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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 | ||
56316147 | 18 | //----------------------------------------------------------------------------- |
19 | // Class AliMUONTrackExtrap | |
20 | // ------------------------ | |
21 | // Tools for track extrapolation in ALICE dimuon spectrometer | |
22 | // Author: Philippe Pillot | |
23 | //----------------------------------------------------------------------------- | |
c04e3238 | 24 | |
c04e3238 | 25 | #include "AliMUONTrackExtrap.h" |
26 | #include "AliMUONTrackParam.h" | |
27 | #include "AliMUONConstants.h" | |
0e894e58 | 28 | #include "AliMUONReconstructor.h" |
29 | #include "AliMUONRecoParam.h" | |
8cde4af5 | 30 | |
c04e3238 | 31 | #include "AliMagF.h" |
8cde4af5 | 32 | |
8cde4af5 | 33 | #include <TMath.h> |
8cde4af5 | 34 | #include <TGeoManager.h> |
c04e3238 | 35 | |
ea94c18b | 36 | #include <Riostream.h> |
37 | ||
78649106 | 38 | /// \cond CLASSIMP |
c04e3238 | 39 | ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context |
78649106 | 40 | /// \endcond |
c04e3238 | 41 | |
42 | const AliMagF* AliMUONTrackExtrap::fgkField = 0x0; | |
4284483e | 43 | const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE; |
208f139e | 44 | const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000; |
4284483e | 45 | const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.; |
46 | const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002; | |
208f139e | 47 | |
690d2205 | 48 | //__________________________________________________________________________ |
208f139e | 49 | Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum) |
50 | { | |
51 | /// Returns impact parameter at vertex in bending plane (cm), | |
52 | /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c), | |
53 | /// using simple values for dipole magnetic field. | |
54 | /// The sign of "BendingMomentum" is the sign of the charge. | |
55 | ||
56 | if (bendingMomentum == 0.) return 1.e10; | |
57 | ||
9bf6860b | 58 | const Double_t kCorrectionFactor = 0.9; // impact parameter is 10% overestimated |
208f139e | 59 | Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ()); |
60 | Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL()); | |
9bf6860b | 61 | Float_t b[3], x[3] = {50.,50.,(Float_t) simpleBPosition}; |
208f139e | 62 | if (fgkField) fgkField->Field(x,b); |
63 | else { | |
64 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
65 | exit(-1); | |
66 | } | |
67 | Double_t simpleBValue = (Double_t) b[0]; | |
68 | ||
9bf6860b | 69 | return kCorrectionFactor * (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum); |
208f139e | 70 | } |
71 | ||
690d2205 | 72 | //__________________________________________________________________________ |
208f139e | 73 | Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam) |
74 | { | |
75 | /// Returns signed bending momentum in bending plane (GeV/c), | |
76 | /// the sign being the sign of the charge for particles moving forward in Z, | |
77 | /// from the impact parameter "ImpactParam" at vertex in bending plane (cm), | |
78 | /// using simple values for dipole magnetic field. | |
79 | ||
80 | if (impactParam == 0.) return 1.e10; | |
81 | ||
9bf6860b | 82 | const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated |
208f139e | 83 | Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ()); |
84 | Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL()); | |
9bf6860b | 85 | Float_t b[3], x[3] = {50.,50.,(Float_t) simpleBPosition}; |
208f139e | 86 | if (fgkField) fgkField->Field(x,b); |
87 | else { | |
88 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
89 | exit(-1); | |
90 | } | |
91 | Double_t simpleBValue = (Double_t) b[0]; | |
92 | ||
0e894e58 | 93 | if (TMath::Abs(simpleBValue) > 0.01) return kCorrectionFactor * (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam); |
94 | else return AliMUONReconstructor::GetRecoParam()->GetMostProbBendingMomentum(); | |
019df241 | 95 | } |
96 | ||
690d2205 | 97 | //__________________________________________________________________________ |
019df241 | 98 | void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd) |
99 | { | |
100 | /// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd". | |
101 | /// On return, results from the extrapolation are updated in trackParam. | |
102 | ||
103 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z | |
104 | ||
105 | // Compute track parameters | |
106 | Double_t dZ = zEnd - trackParam->GetZ(); | |
107 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ); | |
108 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ); | |
109 | trackParam->SetZ(zEnd); | |
110 | ||
111 | // Update track parameters covariances if any | |
112 | if (trackParam->CovariancesExist()) { | |
113 | TMatrixD paramCov(trackParam->GetCovariances()); | |
114 | paramCov(0,0) += dZ * dZ * paramCov(1,1) + 2. * dZ * paramCov(0,1); | |
115 | paramCov(0,1) += dZ * paramCov(1,1); | |
116 | paramCov(1,0) = paramCov(0,1); | |
117 | paramCov(2,2) += dZ * dZ * paramCov(3,3) + 2. * dZ * paramCov(2,3); | |
118 | paramCov(2,3) += dZ * paramCov(3,3); | |
119 | paramCov(3,2) = paramCov(2,3); | |
120 | trackParam->SetCovariances(paramCov); | |
121 | } | |
122 | ||
208f139e | 123 | } |
c04e3238 | 124 | |
690d2205 | 125 | //__________________________________________________________________________ |
c04e3238 | 126 | void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd) |
127 | { | |
4284483e | 128 | /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm. |
129 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
130 | if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd); | |
131 | else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd); | |
132 | } | |
133 | ||
690d2205 | 134 | //__________________________________________________________________________ |
4284483e | 135 | void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd) |
136 | { | |
137 | /// Track parameter extrapolation to the plane at "Z" using Helix algorithm. | |
c04e3238 | 138 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. |
139 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z | |
140 | Double_t forwardBackward; // +1 if forward, -1 if backward | |
141 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
142 | else forwardBackward = -1.0; | |
dade8580 | 143 | Double_t v3[7], v3New[7]; // 7 in parameter ???? |
144 | Int_t i3, stepNumber; | |
c04e3238 | 145 | // For safety: return kTRUE or kFALSE ???? |
146 | // Parameter vector for calling EXTRAP_ONESTEP | |
4284483e | 147 | ConvertTrackParamForExtrap(trackParam, forwardBackward, v3); |
c04e3238 | 148 | // sign of charge (sign of fInverseBendingMomentum if forward motion) |
149 | // must be changed if backward extrapolation | |
208f139e | 150 | Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); |
c04e3238 | 151 | // Extrapolation loop |
152 | stepNumber = 0; | |
208f139e | 153 | while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0 |
c04e3238 | 154 | stepNumber++; |
4284483e | 155 | ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New); |
dade8580 | 156 | if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0 |
690d2205 | 157 | // better use TArray ???? |
208f139e | 158 | for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];} |
c04e3238 | 159 | } |
208f139e | 160 | // check fgkMaxStepNumber ???? |
c04e3238 | 161 | // Interpolation back to exact Z (2nd order) |
162 | // should be in function ???? using TArray ???? | |
dade8580 | 163 | Double_t dZ12 = v3New[2] - v3[2]; // 1->2 |
c04e3238 | 164 | if (TMath::Abs(dZ12) > 0) { |
dade8580 | 165 | Double_t dZ1i = zEnd - v3[2]; // 1-i |
166 | Double_t dZi2 = v3New[2] - zEnd; // i->2 | |
167 | Double_t xPrime = (v3New[0] - v3[0]) / dZ12; | |
168 | Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12; | |
169 | Double_t yPrime = (v3New[1] - v3[1]) / dZ12; | |
170 | Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12; | |
171 | v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X | |
172 | v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y | |
173 | v3[2] = zEnd; // Z | |
c04e3238 | 174 | Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i); |
175 | Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i); | |
176 | // (PX, PY, PZ)/PTOT assuming forward motion | |
208f139e | 177 | v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT |
dade8580 | 178 | v3[3] = xPrimeI * v3[5]; // PX/PTOT |
179 | v3[4] = yPrimeI * v3[5]; // PY/PTOT | |
c04e3238 | 180 | } else { |
4284483e | 181 | cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl; |
c04e3238 | 182 | } |
4284483e | 183 | // Recover track parameters (charge back for forward motion) |
dade8580 | 184 | RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam); |
c04e3238 | 185 | } |
186 | ||
690d2205 | 187 | //__________________________________________________________________________ |
4284483e | 188 | void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd) |
189 | { | |
190 | /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm. | |
191 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
192 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z | |
193 | Double_t forwardBackward; // +1 if forward, -1 if backward | |
194 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
195 | else forwardBackward = -1.0; | |
196 | // sign of charge (sign of fInverseBendingMomentum if forward motion) | |
197 | // must be changed if backward extrapolation | |
198 | Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); | |
199 | Double_t v3[7], v3New[7]; | |
200 | Double_t dZ, step; | |
201 | Int_t stepNumber = 0; | |
202 | ||
203 | // Extrapolation loop (until within tolerance) | |
204 | Double_t residue = zEnd - trackParam->GetZ(); | |
205 | while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) { | |
206 | dZ = zEnd - trackParam->GetZ(); | |
207 | // step lenght assuming linear trajectory | |
208 | step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() + | |
690d2205 | 209 | trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope()); |
4284483e | 210 | ConvertTrackParamForExtrap(trackParam, forwardBackward, v3); |
211 | do { // reduce step lenght while zEnd oversteped | |
212 | if (stepNumber > fgkMaxStepNumber) { | |
213 | cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl; | |
214 | break; | |
215 | } | |
216 | stepNumber ++; | |
217 | step = TMath::Abs(step); | |
218 | AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New); | |
219 | residue = zEnd - v3New[2]; | |
220 | step *= dZ/(v3New[2]-trackParam->GetZ()); | |
221 | } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue); | |
222 | RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam); | |
223 | } | |
224 | ||
225 | // terminate the extropolation with a straight line up to the exact "zEnd" value | |
226 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope()); | |
227 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope()); | |
228 | trackParam->SetZ(zEnd); | |
229 | } | |
230 | ||
690d2205 | 231 | //__________________________________________________________________________ |
4284483e | 232 | void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3) |
c04e3238 | 233 | { |
dade8580 | 234 | /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam. |
c04e3238 | 235 | /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward" |
236 | /// to know whether the particle is going forward (+1) or backward (-1). | |
dade8580 | 237 | v3[0] = trackParam->GetNonBendingCoor(); // X |
238 | v3[1] = trackParam->GetBendingCoor(); // Y | |
239 | v3[2] = trackParam->GetZ(); // Z | |
c04e3238 | 240 | Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); |
241 | Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()); | |
dade8580 | 242 | v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT |
243 | v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0 | |
244 | v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT | |
245 | v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT | |
c04e3238 | 246 | } |
247 | ||
690d2205 | 248 | //__________________________________________________________________________ |
dade8580 | 249 | void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam) |
c04e3238 | 250 | { |
dade8580 | 251 | /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3", |
c04e3238 | 252 | /// assumed to be calculated for forward motion in Z. |
253 | /// "InverseBendingMomentum" is signed with "charge". | |
dade8580 | 254 | trackParam->SetNonBendingCoor(v3[0]); // X |
255 | trackParam->SetBendingCoor(v3[1]); // Y | |
256 | trackParam->SetZ(v3[2]); // Z | |
257 | Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]); | |
c04e3238 | 258 | trackParam->SetInverseBendingMomentum(charge/pYZ); |
dade8580 | 259 | trackParam->SetBendingSlope(v3[4]/v3[5]); |
260 | trackParam->SetNonBendingSlope(v3[3]/v3[5]); | |
208f139e | 261 | } |
262 | ||
690d2205 | 263 | //__________________________________________________________________________ |
ea94c18b | 264 | void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator) |
208f139e | 265 | { |
266 | /// Track parameters and their covariances extrapolated to the plane at "zEnd". | |
267 | /// On return, results from the extrapolation are updated in trackParam. | |
268 | ||
269 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z | |
270 | ||
ea94c18b | 271 | // No need to propagate the covariance matrix if it does not exist |
272 | if (!trackParam->CovariancesExist()) { | |
273 | cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl; | |
274 | // Extrapolate track parameters to "zEnd" | |
275 | ExtrapToZ(trackParam,zEnd); | |
276 | return; | |
277 | } | |
278 | ||
208f139e | 279 | // Save the actual track parameters |
280 | AliMUONTrackParam trackParamSave(*trackParam); | |
ea94c18b | 281 | TMatrixD paramSave(trackParamSave.GetParameters()); |
282 | Double_t zBegin = trackParamSave.GetZ(); | |
283 | ||
284 | // Get reference to the parameter covariance matrix | |
285 | const TMatrixD& kParamCov = trackParam->GetCovariances(); | |
9bf6860b | 286 | |
208f139e | 287 | // Extrapolate track parameters to "zEnd" |
288 | ExtrapToZ(trackParam,zEnd); | |
208f139e | 289 | |
ea94c18b | 290 | // Get reference to the extrapolated parameters |
291 | const TMatrixD& extrapParam = trackParam->GetParameters(); | |
208f139e | 292 | |
293 | // Calculate the jacobian related to the track parameters extrapolation to "zEnd" | |
294 | TMatrixD jacob(5,5); | |
ea94c18b | 295 | jacob.Zero(); |
296 | TMatrixD dParam(5,1); | |
208f139e | 297 | for (Int_t i=0; i<5; i++) { |
298 | // Skip jacobian calculation for parameters with no associated error | |
18abc511 | 299 | if (kParamCov(i,i) <= 0.) continue; |
ea94c18b | 300 | |
208f139e | 301 | // Small variation of parameter i only |
302 | for (Int_t j=0; j<5; j++) { | |
303 | if (j==i) { | |
ea94c18b | 304 | dParam(j,0) = TMath::Sqrt(kParamCov(i,i)); |
305 | if (j == 4) dParam(j,0) *= TMath::Sign(1.,-paramSave(4,0)); // variation always in the same direction | |
306 | } else dParam(j,0) = 0.; | |
208f139e | 307 | } |
ea94c18b | 308 | |
208f139e | 309 | // Set new parameters |
ea94c18b | 310 | trackParamSave.SetParameters(paramSave); |
311 | trackParamSave.AddParameters(dParam); | |
312 | trackParamSave.SetZ(zBegin); | |
313 | ||
208f139e | 314 | // Extrapolate new track parameters to "zEnd" |
315 | ExtrapToZ(&trackParamSave,zEnd); | |
ea94c18b | 316 | |
208f139e | 317 | // Calculate the jacobian |
ea94c18b | 318 | TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam); |
319 | jacobji *= 1. / dParam(i,0); | |
320 | jacob.SetSub(0,i,jacobji); | |
208f139e | 321 | } |
322 | ||
323 | // Extrapolate track parameter covariances to "zEnd" | |
ea94c18b | 324 | TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob); |
325 | TMatrixD tmp2(jacob,TMatrixD::kMult,tmp); | |
326 | trackParam->SetCovariances(tmp2); | |
327 | ||
328 | // Update the propagator if required | |
329 | if (updatePropagator) trackParam->UpdatePropagator(jacob); | |
208f139e | 330 | } |
331 | ||
690d2205 | 332 | //__________________________________________________________________________ |
8cde4af5 | 333 | void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2) |
334 | { | |
335 | /// Add to the track parameter covariances the effects of multiple Coulomb scattering | |
690d2205 | 336 | /// The absorber correction parameters are supposed to be calculated at the current track z-position |
8cde4af5 | 337 | |
338 | // absorber related covariance parameters | |
339 | Double_t bendingSlope = param->GetBendingSlope(); | |
340 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
341 | Double_t inverseBendingMomentum = param->GetInverseBendingMomentum(); | |
342 | Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) / | |
690d2205 | 343 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1 |
8cde4af5 | 344 | Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2); |
345 | Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1); | |
346 | Double_t varSlop = alpha2 * f0; | |
347 | ||
690d2205 | 348 | // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX |
349 | Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
350 | Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope / | |
351 | (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
352 | ||
353 | // Set MCS covariance matrix | |
ea94c18b | 354 | TMatrixD newParamCov(param->GetCovariances()); |
8cde4af5 | 355 | // Non bending plane |
ea94c18b | 356 | newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope; |
357 | newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop; | |
8cde4af5 | 358 | // Bending plane |
ea94c18b | 359 | newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope; |
360 | newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop; | |
690d2205 | 361 | // Inverse bending momentum (due to dependences with bending and non bending slopes) |
362 | newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope; | |
363 | newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop; | |
364 | newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope; | |
365 | newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop; | |
366 | newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop; | |
ea94c18b | 367 | |
368 | // Set new covariances | |
369 | param->SetCovariances(newParamCov); | |
690d2205 | 370 | } |
371 | ||
372 | //__________________________________________________________________________ | |
373 | void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param, | |
374 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
375 | Double_t errXVtx, Double_t errYVtx, | |
376 | Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2) | |
377 | { | |
378 | /// Correct parameters and corresponding covariances using Branson correction | |
379 | /// - input param are parameters and covariances at the end of absorber | |
380 | /// - output param are parameters and covariances at vertex | |
381 | /// Absorber correction parameters are supposed to be calculated at the current track z-position | |
382 | ||
383 | // Position of the Branson plane (spectro. (z<0)) | |
384 | Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.; | |
385 | ||
386 | // Add MCS effects to current parameter covariances | |
387 | AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2); | |
388 | ||
389 | // Get track parameters and covariances in the Branson plane corrected for magnetic field effect | |
390 | ExtrapToZCov(param,zVtx); | |
391 | LinearExtrapToZ(param,zB); | |
392 | ||
393 | // compute track parameters at vertex | |
394 | TMatrixD newParam(5,1); | |
395 | newParam(0,0) = xVtx; | |
396 | newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx); | |
397 | newParam(2,0) = yVtx; | |
398 | newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx); | |
399 | newParam(4,0) = param->GetCharge() / param->P() * | |
400 | TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) / | |
401 | TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0)); | |
402 | ||
403 | // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system | |
404 | TMatrixD paramCovP(param->GetCovariances()); | |
405 | Cov2CovP(param->GetParameters(),paramCovP); | |
406 | ||
407 | // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system | |
408 | TMatrixD paramCovVtx(5,5); | |
409 | paramCovVtx.Zero(); | |
410 | paramCovVtx(0,0) = errXVtx * errXVtx; | |
411 | paramCovVtx(1,1) = paramCovP(0,0); | |
412 | paramCovVtx(2,2) = errYVtx * errYVtx; | |
413 | paramCovVtx(3,3) = paramCovP(2,2); | |
414 | paramCovVtx(4,4) = paramCovP(4,4); | |
415 | paramCovVtx(1,3) = paramCovP(0,2); | |
416 | paramCovVtx(3,1) = paramCovP(2,0); | |
417 | paramCovVtx(1,4) = paramCovP(0,4); | |
418 | paramCovVtx(4,1) = paramCovP(4,0); | |
419 | paramCovVtx(3,4) = paramCovP(2,4); | |
420 | paramCovVtx(4,3) = paramCovP(4,2); | |
421 | ||
422 | // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) | |
423 | TMatrixD jacob(5,5); | |
424 | jacob.UnitMatrix(); | |
425 | jacob(1,0) = - 1. / (zB - zVtx); | |
426 | jacob(1,1) = 1. / (zB - zVtx); | |
427 | jacob(3,2) = - 1. / (zB - zVtx); | |
428 | jacob(3,3) = 1. / (zB - zVtx); | |
8cde4af5 | 429 | |
690d2205 | 430 | // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system |
431 | TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob); | |
432 | TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp); | |
433 | ||
434 | // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system | |
435 | CovP2Cov(newParam,newParamCov); | |
436 | ||
437 | // Set parameters and covariances at vertex | |
438 | param->SetParameters(newParam); | |
439 | param->SetZ(zVtx); | |
440 | param->SetCovariances(newParamCov); | |
8cde4af5 | 441 | } |
442 | ||
690d2205 | 443 | //__________________________________________________________________________ |
444 | void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2) | |
445 | { | |
446 | /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances | |
447 | ||
448 | // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system | |
449 | TMatrixD newParamCov(param->GetCovariances()); | |
450 | Cov2CovP(param->GetParameters(),newParamCov); | |
451 | ||
452 | // Add effects of energy loss fluctuation to covariances | |
453 | newParamCov(4,4) += sigmaELoss2; | |
454 | ||
455 | // Compute new parameters corrected for energy loss | |
456 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
457 | Double_t bendingSlope = param->GetBendingSlope(); | |
458 | param->SetInverseBendingMomentum(param->GetCharge() / (param->P() + eLoss) * | |
459 | TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) / | |
460 | TMath::Sqrt(1.0 + bendingSlope*bendingSlope)); | |
461 | ||
462 | // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system | |
463 | CovP2Cov(param->GetParameters(),newParamCov); | |
464 | ||
465 | // Set new parameter covariances | |
466 | param->SetCovariances(newParamCov); | |
467 | } | |
468 | ||
469 | //__________________________________________________________________________ | |
18abc511 | 470 | Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal, |
471 | Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2, | |
472 | Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2) | |
8cde4af5 | 473 | { |
474 | /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber | |
690d2205 | 475 | /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important) |
8cde4af5 | 476 | // pathLength: path length between trackXYZIn and trackXYZOut (cm) |
477 | // f0: 0th moment of z calculated with the inverse radiation-length distribution | |
478 | // f1: 1st moment of z calculated with the inverse radiation-length distribution | |
479 | // f2: 2nd moment of z calculated with the inverse radiation-length distribution | |
480 | // meanRho: average density of crossed material (g/cm3) | |
84f061ef | 481 | // totalELoss: total energy loss in absorber |
8cde4af5 | 482 | |
483 | // Reset absorber's parameters | |
484 | pathLength = 0.; | |
485 | f0 = 0.; | |
486 | f1 = 0.; | |
487 | f2 = 0.; | |
488 | meanRho = 0.; | |
84f061ef | 489 | totalELoss = 0.; |
690d2205 | 490 | sigmaELoss2 = 0.; |
8cde4af5 | 491 | |
492 | // Check whether the geometry is available | |
493 | if (!gGeoManager) { | |
494 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl; | |
18abc511 | 495 | return kFALSE; |
8cde4af5 | 496 | } |
497 | ||
498 | // Initialize starting point and direction | |
499 | pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+ | |
500 | (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+ | |
501 | (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2])); | |
18abc511 | 502 | if (pathLength < TGeoShape::Tolerance()) return kFALSE; |
8cde4af5 | 503 | Double_t b[3]; |
504 | b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength; | |
505 | b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength; | |
506 | b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength; | |
507 | TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b); | |
508 | if (!currentnode) { | |
509 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl; | |
18abc511 | 510 | return kFALSE; |
8cde4af5 | 511 | } |
512 | ||
513 | // loop over absorber slices and calculate absorber's parameters | |
514 | Double_t rho = 0.; // material density (g/cm3) | |
515 | Double_t x0 = 0.; // radiation-length (cm-1) | |
84f061ef | 516 | Double_t atomicA = 0.; // A of material |
517 | Double_t atomicZ = 0.; // Z of material | |
8cde4af5 | 518 | Double_t localPathLength = 0; |
519 | Double_t remainingPathLength = pathLength; | |
520 | Double_t zB = trackXYZIn[2]; | |
521 | Double_t zE, dzB, dzE; | |
522 | do { | |
523 | // Get material properties | |
524 | TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial(); | |
525 | rho = material->GetDensity(); | |
526 | x0 = material->GetRadLen(); | |
527 | if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture | |
84f061ef | 528 | atomicA = material->GetA(); |
529 | atomicZ = material->GetZ(); | |
8cde4af5 | 530 | |
531 | // Get path length within this material | |
532 | gGeoManager->FindNextBoundary(remainingPathLength); | |
533 | localPathLength = gGeoManager->GetStep() + 1.e-6; | |
534 | // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step | |
535 | if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength; | |
536 | else { | |
537 | currentnode = gGeoManager->Step(); | |
538 | if (!currentnode) { | |
539 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl; | |
18abc511 | 540 | f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.; |
541 | return kFALSE; | |
8cde4af5 | 542 | } |
543 | if (!gGeoManager->IsEntering()) { | |
544 | // make another small step to try to enter in new absorber slice | |
545 | gGeoManager->SetStep(0.001); | |
546 | currentnode = gGeoManager->Step(); | |
547 | if (!gGeoManager->IsEntering() || !currentnode) { | |
548 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl; | |
18abc511 | 549 | f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.; |
550 | return kFALSE; | |
8cde4af5 | 551 | } |
552 | localPathLength += 0.001; | |
553 | } | |
554 | } | |
555 | ||
556 | // calculate absorber's parameters | |
557 | zE = b[2] * localPathLength + zB; | |
558 | dzB = zB - trackXYZIn[2]; | |
559 | dzE = zE - trackXYZIn[2]; | |
560 | f0 += localPathLength / x0; | |
561 | f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.; | |
562 | f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.; | |
563 | meanRho += localPathLength * rho; | |
84f061ef | 564 | totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ); |
690d2205 | 565 | sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicA, atomicZ); |
8cde4af5 | 566 | |
567 | // prepare next step | |
568 | zB = zE; | |
569 | remainingPathLength -= localPathLength; | |
570 | } while (remainingPathLength > TGeoShape::Tolerance()); | |
571 | ||
572 | meanRho /= pathLength; | |
18abc511 | 573 | |
574 | return kTRUE; | |
8cde4af5 | 575 | } |
576 | ||
690d2205 | 577 | //__________________________________________________________________________ |
ea94c18b | 578 | Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0) |
579 | { | |
580 | /// Return the angular dispersion square due to multiple Coulomb scattering | |
581 | /// through a material of thickness "dZ" and of radiation length "x0" | |
582 | /// assuming linear propagation and using the small angle approximation. | |
583 | ||
584 | Double_t bendingSlope = param.GetBendingSlope(); | |
585 | Double_t nonBendingSlope = param.GetNonBendingSlope(); | |
586 | Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() * | |
690d2205 | 587 | (1.0 + bendingSlope * bendingSlope) / |
588 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); | |
ea94c18b | 589 | // Path length in the material |
590 | Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope); | |
591 | // relativistic velocity | |
592 | Double_t velo = 1.; | |
593 | // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory | |
594 | Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0)); | |
595 | ||
596 | return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0; | |
597 | } | |
598 | ||
690d2205 | 599 | //__________________________________________________________________________ |
8cde4af5 | 600 | void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0) |
208f139e | 601 | { |
602 | /// Add to the track parameter covariances the effects of multiple Coulomb scattering | |
603 | /// through a material of thickness "dZ" and of radiation length "x0" | |
604 | /// assuming linear propagation and using the small angle approximation. | |
605 | ||
606 | Double_t bendingSlope = param->GetBendingSlope(); | |
607 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
690d2205 | 608 | Double_t inverseBendingMomentum = param->GetInverseBendingMomentum(); |
609 | Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum * | |
610 | (1.0 + bendingSlope * bendingSlope) / | |
611 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); | |
208f139e | 612 | // Path length in the material |
613 | Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope); | |
614 | Double_t pathLength2 = pathLength * pathLength; | |
615 | // relativistic velocity | |
616 | Double_t velo = 1.; | |
617 | // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory | |
618 | Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0)); | |
619 | theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0; | |
620 | ||
208f139e | 621 | Double_t varCoor = pathLength2 * theta02 / 3.; |
622 | Double_t varSlop = theta02; | |
623 | Double_t covCorrSlope = pathLength * theta02 / 2.; | |
ea94c18b | 624 | |
690d2205 | 625 | // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX |
626 | Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
627 | Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope / | |
628 | (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
629 | ||
630 | // Set MCS covariance matrix | |
ea94c18b | 631 | TMatrixD newParamCov(param->GetCovariances()); |
208f139e | 632 | // Non bending plane |
ea94c18b | 633 | newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope; |
634 | newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop; | |
208f139e | 635 | // Bending plane |
ea94c18b | 636 | newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope; |
637 | newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop; | |
690d2205 | 638 | // Inverse bending momentum (due to dependences with bending and non bending slopes) |
639 | newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope; | |
640 | newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop; | |
641 | newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope; | |
642 | newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop; | |
643 | newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop; | |
208f139e | 644 | |
ea94c18b | 645 | // Set new covariances |
646 | param->SetCovariances(newParamCov); | |
c04e3238 | 647 | } |
648 | ||
690d2205 | 649 | //__________________________________________________________________________ |
650 | void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, | |
651 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
652 | Double_t errXVtx, Double_t errYVtx, | |
653 | Bool_t correctForMCS, Bool_t correctForEnergyLoss) | |
c04e3238 | 654 | { |
690d2205 | 655 | /// Main method for extrapolation to the vertex: |
656 | /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam | |
657 | /// Changes parameters and covariances according to multiple scattering and energy loss corrections: | |
658 | /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances | |
659 | /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances | |
660 | /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances | |
661 | /// if correctForEnergyLoss=kFALSE: do nothing about energy loss | |
c04e3238 | 662 | |
8cde4af5 | 663 | if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex |
c04e3238 | 664 | |
8cde4af5 | 665 | if (trackParam->GetZ() > zVtx) { // spectro. (z<0) |
690d2205 | 666 | cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() |
667 | <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl; | |
fac70e25 | 668 | return; |
669 | } | |
670 | ||
8cde4af5 | 671 | // Check the vertex position relatively to the absorber |
ea94c18b | 672 | if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0) |
8cde4af5 | 673 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx |
690d2205 | 674 | <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl; |
ea94c18b | 675 | } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0) |
8cde4af5 | 676 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx |
690d2205 | 677 | <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl; |
678 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx); | |
679 | else ExtrapToZ(trackParam,zVtx); | |
8cde4af5 | 680 | return; |
681 | } | |
682 | ||
683 | // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed | |
ea94c18b | 684 | if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0) |
8cde4af5 | 685 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() |
690d2205 | 686 | <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl; |
687 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx); | |
688 | else ExtrapToZ(trackParam,zVtx); | |
8cde4af5 | 689 | return; |
ea94c18b | 690 | } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0) |
8cde4af5 | 691 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() |
690d2205 | 692 | <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl; |
c04e3238 | 693 | } else { |
690d2205 | 694 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd()); |
695 | else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd()); | |
c04e3238 | 696 | } |
c04e3238 | 697 | |
690d2205 | 698 | // Get absorber correction parameters assuming linear propagation in absorber |
8cde4af5 | 699 | Double_t trackXYZOut[3]; |
700 | trackXYZOut[0] = trackParam->GetNonBendingCoor(); | |
701 | trackXYZOut[1] = trackParam->GetBendingCoor(); | |
702 | trackXYZOut[2] = trackParam->GetZ(); | |
703 | Double_t trackXYZIn[3]; | |
690d2205 | 704 | if (correctForMCS) { // assume linear propagation until the vertex |
705 | trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0) | |
706 | trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]); | |
707 | trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]); | |
708 | } else { | |
709 | AliMUONTrackParam trackParamIn(*trackParam); | |
710 | ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg())); | |
711 | trackXYZIn[0] = trackParamIn.GetNonBendingCoor(); | |
712 | trackXYZIn[1] = trackParamIn.GetBendingCoor(); | |
713 | trackXYZIn[2] = trackParamIn.GetZ(); | |
714 | } | |
84f061ef | 715 | Double_t pTot = trackParam->P(); |
18abc511 | 716 | Double_t pathLength, f0, f1, f2, meanRho, deltaP, sigmaDeltaP2; |
717 | if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP,sigmaDeltaP2)) { | |
718 | cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl; | |
719 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx); | |
720 | else ExtrapToZ(trackParam,zVtx); | |
721 | return; | |
722 | } | |
8cde4af5 | 723 | |
690d2205 | 724 | // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags |
725 | if (correctForMCS) { | |
fac70e25 | 726 | |
690d2205 | 727 | if (correctForEnergyLoss) { |
728 | ||
729 | // Correct for multiple scattering and energy loss | |
730 | CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2); | |
731 | CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, | |
732 | trackXYZIn[2], pathLength, f0, f1, f2); | |
733 | CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2); | |
734 | ||
735 | } else { | |
736 | ||
737 | // Correct for multiple scattering | |
738 | CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, | |
739 | trackXYZIn[2], pathLength, f0, f1, f2); | |
740 | } | |
fac70e25 | 741 | |
fac70e25 | 742 | } else { |
690d2205 | 743 | |
744 | if (correctForEnergyLoss) { | |
745 | ||
18abc511 | 746 | // Correct for energy loss add multiple scattering dispersion in covariance matrix |
690d2205 | 747 | CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2); |
748 | AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2); | |
749 | ExtrapToZCov(trackParam, trackXYZIn[2]); | |
750 | CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2); | |
751 | ExtrapToZCov(trackParam, zVtx); | |
752 | ||
753 | } else { | |
754 | ||
18abc511 | 755 | // add multiple scattering dispersion in covariance matrix |
690d2205 | 756 | AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2); |
757 | ExtrapToZCov(trackParam, zVtx); | |
758 | ||
759 | } | |
760 | ||
fac70e25 | 761 | } |
8cde4af5 | 762 | |
fac70e25 | 763 | } |
764 | ||
690d2205 | 765 | //__________________________________________________________________________ |
766 | void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, | |
767 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
768 | Double_t errXVtx, Double_t errYVtx) | |
769 | { | |
770 | /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects | |
771 | /// Add branson correction resolution and energy loss fluctuation to parameter covariances | |
772 | ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE); | |
773 | } | |
774 | ||
775 | //__________________________________________________________________________ | |
776 | void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam, | |
777 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
778 | Double_t errXVtx, Double_t errYVtx) | |
779 | { | |
780 | /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only | |
781 | /// Add branson correction resolution to parameter covariances | |
782 | ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE); | |
783 | } | |
784 | ||
785 | //__________________________________________________________________________ | |
786 | void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx) | |
787 | { | |
788 | /// Extrapolate track parameters to vertex, corrected for energy loss effects only | |
789 | /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances | |
790 | ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE); | |
791 | } | |
792 | ||
793 | //__________________________________________________________________________ | |
794 | void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx) | |
795 | { | |
796 | /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections | |
797 | /// Add dispersion due to multiple scattering to parameter covariances | |
798 | ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE); | |
799 | } | |
800 | ||
801 | //__________________________________________________________________________ | |
fac70e25 | 802 | Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx) |
803 | { | |
804 | /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation | |
805 | ||
806 | if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex | |
8cde4af5 | 807 | |
fac70e25 | 808 | // Check whether the geometry is available |
809 | if (!gGeoManager) { | |
810 | cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl; | |
811 | return 0.; | |
812 | } | |
813 | ||
814 | // Get encountered material correction parameters assuming linear propagation from vertex to the track position | |
815 | Double_t trackXYZOut[3]; | |
816 | trackXYZOut[0] = trackParam->GetNonBendingCoor(); | |
817 | trackXYZOut[1] = trackParam->GetBendingCoor(); | |
818 | trackXYZOut[2] = trackParam->GetZ(); | |
819 | Double_t trackXYZIn[3]; | |
820 | trackXYZIn[0] = xVtx; | |
821 | trackXYZIn[1] = yVtx; | |
822 | trackXYZIn[2] = zVtx; | |
84f061ef | 823 | Double_t pTot = trackParam->P(); |
18abc511 | 824 | Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2; |
690d2205 | 825 | GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2); |
fac70e25 | 826 | |
84f061ef | 827 | return totalELoss; |
c04e3238 | 828 | } |
829 | ||
690d2205 | 830 | //__________________________________________________________________________ |
84f061ef | 831 | Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ) |
c04e3238 | 832 | { |
84f061ef | 833 | /// Returns the mean total momentum energy loss of muon with total momentum='pTotal' |
834 | /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ' | |
835 | Double_t muMass = 0.105658369; // GeV | |
836 | Double_t eMass = 0.510998918e-3; // GeV | |
837 | Double_t k = 0.307075e-3; // GeV.g^-1.cm^2 | |
838 | Double_t i = 9.5e-9; // mean exitation energy per atomic Z (GeV) | |
8cde4af5 | 839 | Double_t p2=pTotal*pTotal; |
840 | Double_t beta2=p2/(p2 + muMass*muMass); | |
8cde4af5 | 841 | |
84f061ef | 842 | Double_t w = k * rho * pathLength * atomicZ / atomicA / beta2; |
843 | ||
8cde4af5 | 844 | if (beta2/(1-beta2)>3.5*3.5) |
690d2205 | 845 | return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2); |
846 | ||
84f061ef | 847 | return w * (log(2.*eMass*beta2/(1-beta2)/(i*atomicZ)) - beta2); |
c04e3238 | 848 | } |
849 | ||
690d2205 | 850 | //__________________________________________________________________________ |
851 | Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ) | |
852 | { | |
853 | /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal' | |
854 | /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ' | |
855 | Double_t muMass = 0.105658369; // GeV | |
856 | //Double_t eMass = 0.510998918e-3; // GeV | |
857 | Double_t k = 0.307075e-3; // GeV.g^-1.cm^2 | |
858 | Double_t p2=pTotal*pTotal; | |
859 | Double_t beta2=p2/(p2 + muMass*muMass); | |
860 | ||
861 | Double_t fwhm = 2. * k * rho * pathLength * atomicZ / atomicA / beta2; // FWHM of the energy loss Landau distribution | |
862 | Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma) | |
863 | ||
864 | //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution | |
865 | ||
866 | return sigma2; | |
867 | } | |
868 | ||
869 | //__________________________________________________________________________ | |
870 | void AliMUONTrackExtrap::Cov2CovP(const TMatrixD ¶m, TMatrixD &cov) | |
871 | { | |
872 | /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot) | |
873 | /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system | |
874 | ||
875 | // charge * total momentum | |
876 | Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) / | |
877 | TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0); | |
878 | ||
879 | // Jacobian of the opposite transformation | |
880 | TMatrixD jacob(5,5); | |
881 | jacob.UnitMatrix(); | |
882 | jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
883 | jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) / | |
884 | (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
885 | jacob(4,4) = - qPTot / param(4,0); | |
886 | ||
887 | // compute covariances in new coordinate system | |
888 | TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob); | |
889 | cov.Mult(jacob,tmp); | |
890 | } | |
891 | ||
892 | //__________________________________________________________________________ | |
893 | void AliMUONTrackExtrap::CovP2Cov(const TMatrixD ¶m, TMatrixD &covP) | |
894 | { | |
895 | /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz) | |
896 | /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system | |
897 | ||
898 | // charge * total momentum | |
899 | Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) / | |
900 | TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0); | |
901 | ||
902 | // Jacobian of the transformation | |
903 | TMatrixD jacob(5,5); | |
904 | jacob.UnitMatrix(); | |
905 | jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
906 | jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) / | |
907 | (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
908 | jacob(4,4) = - param(4,0) / qPTot; | |
909 | ||
910 | // compute covariances in new coordinate system | |
911 | TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob); | |
912 | covP.Mult(jacob,tmp); | |
913 | } | |
914 | ||
c04e3238 | 915 | //__________________________________________________________________________ |
916 | void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout) | |
917 | { | |
71a2d3aa | 918 | /// <pre> |
c04e3238 | 919 | /// ****************************************************************** |
920 | /// * * | |
921 | /// * Performs the tracking of one step in a magnetic field * | |
922 | /// * The trajectory is assumed to be a helix in a constant field * | |
923 | /// * taken at the mid point of the step. * | |
924 | /// * Parameters: * | |
925 | /// * input * | |
926 | /// * STEP =arc length of the step asked * | |
927 | /// * VECT =input vector (position,direction cos and momentum) * | |
928 | /// * CHARGE= electric charge of the particle * | |
929 | /// * output * | |
930 | /// * VOUT = same as VECT after completion of the step * | |
931 | /// * * | |
2060b217 | 932 | /// * ==>Called by : USER, GUSWIM * |
c04e3238 | 933 | /// * Author m.hansroul ********* * |
934 | /// * modified s.egli, s.v.levonian * | |
935 | /// * modified v.perevoztchikov | |
936 | /// * * | |
937 | /// ****************************************************************** | |
71a2d3aa | 938 | /// </pre> |
c04e3238 | 939 | |
940 | // modif: everything in double precision | |
941 | ||
942 | Double_t xyz[3], h[4], hxp[3]; | |
943 | Double_t h2xy, hp, rho, tet; | |
944 | Double_t sint, sintt, tsint, cos1t; | |
945 | Double_t f1, f2, f3, f4, f5, f6; | |
946 | ||
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 | const Int_t kipp = 6; | |
954 | ||
955 | const Double_t kec = 2.9979251e-4; | |
956 | // | |
957 | // ------------------------------------------------------------------ | |
958 | // | |
959 | // units are kgauss,centimeters,gev/c | |
960 | // | |
961 | vout[kipp] = vect[kipp]; | |
962 | if (TMath::Abs(charge) < 0.00001) { | |
963 | for (Int_t i = 0; i < 3; i++) { | |
964 | vout[i] = vect[i] + step * vect[i+3]; | |
965 | vout[i+3] = vect[i+3]; | |
966 | } | |
967 | return; | |
968 | } | |
969 | xyz[0] = vect[kix] + 0.5 * step * vect[kipx]; | |
970 | xyz[1] = vect[kiy] + 0.5 * step * vect[kipy]; | |
971 | xyz[2] = vect[kiz] + 0.5 * step * vect[kipz]; | |
972 | ||
973 | //cmodif: call gufld (xyz, h) changed into: | |
974 | GetField (xyz, h); | |
975 | ||
976 | h2xy = h[0]*h[0] + h[1]*h[1]; | |
977 | h[3] = h[2]*h[2]+ h2xy; | |
978 | if (h[3] < 1.e-12) { | |
979 | for (Int_t i = 0; i < 3; i++) { | |
980 | vout[i] = vect[i] + step * vect[i+3]; | |
981 | vout[i+3] = vect[i+3]; | |
982 | } | |
983 | return; | |
984 | } | |
985 | if (h2xy < 1.e-12*h[3]) { | |
986 | ExtrapOneStepHelix3(charge*h[2], step, vect, vout); | |
987 | return; | |
988 | } | |
989 | h[3] = TMath::Sqrt(h[3]); | |
990 | h[0] /= h[3]; | |
991 | h[1] /= h[3]; | |
992 | h[2] /= h[3]; | |
993 | h[3] *= kec; | |
994 | ||
995 | hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy]; | |
996 | hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz]; | |
997 | hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx]; | |
998 | ||
999 | hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz]; | |
1000 | ||
1001 | rho = -charge*h[3]/vect[kipp]; | |
1002 | tet = rho * step; | |
1003 | ||
1004 | if (TMath::Abs(tet) > 0.15) { | |
1005 | sint = TMath::Sin(tet); | |
1006 | sintt = (sint/tet); | |
1007 | tsint = (tet-sint)/tet; | |
1008 | cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet; | |
1009 | } else { | |
1010 | tsint = tet*tet/36.; | |
1011 | sintt = (1. - tsint); | |
1012 | sint = tet*sintt; | |
1013 | cos1t = 0.5*tet; | |
1014 | } | |
1015 | ||
1016 | f1 = step * sintt; | |
1017 | f2 = step * cos1t; | |
1018 | f3 = step * tsint * hp; | |
1019 | f4 = -tet*cos1t; | |
1020 | f5 = sint; | |
1021 | f6 = tet * cos1t * hp; | |
1022 | ||
1023 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0]; | |
1024 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1]; | |
1025 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2]; | |
1026 | ||
1027 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0]; | |
1028 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1]; | |
1029 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2]; | |
1030 | ||
1031 | return; | |
1032 | } | |
1033 | ||
1034 | //__________________________________________________________________________ | |
1035 | void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout) | |
1036 | { | |
71a2d3aa | 1037 | /// <pre> |
c04e3238 | 1038 | /// ****************************************************************** |
1039 | /// * * | |
1040 | /// * Tracking routine in a constant field oriented * | |
1041 | /// * along axis 3 * | |
1042 | /// * Tracking is performed with a conventional * | |
1043 | /// * helix step method * | |
1044 | /// * * | |
2060b217 | 1045 | /// * ==>Called by : USER, GUSWIM * |
c04e3238 | 1046 | /// * Authors R.Brun, M.Hansroul ********* * |
1047 | /// * Rewritten V.Perevoztchikov | |
1048 | /// * * | |
1049 | /// ****************************************************************** | |
71a2d3aa | 1050 | /// </pre> |
c04e3238 | 1051 | |
1052 | Double_t hxp[3]; | |
1053 | Double_t h4, hp, rho, tet; | |
1054 | Double_t sint, sintt, tsint, cos1t; | |
1055 | Double_t f1, f2, f3, f4, f5, f6; | |
1056 | ||
1057 | const Int_t kix = 0; | |
1058 | const Int_t kiy = 1; | |
1059 | const Int_t kiz = 2; | |
1060 | const Int_t kipx = 3; | |
1061 | const Int_t kipy = 4; | |
1062 | const Int_t kipz = 5; | |
1063 | const Int_t kipp = 6; | |
1064 | ||
1065 | const Double_t kec = 2.9979251e-4; | |
1066 | ||
1067 | // | |
1068 | // ------------------------------------------------------------------ | |
1069 | // | |
1070 | // units are kgauss,centimeters,gev/c | |
1071 | // | |
1072 | vout[kipp] = vect[kipp]; | |
1073 | h4 = field * kec; | |
1074 | ||
1075 | hxp[0] = - vect[kipy]; | |
1076 | hxp[1] = + vect[kipx]; | |
1077 | ||
1078 | hp = vect[kipz]; | |
1079 | ||
1080 | rho = -h4/vect[kipp]; | |
1081 | tet = rho * step; | |
1082 | if (TMath::Abs(tet) > 0.15) { | |
1083 | sint = TMath::Sin(tet); | |
1084 | sintt = (sint/tet); | |
1085 | tsint = (tet-sint)/tet; | |
1086 | cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet; | |
1087 | } else { | |
1088 | tsint = tet*tet/36.; | |
1089 | sintt = (1. - tsint); | |
1090 | sint = tet*sintt; | |
1091 | cos1t = 0.5*tet; | |
1092 | } | |
1093 | ||
1094 | f1 = step * sintt; | |
1095 | f2 = step * cos1t; | |
1096 | f3 = step * tsint * hp; | |
1097 | f4 = -tet*cos1t; | |
1098 | f5 = sint; | |
1099 | f6 = tet * cos1t * hp; | |
1100 | ||
1101 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0]; | |
1102 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1]; | |
1103 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f3; | |
1104 | ||
1105 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0]; | |
1106 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1]; | |
1107 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f6; | |
1108 | ||
1109 | return; | |
1110 | } | |
8cde4af5 | 1111 | |
c04e3238 | 1112 | //__________________________________________________________________________ |
1113 | void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout) | |
1114 | { | |
71a2d3aa | 1115 | /// <pre> |
c04e3238 | 1116 | /// ****************************************************************** |
1117 | /// * * | |
1118 | /// * Runge-Kutta method for tracking a particle through a magnetic * | |
1119 | /// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of * | |
1120 | /// * Standards, procedure 25.5.20) * | |
1121 | /// * * | |
1122 | /// * Input parameters * | |
1123 | /// * CHARGE Particle charge * | |
1124 | /// * STEP Step size * | |
1125 | /// * VECT Initial co-ords,direction cosines,momentum * | |
1126 | /// * Output parameters * | |
1127 | /// * VOUT Output co-ords,direction cosines,momentum * | |
1128 | /// * User routine called * | |
1129 | /// * CALL GUFLD(X,F) * | |
1130 | /// * * | |
2060b217 | 1131 | /// * ==>Called by : USER, GUSWIM * |
c04e3238 | 1132 | /// * Authors R.Brun, M.Hansroul ********* * |
1133 | /// * V.Perevoztchikov (CUT STEP implementation) * | |
1134 | /// * * | |
1135 | /// * * | |
1136 | /// ****************************************************************** | |
71a2d3aa | 1137 | /// </pre> |
c04e3238 | 1138 | |
1139 | Double_t h2, h4, f[4]; | |
1140 | Double_t xyzt[3], a, b, c, ph,ph2; | |
1141 | Double_t secxs[4],secys[4],seczs[4],hxp[3]; | |
1142 | Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt; | |
1143 | Double_t est, at, bt, ct, cba; | |
1144 | Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost; | |
1145 | ||
1146 | Double_t x; | |
1147 | Double_t y; | |
1148 | Double_t z; | |
1149 | ||
1150 | Double_t xt; | |
1151 | Double_t yt; | |
1152 | Double_t zt; | |
1153 | ||
1154 | Double_t maxit = 1992; | |
1155 | Double_t maxcut = 11; | |
1156 | ||
1157 | const Double_t kdlt = 1e-4; | |
1158 | const Double_t kdlt32 = kdlt/32.; | |
1159 | const Double_t kthird = 1./3.; | |
1160 | const Double_t khalf = 0.5; | |
1161 | const Double_t kec = 2.9979251e-4; | |
1162 | ||
1163 | const Double_t kpisqua = 9.86960440109; | |
1164 | const Int_t kix = 0; | |
1165 | const Int_t kiy = 1; | |
1166 | const Int_t kiz = 2; | |
1167 | const Int_t kipx = 3; | |
1168 | const Int_t kipy = 4; | |
1169 | const Int_t kipz = 5; | |
1170 | ||
1171 | // *. | |
1172 | // *. ------------------------------------------------------------------ | |
1173 | // *. | |
1174 | // * this constant is for units cm,gev/c and kgauss | |
1175 | // * | |
1176 | Int_t iter = 0; | |
1177 | Int_t ncut = 0; | |
1178 | for(Int_t j = 0; j < 7; j++) | |
1179 | vout[j] = vect[j]; | |
1180 | ||
1181 | Double_t pinv = kec * charge / vect[6]; | |
1182 | Double_t tl = 0.; | |
1183 | Double_t h = step; | |
1184 | Double_t rest; | |
1185 | ||
1186 | ||
1187 | do { | |
1188 | rest = step - tl; | |
1189 | if (TMath::Abs(h) > TMath::Abs(rest)) h = rest; | |
1190 | //cmodif: call gufld(vout,f) changed into: | |
1191 | ||
1192 | GetField(vout,f); | |
1193 | ||
1194 | // * | |
1195 | // * start of integration | |
1196 | // * | |
1197 | x = vout[0]; | |
1198 | y = vout[1]; | |
1199 | z = vout[2]; | |
1200 | a = vout[3]; | |
1201 | b = vout[4]; | |
1202 | c = vout[5]; | |
1203 | ||
1204 | h2 = khalf * h; | |
1205 | h4 = khalf * h2; | |
1206 | ph = pinv * h; | |
1207 | ph2 = khalf * ph; | |
1208 | secxs[0] = (b * f[2] - c * f[1]) * ph2; | |
1209 | secys[0] = (c * f[0] - a * f[2]) * ph2; | |
1210 | seczs[0] = (a * f[1] - b * f[0]) * ph2; | |
1211 | ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]); | |
1212 | if (ang2 > kpisqua) break; | |
1213 | ||
1214 | dxt = h2 * a + h4 * secxs[0]; | |
1215 | dyt = h2 * b + h4 * secys[0]; | |
1216 | dzt = h2 * c + h4 * seczs[0]; | |
1217 | xt = x + dxt; | |
1218 | yt = y + dyt; | |
1219 | zt = z + dzt; | |
1220 | // * | |
1221 | // * second intermediate point | |
1222 | // * | |
1223 | ||
1224 | est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt); | |
1225 | if (est > h) { | |
1226 | if (ncut++ > maxcut) break; | |
1227 | h *= khalf; | |
1228 | continue; | |
1229 | } | |
1230 | ||
1231 | xyzt[0] = xt; | |
1232 | xyzt[1] = yt; | |
1233 | xyzt[2] = zt; | |
1234 | ||
1235 | //cmodif: call gufld(xyzt,f) changed into: | |
1236 | GetField(xyzt,f); | |
1237 | ||
1238 | at = a + secxs[0]; | |
1239 | bt = b + secys[0]; | |
1240 | ct = c + seczs[0]; | |
1241 | ||
1242 | secxs[1] = (bt * f[2] - ct * f[1]) * ph2; | |
1243 | secys[1] = (ct * f[0] - at * f[2]) * ph2; | |
1244 | seczs[1] = (at * f[1] - bt * f[0]) * ph2; | |
1245 | at = a + secxs[1]; | |
1246 | bt = b + secys[1]; | |
1247 | ct = c + seczs[1]; | |
1248 | secxs[2] = (bt * f[2] - ct * f[1]) * ph2; | |
1249 | secys[2] = (ct * f[0] - at * f[2]) * ph2; | |
1250 | seczs[2] = (at * f[1] - bt * f[0]) * ph2; | |
1251 | dxt = h * (a + secxs[2]); | |
1252 | dyt = h * (b + secys[2]); | |
1253 | dzt = h * (c + seczs[2]); | |
1254 | xt = x + dxt; | |
1255 | yt = y + dyt; | |
1256 | zt = z + dzt; | |
1257 | at = a + 2.*secxs[2]; | |
1258 | bt = b + 2.*secys[2]; | |
1259 | ct = c + 2.*seczs[2]; | |
1260 | ||
1261 | est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt); | |
1262 | if (est > 2.*TMath::Abs(h)) { | |
1263 | if (ncut++ > maxcut) break; | |
1264 | h *= khalf; | |
1265 | continue; | |
1266 | } | |
1267 | ||
1268 | xyzt[0] = xt; | |
1269 | xyzt[1] = yt; | |
1270 | xyzt[2] = zt; | |
1271 | ||
1272 | //cmodif: call gufld(xyzt,f) changed into: | |
1273 | GetField(xyzt,f); | |
1274 | ||
1275 | z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h; | |
1276 | y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h; | |
1277 | x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h; | |
1278 | ||
1279 | secxs[3] = (bt*f[2] - ct*f[1])* ph2; | |
1280 | secys[3] = (ct*f[0] - at*f[2])* ph2; | |
1281 | seczs[3] = (at*f[1] - bt*f[0])* ph2; | |
1282 | a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird; | |
1283 | b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird; | |
1284 | c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird; | |
1285 | ||
1286 | est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2])) | |
1287 | + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2])) | |
1288 | + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2])); | |
1289 | ||
1290 | if (est > kdlt && TMath::Abs(h) > 1.e-4) { | |
1291 | if (ncut++ > maxcut) break; | |
1292 | h *= khalf; | |
1293 | continue; | |
1294 | } | |
1295 | ||
1296 | ncut = 0; | |
1297 | // * if too many iterations, go to helix | |
1298 | if (iter++ > maxit) break; | |
1299 | ||
1300 | tl += h; | |
1301 | if (est < kdlt32) | |
1302 | h *= 2.; | |
1303 | cba = 1./ TMath::Sqrt(a*a + b*b + c*c); | |
1304 | vout[0] = x; | |
1305 | vout[1] = y; | |
1306 | vout[2] = z; | |
1307 | vout[3] = cba*a; | |
1308 | vout[4] = cba*b; | |
1309 | vout[5] = cba*c; | |
1310 | rest = step - tl; | |
1311 | if (step < 0.) rest = -rest; | |
1312 | if (rest < 1.e-5*TMath::Abs(step)) return; | |
1313 | ||
1314 | } while(1); | |
1315 | ||
1316 | // angle too big, use helix | |
1317 | ||
1318 | f1 = f[0]; | |
1319 | f2 = f[1]; | |
1320 | f3 = f[2]; | |
1321 | f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3); | |
1322 | rho = -f4*pinv; | |
1323 | tet = rho * step; | |
1324 | ||
1325 | hnorm = 1./f4; | |
1326 | f1 = f1*hnorm; | |
1327 | f2 = f2*hnorm; | |
1328 | f3 = f3*hnorm; | |
1329 | ||
1330 | hxp[0] = f2*vect[kipz] - f3*vect[kipy]; | |
1331 | hxp[1] = f3*vect[kipx] - f1*vect[kipz]; | |
1332 | hxp[2] = f1*vect[kipy] - f2*vect[kipx]; | |
1333 | ||
1334 | hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz]; | |
1335 | ||
1336 | rho1 = 1./rho; | |
1337 | sint = TMath::Sin(tet); | |
1338 | cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet); | |
1339 | ||
1340 | g1 = sint*rho1; | |
1341 | g2 = cost*rho1; | |
1342 | g3 = (tet-sint) * hp*rho1; | |
1343 | g4 = -cost; | |
1344 | g5 = sint; | |
1345 | g6 = cost * hp; | |
1346 | ||
1347 | vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1; | |
1348 | vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2; | |
1349 | vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3; | |
1350 | ||
1351 | vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1; | |
1352 | vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2; | |
1353 | vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3; | |
1354 | ||
1355 | return; | |
1356 | } | |
8cde4af5 | 1357 | |
c04e3238 | 1358 | //___________________________________________________________ |
690d2205 | 1359 | void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field) |
c04e3238 | 1360 | { |
1361 | /// interface for arguments in double precision (Why ? ChF) | |
1362 | Float_t x[3], b[3]; | |
690d2205 | 1363 | |
c04e3238 | 1364 | x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2]; |
690d2205 | 1365 | |
c04e3238 | 1366 | if (fgkField) fgkField->Field(x,b); |
1367 | else { | |
1368 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
1369 | exit(-1); | |
1370 | } | |
1371 | ||
1372 | Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2]; | |
690d2205 | 1373 | |
c04e3238 | 1374 | return; |
1375 | } |