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c04e3238 | 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 | // | |
20 | // Tools | |
21 | // for | |
22 | // track | |
23 | // extrapolation | |
24 | // in | |
25 | // ALICE | |
26 | // dimuon | |
27 | // spectrometer | |
28 | // | |
29 | /////////////////////////////////////////////////// | |
30 | ||
c04e3238 | 31 | #include "AliMUONTrackExtrap.h" |
32 | #include "AliMUONTrackParam.h" | |
33 | #include "AliMUONConstants.h" | |
8cde4af5 | 34 | |
c04e3238 | 35 | #include "AliMagF.h" |
8cde4af5 | 36 | |
37 | #include <Riostream.h> | |
38 | #include <TMath.h> | |
39 | #include <TMatrixD.h> | |
40 | #include <TGeoManager.h> | |
c04e3238 | 41 | |
78649106 | 42 | /// \cond CLASSIMP |
c04e3238 | 43 | ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context |
78649106 | 44 | /// \endcond |
c04e3238 | 45 | |
46 | const AliMagF* AliMUONTrackExtrap::fgkField = 0x0; | |
4284483e | 47 | const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE; |
208f139e | 48 | const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000; |
4284483e | 49 | const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.; |
50 | const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002; | |
208f139e | 51 | |
52 | //__________________________________________________________________________ | |
53 | Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum) | |
54 | { | |
55 | /// Returns impact parameter at vertex in bending plane (cm), | |
56 | /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c), | |
57 | /// using simple values for dipole magnetic field. | |
58 | /// The sign of "BendingMomentum" is the sign of the charge. | |
59 | ||
60 | if (bendingMomentum == 0.) return 1.e10; | |
61 | ||
62 | Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ()); | |
63 | Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL()); | |
64 | Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition}; | |
65 | if (fgkField) fgkField->Field(x,b); | |
66 | else { | |
67 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
68 | exit(-1); | |
69 | } | |
70 | Double_t simpleBValue = (Double_t) b[0]; | |
71 | ||
72 | return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum); | |
73 | } | |
74 | ||
75 | //__________________________________________________________________________ | |
76 | Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam) | |
77 | { | |
78 | /// Returns signed bending momentum in bending plane (GeV/c), | |
79 | /// the sign being the sign of the charge for particles moving forward in Z, | |
80 | /// from the impact parameter "ImpactParam" at vertex in bending plane (cm), | |
81 | /// using simple values for dipole magnetic field. | |
82 | ||
83 | if (impactParam == 0.) return 1.e10; | |
84 | ||
85 | Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ()); | |
86 | Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL()); | |
87 | Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition}; | |
88 | if (fgkField) fgkField->Field(x,b); | |
89 | else { | |
90 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
91 | exit(-1); | |
92 | } | |
93 | Double_t simpleBValue = (Double_t) b[0]; | |
94 | ||
95 | return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam); | |
96 | } | |
c04e3238 | 97 | |
98 | //__________________________________________________________________________ | |
99 | void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd) | |
100 | { | |
4284483e | 101 | /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm. |
102 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
103 | if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd); | |
104 | else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd); | |
105 | } | |
106 | ||
107 | //__________________________________________________________________________ | |
108 | void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd) | |
109 | { | |
110 | /// Track parameter extrapolation to the plane at "Z" using Helix algorithm. | |
c04e3238 | 111 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. |
112 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z | |
113 | Double_t forwardBackward; // +1 if forward, -1 if backward | |
114 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
115 | else forwardBackward = -1.0; | |
dade8580 | 116 | Double_t v3[7], v3New[7]; // 7 in parameter ???? |
117 | Int_t i3, stepNumber; | |
c04e3238 | 118 | // For safety: return kTRUE or kFALSE ???? |
119 | // Parameter vector for calling EXTRAP_ONESTEP | |
4284483e | 120 | ConvertTrackParamForExtrap(trackParam, forwardBackward, v3); |
c04e3238 | 121 | // sign of charge (sign of fInverseBendingMomentum if forward motion) |
122 | // must be changed if backward extrapolation | |
208f139e | 123 | Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); |
c04e3238 | 124 | // Extrapolation loop |
125 | stepNumber = 0; | |
208f139e | 126 | while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0 |
c04e3238 | 127 | stepNumber++; |
4284483e | 128 | ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New); |
dade8580 | 129 | if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0 |
c04e3238 | 130 | // better use TArray ???? |
208f139e | 131 | for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];} |
c04e3238 | 132 | } |
208f139e | 133 | // check fgkMaxStepNumber ???? |
c04e3238 | 134 | // Interpolation back to exact Z (2nd order) |
135 | // should be in function ???? using TArray ???? | |
dade8580 | 136 | Double_t dZ12 = v3New[2] - v3[2]; // 1->2 |
c04e3238 | 137 | if (TMath::Abs(dZ12) > 0) { |
dade8580 | 138 | Double_t dZ1i = zEnd - v3[2]; // 1-i |
139 | Double_t dZi2 = v3New[2] - zEnd; // i->2 | |
140 | Double_t xPrime = (v3New[0] - v3[0]) / dZ12; | |
141 | Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12; | |
142 | Double_t yPrime = (v3New[1] - v3[1]) / dZ12; | |
143 | Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12; | |
144 | v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X | |
145 | v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y | |
146 | v3[2] = zEnd; // Z | |
c04e3238 | 147 | Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i); |
148 | Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i); | |
149 | // (PX, PY, PZ)/PTOT assuming forward motion | |
208f139e | 150 | v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT |
dade8580 | 151 | v3[3] = xPrimeI * v3[5]; // PX/PTOT |
152 | v3[4] = yPrimeI * v3[5]; // PY/PTOT | |
c04e3238 | 153 | } else { |
4284483e | 154 | cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl; |
c04e3238 | 155 | } |
4284483e | 156 | // Recover track parameters (charge back for forward motion) |
dade8580 | 157 | RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam); |
c04e3238 | 158 | } |
159 | ||
160 | //__________________________________________________________________________ | |
4284483e | 161 | void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd) |
162 | { | |
163 | /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm. | |
164 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
165 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z | |
166 | Double_t forwardBackward; // +1 if forward, -1 if backward | |
167 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
168 | else forwardBackward = -1.0; | |
169 | // sign of charge (sign of fInverseBendingMomentum if forward motion) | |
170 | // must be changed if backward extrapolation | |
171 | Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); | |
172 | Double_t v3[7], v3New[7]; | |
173 | Double_t dZ, step; | |
174 | Int_t stepNumber = 0; | |
175 | ||
176 | // Extrapolation loop (until within tolerance) | |
177 | Double_t residue = zEnd - trackParam->GetZ(); | |
178 | while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) { | |
179 | dZ = zEnd - trackParam->GetZ(); | |
180 | // step lenght assuming linear trajectory | |
181 | step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() + | |
182 | trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope()); | |
183 | ConvertTrackParamForExtrap(trackParam, forwardBackward, v3); | |
184 | do { // reduce step lenght while zEnd oversteped | |
185 | if (stepNumber > fgkMaxStepNumber) { | |
186 | cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl; | |
187 | break; | |
188 | } | |
189 | stepNumber ++; | |
190 | step = TMath::Abs(step); | |
191 | AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New); | |
192 | residue = zEnd - v3New[2]; | |
193 | step *= dZ/(v3New[2]-trackParam->GetZ()); | |
194 | } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue); | |
195 | RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam); | |
196 | } | |
197 | ||
198 | // terminate the extropolation with a straight line up to the exact "zEnd" value | |
199 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope()); | |
200 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope()); | |
201 | trackParam->SetZ(zEnd); | |
202 | } | |
203 | ||
204 | //__________________________________________________________________________ | |
205 | void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3) | |
c04e3238 | 206 | { |
dade8580 | 207 | /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam. |
c04e3238 | 208 | /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward" |
209 | /// to know whether the particle is going forward (+1) or backward (-1). | |
dade8580 | 210 | v3[0] = trackParam->GetNonBendingCoor(); // X |
211 | v3[1] = trackParam->GetBendingCoor(); // Y | |
212 | v3[2] = trackParam->GetZ(); // Z | |
c04e3238 | 213 | Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); |
214 | Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()); | |
dade8580 | 215 | v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT |
216 | v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0 | |
217 | v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT | |
218 | v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT | |
c04e3238 | 219 | } |
220 | ||
221 | //__________________________________________________________________________ | |
dade8580 | 222 | void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam) |
c04e3238 | 223 | { |
dade8580 | 224 | /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3", |
c04e3238 | 225 | /// assumed to be calculated for forward motion in Z. |
226 | /// "InverseBendingMomentum" is signed with "charge". | |
dade8580 | 227 | trackParam->SetNonBendingCoor(v3[0]); // X |
228 | trackParam->SetBendingCoor(v3[1]); // Y | |
229 | trackParam->SetZ(v3[2]); // Z | |
230 | Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]); | |
c04e3238 | 231 | trackParam->SetInverseBendingMomentum(charge/pYZ); |
dade8580 | 232 | trackParam->SetBendingSlope(v3[4]/v3[5]); |
233 | trackParam->SetNonBendingSlope(v3[3]/v3[5]); | |
208f139e | 234 | } |
235 | ||
236 | //__________________________________________________________________________ | |
237 | void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd) | |
238 | { | |
239 | /// Track parameters and their covariances extrapolated to the plane at "zEnd". | |
240 | /// On return, results from the extrapolation are updated in trackParam. | |
241 | ||
242 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z | |
243 | ||
244 | // Save the actual track parameters | |
245 | AliMUONTrackParam trackParamSave(*trackParam); | |
246 | Double_t nonBendingCoor = trackParamSave.GetNonBendingCoor(); | |
247 | Double_t nonBendingSlope = trackParamSave.GetNonBendingSlope(); | |
248 | Double_t bendingCoor = trackParamSave.GetBendingCoor(); | |
249 | Double_t bendingSlope = trackParamSave.GetBendingSlope(); | |
250 | Double_t inverseBendingMomentum = trackParamSave.GetInverseBendingMomentum(); | |
251 | Double_t zBegin = trackParamSave.GetZ(); | |
252 | ||
253 | // Extrapolate track parameters to "zEnd" | |
254 | ExtrapToZ(trackParam,zEnd); | |
255 | Double_t extrapNonBendingCoor = trackParam->GetNonBendingCoor(); | |
256 | Double_t extrapNonBendingSlope = trackParam->GetNonBendingSlope(); | |
257 | Double_t extrapBendingCoor = trackParam->GetBendingCoor(); | |
258 | Double_t extrapBendingSlope = trackParam->GetBendingSlope(); | |
259 | Double_t extrapInverseBendingMomentum = trackParam->GetInverseBendingMomentum(); | |
260 | ||
261 | // Get the pointer to the parameter covariance matrix | |
262 | if (!trackParam->CovariancesExist()) { | |
263 | //cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: track parameter covariance matrix does not exist"<<endl; | |
264 | //cout<<" -> nothing to extrapolate !!"<<endl; | |
265 | return; | |
266 | } | |
267 | TMatrixD* paramCov = trackParam->GetCovariances(); | |
268 | ||
269 | // Calculate the jacobian related to the track parameters extrapolation to "zEnd" | |
270 | TMatrixD jacob(5,5); | |
271 | jacob = 0.; | |
272 | Double_t dParam[5]; | |
273 | for (Int_t i=0; i<5; i++) { | |
274 | // Skip jacobian calculation for parameters with no associated error | |
275 | if ((*paramCov)(i,i) == 0.) continue; | |
276 | // Small variation of parameter i only | |
277 | for (Int_t j=0; j<5; j++) { | |
278 | if (j==i) { | |
279 | dParam[j] = TMath::Sqrt((*paramCov)(i,i)); | |
280 | if (j == 4) dParam[j] *= TMath::Sign(1.,-inverseBendingMomentum); // variation always in the same direction | |
281 | } else dParam[j] = 0.; | |
282 | } | |
283 | // Set new parameters | |
284 | trackParamSave.SetNonBendingCoor (nonBendingCoor + dParam[0]); | |
285 | trackParamSave.SetNonBendingSlope (nonBendingSlope + dParam[1]); | |
286 | trackParamSave.SetBendingCoor (bendingCoor + dParam[2]); | |
287 | trackParamSave.SetBendingSlope (bendingSlope + dParam[3]); | |
288 | trackParamSave.SetInverseBendingMomentum(inverseBendingMomentum + dParam[4]); | |
289 | trackParamSave.SetZ (zBegin); | |
290 | // Extrapolate new track parameters to "zEnd" | |
291 | ExtrapToZ(&trackParamSave,zEnd); | |
292 | // Calculate the jacobian | |
293 | jacob(0,i) = (trackParamSave.GetNonBendingCoor() - extrapNonBendingCoor ) / dParam[i]; | |
294 | jacob(1,i) = (trackParamSave.GetNonBendingSlope() - extrapNonBendingSlope ) / dParam[i]; | |
295 | jacob(2,i) = (trackParamSave.GetBendingCoor() - extrapBendingCoor ) / dParam[i]; | |
296 | jacob(3,i) = (trackParamSave.GetBendingSlope() - extrapBendingSlope ) / dParam[i]; | |
297 | jacob(4,i) = (trackParamSave.GetInverseBendingMomentum() - extrapInverseBendingMomentum) / dParam[i]; | |
298 | } | |
299 | ||
300 | // Extrapolate track parameter covariances to "zEnd" | |
301 | TMatrixD tmp((*paramCov),TMatrixD::kMultTranspose,jacob); | |
302 | (*paramCov) = TMatrixD(jacob,TMatrixD::kMult,tmp); | |
303 | ||
c04e3238 | 304 | } |
305 | ||
306 | //__________________________________________________________________________ | |
307 | void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut) | |
308 | { | |
309 | /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station" | |
310 | /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut" | |
311 | /// (index 0 and 1 for first and second chambers). | |
312 | Double_t extZ[2], z1, z2; | |
313 | Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings | |
314 | // range of station to be checked ???? | |
315 | z1 = AliMUONConstants::DefaultChamberZ(2 * station); | |
316 | z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1); | |
317 | // First and second Z to extrapolate at | |
318 | if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;} | |
319 | else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;} | |
320 | else { | |
208f139e | 321 | cout<<"E-AliMUONTrackExtrap::ExtrapToStation: Starting Z ("<<trackParamIn->GetZ() |
c04e3238 | 322 | <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl; |
323 | exit(-1); | |
324 | } | |
325 | extZ[i1] = z1; | |
326 | extZ[i2] = z2; | |
327 | // copy of track parameters | |
328 | trackParamOut[i1] = *trackParamIn; | |
329 | // first extrapolation | |
330 | ExtrapToZ(&(trackParamOut[i1]),extZ[0]); | |
331 | trackParamOut[i2] = trackParamOut[i1]; | |
332 | // second extrapolation | |
333 | ExtrapToZ(&(trackParamOut[i2]),extZ[1]); | |
334 | return; | |
208f139e | 335 | } |
336 | ||
337 | //__________________________________________________________________________ | |
338 | void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx) | |
339 | { | |
8cde4af5 | 340 | /// Extrapolation to the vertex (at the z position "zVtx") without Branson and energy loss corrections. |
208f139e | 341 | /// Returns the track parameters resulting from the extrapolation in the current TrackParam. |
342 | /// Include multiple Coulomb scattering effects in trackParam covariances. | |
343 | ||
8cde4af5 | 344 | if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex |
345 | ||
208f139e | 346 | if (trackParam->GetZ() > zVtx) { // spectro. (z<0) |
347 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertexUncorrected: Starting Z ("<<trackParam->GetZ() | |
348 | <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl; | |
349 | exit(-1); | |
350 | } | |
351 | ||
8cde4af5 | 352 | // Check whether the geometry is available and get absorber boundaries |
353 | if (!gGeoManager) { | |
354 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl; | |
355 | return; | |
356 | } | |
357 | TGeoNode *absNode = gGeoManager->GetVolume("ALIC")->GetNode("ABSM_1"); | |
358 | if (!absNode) { | |
359 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: failed to get absorber node"<<endl; | |
360 | return; | |
361 | } | |
362 | Double_t zAbsBeg, zAbsEnd; | |
363 | absNode->GetVolume()->GetShape()->GetAxisRange(3,zAbsBeg,zAbsEnd); | |
364 | const Double_t *absPos = absNode->GetMatrix()->GetTranslation(); | |
365 | zAbsBeg = absPos[2] - zAbsBeg; // spectro. (z<0) | |
366 | zAbsEnd = absPos[2] - zAbsEnd; // spectro. (z<0) | |
367 | ||
368 | // Check the vertex position relatively to the absorber | |
369 | if (zVtx < zAbsBeg && zVtx > zAbsEnd) { // spectro. (z<0) | |
370 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx | |
371 | <<") inside the front absorber ("<<zAbsBeg<<","<<zAbsEnd<<")"<<endl; | |
372 | } else if (zVtx < zAbsEnd ) { // spectro. (z<0) | |
373 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx | |
374 | <<") downstream the front absorber (zAbsorberEnd = "<<zAbsEnd<<")"<<endl; | |
208f139e | 375 | ExtrapToZCov(trackParam,zVtx); |
376 | return; | |
377 | } | |
378 | ||
8cde4af5 | 379 | // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed |
380 | if (trackParam->GetZ() > zAbsBeg) { // spectro. (z<0) | |
381 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() | |
382 | <<") upstream the front absorber (zAbsorberBegin = "<<zAbsBeg<<")"<<endl; | |
383 | ExtrapToZCov(trackParam,zVtx); | |
384 | return; | |
385 | } else if (trackParam->GetZ() > zAbsEnd) { // spectro. (z<0) | |
386 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() | |
387 | <<") inside the front absorber ("<<zAbsBeg<<","<<zAbsEnd<<")"<<endl; | |
208f139e | 388 | } else { |
8cde4af5 | 389 | ExtrapToZCov(trackParam,zAbsEnd); |
208f139e | 390 | } |
391 | ||
8cde4af5 | 392 | // Then add MCS effect in absorber to the parameters covariances |
393 | AliMUONTrackParam trackParamIn(*trackParam); | |
394 | ExtrapToZ(&trackParamIn, TMath::Min(zVtx, zAbsBeg)); | |
395 | Double_t trackXYZIn[3]; | |
396 | trackXYZIn[0] = trackParamIn.GetNonBendingCoor(); | |
397 | trackXYZIn[1] = trackParamIn.GetBendingCoor(); | |
398 | trackXYZIn[2] = trackParamIn.GetZ(); | |
399 | Double_t trackXYZOut[3]; | |
400 | trackXYZOut[0] = trackParam->GetNonBendingCoor(); | |
401 | trackXYZOut[1] = trackParam->GetBendingCoor(); | |
402 | trackXYZOut[2] = trackParam->GetZ(); | |
403 | Double_t pathLength = 0.; | |
404 | Double_t f0 = 0.; | |
405 | Double_t f1 = 0.; | |
406 | Double_t f2 = 0.; | |
407 | Double_t meanRho = 0.; | |
408 | GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho); | |
409 | AddMCSEffectInAbsorber(trackParam,pathLength,f0,f1,f2); | |
208f139e | 410 | |
411 | // finally go to the vertex | |
412 | ExtrapToZCov(trackParam,zVtx); | |
413 | ||
414 | } | |
415 | ||
416 | //__________________________________________________________________________ | |
8cde4af5 | 417 | void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2) |
418 | { | |
419 | /// Add to the track parameter covariances the effects of multiple Coulomb scattering | |
420 | /// at the end of the front absorber using the absorber correction parameters | |
421 | ||
422 | // absorber related covariance parameters | |
423 | Double_t bendingSlope = param->GetBendingSlope(); | |
424 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
425 | Double_t inverseBendingMomentum = param->GetInverseBendingMomentum(); | |
426 | Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) / | |
427 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1 | |
428 | Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2); | |
429 | Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1); | |
430 | Double_t varSlop = alpha2 * f0; | |
431 | ||
432 | TMatrixD* paramCov = param->GetCovariances(); | |
433 | // Non bending plane | |
434 | (*paramCov)(0,0) += varCoor; (*paramCov)(0,1) += covCorrSlope; | |
435 | (*paramCov)(1,0) += covCorrSlope; (*paramCov)(1,1) += varSlop; | |
436 | // Bending plane | |
437 | (*paramCov)(2,2) += varCoor; (*paramCov)(2,3) += covCorrSlope; | |
438 | (*paramCov)(3,2) += covCorrSlope; (*paramCov)(3,3) += varSlop; | |
439 | ||
440 | } | |
441 | ||
442 | //__________________________________________________________________________ | |
443 | void AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t &pathLength, | |
444 | Double_t &f0, Double_t &f1, Double_t &f2, Double_t &meanRho) | |
445 | { | |
446 | /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber | |
447 | /// Calculated assuming a linear propagation between track positions trackXYZIn and trackXYZOut | |
448 | // pathLength: path length between trackXYZIn and trackXYZOut (cm) | |
449 | // f0: 0th moment of z calculated with the inverse radiation-length distribution | |
450 | // f1: 1st moment of z calculated with the inverse radiation-length distribution | |
451 | // f2: 2nd moment of z calculated with the inverse radiation-length distribution | |
452 | // meanRho: average density of crossed material (g/cm3) | |
453 | ||
454 | // Reset absorber's parameters | |
455 | pathLength = 0.; | |
456 | f0 = 0.; | |
457 | f1 = 0.; | |
458 | f2 = 0.; | |
459 | meanRho = 0.; | |
460 | ||
461 | // Check whether the geometry is available | |
462 | if (!gGeoManager) { | |
463 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl; | |
464 | return; | |
465 | } | |
466 | ||
467 | // Initialize starting point and direction | |
468 | pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+ | |
469 | (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+ | |
470 | (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2])); | |
471 | if (pathLength < TGeoShape::Tolerance()) return; | |
472 | Double_t b[3]; | |
473 | b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength; | |
474 | b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength; | |
475 | b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength; | |
476 | TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b); | |
477 | if (!currentnode) { | |
478 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl; | |
479 | return; | |
480 | } | |
481 | ||
482 | // loop over absorber slices and calculate absorber's parameters | |
483 | Double_t rho = 0.; // material density (g/cm3) | |
484 | Double_t x0 = 0.; // radiation-length (cm-1) | |
485 | Double_t localPathLength = 0; | |
486 | Double_t remainingPathLength = pathLength; | |
487 | Double_t zB = trackXYZIn[2]; | |
488 | Double_t zE, dzB, dzE; | |
489 | do { | |
490 | // Get material properties | |
491 | TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial(); | |
492 | rho = material->GetDensity(); | |
493 | x0 = material->GetRadLen(); | |
494 | if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture | |
495 | ||
496 | // Get path length within this material | |
497 | gGeoManager->FindNextBoundary(remainingPathLength); | |
498 | localPathLength = gGeoManager->GetStep() + 1.e-6; | |
499 | // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step | |
500 | if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength; | |
501 | else { | |
502 | currentnode = gGeoManager->Step(); | |
503 | if (!currentnode) { | |
504 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl; | |
505 | f0 = f1 = f2 = meanRho = 0.; | |
506 | return; | |
507 | } | |
508 | if (!gGeoManager->IsEntering()) { | |
509 | // make another small step to try to enter in new absorber slice | |
510 | gGeoManager->SetStep(0.001); | |
511 | currentnode = gGeoManager->Step(); | |
512 | if (!gGeoManager->IsEntering() || !currentnode) { | |
513 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl; | |
514 | f0 = f1 = f2 = meanRho = 0.; | |
515 | return; | |
516 | } | |
517 | localPathLength += 0.001; | |
518 | } | |
519 | } | |
520 | ||
521 | // calculate absorber's parameters | |
522 | zE = b[2] * localPathLength + zB; | |
523 | dzB = zB - trackXYZIn[2]; | |
524 | dzE = zE - trackXYZIn[2]; | |
525 | f0 += localPathLength / x0; | |
526 | f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.; | |
527 | f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.; | |
528 | meanRho += localPathLength * rho; | |
529 | ||
530 | // prepare next step | |
531 | zB = zE; | |
532 | remainingPathLength -= localPathLength; | |
533 | } while (remainingPathLength > TGeoShape::Tolerance()); | |
534 | ||
535 | meanRho /= pathLength; | |
536 | } | |
537 | ||
538 | //__________________________________________________________________________ | |
539 | void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0) | |
208f139e | 540 | { |
541 | /// Add to the track parameter covariances the effects of multiple Coulomb scattering | |
542 | /// through a material of thickness "dZ" and of radiation length "x0" | |
543 | /// assuming linear propagation and using the small angle approximation. | |
544 | ||
545 | Double_t bendingSlope = param->GetBendingSlope(); | |
546 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
547 | Double_t inverseTotalMomentum2 = param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum() * | |
548 | (1.0 + bendingSlope * bendingSlope) / | |
549 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); | |
550 | // Path length in the material | |
551 | Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope); | |
552 | Double_t pathLength2 = pathLength * pathLength; | |
553 | // relativistic velocity | |
554 | Double_t velo = 1.; | |
555 | // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory | |
556 | Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0)); | |
557 | theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0; | |
558 | ||
559 | // Add effects of multiple Coulomb scattering in track parameter covariances | |
560 | TMatrixD* paramCov = param->GetCovariances(); | |
561 | Double_t varCoor = pathLength2 * theta02 / 3.; | |
562 | Double_t varSlop = theta02; | |
563 | Double_t covCorrSlope = pathLength * theta02 / 2.; | |
564 | // Non bending plane | |
565 | (*paramCov)(0,0) += varCoor; (*paramCov)(0,1) += covCorrSlope; | |
566 | (*paramCov)(1,0) += covCorrSlope; (*paramCov)(1,1) += varSlop; | |
567 | // Bending plane | |
568 | (*paramCov)(2,2) += varCoor; (*paramCov)(2,3) += covCorrSlope; | |
569 | (*paramCov)(3,2) += covCorrSlope; (*paramCov)(3,3) += varSlop; | |
570 | ||
c04e3238 | 571 | } |
572 | ||
573 | //__________________________________________________________________________ | |
574 | void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx) | |
575 | { | |
576 | /// Extrapolation to the vertex. | |
577 | /// Returns the track parameters resulting from the extrapolation in the current TrackParam. | |
8cde4af5 | 578 | /// Changes parameters according to Branson correction through the absorber and energy loss |
c04e3238 | 579 | |
8cde4af5 | 580 | if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex |
c04e3238 | 581 | |
8cde4af5 | 582 | if (trackParam->GetZ() > zVtx) { // spectro. (z<0) |
583 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() | |
584 | <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl; | |
585 | exit(-1); | |
c04e3238 | 586 | } |
8cde4af5 | 587 | |
588 | // Check whether the geometry is available and get absorber boundaries | |
589 | if (!gGeoManager) { | |
590 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl; | |
591 | return; | |
592 | } | |
593 | TGeoNode *absNode = gGeoManager->GetVolume("ALIC")->GetNode("ABSM_1"); | |
594 | if (!absNode) { | |
595 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: failed to get absorber node"<<endl; | |
596 | return; | |
597 | } | |
598 | Double_t zAbsBeg, zAbsEnd; | |
599 | absNode->GetVolume()->GetShape()->GetAxisRange(3,zAbsBeg,zAbsEnd); | |
600 | const Double_t *absPos = absNode->GetMatrix()->GetTranslation(); | |
601 | zAbsBeg = absPos[2] - zAbsBeg; // spectro. (z<0) | |
602 | zAbsEnd = absPos[2] - zAbsEnd; // spectro. (z<0) | |
603 | ||
604 | // Check the vertex position relatively to the absorber | |
605 | if (zVtx < zAbsBeg && zVtx > zAbsEnd) { // spectro. (z<0) | |
606 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx | |
607 | <<") inside the front absorber ("<<zAbsBeg<<","<<zAbsEnd<<")"<<endl; | |
608 | } else if (zVtx < zAbsEnd ) { // spectro. (z<0) | |
609 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx | |
610 | <<") downstream the front absorber (zAbsorberEnd = "<<zAbsEnd<<")"<<endl; | |
611 | ExtrapToZ(trackParam,zVtx); | |
612 | return; | |
613 | } | |
614 | ||
615 | // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed | |
616 | if (trackParam->GetZ() > zAbsBeg) { // spectro. (z<0) | |
617 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() | |
618 | <<") upstream the front absorber (zAbsorberBegin = "<<zAbsBeg<<")"<<endl; | |
619 | ExtrapToZ(trackParam,zVtx); | |
620 | return; | |
621 | } else if (trackParam->GetZ() > zAbsEnd) { // spectro. (z<0) | |
622 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() | |
623 | <<") inside the front absorber ("<<zAbsBeg<<","<<zAbsEnd<<")"<<endl; | |
c04e3238 | 624 | } else { |
8cde4af5 | 625 | ExtrapToZ(trackParam,zAbsEnd); |
c04e3238 | 626 | } |
c04e3238 | 627 | |
8cde4af5 | 628 | // Get absorber correction parameters assuming linear propagation from vertex to the track position |
629 | Double_t trackXYZOut[3]; | |
630 | trackXYZOut[0] = trackParam->GetNonBendingCoor(); | |
631 | trackXYZOut[1] = trackParam->GetBendingCoor(); | |
632 | trackXYZOut[2] = trackParam->GetZ(); | |
633 | Double_t trackXYZIn[3]; | |
634 | trackXYZIn[2] = TMath::Min(zVtx, zAbsBeg); // spectro. (z<0) | |
635 | trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]); | |
636 | trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]); | |
637 | Double_t pathLength = 0.; | |
638 | Double_t f0 = 0.; | |
639 | Double_t f1 = 0.; | |
640 | Double_t f2 = 0.; | |
641 | Double_t meanRho = 0.; | |
642 | GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho); | |
c04e3238 | 643 | |
8cde4af5 | 644 | // Calculate energy loss |
645 | Double_t pTot = trackParam->P(); | |
646 | Double_t charge = TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); | |
647 | Double_t deltaP = TotalMomentumEnergyLoss(pTot,pathLength,meanRho); | |
648 | ||
649 | // Correct for half of energy loss | |
650 | pTot += 0.5 * deltaP; | |
651 | ||
652 | // Position of the Branson plane (spectro. (z<0)) | |
653 | Double_t zB = (f1>0.) ? trackXYZIn[2] - f2/f1 : 0.; | |
654 | ||
655 | // Get track position in the Branson plane corrected for magnetic field effect | |
656 | ExtrapToZ(trackParam,zVtx); | |
657 | Double_t xB = trackParam->GetNonBendingCoor() + (zB - zVtx) * trackParam->GetNonBendingSlope(); | |
658 | Double_t yB = trackParam->GetBendingCoor() + (zB - zVtx) * trackParam->GetBendingSlope(); | |
659 | ||
660 | // Get track slopes corrected for multiple scattering (spectro. (z<0)) | |
661 | Double_t nonBendingSlope = (zB<0.) ? (xB - xVtx) / (zB - zVtx) : trackParam->GetNonBendingSlope(); | |
662 | Double_t bendingSlope = (zB<0.) ? (yB - yVtx) / (zB - zVtx) : trackParam->GetBendingSlope(); | |
663 | ||
664 | // Correct for second half of energy loss | |
665 | pTot += 0.5 * deltaP; | |
666 | ||
667 | // Set track parameters at vertex | |
668 | trackParam->SetNonBendingCoor(xVtx); | |
669 | trackParam->SetBendingCoor(yVtx); | |
c04e3238 | 670 | trackParam->SetZ(zVtx); |
8cde4af5 | 671 | trackParam->SetNonBendingSlope(nonBendingSlope); |
672 | trackParam->SetBendingSlope(bendingSlope); | |
673 | trackParam->SetInverseBendingMomentum(charge / pTot * | |
674 | TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) / | |
675 | TMath::Sqrt(1.0 + bendingSlope*bendingSlope)); | |
676 | ||
c04e3238 | 677 | } |
678 | ||
679 | //__________________________________________________________________________ | |
8cde4af5 | 680 | Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t pTotal, Double_t pathLength, Double_t rho) |
c04e3238 | 681 | { |
8cde4af5 | 682 | /// Returns the total momentum energy loss in the front absorber |
683 | Double_t muMass = 0.10566; | |
684 | Double_t p2=pTotal*pTotal; | |
685 | Double_t beta2=p2/(p2 + muMass*muMass); | |
686 | Double_t dE=ApproximateBetheBloch(beta2)*pathLength*rho; | |
687 | ||
688 | return dE; | |
c04e3238 | 689 | } |
690 | ||
691 | //__________________________________________________________________________ | |
8cde4af5 | 692 | Double_t AliMUONTrackExtrap::ApproximateBetheBloch(Double_t beta2) { |
693 | //------------------------------------------------------------------ | |
694 | // This is an approximation of the Bethe-Bloch formula with | |
695 | // the density effect taken into account at beta*gamma > 3.5 | |
696 | // (the approximation is reasonable only for solid materials) | |
697 | //------------------------------------------------------------------ | |
698 | if (beta2/(1-beta2)>3.5*3.5) | |
699 | return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); | |
700 | ||
701 | return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); | |
c04e3238 | 702 | } |
703 | ||
704 | //__________________________________________________________________________ | |
705 | void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout) | |
706 | { | |
707 | /// ****************************************************************** | |
708 | /// * * | |
709 | /// * Performs the tracking of one step in a magnetic field * | |
710 | /// * The trajectory is assumed to be a helix in a constant field * | |
711 | /// * taken at the mid point of the step. * | |
712 | /// * Parameters: * | |
713 | /// * input * | |
714 | /// * STEP =arc length of the step asked * | |
715 | /// * VECT =input vector (position,direction cos and momentum) * | |
716 | /// * CHARGE= electric charge of the particle * | |
717 | /// * output * | |
718 | /// * VOUT = same as VECT after completion of the step * | |
719 | /// * * | |
720 | /// * ==>Called by : <USER>, GUSWIM * | |
721 | /// * Author m.hansroul ********* * | |
722 | /// * modified s.egli, s.v.levonian * | |
723 | /// * modified v.perevoztchikov | |
724 | /// * * | |
725 | /// ****************************************************************** | |
726 | ||
727 | // modif: everything in double precision | |
728 | ||
729 | Double_t xyz[3], h[4], hxp[3]; | |
730 | Double_t h2xy, hp, rho, tet; | |
731 | Double_t sint, sintt, tsint, cos1t; | |
732 | Double_t f1, f2, f3, f4, f5, f6; | |
733 | ||
734 | const Int_t kix = 0; | |
735 | const Int_t kiy = 1; | |
736 | const Int_t kiz = 2; | |
737 | const Int_t kipx = 3; | |
738 | const Int_t kipy = 4; | |
739 | const Int_t kipz = 5; | |
740 | const Int_t kipp = 6; | |
741 | ||
742 | const Double_t kec = 2.9979251e-4; | |
743 | // | |
744 | // ------------------------------------------------------------------ | |
745 | // | |
746 | // units are kgauss,centimeters,gev/c | |
747 | // | |
748 | vout[kipp] = vect[kipp]; | |
749 | if (TMath::Abs(charge) < 0.00001) { | |
750 | for (Int_t i = 0; i < 3; i++) { | |
751 | vout[i] = vect[i] + step * vect[i+3]; | |
752 | vout[i+3] = vect[i+3]; | |
753 | } | |
754 | return; | |
755 | } | |
756 | xyz[0] = vect[kix] + 0.5 * step * vect[kipx]; | |
757 | xyz[1] = vect[kiy] + 0.5 * step * vect[kipy]; | |
758 | xyz[2] = vect[kiz] + 0.5 * step * vect[kipz]; | |
759 | ||
760 | //cmodif: call gufld (xyz, h) changed into: | |
761 | GetField (xyz, h); | |
762 | ||
763 | h2xy = h[0]*h[0] + h[1]*h[1]; | |
764 | h[3] = h[2]*h[2]+ h2xy; | |
765 | if (h[3] < 1.e-12) { | |
766 | for (Int_t i = 0; i < 3; i++) { | |
767 | vout[i] = vect[i] + step * vect[i+3]; | |
768 | vout[i+3] = vect[i+3]; | |
769 | } | |
770 | return; | |
771 | } | |
772 | if (h2xy < 1.e-12*h[3]) { | |
773 | ExtrapOneStepHelix3(charge*h[2], step, vect, vout); | |
774 | return; | |
775 | } | |
776 | h[3] = TMath::Sqrt(h[3]); | |
777 | h[0] /= h[3]; | |
778 | h[1] /= h[3]; | |
779 | h[2] /= h[3]; | |
780 | h[3] *= kec; | |
781 | ||
782 | hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy]; | |
783 | hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz]; | |
784 | hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx]; | |
785 | ||
786 | hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz]; | |
787 | ||
788 | rho = -charge*h[3]/vect[kipp]; | |
789 | tet = rho * step; | |
790 | ||
791 | if (TMath::Abs(tet) > 0.15) { | |
792 | sint = TMath::Sin(tet); | |
793 | sintt = (sint/tet); | |
794 | tsint = (tet-sint)/tet; | |
795 | cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet; | |
796 | } else { | |
797 | tsint = tet*tet/36.; | |
798 | sintt = (1. - tsint); | |
799 | sint = tet*sintt; | |
800 | cos1t = 0.5*tet; | |
801 | } | |
802 | ||
803 | f1 = step * sintt; | |
804 | f2 = step * cos1t; | |
805 | f3 = step * tsint * hp; | |
806 | f4 = -tet*cos1t; | |
807 | f5 = sint; | |
808 | f6 = tet * cos1t * hp; | |
809 | ||
810 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0]; | |
811 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1]; | |
812 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2]; | |
813 | ||
814 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0]; | |
815 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1]; | |
816 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2]; | |
817 | ||
818 | return; | |
819 | } | |
820 | ||
821 | //__________________________________________________________________________ | |
822 | void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout) | |
823 | { | |
824 | /// ****************************************************************** | |
825 | /// * * | |
826 | /// * Tracking routine in a constant field oriented * | |
827 | /// * along axis 3 * | |
828 | /// * Tracking is performed with a conventional * | |
829 | /// * helix step method * | |
830 | /// * * | |
831 | /// * ==>Called by : <USER>, GUSWIM * | |
832 | /// * Authors R.Brun, M.Hansroul ********* * | |
833 | /// * Rewritten V.Perevoztchikov | |
834 | /// * * | |
835 | /// ****************************************************************** | |
836 | ||
837 | Double_t hxp[3]; | |
838 | Double_t h4, hp, rho, tet; | |
839 | Double_t sint, sintt, tsint, cos1t; | |
840 | Double_t f1, f2, f3, f4, f5, f6; | |
841 | ||
842 | const Int_t kix = 0; | |
843 | const Int_t kiy = 1; | |
844 | const Int_t kiz = 2; | |
845 | const Int_t kipx = 3; | |
846 | const Int_t kipy = 4; | |
847 | const Int_t kipz = 5; | |
848 | const Int_t kipp = 6; | |
849 | ||
850 | const Double_t kec = 2.9979251e-4; | |
851 | ||
852 | // | |
853 | // ------------------------------------------------------------------ | |
854 | // | |
855 | // units are kgauss,centimeters,gev/c | |
856 | // | |
857 | vout[kipp] = vect[kipp]; | |
858 | h4 = field * kec; | |
859 | ||
860 | hxp[0] = - vect[kipy]; | |
861 | hxp[1] = + vect[kipx]; | |
862 | ||
863 | hp = vect[kipz]; | |
864 | ||
865 | rho = -h4/vect[kipp]; | |
866 | tet = rho * step; | |
867 | if (TMath::Abs(tet) > 0.15) { | |
868 | sint = TMath::Sin(tet); | |
869 | sintt = (sint/tet); | |
870 | tsint = (tet-sint)/tet; | |
871 | cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet; | |
872 | } else { | |
873 | tsint = tet*tet/36.; | |
874 | sintt = (1. - tsint); | |
875 | sint = tet*sintt; | |
876 | cos1t = 0.5*tet; | |
877 | } | |
878 | ||
879 | f1 = step * sintt; | |
880 | f2 = step * cos1t; | |
881 | f3 = step * tsint * hp; | |
882 | f4 = -tet*cos1t; | |
883 | f5 = sint; | |
884 | f6 = tet * cos1t * hp; | |
885 | ||
886 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0]; | |
887 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1]; | |
888 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f3; | |
889 | ||
890 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0]; | |
891 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1]; | |
892 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f6; | |
893 | ||
894 | return; | |
895 | } | |
8cde4af5 | 896 | |
c04e3238 | 897 | //__________________________________________________________________________ |
898 | void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout) | |
899 | { | |
900 | /// ****************************************************************** | |
901 | /// * * | |
902 | /// * Runge-Kutta method for tracking a particle through a magnetic * | |
903 | /// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of * | |
904 | /// * Standards, procedure 25.5.20) * | |
905 | /// * * | |
906 | /// * Input parameters * | |
907 | /// * CHARGE Particle charge * | |
908 | /// * STEP Step size * | |
909 | /// * VECT Initial co-ords,direction cosines,momentum * | |
910 | /// * Output parameters * | |
911 | /// * VOUT Output co-ords,direction cosines,momentum * | |
912 | /// * User routine called * | |
913 | /// * CALL GUFLD(X,F) * | |
914 | /// * * | |
915 | /// * ==>Called by : <USER>, GUSWIM * | |
916 | /// * Authors R.Brun, M.Hansroul ********* * | |
917 | /// * V.Perevoztchikov (CUT STEP implementation) * | |
918 | /// * * | |
919 | /// * * | |
920 | /// ****************************************************************** | |
921 | ||
922 | Double_t h2, h4, f[4]; | |
923 | Double_t xyzt[3], a, b, c, ph,ph2; | |
924 | Double_t secxs[4],secys[4],seczs[4],hxp[3]; | |
925 | Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt; | |
926 | Double_t est, at, bt, ct, cba; | |
927 | Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost; | |
928 | ||
929 | Double_t x; | |
930 | Double_t y; | |
931 | Double_t z; | |
932 | ||
933 | Double_t xt; | |
934 | Double_t yt; | |
935 | Double_t zt; | |
936 | ||
937 | Double_t maxit = 1992; | |
938 | Double_t maxcut = 11; | |
939 | ||
940 | const Double_t kdlt = 1e-4; | |
941 | const Double_t kdlt32 = kdlt/32.; | |
942 | const Double_t kthird = 1./3.; | |
943 | const Double_t khalf = 0.5; | |
944 | const Double_t kec = 2.9979251e-4; | |
945 | ||
946 | const Double_t kpisqua = 9.86960440109; | |
947 | const Int_t kix = 0; | |
948 | const Int_t kiy = 1; | |
949 | const Int_t kiz = 2; | |
950 | const Int_t kipx = 3; | |
951 | const Int_t kipy = 4; | |
952 | const Int_t kipz = 5; | |
953 | ||
954 | // *. | |
955 | // *. ------------------------------------------------------------------ | |
956 | // *. | |
957 | // * this constant is for units cm,gev/c and kgauss | |
958 | // * | |
959 | Int_t iter = 0; | |
960 | Int_t ncut = 0; | |
961 | for(Int_t j = 0; j < 7; j++) | |
962 | vout[j] = vect[j]; | |
963 | ||
964 | Double_t pinv = kec * charge / vect[6]; | |
965 | Double_t tl = 0.; | |
966 | Double_t h = step; | |
967 | Double_t rest; | |
968 | ||
969 | ||
970 | do { | |
971 | rest = step - tl; | |
972 | if (TMath::Abs(h) > TMath::Abs(rest)) h = rest; | |
973 | //cmodif: call gufld(vout,f) changed into: | |
974 | ||
975 | GetField(vout,f); | |
976 | ||
977 | // * | |
978 | // * start of integration | |
979 | // * | |
980 | x = vout[0]; | |
981 | y = vout[1]; | |
982 | z = vout[2]; | |
983 | a = vout[3]; | |
984 | b = vout[4]; | |
985 | c = vout[5]; | |
986 | ||
987 | h2 = khalf * h; | |
988 | h4 = khalf * h2; | |
989 | ph = pinv * h; | |
990 | ph2 = khalf * ph; | |
991 | secxs[0] = (b * f[2] - c * f[1]) * ph2; | |
992 | secys[0] = (c * f[0] - a * f[2]) * ph2; | |
993 | seczs[0] = (a * f[1] - b * f[0]) * ph2; | |
994 | ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]); | |
995 | if (ang2 > kpisqua) break; | |
996 | ||
997 | dxt = h2 * a + h4 * secxs[0]; | |
998 | dyt = h2 * b + h4 * secys[0]; | |
999 | dzt = h2 * c + h4 * seczs[0]; | |
1000 | xt = x + dxt; | |
1001 | yt = y + dyt; | |
1002 | zt = z + dzt; | |
1003 | // * | |
1004 | // * second intermediate point | |
1005 | // * | |
1006 | ||
1007 | est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt); | |
1008 | if (est > h) { | |
1009 | if (ncut++ > maxcut) break; | |
1010 | h *= khalf; | |
1011 | continue; | |
1012 | } | |
1013 | ||
1014 | xyzt[0] = xt; | |
1015 | xyzt[1] = yt; | |
1016 | xyzt[2] = zt; | |
1017 | ||
1018 | //cmodif: call gufld(xyzt,f) changed into: | |
1019 | GetField(xyzt,f); | |
1020 | ||
1021 | at = a + secxs[0]; | |
1022 | bt = b + secys[0]; | |
1023 | ct = c + seczs[0]; | |
1024 | ||
1025 | secxs[1] = (bt * f[2] - ct * f[1]) * ph2; | |
1026 | secys[1] = (ct * f[0] - at * f[2]) * ph2; | |
1027 | seczs[1] = (at * f[1] - bt * f[0]) * ph2; | |
1028 | at = a + secxs[1]; | |
1029 | bt = b + secys[1]; | |
1030 | ct = c + seczs[1]; | |
1031 | secxs[2] = (bt * f[2] - ct * f[1]) * ph2; | |
1032 | secys[2] = (ct * f[0] - at * f[2]) * ph2; | |
1033 | seczs[2] = (at * f[1] - bt * f[0]) * ph2; | |
1034 | dxt = h * (a + secxs[2]); | |
1035 | dyt = h * (b + secys[2]); | |
1036 | dzt = h * (c + seczs[2]); | |
1037 | xt = x + dxt; | |
1038 | yt = y + dyt; | |
1039 | zt = z + dzt; | |
1040 | at = a + 2.*secxs[2]; | |
1041 | bt = b + 2.*secys[2]; | |
1042 | ct = c + 2.*seczs[2]; | |
1043 | ||
1044 | est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt); | |
1045 | if (est > 2.*TMath::Abs(h)) { | |
1046 | if (ncut++ > maxcut) break; | |
1047 | h *= khalf; | |
1048 | continue; | |
1049 | } | |
1050 | ||
1051 | xyzt[0] = xt; | |
1052 | xyzt[1] = yt; | |
1053 | xyzt[2] = zt; | |
1054 | ||
1055 | //cmodif: call gufld(xyzt,f) changed into: | |
1056 | GetField(xyzt,f); | |
1057 | ||
1058 | z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h; | |
1059 | y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h; | |
1060 | x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h; | |
1061 | ||
1062 | secxs[3] = (bt*f[2] - ct*f[1])* ph2; | |
1063 | secys[3] = (ct*f[0] - at*f[2])* ph2; | |
1064 | seczs[3] = (at*f[1] - bt*f[0])* ph2; | |
1065 | a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird; | |
1066 | b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird; | |
1067 | c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird; | |
1068 | ||
1069 | est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2])) | |
1070 | + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2])) | |
1071 | + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2])); | |
1072 | ||
1073 | if (est > kdlt && TMath::Abs(h) > 1.e-4) { | |
1074 | if (ncut++ > maxcut) break; | |
1075 | h *= khalf; | |
1076 | continue; | |
1077 | } | |
1078 | ||
1079 | ncut = 0; | |
1080 | // * if too many iterations, go to helix | |
1081 | if (iter++ > maxit) break; | |
1082 | ||
1083 | tl += h; | |
1084 | if (est < kdlt32) | |
1085 | h *= 2.; | |
1086 | cba = 1./ TMath::Sqrt(a*a + b*b + c*c); | |
1087 | vout[0] = x; | |
1088 | vout[1] = y; | |
1089 | vout[2] = z; | |
1090 | vout[3] = cba*a; | |
1091 | vout[4] = cba*b; | |
1092 | vout[5] = cba*c; | |
1093 | rest = step - tl; | |
1094 | if (step < 0.) rest = -rest; | |
1095 | if (rest < 1.e-5*TMath::Abs(step)) return; | |
1096 | ||
1097 | } while(1); | |
1098 | ||
1099 | // angle too big, use helix | |
1100 | ||
1101 | f1 = f[0]; | |
1102 | f2 = f[1]; | |
1103 | f3 = f[2]; | |
1104 | f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3); | |
1105 | rho = -f4*pinv; | |
1106 | tet = rho * step; | |
1107 | ||
1108 | hnorm = 1./f4; | |
1109 | f1 = f1*hnorm; | |
1110 | f2 = f2*hnorm; | |
1111 | f3 = f3*hnorm; | |
1112 | ||
1113 | hxp[0] = f2*vect[kipz] - f3*vect[kipy]; | |
1114 | hxp[1] = f3*vect[kipx] - f1*vect[kipz]; | |
1115 | hxp[2] = f1*vect[kipy] - f2*vect[kipx]; | |
1116 | ||
1117 | hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz]; | |
1118 | ||
1119 | rho1 = 1./rho; | |
1120 | sint = TMath::Sin(tet); | |
1121 | cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet); | |
1122 | ||
1123 | g1 = sint*rho1; | |
1124 | g2 = cost*rho1; | |
1125 | g3 = (tet-sint) * hp*rho1; | |
1126 | g4 = -cost; | |
1127 | g5 = sint; | |
1128 | g6 = cost * hp; | |
1129 | ||
1130 | vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1; | |
1131 | vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2; | |
1132 | vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3; | |
1133 | ||
1134 | vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1; | |
1135 | vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2; | |
1136 | vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3; | |
1137 | ||
1138 | return; | |
1139 | } | |
8cde4af5 | 1140 | |
c04e3238 | 1141 | //___________________________________________________________ |
1142 | void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field) | |
1143 | { | |
1144 | /// interface for arguments in double precision (Why ? ChF) | |
1145 | Float_t x[3], b[3]; | |
1146 | ||
1147 | x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2]; | |
1148 | ||
1149 | if (fgkField) fgkField->Field(x,b); | |
1150 | else { | |
1151 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
1152 | exit(-1); | |
1153 | } | |
1154 | ||
1155 | Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2]; | |
1156 | ||
1157 | return; | |
1158 | } |