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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" |
f76701bf | 29 | #include "AliESDVertex.h" |
6c94f330 | 30 | #include "AliLog.h" |
51ad6848 | 31 | |
32 | ClassImp(AliExternalTrackParam) | |
33 | ||
51ad6848 | 34 | //_____________________________________________________________________________ |
90e48c0c | 35 | AliExternalTrackParam::AliExternalTrackParam() : |
6c94f330 | 36 | TObject(), |
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 | ||
6c94f330 | 47 | //_____________________________________________________________________________ |
48 | AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): | |
49 | TObject(track), | |
50 | fX(track.fX), | |
51 | fAlpha(track.fAlpha) | |
52 | { | |
53 | // | |
54 | // copy constructor | |
55 | // | |
56 | for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i]; | |
57 | for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i]; | |
58 | } | |
59 | ||
51ad6848 | 60 | //_____________________________________________________________________________ |
61 | AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, | |
62 | const Double_t param[5], | |
90e48c0c | 63 | const Double_t covar[15]) : |
6c94f330 | 64 | TObject(), |
90e48c0c | 65 | fX(x), |
c9ec41e8 | 66 | fAlpha(alpha) |
51ad6848 | 67 | { |
90e48c0c | 68 | // |
69 | // create external track parameters from given arguments | |
70 | // | |
c9ec41e8 | 71 | for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; |
72 | for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; | |
51ad6848 | 73 | } |
74 | ||
90e48c0c | 75 | //_____________________________________________________________________________ |
6c94f330 | 76 | void AliExternalTrackParam::Set(Double_t x, Double_t alpha, |
77 | const Double_t p[5], const Double_t cov[15]) { | |
c9ec41e8 | 78 | // |
6c94f330 | 79 | // Sets the parameters |
c9ec41e8 | 80 | // |
6c94f330 | 81 | fX=x; |
82 | fAlpha=alpha; | |
83 | for (Int_t i = 0; i < 5; i++) fP[i] = p[i]; | |
84 | for (Int_t i = 0; i < 15; i++) fC[i] = cov[i]; | |
51ad6848 | 85 | } |
86 | ||
87 | //_____________________________________________________________________________ | |
c9ec41e8 | 88 | void AliExternalTrackParam::Reset() { |
1530f89c | 89 | // |
90 | // Resets all the parameters to 0 | |
91 | // | |
c9ec41e8 | 92 | fX=fAlpha=0.; |
93 | for (Int_t i = 0; i < 5; i++) fP[i] = 0; | |
94 | for (Int_t i = 0; i < 15; i++) fC[i] = 0; | |
51ad6848 | 95 | } |
96 | ||
c9ec41e8 | 97 | Double_t AliExternalTrackParam::GetP() const { |
98 | //--------------------------------------------------------------------- | |
99 | // This function returns the track momentum | |
100 | // Results for (nearly) straight tracks are meaningless ! | |
101 | //--------------------------------------------------------------------- | |
06fb4a2f | 102 | if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig; |
c9ec41e8 | 103 | return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]); |
51ad6848 | 104 | } |
105 | ||
1d99986f | 106 | Double_t AliExternalTrackParam::Get1P() const { |
107 | //--------------------------------------------------------------------- | |
108 | // This function returns the 1/(track momentum) | |
109 | //--------------------------------------------------------------------- | |
110 | return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]); | |
111 | } | |
112 | ||
c9ec41e8 | 113 | //_______________________________________________________________________ |
c7bafca9 | 114 | Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { |
c9ec41e8 | 115 | //------------------------------------------------------------------ |
116 | // This function calculates the transverse impact parameter | |
117 | // with respect to a point with global coordinates (x,y) | |
118 | // in the magnetic field "b" (kG) | |
119 | //------------------------------------------------------------------ | |
5773defd | 120 | if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y); |
1530f89c | 121 | Double_t rp4=GetC(b); |
c9ec41e8 | 122 | |
123 | Double_t xt=fX, yt=fP[0]; | |
124 | ||
125 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
126 | Double_t a = x*cs + y*sn; | |
127 | y = -x*sn + y*cs; x=a; | |
128 | xt-=x; yt-=y; | |
129 | ||
130 | sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]); | |
131 | a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt); | |
1530f89c | 132 | return -a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
133 | } | |
134 | ||
135 | //_______________________________________________________________________ | |
136 | void AliExternalTrackParam:: | |
137 | GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { | |
138 | //------------------------------------------------------------------ | |
139 | // This function calculates the transverse and longitudinal impact parameters | |
140 | // with respect to a point with global coordinates (x,y) | |
141 | // in the magnetic field "b" (kG) | |
142 | //------------------------------------------------------------------ | |
143 | Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1); | |
144 | Double_t xt=fX, yt=fP[0]; | |
145 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
146 | Double_t a = x*cs + y*sn; | |
147 | y = -x*sn + y*cs; x=a; | |
148 | xt-=x; yt-=y; | |
149 | ||
150 | Double_t rp4=GetC(b); | |
151 | if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) { | |
152 | dz[0] = -(xt*f1 - yt*r1); | |
153 | dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z; | |
154 | return; | |
155 | } | |
156 | ||
157 | sn=rp4*xt - f1; cs=rp4*yt + r1; | |
158 | a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt); | |
159 | Double_t rr=TMath::Sqrt(sn*sn + cs*cs); | |
160 | dz[0] = -a/(1 + rr); | |
161 | Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2); | |
162 | dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z; | |
51ad6848 | 163 | } |
164 | ||
49d13e89 | 165 | //_______________________________________________________________________ |
166 | Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { | |
167 | //------------------------------------------------------------------ | |
168 | // This function calculates the transverse impact parameter | |
169 | // with respect to a point with global coordinates (xv,yv) | |
170 | // neglecting the track curvature. | |
171 | //------------------------------------------------------------------ | |
172 | Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha); | |
173 | Double_t x= xv*cs + yv*sn; | |
174 | Double_t y=-xv*sn + yv*cs; | |
175 | ||
176 | Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); | |
177 | ||
1530f89c | 178 | return -d; |
49d13e89 | 179 | } |
180 | ||
c7bafca9 | 181 | Bool_t AliExternalTrackParam:: |
182 | CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) { | |
183 | //------------------------------------------------------------------ | |
184 | // This function corrects the track parameters for the crossed material | |
185 | // "d" - the thickness (fraction of the radiation length) | |
186 | // "x0" - the radiation length (g/cm^2) | |
187 | // "mass" - the mass of this particle (GeV/c^2) | |
188 | //------------------------------------------------------------------ | |
189 | Double_t &fP2=fP[2]; | |
190 | Double_t &fP3=fP[3]; | |
191 | Double_t &fP4=fP[4]; | |
192 | ||
193 | Double_t &fC22=fC[5]; | |
194 | Double_t &fC33=fC[9]; | |
195 | Double_t &fC43=fC[13]; | |
196 | Double_t &fC44=fC[14]; | |
197 | ||
7b5ef2e6 | 198 | Double_t p=GetP(); |
199 | Double_t p2=p*p; | |
c7bafca9 | 200 | Double_t beta2=p2/(p2 + mass*mass); |
201 | d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); | |
202 | ||
203 | //Multiple scattering****************** | |
204 | if (d!=0) { | |
205 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d); | |
206 | //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; | |
207 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); | |
208 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); | |
209 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); | |
210 | fC44 += theta2*fP3*fP4*fP3*fP4; | |
211 | } | |
212 | ||
213 | //Energy losses************************ | |
8fc1985d | 214 | if (x0!=0. && beta2<1) { |
c7bafca9 | 215 | d*=x0; |
216 | Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d; | |
217 | if (beta2/(1-beta2)>3.5*3.5) | |
218 | dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d; | |
219 | ||
220 | fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE); | |
221 | } | |
222 | ||
223 | return kTRUE; | |
224 | } | |
225 | ||
49d13e89 | 226 | Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { |
227 | //------------------------------------------------------------------ | |
228 | // Transform this track to the local coord. system rotated | |
229 | // by angle "alpha" (rad) with respect to the global coord. system. | |
230 | //------------------------------------------------------------------ | |
dfcef74c | 231 | if (TMath::Abs(fP[2]) >= kAlmost1) { |
232 | AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2])); | |
233 | return kFALSE; | |
234 | } | |
235 | ||
49d13e89 | 236 | if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi(); |
237 | else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi(); | |
238 | ||
239 | Double_t &fP0=fP[0]; | |
240 | Double_t &fP2=fP[2]; | |
241 | Double_t &fC00=fC[0]; | |
242 | Double_t &fC10=fC[1]; | |
243 | Double_t &fC20=fC[3]; | |
244 | Double_t &fC21=fC[4]; | |
245 | Double_t &fC22=fC[5]; | |
246 | Double_t &fC30=fC[6]; | |
247 | Double_t &fC32=fC[8]; | |
248 | Double_t &fC40=fC[10]; | |
249 | Double_t &fC42=fC[12]; | |
250 | ||
251 | Double_t x=fX; | |
252 | Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha); | |
253 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); | |
254 | ||
dfcef74c | 255 | Double_t tmp=sf*ca - cf*sa; |
256 | if (TMath::Abs(tmp) >= kAlmost1) return kFALSE; | |
257 | ||
49d13e89 | 258 | fAlpha = alpha; |
259 | fX = x*ca + fP0*sa; | |
260 | fP0= -x*sa + fP0*ca; | |
dfcef74c | 261 | fP2= tmp; |
49d13e89 | 262 | |
06fb4a2f | 263 | if (TMath::Abs(cf)<kAlmost0) { |
264 | AliError(Form("Too small cosine value %f",cf)); | |
265 | cf = kAlmost0; | |
266 | } | |
267 | ||
49d13e89 | 268 | Double_t rr=(ca+sf/cf*sa); |
269 | ||
270 | fC00 *= (ca*ca); | |
271 | fC10 *= ca; | |
272 | fC20 *= ca*rr; | |
273 | fC21 *= rr; | |
274 | fC22 *= rr*rr; | |
275 | fC30 *= ca; | |
276 | fC32 *= rr; | |
277 | fC40 *= ca; | |
278 | fC42 *= rr; | |
279 | ||
280 | return kTRUE; | |
281 | } | |
282 | ||
283 | Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { | |
284 | //---------------------------------------------------------------- | |
285 | // Propagate this track to the plane X=xk (cm) in the field "b" (kG) | |
286 | //---------------------------------------------------------------- | |
49d13e89 | 287 | Double_t dx=xk-fX; |
e421f556 | 288 | if (TMath::Abs(dx)<=kAlmost0) return kTRUE; |
18ebc5ef | 289 | |
1530f89c | 290 | Double_t crv=GetC(b); |
5773defd | 291 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
292 | ||
49d13e89 | 293 | Double_t f1=fP[2], f2=f1 + crv*dx; |
bbefa4c4 | 294 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 295 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
296 | ||
297 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
298 | Double_t | |
299 | &fC00=fC[0], | |
300 | &fC10=fC[1], &fC11=fC[2], | |
301 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
302 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
303 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
304 | ||
305 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
306 | ||
307 | fX=xk; | |
308 | fP0 += dx*(f1+f2)/(r1+r2); | |
18ebc5ef | 309 | fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov ! |
49d13e89 | 310 | fP2 += dx*crv; |
311 | ||
312 | //f = F - 1 | |
313 | ||
314 | Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4; | |
315 | Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc; | |
316 | Double_t f12= dx*fP3*f1/(r1*r1*r1); | |
317 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc; | |
318 | Double_t f13= dx/r1; | |
319 | Double_t f24= dx; f24*=cc; | |
320 | ||
321 | //b = C*ft | |
322 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; | |
323 | Double_t b02=f24*fC40; | |
324 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; | |
325 | Double_t b12=f24*fC41; | |
326 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; | |
327 | Double_t b22=f24*fC42; | |
328 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; | |
329 | Double_t b42=f24*fC44; | |
330 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; | |
331 | Double_t b32=f24*fC43; | |
332 | ||
333 | //a = f*b = f*C*ft | |
334 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; | |
335 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; | |
336 | Double_t a22=f24*b42; | |
337 | ||
338 | //F*C*Ft = C + (b + bt + a) | |
339 | fC00 += b00 + b00 + a00; | |
340 | fC10 += b10 + b01 + a01; | |
341 | fC20 += b20 + b02 + a02; | |
342 | fC30 += b30; | |
343 | fC40 += b40; | |
344 | fC11 += b11 + b11 + a11; | |
345 | fC21 += b21 + b12 + a12; | |
346 | fC31 += b31; | |
347 | fC41 += b41; | |
348 | fC22 += b22 + b22 + a22; | |
349 | fC32 += b32; | |
350 | fC42 += b42; | |
351 | ||
352 | return kTRUE; | |
353 | } | |
354 | ||
052daaff | 355 | void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3], |
356 | Double_t p[3], Double_t bz) const { | |
357 | //+++++++++++++++++++++++++++++++++++++++++ | |
358 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
359 | // Extrapolate track along simple helix in magnetic field | |
360 | // Arguments: len -distance alogn helix, [cm] | |
361 | // bz - mag field, [kGaus] | |
362 | // Returns: x and p contain extrapolated positon and momentum | |
363 | // The momentum returned for straight-line tracks is meaningless ! | |
364 | //+++++++++++++++++++++++++++++++++++++++++ | |
365 | GetXYZ(x); | |
366 | ||
367 | if (TMath::Abs(Get1Pt()) < kAlmost0){ //straight-line tracks | |
368 | Double_t unit[3]; GetDirection(unit); | |
369 | x[0]+=unit[0]*len; | |
370 | x[1]+=unit[1]*len; | |
371 | x[2]+=unit[2]*len; | |
372 | ||
373 | p[0]=unit[0]/kAlmost0; | |
374 | p[1]=unit[1]/kAlmost0; | |
375 | p[2]=unit[2]/kAlmost0; | |
376 | } else { | |
377 | GetPxPyPz(p); | |
378 | Double_t pp=GetP(); | |
379 | Double_t a = -kB2C*bz*GetSign(); | |
380 | Double_t rho = a/pp; | |
381 | x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a; | |
382 | x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a; | |
383 | x[2] += p[2]*len/pp; | |
384 | ||
385 | Double_t p0=p[0]; | |
386 | p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len); | |
387 | p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len); | |
388 | } | |
389 | } | |
390 | ||
391 | Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3], | |
392 | Double_t bz) const { | |
393 | //+++++++++++++++++++++++++++++++++++++++++ | |
394 | // Origin: K. Shileev (Kirill.Shileev@cern.ch) | |
395 | // Finds point of intersection (if exists) of the helix with the plane. | |
396 | // Stores result in fX and fP. | |
397 | // Arguments: planePoint,planeNorm - the plane defined by any plane's point | |
398 | // and vector, normal to the plane | |
399 | // Returns: kTrue if helix intersects the plane, kFALSE otherwise. | |
400 | //+++++++++++++++++++++++++++++++++++++++++ | |
401 | Double_t x0[3]; GetXYZ(x0); //get track position in MARS | |
402 | ||
403 | //estimates initial helix length up to plane | |
404 | Double_t s= | |
405 | (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2]; | |
406 | Double_t dist=99999,distPrev=dist; | |
407 | Double_t x[3],p[3]; | |
408 | while(TMath::Abs(dist)>0.00001){ | |
409 | //calculates helix at the distance s from x0 ALONG the helix | |
410 | Propagate(s,x,p,bz); | |
411 | ||
412 | //distance between current helix position and plane | |
413 | dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2]; | |
414 | ||
415 | if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;} | |
416 | distPrev=dist; | |
417 | s-=dist; | |
418 | } | |
419 | //on exit pnt is intersection point,norm is track vector at that point, | |
420 | //all in MARS | |
421 | for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];} | |
422 | return kTRUE; | |
423 | } | |
424 | ||
49d13e89 | 425 | Double_t |
426 | AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const { | |
427 | //---------------------------------------------------------------- | |
428 | // Estimate the chi2 of the space point "p" with the cov. matrix "cov" | |
429 | //---------------------------------------------------------------- | |
430 | Double_t sdd = fC[0] + cov[0]; | |
431 | Double_t sdz = fC[1] + cov[1]; | |
432 | Double_t szz = fC[2] + cov[2]; | |
433 | Double_t det = sdd*szz - sdz*sdz; | |
434 | ||
435 | if (TMath::Abs(det) < kAlmost0) return kVeryBig; | |
436 | ||
437 | Double_t d = fP[0] - p[0]; | |
438 | Double_t z = fP[1] - p[1]; | |
439 | ||
440 | return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det; | |
441 | } | |
442 | ||
443 | Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { | |
444 | //------------------------------------------------------------------ | |
445 | // Update the track parameters with the space point "p" having | |
446 | // the covariance matrix "cov" | |
447 | //------------------------------------------------------------------ | |
448 | Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4]; | |
449 | Double_t | |
450 | &fC00=fC[0], | |
451 | &fC10=fC[1], &fC11=fC[2], | |
452 | &fC20=fC[3], &fC21=fC[4], &fC22=fC[5], | |
453 | &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9], | |
454 | &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14]; | |
455 | ||
456 | Double_t r00=cov[0], r01=cov[1], r11=cov[2]; | |
457 | r00+=fC00; r01+=fC10; r11+=fC11; | |
458 | Double_t det=r00*r11 - r01*r01; | |
459 | ||
460 | if (TMath::Abs(det) < kAlmost0) return kFALSE; | |
461 | ||
462 | ||
463 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; | |
464 | ||
465 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; | |
466 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; | |
467 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; | |
468 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; | |
469 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; | |
470 | ||
471 | Double_t dy=p[0] - fP0, dz=p[1] - fP1; | |
472 | Double_t sf=fP2 + k20*dy + k21*dz; | |
473 | if (TMath::Abs(sf) > kAlmost1) return kFALSE; | |
474 | ||
475 | fP0 += k00*dy + k01*dz; | |
476 | fP1 += k10*dy + k11*dz; | |
477 | fP2 = sf; | |
478 | fP3 += k30*dy + k31*dz; | |
479 | fP4 += k40*dy + k41*dz; | |
480 | ||
481 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; | |
482 | Double_t c12=fC21, c13=fC31, c14=fC41; | |
483 | ||
484 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; | |
485 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; | |
486 | fC40-=k00*c04+k01*c14; | |
487 | ||
488 | fC11-=k10*c01+k11*fC11; | |
489 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; | |
490 | fC41-=k10*c04+k11*c14; | |
491 | ||
492 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; | |
493 | fC42-=k20*c04+k21*c14; | |
494 | ||
495 | fC33-=k30*c03+k31*c13; | |
496 | fC43-=k30*c04+k31*c14; | |
497 | ||
498 | fC44-=k40*c04+k41*c14; | |
499 | ||
500 | return kTRUE; | |
501 | } | |
502 | ||
c7bafca9 | 503 | void |
504 | AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const { | |
505 | //-------------------------------------------------------------------- | |
506 | // External track parameters -> helix parameters | |
507 | // "b" - magnetic field (kG) | |
508 | //-------------------------------------------------------------------- | |
509 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
510 | ||
1530f89c | 511 | hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3]; |
c7bafca9 | 512 | |
513 | hlx[5]=fX*cs - hlx[0]*sn; // x0 | |
514 | hlx[0]=fX*sn + hlx[0]*cs; // y0 | |
515 | //hlx[1]= // z0 | |
516 | hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0 | |
517 | //hlx[3]= // tgl | |
1530f89c | 518 | hlx[4]=GetC(b); // C |
c7bafca9 | 519 | } |
520 | ||
521 | ||
522 | static void Evaluate(const Double_t *h, Double_t t, | |
523 | Double_t r[3], //radius vector | |
524 | Double_t g[3], //first defivatives | |
525 | Double_t gg[3]) //second derivatives | |
526 | { | |
527 | //-------------------------------------------------------------------- | |
528 | // Calculate position of a point on a track and some derivatives | |
529 | //-------------------------------------------------------------------- | |
530 | Double_t phase=h[4]*t+h[2]; | |
531 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
532 | ||
533 | r[0] = h[5] + (sn - h[6])/h[4]; | |
534 | r[1] = h[0] - (cs - h[7])/h[4]; | |
535 | r[2] = h[1] + h[3]*t; | |
536 | ||
537 | g[0] = cs; g[1]=sn; g[2]=h[3]; | |
538 | ||
539 | gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; | |
540 | } | |
541 | ||
542 | Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p, | |
543 | Double_t b, Double_t &xthis, Double_t &xp) const { | |
544 | //------------------------------------------------------------ | |
545 | // Returns the (weighed !) distance of closest approach between | |
546 | // this track and the track "p". | |
547 | // Other returned values: | |
548 | // xthis, xt - coordinates of tracks' reference planes at the DCA | |
549 | //----------------------------------------------------------- | |
550 | Double_t dy2=GetSigmaY2() + p->GetSigmaY2(); | |
551 | Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); | |
552 | Double_t dx2=dy2; | |
553 | ||
554 | //dx2=dy2=dz2=1.; | |
555 | ||
556 | Double_t p1[8]; GetHelixParameters(p1,b); | |
557 | p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]); | |
558 | Double_t p2[8]; p->GetHelixParameters(p2,b); | |
559 | p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]); | |
560 | ||
561 | ||
562 | Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.; | |
563 | Evaluate(p1,t1,r1,g1,gg1); | |
564 | Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.; | |
565 | Evaluate(p2,t2,r2,g2,gg2); | |
566 | ||
567 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
568 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
569 | ||
570 | Int_t max=27; | |
571 | while (max--) { | |
572 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
573 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
574 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
575 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
576 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
577 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
578 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
579 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
580 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
581 | ||
582 | Double_t det=h11*h22-h12*h12; | |
583 | ||
584 | Double_t dt1,dt2; | |
585 | if (TMath::Abs(det)<1.e-33) { | |
586 | //(quasi)singular Hessian | |
587 | dt1=-gt1; dt2=-gt2; | |
588 | } else { | |
589 | dt1=-(gt1*h22 - gt2*h12)/det; | |
590 | dt2=-(h11*gt2 - h12*gt1)/det; | |
591 | } | |
592 | ||
593 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
594 | ||
595 | //check delta(phase1) ? | |
596 | //check delta(phase2) ? | |
597 | ||
598 | if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
599 | if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
600 | if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) | |
601 | AliWarning(" stopped at not a stationary point !"); | |
602 | Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); | |
603 | if (lmb < 0.) | |
604 | AliWarning(" stopped at not a minimum !"); | |
605 | break; | |
606 | } | |
607 | ||
608 | Double_t dd=dm; | |
609 | for (Int_t div=1 ; ; div*=2) { | |
610 | Evaluate(p1,t1+dt1,r1,g1,gg1); | |
611 | Evaluate(p2,t2+dt2,r2,g2,gg2); | |
612 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
613 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
614 | if (dd<dm) break; | |
615 | dt1*=0.5; dt2*=0.5; | |
616 | if (div>512) { | |
617 | AliWarning(" overshoot !"); break; | |
618 | } | |
619 | } | |
620 | dm=dd; | |
621 | ||
622 | t1+=dt1; | |
623 | t2+=dt2; | |
624 | ||
625 | } | |
626 | ||
627 | if (max<=0) AliWarning(" too many iterations !"); | |
628 | ||
629 | Double_t cs=TMath::Cos(GetAlpha()); | |
630 | Double_t sn=TMath::Sin(GetAlpha()); | |
631 | xthis=r1[0]*cs + r1[1]*sn; | |
632 | ||
633 | cs=TMath::Cos(p->GetAlpha()); | |
634 | sn=TMath::Sin(p->GetAlpha()); | |
635 | xp=r2[0]*cs + r2[1]*sn; | |
636 | ||
637 | return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2)); | |
638 | } | |
639 | ||
640 | Double_t AliExternalTrackParam:: | |
641 | PropagateToDCA(AliExternalTrackParam *p, Double_t b) { | |
642 | //-------------------------------------------------------------- | |
643 | // Propagates this track and the argument track to the position of the | |
644 | // distance of closest approach. | |
645 | // Returns the (weighed !) distance of closest approach. | |
646 | //-------------------------------------------------------------- | |
647 | Double_t xthis,xp; | |
648 | Double_t dca=GetDCA(p,b,xthis,xp); | |
649 | ||
650 | if (!PropagateTo(xthis,b)) { | |
651 | //AliWarning(" propagation failed !"); | |
652 | return 1e+33; | |
653 | } | |
654 | ||
655 | if (!p->PropagateTo(xp,b)) { | |
656 | //AliWarning(" propagation failed !"; | |
657 | return 1e+33; | |
658 | } | |
659 | ||
660 | return dca; | |
661 | } | |
662 | ||
663 | ||
664 | ||
f76701bf | 665 | |
666 | Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){ | |
667 | // | |
668 | // Try to relate this track to the vertex "vtx", | |
669 | // if the (rough) transverse impact parameter is not bigger then "maxd". | |
670 | // Magnetic field is "b" (kG). | |
671 | // | |
672 | // a) The track gets extapolated to the DCA to the vertex. | |
673 | // b) The impact parameters and their covariance matrix are calculated. | |
674 | // | |
675 | // In the case of success, the returned value is kTRUE | |
676 | // (otherwise, it's kFALSE) | |
677 | // | |
678 | Double_t alpha=GetAlpha(); | |
679 | Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha); | |
680 | Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2]; | |
681 | Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn; | |
29fbcc93 | 682 | Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs; |
f76701bf | 683 | x-=xv; y-=yv; |
684 | ||
685 | //Estimate the impact parameter neglecting the track curvature | |
686 | Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp)); | |
687 | if (d > maxd) return kFALSE; | |
688 | ||
689 | //Propagate to the DCA | |
690 | Double_t crv=0.299792458e-3*b*GetParameter()[4]; | |
691 | Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp)); | |
692 | sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn); | |
693 | ||
694 | x = xv*cs + yv*sn; | |
695 | yv=-xv*sn + yv*cs; xv=x; | |
696 | ||
697 | if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; | |
29fbcc93 | 698 | return kTRUE; |
f76701bf | 699 | } |
700 | ||
701 | ||
702 | ||
703 | ||
c9ec41e8 | 704 | Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) { |
705 | //---------------------------------------------------------------- | |
706 | // This function performs local->global transformation of the | |
707 | // track momentum. | |
708 | // When called, the arguments are: | |
709 | // p[0] = 1/pt of the track; | |
710 | // p[1] = sine of local azim. angle of the track momentum; | |
711 | // p[2] = tangent of the track momentum dip angle; | |
712 | // alpha - rotation angle. | |
713 | // The result is returned as: | |
714 | // p[0] = px | |
715 | // p[1] = py | |
716 | // p[2] = pz | |
717 | // Results for (nearly) straight tracks are meaningless ! | |
718 | //---------------------------------------------------------------- | |
e421f556 | 719 | if (TMath::Abs(p[0])<=kAlmost0) return kFALSE; |
49d13e89 | 720 | if (TMath::Abs(p[1])> kAlmost1) return kFALSE; |
c9ec41e8 | 721 | |
722 | Double_t pt=1./TMath::Abs(p[0]); | |
723 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha); | |
724 | Double_t r=TMath::Sqrt(1 - p[1]*p[1]); | |
725 | p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2]; | |
a5e407e9 | 726 | |
727 | return kTRUE; | |
728 | } | |
729 | ||
c9ec41e8 | 730 | Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) { |
731 | //---------------------------------------------------------------- | |
732 | // This function performs local->global transformation of the | |
733 | // track position. | |
734 | // When called, the arguments are: | |
735 | // r[0] = local x | |
736 | // r[1] = local y | |
737 | // r[2] = local z | |
738 | // alpha - rotation angle. | |
739 | // The result is returned as: | |
740 | // r[0] = global x | |
741 | // r[1] = global y | |
742 | // r[2] = global z | |
743 | //---------------------------------------------------------------- | |
744 | Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0]; | |
745 | r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs; | |
a5e407e9 | 746 | |
a5e407e9 | 747 | return kTRUE; |
51ad6848 | 748 | } |
749 | ||
b1149664 | 750 | void AliExternalTrackParam::GetDirection(Double_t d[3]) const { |
751 | //---------------------------------------------------------------- | |
752 | // This function returns a unit vector along the track direction | |
753 | // in the global coordinate system. | |
754 | //---------------------------------------------------------------- | |
755 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
756 | Double_t snp=fP[2]; | |
757 | Double_t csp =TMath::Sqrt(1.- snp*snp); | |
758 | Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]); | |
759 | d[0]=(csp*cs - snp*sn)/norm; | |
760 | d[1]=(snp*cs + csp*sn)/norm; | |
761 | d[2]=fP[3]/norm; | |
762 | } | |
763 | ||
c9ec41e8 | 764 | Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const { |
765 | //--------------------------------------------------------------------- | |
766 | // This function returns the global track momentum components | |
767 | // Results for (nearly) straight tracks are meaningless ! | |
768 | //--------------------------------------------------------------------- | |
769 | p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3]; | |
770 | return Local2GlobalMomentum(p,fAlpha); | |
771 | } | |
a5e407e9 | 772 | |
c9ec41e8 | 773 | Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const { |
774 | //--------------------------------------------------------------------- | |
775 | // This function returns the global track position | |
776 | //--------------------------------------------------------------------- | |
777 | r[0]=fX; r[1]=fP[0]; r[2]=fP[1]; | |
778 | return Local2GlobalPosition(r,fAlpha); | |
51ad6848 | 779 | } |
780 | ||
c9ec41e8 | 781 | Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const { |
782 | //--------------------------------------------------------------------- | |
783 | // This function returns the global covariance matrix of the track params | |
784 | // | |
785 | // Cov(x,x) ... : cv[0] | |
786 | // Cov(y,x) ... : cv[1] cv[2] | |
787 | // Cov(z,x) ... : cv[3] cv[4] cv[5] | |
788 | // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9] | |
789 | // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14] | |
790 | // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20] | |
a5e407e9 | 791 | // |
c9ec41e8 | 792 | // Results for (nearly) straight tracks are meaningless ! |
793 | //--------------------------------------------------------------------- | |
e421f556 | 794 | if (TMath::Abs(fP[4])<=kAlmost0) { |
c9ec41e8 | 795 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
796 | return kFALSE; | |
a5e407e9 | 797 | } |
49d13e89 | 798 | if (TMath::Abs(fP[2]) > kAlmost1) { |
c9ec41e8 | 799 | for (Int_t i=0; i<21; i++) cv[i]=0.; |
800 | return kFALSE; | |
801 | } | |
802 | Double_t pt=1./TMath::Abs(fP[4]); | |
803 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); | |
804 | Double_t r=TMath::Sqrt(1-fP[2]*fP[2]); | |
805 | ||
806 | Double_t m00=-sn, m10=cs; | |
807 | Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn); | |
808 | Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs); | |
809 | Double_t m35=pt, m45=-pt*pt*fP[3]; | |
810 | ||
811 | cv[0 ] = fC[0]*m00*m00; | |
812 | cv[1 ] = fC[0]*m00*m10; | |
813 | cv[2 ] = fC[0]*m10*m10; | |
814 | cv[3 ] = fC[1]*m00; | |
815 | cv[4 ] = fC[1]*m10; | |
816 | cv[5 ] = fC[2]; | |
817 | cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43); | |
818 | cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43); | |
819 | cv[8 ] = fC[4]*m23 + fC[11]*m43; | |
820 | cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43); | |
821 | cv[10] = m00*(fC[3]*m24 + fC[10]*m44); | |
822 | cv[11] = m10*(fC[3]*m24 + fC[10]*m44); | |
823 | cv[12] = fC[4]*m24 + fC[11]*m44; | |
824 | cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44); | |
825 | cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44); | |
826 | cv[15] = m00*(fC[6]*m35 + fC[10]*m45); | |
827 | cv[16] = m10*(fC[6]*m35 + fC[10]*m45); | |
828 | cv[17] = fC[7]*m35 + fC[11]*m45; | |
829 | cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45); | |
830 | cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45); | |
831 | cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45); | |
51ad6848 | 832 | |
c9ec41e8 | 833 | return kTRUE; |
51ad6848 | 834 | } |
835 | ||
51ad6848 | 836 | |
c9ec41e8 | 837 | Bool_t |
838 | AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const { | |
839 | //--------------------------------------------------------------------- | |
840 | // This function returns the global track momentum extrapolated to | |
841 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
842 | //--------------------------------------------------------------------- | |
c9ec41e8 | 843 | p[0]=fP[4]; |
1530f89c | 844 | p[1]=fP[2]+(x-fX)*GetC(b); |
c9ec41e8 | 845 | p[2]=fP[3]; |
846 | return Local2GlobalMomentum(p,fAlpha); | |
51ad6848 | 847 | } |
848 | ||
7cf7bb6c | 849 | Bool_t |
850 | AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { | |
851 | //--------------------------------------------------------------------- | |
852 | // This function returns the local Y-coordinate of the intersection | |
853 | // point between this track and the reference plane "x" (cm). | |
854 | // Magnetic field "b" (kG) | |
855 | //--------------------------------------------------------------------- | |
856 | Double_t dx=x-fX; | |
857 | if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;} | |
858 | ||
1530f89c | 859 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
7cf7bb6c | 860 | |
861 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
862 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
863 | ||
864 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
865 | y = fP[0] + dx*(f1+f2)/(r1+r2); | |
866 | return kTRUE; | |
867 | } | |
868 | ||
6c94f330 | 869 | Bool_t |
870 | AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { | |
871 | //--------------------------------------------------------------------- | |
872 | // This function returns the local Z-coordinate of the intersection | |
873 | // point between this track and the reference plane "x" (cm). | |
874 | // Magnetic field "b" (kG) | |
875 | //--------------------------------------------------------------------- | |
876 | Double_t dx=x-fX; | |
877 | if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} | |
878 | ||
879 | Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; | |
880 | ||
881 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; | |
882 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; | |
883 | ||
884 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); | |
885 | z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov ! | |
886 | return kTRUE; | |
887 | } | |
888 | ||
c9ec41e8 | 889 | Bool_t |
890 | AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { | |
891 | //--------------------------------------------------------------------- | |
892 | // This function returns the global track position extrapolated to | |
893 | // the radial position "x" (cm) in the magnetic field "b" (kG) | |
894 | //--------------------------------------------------------------------- | |
c9ec41e8 | 895 | Double_t dx=x-fX; |
e421f556 | 896 | if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r); |
897 | ||
1530f89c | 898 | Double_t f1=fP[2], f2=f1 + dx*GetC(b); |
c9ec41e8 | 899 | |
e421f556 | 900 | if (TMath::Abs(f1) >= kAlmost1) return kFALSE; |
49d13e89 | 901 | if (TMath::Abs(f2) >= kAlmost1) return kFALSE; |
c9ec41e8 | 902 | |
903 | Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2); | |
904 | r[0] = x; | |
905 | r[1] = fP[0] + dx*(f1+f2)/(r1+r2); | |
6c94f330 | 906 | r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; |
c9ec41e8 | 907 | return Local2GlobalPosition(r,fAlpha); |
51ad6848 | 908 | } |
909 | ||
51ad6848 | 910 | //_____________________________________________________________________________ |
911 | void AliExternalTrackParam::Print(Option_t* /*option*/) const | |
912 | { | |
913 | // print the parameters and the covariance matrix | |
914 | ||
915 | printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); | |
916 | printf(" parameters: %12g %12g %12g %12g %12g\n", | |
c9ec41e8 | 917 | fP[0], fP[1], fP[2], fP[3], fP[4]); |
918 | printf(" covariance: %12g\n", fC[0]); | |
919 | printf(" %12g %12g\n", fC[1], fC[2]); | |
920 | printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]); | |
51ad6848 | 921 | printf(" %12g %12g %12g %12g\n", |
c9ec41e8 | 922 | fC[6], fC[7], fC[8], fC[9]); |
51ad6848 | 923 | printf(" %12g %12g %12g %12g %12g\n", |
c9ec41e8 | 924 | fC[10], fC[11], fC[12], fC[13], fC[14]); |
51ad6848 | 925 | } |
5b77d93c | 926 | |
c194ba83 | 927 | Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const { |
928 | // | |
929 | // Get sinus at given x | |
930 | // | |
1530f89c | 931 | Double_t crv=GetC(b); |
c194ba83 | 932 | if (TMath::Abs(b) < kAlmost0Field) crv=0.; |
933 | Double_t dx = x-fX; | |
934 | Double_t res = fP[2]+dx*crv; | |
935 | return res; | |
936 | } |