------------------------------------------------------ | |
193 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); | |
194 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
195 | ||
196 | Double_t &fP0=fP[0]; | |
197 | Double_t &fP2=fP[2]; | |
198 | Double_t &fC00=fC[0]; | |
199 | Double_t &fC10=fC[1]; | |
200 | Double_t &fC20=fC[3]; | |
201 | Double_t &fC21=fC[4]; | |
202 | Double_t &fC22=fC[5]; | |
203 | Double_t &fC30=fC[6]; | |
204 | Double_t &fC32=fC[8]; | |
205 | Double_t &fC40=fC[10]; | |
206 | Double_t &fC42=fC[12]; | |
207 | ||
208 | Double_t x=fX; | |
209 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
210 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
211 | ||
212 | fAlpha = alpha; | |
213 | fX = x*ca + fP0*sa; | |
214 | fP0= -x*sa + fP0*ca; | |
215 | fP2= sf*ca - cf*sa; | |
216 | ||
06fb4a2f | 217 | if (TMath::Abs(cf)<kAlmost0) { |
218 | AliError(Form("Too small cosine value %f",cf)); | |
219 | cf = kAlmost0; | |
220 | } | |
221 | ||
49d13e89 | 222 | Double_t rr=(ca+sf/cf*sa); |
223 | ||
224 | fC00 *= (ca*ca); | |
225 | fC10 *= ca; | |
226 | fC20 *= ca*rr; | |
227 | fC21 *= rr; | |
228 | fC22 *= rr*rr; | |
229 | fC30 *= ca; | |
230 | fC32 *= rr; | |
231 | fC40 *= ca; | |
232 | fC42 *= rr; | |
233 | ||
234 | return kTRUE; | |
235 | } | |
236 | ||
237 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
238 | //---------------------------------------------------------------- | |
239 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
240 | //---------------------------------------------------------------- | |
49d13e89 | 241 | Double_t dx=xk-fX; |
606833e7 | 242 | if (TMath::Abs(dx)<=0) return kTRUE; |
18ebc5ef | 243 | |
244 | Double_t crv=kB2C*b*fP[4]; | |
5773defd | 245 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
246 | ||
49d13e89 | 247 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 248 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 249 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
250 | ||
251 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
252 | Double_t | |
253 | &fC00=fC[0], | |
254 | &fC10=fC[1], &fC11=fC[2], | |
255 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
256 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
257 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
258 | ||
259 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
260 | ||
261 | fX=xk; | |
262 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 263 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 264 | fP2 += dx*crv; |
265 | ||
266 | //f = F - 1 | |
267 | ||
268 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
269 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
270 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
271 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
272 | Double_t f13= dx/r1; | |
273 | Double_t f24= dx; f24*=cc; | |
274 | ||
275 | //b = C*ft | |
276 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
277 | Double_t b02=f24*fC40; | |
278 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
279 | Double_t b12=f24*fC41; | |
280 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
281 | Double_t b22=f24*fC42; | |
282 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
283 | Double_t b42=f24*fC44; | |
284 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
285 | Double_t b32=f24*fC43; | |
286 | ||
287 | //a = f*b = f*C*ft | |
288 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
289 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
290 | Double_t a22=f24*b42; | |
291 | ||
292 | //F*C*Ft = C + (b + bt + a) | |
293 | fC00 += b00 + b00 + a00; | |
294 | fC10 += b10 + b01 + a01; | |
295 | fC20 += b20 + b02 + a02; | |
296 | fC30 += b30; | |
297 | fC40 += b40; | |
298 | fC11 += b11 + b11 + a11; | |
299 | fC21 += b21 + b12 + a12; | |
300 | fC31 += b31; | |
301 | fC41 += b41; | |
302 | fC22 += b22 + b22 + a22; | |
303 | fC32 += b32; | |
304 | fC42 += b42; | |
305 | ||
306 | return kTRUE; | |
307 | } | |
308 | ||
309 | Double_t | |
310 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
311 | //---------------------------------------------------------------- | |
312 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
313 | //---------------------------------------------------------------- | |
314 | Double_t sdd = fC[0] + cov[0]; | |
315 | Double_t sdz = fC[1] + cov[1]; | |
316 | Double_t szz = fC[2] + cov[2]; | |
317 | Double_t det = sdd*szz - sdz*sdz; | |
318 | ||
319 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
320 | ||
321 | Double_t d = fP[0] - p[0]; | |
322 | Double_t z = fP[1] - p[1]; | |
323 | ||
324 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
325 | } | |
326 | ||
327 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { | |
328 | //------------------------------------------------------------------ | |
329 | // Update the track parameters with the space point "p" having | |
330 | // the covariance matrix "cov" | |
331 | //------------------------------------------------------------------ | |
332 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
333 | Double_t | |
334 | &fC00=fC[0], | |
335 | &fC10=fC[1], &fC11=fC[2], | |
336 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
337 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
338 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
339 | ||
340 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
341 | r00+=fC00; r01+=fC10; r11+=fC11; | |
342 | Double_t det=r00*r11 - r01*r01; | |
343 | ||
344 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
345 | ||
346 | ||
347 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
348 | ||
349 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
350 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
351 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
352 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
353 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
354 | ||
355 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
356 | Double_t sf=fP2 + k20*dy + k21*dz; | |
357 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
358 | ||
359 | fP0 += k00*dy + k01*dz; | |
360 | fP1 += k10*dy + k11*dz; | |
361 | fP2 = sf; | |
362 | fP3 += k30*dy + k31*dz; | |
363 | fP4 += k40*dy + k41*dz; | |
364 | ||
365 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
366 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
367 | ||
368 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
369 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
370 | fC40-=k00*c04+k01*c14; | |
371 | ||
372 | fC11-=k10*c01+k11*fC11; | |
373 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
374 | fC41-=k10*c04+k11*c14; | |
375 | ||
376 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
377 | fC42-=k20*c04+k21*c14; | |
378 | ||
379 | fC33-=k30*c03+k31*c13; | |
380 | fC43-=k30*c04+k31*c14; | |
381 | ||
382 | fC44-=k40*c04+k41*c14; | |
383 | ||
384 | return kTRUE; | |
385 | } | |
386 | ||
c7bafca9 | 387 | void |
388 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
389 | //-------------------------------------------------------------------- | |
390 | // External track parameters -> helix parameters | |
391 | // "b" - magnetic field (kG) | |
392 | //-------------------------------------------------------------------- | |
393 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
394 | ||
395 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; hlx[4]=fP[4]; | |
396 | ||
397 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
398 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
399 | //hlx[1]= // z0 | |
400 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
401 | //hlx[3]= // tgl | |
402 | hlx[4]=hlx[4]*kB2C*b; // C | |
403 | } | |
404 | ||
405 | ||
406 | static void Evaluate(const Double_t *h, Double_t t, | |
407 | Double_t r[3], //radius vector | |
408 | Double_t g[3], //first defivatives | |
409 | Double_t gg[3]) //second derivatives | |
410 | { | |
411 | //-------------------------------------------------------------------- | |
412 | // Calculate position of a point on a track and some derivatives | |
413 | //-------------------------------------------------------------------- | |
414 | Double_t phase=h[4]*t+h[2]; | |
415 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
416 | ||
417 | r[0] = h[5] + (sn - h[6])/h[4]; | |
418 | r[1] = h[0] - (cs - h[7])/h[4]; | |
419 | r[2] = h[1] + h[3]*t; | |
420 | ||
421 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
422 | ||
423 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
424 | } | |
425 | ||
426 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
427 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
428 | //------------------------------------------------------------ | |
429 | // Returns the (weighed !) distance of closest approach between | |
430 | // this track and the track "p". | |
431 | // Other returned values: | |
432 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
433 | //----------------------------------------------------------- | |
434 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
435 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
436 | Double_t dx2=dy2; | |
437 | ||
438 | //dx2=dy2=dz2=1.; | |
439 | ||
440 | Double_t p1[8]; GetHelixParameters(p1,b); | |
441 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
442 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
443 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
444 | ||
445 | ||
446 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
447 | Evaluate(p1,t1,r1,g1,gg1); | |
448 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
449 | Evaluate(p2,t2,r2,g2,gg2); | |
450 | ||
451 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
452 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
453 | ||
454 | Int_t max=27; | |
455 | while (max--) { | |
456 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
457 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
458 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
459 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
460 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
461 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
462 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
463 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
464 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
465 | ||
466 | Double_t det=h11*h22-h12*h12; | |
467 | ||
468 | Double_t dt1,dt2; | |
469 | if (TMath::Abs(det)<1.e-33) { | |
470 | //(quasi)singular Hessian | |
471 | dt1=-gt1; dt2=-gt2; | |
472 | } else { | |
473 | dt1=-(gt1*h22 - gt2*h12)/det; | |
474 | dt2=-(h11*gt2 - h12*gt1)/det; | |
475 | } | |
476 | ||
477 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
478 | ||
479 | //check delta(phase1) ? | |
480 | //check delta(phase2) ? | |
481 | ||
482 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
483 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
484 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
485 | AliWarning(" stopped at not a stationary point !"); | |
486 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); | |
487 | if (lmb < 0.) | |
488 | AliWarning(" stopped at not a minimum !"); | |
489 | break; | |
490 | } | |
491 | ||
492 | Double_t dd=dm; | |
493 | for (Int_t div=1 ; ; div*=2) { | |
494 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
495 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
496 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
497 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
498 | if (dd<dm) break; | |
499 | dt1*=0.5; dt2*=0.5; | |
500 | if (div>512) { | |
501 | AliWarning(" overshoot !"); break; | |
502 | } | |
503 | } | |
504 | dm=dd; | |
505 | ||
506 | t1+=dt1; | |
507 | t2+=dt2; | |
508 | ||
509 | } | |
510 | ||
511 | if (max<=0) AliWarning(" too many iterations !"); | |
512 | ||
513 | Double_t cs=TMath::Cos(GetAlpha()); | |
514 | Double_t sn=TMath::Sin(GetAlpha()); | |
515 | xthis=r1[0]*cs + r1[1]*sn; | |
516 | ||
517 | cs=TMath::Cos(p->GetAlpha()); | |
518 | sn=TMath::Sin(p->GetAlpha()); | |
519 | xp=r2[0]*cs + r2[1]*sn; | |
520 | ||
521 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
522 | } | |
523 | ||
524 | Double_t AliExternalTrackParam:: | |
525 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
526 | //-------------------------------------------------------------- | |
527 | // Propagates this track and the argument track to the position of the | |
528 | // distance of closest approach. | |
529 | // Returns the (weighed !) distance of closest approach. | |
530 | //-------------------------------------------------------------- | |
531 | Double_t xthis,xp; | |
532 | Double_t dca=GetDCA(p,b,xthis,xp); | |
533 | ||
534 | if (!PropagateTo(xthis,b)) { | |
535 | //AliWarning(" propagation failed !"); | |
536 | return 1e+33; | |
537 | } | |
538 | ||
539 | if (!p->PropagateTo(xp,b)) { | |
540 | //AliWarning(" propagation failed !"; | |
541 | return 1e+33; | |
542 | } | |
543 | ||
544 | return dca; | |
545 | } | |
546 | ||
547 | ||
548 | ||
f76701bf | 549 | |
550 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){ | |
551 | // | |
552 | // Try to relate this track to the vertex "vtx", | |
553 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
554 | // Magnetic field is "b" (kG). | |
555 | // | |
556 | // a) The track gets extapolated to the DCA to the vertex. | |
557 | // b) The impact parameters and their covariance matrix are calculated. | |
558 | // | |
559 | // In the case of success, the returned value is kTRUE | |
560 | // (otherwise, it's kFALSE) | |
561 | // | |
562 | Double_t alpha=GetAlpha(); | |
563 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
564 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
565 | Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn; | |
29fbcc93 | 566 | Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs; |
f76701bf | 567 | x-=xv; y-=yv; |
568 | ||
569 | //Estimate the impact parameter neglecting the track curvature | |
570 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
571 | if (d > maxd) return kFALSE; | |
572 | ||
573 | //Propagate to the DCA | |
574 | Double_t crv=0.299792458e-3*b*GetParameter()[4]; | |
575 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); | |
576 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
577 | ||
578 | x = xv*cs + yv*sn; | |
579 | yv=-xv*sn + yv*cs; xv=x; | |
580 | ||
581 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
29fbcc93 | 582 | return kTRUE; |
f76701bf | 583 | } |
584 | ||
585 | ||
586 | ||
587 | ||
c9ec41e8 | 588 | Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) { |
589 | //---------------------------------------------------------------- | |
590 | // This function performs local->global transformation of the | |
591 | // track momentum. | |
592 | // When called, the arguments are: | |
593 | // p[0] = 1/pt of the track; | |
594 | // p[1] = sine of local azim. angle of the track momentum; | |
595 | // p[2] = tangent of the track momentum dip angle; | |
596 | // alpha - rotation angle. | |
597 | // The result is returned as: | |
598 | // p[0] = px | |
599 | // p[1] = py | |
600 | // p[2] = pz | |
601 | // Results for (nearly) straight tracks are meaningless ! | |
602 | //---------------------------------------------------------------- | |
603 | if (TMath::Abs(p[0])<=0) return kFALSE; | |
49d13e89 | 604 | if (TMath::Abs(p[1])> kAlmost1) return kFALSE; |
c9ec41e8 | 605 | |
606 | Double_t pt=1./TMath::Abs(p[0]); | |
607 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha); | |
608 | Double_t r=TMath::Sqrt(1 - p[1]*p[1]); | |
609 | p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2]; | |
a5e407e9 | 610 | |
611 | return kTRUE; | |
612 | } | |
613 | ||
c9ec41e8 | 614 | Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) { |
615 | //---------------------------------------------------------------- | |
616 | // This function performs local->global transformation of the | |
617 | // track position. | |
618 | // When called, the arguments are: | |
619 | // r[0] = local x | |
620 | // r[1] = local y | |
621 | // r[2] = local z | |
622 | // alpha - rotation angle. | |
623 | // The result is returned as: | |
624 | // r[0] = global x | |
625 | // r[1] = global y | |
626 | // r[2] = global z | |
627 | //---------------------------------------------------------------- | |
628 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0]; | |
629 | r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs; | |
a5e407e9 | 630 | |
a5e407e9 | 631 | return kTRUE; |
51ad6848 | 632 | } |
633 | ||
c9ec41e8 | 634 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const { |
635 | //--------------------------------------------------------------------- | |
636 | // This function returns the global track momentum components | |
637 | // Results for (nearly) straight tracks are meaningless ! | |
638 | //--------------------------------------------------------------------- | |
639 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
640 | return Local2GlobalMomentum(p,fAlpha); | |
641 | } | |
a5e407e9 | 642 | |
c9ec41e8 | 643 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
644 | //--------------------------------------------------------------------- | |
645 | // This function returns the global track position | |
646 | //--------------------------------------------------------------------- | |
647 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
648 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 649 | } |
650 | ||
c9ec41e8 | 651 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
652 | //--------------------------------------------------------------------- | |
653 | // This function returns the global covariance matrix of the track params | |
654 | // | |
655 | // Cov(x,x) ... : cv[0] | |
656 | // Cov(y,x) ... : cv[1] cv[2] | |
657 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
658 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
659 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
660 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 661 | // |
c9ec41e8 | 662 | // Results for (nearly) straight tracks are meaningless ! |
663 | //--------------------------------------------------------------------- | |
664 | if (TMath::Abs(fP[4])<=0) { | |
665 | for (Int_t i=0; i<21; i++) cv[i]=0.; | |
666 | return kFALSE; | |
a5e407e9 | 667 | } |
49d13e89 | 668 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 669 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
670 | return kFALSE; | |
671 | } | |
672 | Double_t pt=1./TMath::Abs(fP[4]); | |
673 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
674 | Double_t r=TMath::Sqrt(1-fP[2]*fP[2]); | |
675 | ||
676 | Double_t m00=-sn, m10=cs; | |
677 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
678 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
679 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
680 | ||
681 | cv[0 ] = fC[0]*m00*m00; | |
682 | cv[1 ] = fC[0]*m00*m10; | |
683 | cv[2 ] = fC[0]*m10*m10; | |
684 | cv[3 ] = fC[1]*m00; | |
685 | cv[4 ] = fC[1]*m10; | |
686 | cv[5 ] = fC[2]; | |
687 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
688 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
689 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
690 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
691 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
692 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
693 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
694 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
695 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
696 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
697 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
698 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
699 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
700 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
701 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 702 | |
c9ec41e8 | 703 | return kTRUE; |
51ad6848 | 704 | } |
705 | ||
51ad6848 | 706 | |
c9ec41e8 | 707 | Bool_t |
708 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
709 | //--------------------------------------------------------------------- | |
710 | // This function returns the global track momentum extrapolated to | |
711 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
712 | //--------------------------------------------------------------------- | |
c9ec41e8 | 713 | p[0]=fP[4]; |
49d13e89 | 714 | p[1]=fP[2]+(x-fX)*fP[4]*b*kB2C; |
c9ec41e8 | 715 | p[2]=fP[3]; |
716 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 717 | } |
718 | ||
c9ec41e8 | 719 | Bool_t |
720 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
721 | //--------------------------------------------------------------------- | |
722 | // This function returns the global track position extrapolated to | |
723 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
724 | //--------------------------------------------------------------------- | |
c9ec41e8 | 725 | Double_t dx=x-fX; |
49d13e89 | 726 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; |
c9ec41e8 | 727 | |
49d13e89 | 728 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 729 | |
730 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
731 | r[0] = x; | |
732 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
733 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; | |
734 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 735 | } |
736 | ||
737 | ||
edc97986 | 738 | //_____________________________________________________________________________ |
739 | void AliExternalTrackParam::ApproximateHelixWithLine(Double_t xk, Double_t b, AliStrLine *line) | |
740 | { | |
741 | //------------------------------------------------------------ | |
742 | // Approximate the track (helix) with a straight line tangent to the | |
743 | // helix in the point defined by r (F. Prino, prino@to.infn.it) | |
744 | //------------------------------------------------------------ | |
745 | Double_t mom[3]; | |
746 | Double_t azim = TMath::ASin(fP[2])+fAlpha; | |
747 | Double_t theta = TMath::Pi()/2. - TMath::ATan(fP[3]); | |
748 | mom[0] = TMath::Sin(theta)*TMath::Cos(azim); | |
749 | mom[1] = TMath::Sin(theta)*TMath::Sin(azim); | |
750 | mom[2] = TMath::Cos(theta); | |
751 | Double_t pos[3]; | |
752 | GetXYZAt(xk,b,pos); | |
753 | line->SetP0(pos); | |
754 | line->SetCd(mom); | |
755 | } | |
51ad6848 | 756 | //_____________________________________________________________________________ |
757 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
758 | { | |
759 | // print the parameters and the covariance matrix | |
760 | ||
761 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
762 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 763 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
764 | printf(" covariance: %12g\n", fC[0]); | |
765 | printf(" %12g %12g\n", fC[1], fC[2]); | |
766 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 767 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 768 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 769 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 770 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 771 | } |
5b77d93c | 772 | |
773 | ||
774 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t mass, Double_t maxStep, Bool_t rotateTo){ | |
775 | //---------------------------------------------------------------- | |
776 | // Propagate this track to the plane X=xk (cm) | |
777 | // correction for unhomogenity of the magnetic field and the | |
778 | // the correction for the material is included | |
779 | // | |
780 | // Require acces to magnetic field and geomanager | |
781 | // | |
782 | // mass - mass used in propagation - used for energy loss correction | |
783 | // maxStep - maximal step for propagation | |
784 | //---------------------------------------------------------------- | |
785 | const Double_t kEpsilon = 0.00001; | |
786 | Double_t xpos = GetX(); | |
787 | Double_t dir = (xpos<xToGo) ? 1.:-1.; | |
788 | // | |
789 | while ( (xToGo-xpos)*dir > kEpsilon){ | |
790 | Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep); | |
791 | Double_t x = xpos+step; | |
792 | Double_t xyz0[3],xyz1[3],param[7]; | |
793 | GetXYZ(xyz0); //starting global position | |
794 | Float_t pos0[3] = {xyz0[0],xyz0[1],xyz0[2]}; | |
795 | Double_t magZ = AliTracker::GetBz(pos0); | |
796 | if (!GetXYZAt(x,magZ,xyz1)) return kFALSE; // no prolongation | |
797 | AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param); | |
798 | if (!PropagateTo(x,magZ)) return kFALSE; | |
799 | Double_t distance = param[4]; | |
800 | if (!CorrectForMaterial(distance,param[1],param[0],mass)) return kFALSE; | |
801 | if (rotateTo){ | |
802 | GetXYZ(xyz0); // global position | |
803 | Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]); | |
804 | if (!Rotate(alphan)) return kFALSE; | |
805 | } | |
806 | xpos = GetX(); | |
807 | } | |
808 | return kTRUE; | |
809 | } | |
810 | ||
811 | //_____________________________________________________________________________ | |
812 | Bool_t AliExternalTrackParam::CorrectForMaterial(Double_t d, Double_t x0, Double_t rho, Double_t mass) | |
813 | { | |
814 | // | |
815 | // Take into account material effects assuming: | |
816 | // x0 - mean rad length | |
817 | // rho - mean density | |
818 | ||
819 | // | |
820 | // multiple scattering | |
821 | // | |
822 | if (mass<=0) { | |
823 | AliError("Non-positive mass"); | |
824 | return kFALSE; | |
825 | } | |
826 | Double_t p2=(1.+ fP[3]*fP[3])/(fP[4]*fP[4]); | |
827 | Double_t beta2=p2/(p2 + mass*mass); | |
828 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho; | |
829 | // | |
830 | fC[5] += theta2*(1.- fP[2]*fP[2])*(1. + fP[3]*fP[3]); | |
831 | fC[9] += theta2*(1. + fP[3]*fP[3])*(1. + fP[3]*fP[3]); | |
832 | fC[13] += theta2*fP[3]*fP[4]*(1. + fP[3]*fP[3]); | |
833 | fC[14] += theta2*fP[3]*fP[4]*fP[3]*fP[4]; | |
834 | // | |
835 | Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho; | |
836 | fP[4] *=(1.- TMath::Sqrt(p2+mass*mass)/p2*dE); | |
837 | // | |
838 | Double_t sigmade = 0.02*TMath::Sqrt(TMath::Abs(dE)); // energy loss fluctuation | |
839 | Double_t sigmac2 = sigmade*sigmade*fP[4]*fP[4]*(p2+mass*mass)/(p2*p2); | |
840 | fC[14] += sigmac2; | |
841 | return kTRUE; | |
842 | } | |
843 | ||
844 |