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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"
8cde4af5 28
c04e3238 29#include "AliMagF.h"
8cde4af5 30
8cde4af5 31#include <TMath.h>
8cde4af5 32#include <TGeoManager.h>
c04e3238 33
ea94c18b 34#include <Riostream.h>
35
78649106 36/// \cond CLASSIMP
c04e3238 37ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 38/// \endcond
c04e3238 39
40const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
4284483e 41const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 42const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 43const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
44const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 45
690d2205 46//__________________________________________________________________________
208f139e 47Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
48{
49 /// Returns impact parameter at vertex in bending plane (cm),
50 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
51 /// using simple values for dipole magnetic field.
52 /// The sign of "BendingMomentum" is the sign of the charge.
53
54 if (bendingMomentum == 0.) return 1.e10;
55
9bf6860b 56 const Double_t kCorrectionFactor = 0.9; // impact parameter is 10% overestimated
208f139e 57 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
58 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
9bf6860b 59 Float_t b[3], x[3] = {50.,50.,(Float_t) simpleBPosition};
208f139e 60 if (fgkField) fgkField->Field(x,b);
61 else {
62 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
63 exit(-1);
64 }
65 Double_t simpleBValue = (Double_t) b[0];
66
9bf6860b 67 return kCorrectionFactor * (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum);
208f139e 68}
69
690d2205 70//__________________________________________________________________________
208f139e 71Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
72{
73 /// Returns signed bending momentum in bending plane (GeV/c),
74 /// the sign being the sign of the charge for particles moving forward in Z,
75 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
76 /// using simple values for dipole magnetic field.
77
78 if (impactParam == 0.) return 1.e10;
79
9bf6860b 80 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
208f139e 81 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
82 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
9bf6860b 83 Float_t b[3], x[3] = {50.,50.,(Float_t) simpleBPosition};
208f139e 84 if (fgkField) fgkField->Field(x,b);
85 else {
86 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
87 exit(-1);
88 }
89 Double_t simpleBValue = (Double_t) b[0];
90
9bf6860b 91 return kCorrectionFactor * (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam);
019df241 92}
93
690d2205 94//__________________________________________________________________________
019df241 95void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
96{
97 /// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd".
98 /// On return, results from the extrapolation are updated in trackParam.
99
100 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
101
102 // Compute track parameters
103 Double_t dZ = zEnd - trackParam->GetZ();
104 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
105 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
106 trackParam->SetZ(zEnd);
107
108 // Update track parameters covariances if any
109 if (trackParam->CovariancesExist()) {
110 TMatrixD paramCov(trackParam->GetCovariances());
111 paramCov(0,0) += dZ * dZ * paramCov(1,1) + 2. * dZ * paramCov(0,1);
112 paramCov(0,1) += dZ * paramCov(1,1);
113 paramCov(1,0) = paramCov(0,1);
114 paramCov(2,2) += dZ * dZ * paramCov(3,3) + 2. * dZ * paramCov(2,3);
115 paramCov(2,3) += dZ * paramCov(3,3);
116 paramCov(3,2) = paramCov(2,3);
117 trackParam->SetCovariances(paramCov);
118 }
119
208f139e 120}
c04e3238 121
690d2205 122//__________________________________________________________________________
c04e3238 123void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
124{
4284483e 125 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
126 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
127 if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
128 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
129}
130
690d2205 131//__________________________________________________________________________
4284483e 132void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
133{
134 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 135 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
136 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
137 Double_t forwardBackward; // +1 if forward, -1 if backward
138 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
139 else forwardBackward = -1.0;
dade8580 140 Double_t v3[7], v3New[7]; // 7 in parameter ????
141 Int_t i3, stepNumber;
c04e3238 142 // For safety: return kTRUE or kFALSE ????
143 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 144 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 145 // sign of charge (sign of fInverseBendingMomentum if forward motion)
146 // must be changed if backward extrapolation
208f139e 147 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 148 // Extrapolation loop
149 stepNumber = 0;
208f139e 150 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 151 stepNumber++;
4284483e 152 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 153 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 154 // better use TArray ????
208f139e 155 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 156 }
208f139e 157 // check fgkMaxStepNumber ????
c04e3238 158 // Interpolation back to exact Z (2nd order)
159 // should be in function ???? using TArray ????
dade8580 160 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 161 if (TMath::Abs(dZ12) > 0) {
dade8580 162 Double_t dZ1i = zEnd - v3[2]; // 1-i
163 Double_t dZi2 = v3New[2] - zEnd; // i->2
164 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
165 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
166 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
167 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
168 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
169 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
170 v3[2] = zEnd; // Z
c04e3238 171 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
172 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
173 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 174 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 175 v3[3] = xPrimeI * v3[5]; // PX/PTOT
176 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 177 } else {
4284483e 178 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 179 }
4284483e 180 // Recover track parameters (charge back for forward motion)
dade8580 181 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 182}
183
690d2205 184//__________________________________________________________________________
4284483e 185void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
186{
187 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
188 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
189 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
190 Double_t forwardBackward; // +1 if forward, -1 if backward
191 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
192 else forwardBackward = -1.0;
193 // sign of charge (sign of fInverseBendingMomentum if forward motion)
194 // must be changed if backward extrapolation
195 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
196 Double_t v3[7], v3New[7];
197 Double_t dZ, step;
198 Int_t stepNumber = 0;
199
200 // Extrapolation loop (until within tolerance)
201 Double_t residue = zEnd - trackParam->GetZ();
202 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
203 dZ = zEnd - trackParam->GetZ();
204 // step lenght assuming linear trajectory
205 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 206 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 207 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
208 do { // reduce step lenght while zEnd oversteped
209 if (stepNumber > fgkMaxStepNumber) {
210 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
211 break;
212 }
213 stepNumber ++;
214 step = TMath::Abs(step);
215 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
216 residue = zEnd - v3New[2];
217 step *= dZ/(v3New[2]-trackParam->GetZ());
218 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
219 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
220 }
221
222 // terminate the extropolation with a straight line up to the exact "zEnd" value
223 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
224 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
225 trackParam->SetZ(zEnd);
226}
227
690d2205 228//__________________________________________________________________________
4284483e 229void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 230{
dade8580 231 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 232 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
233 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 234 v3[0] = trackParam->GetNonBendingCoor(); // X
235 v3[1] = trackParam->GetBendingCoor(); // Y
236 v3[2] = trackParam->GetZ(); // Z
c04e3238 237 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
238 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 239 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
240 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
241 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
242 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 243}
244
690d2205 245//__________________________________________________________________________
dade8580 246void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 247{
dade8580 248 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 249 /// assumed to be calculated for forward motion in Z.
250 /// "InverseBendingMomentum" is signed with "charge".
dade8580 251 trackParam->SetNonBendingCoor(v3[0]); // X
252 trackParam->SetBendingCoor(v3[1]); // Y
253 trackParam->SetZ(v3[2]); // Z
254 Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]);
c04e3238 255 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 256 trackParam->SetBendingSlope(v3[4]/v3[5]);
257 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
208f139e 258}
259
690d2205 260//__________________________________________________________________________
ea94c18b 261void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 262{
263 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
264 /// On return, results from the extrapolation are updated in trackParam.
265
266 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
267
ea94c18b 268 // No need to propagate the covariance matrix if it does not exist
269 if (!trackParam->CovariancesExist()) {
270 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
271 // Extrapolate track parameters to "zEnd"
272 ExtrapToZ(trackParam,zEnd);
273 return;
274 }
275
208f139e 276 // Save the actual track parameters
277 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 278 TMatrixD paramSave(trackParamSave.GetParameters());
279 Double_t zBegin = trackParamSave.GetZ();
280
281 // Get reference to the parameter covariance matrix
282 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 283
208f139e 284 // Extrapolate track parameters to "zEnd"
285 ExtrapToZ(trackParam,zEnd);
208f139e 286
ea94c18b 287 // Get reference to the extrapolated parameters
288 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 289
290 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
291 TMatrixD jacob(5,5);
ea94c18b 292 jacob.Zero();
293 TMatrixD dParam(5,1);
208f139e 294 for (Int_t i=0; i<5; i++) {
295 // Skip jacobian calculation for parameters with no associated error
18abc511 296 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 297
208f139e 298 // Small variation of parameter i only
299 for (Int_t j=0; j<5; j++) {
300 if (j==i) {
ea94c18b 301 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
302 if (j == 4) dParam(j,0) *= TMath::Sign(1.,-paramSave(4,0)); // variation always in the same direction
303 } else dParam(j,0) = 0.;
208f139e 304 }
ea94c18b 305
208f139e 306 // Set new parameters
ea94c18b 307 trackParamSave.SetParameters(paramSave);
308 trackParamSave.AddParameters(dParam);
309 trackParamSave.SetZ(zBegin);
310
208f139e 311 // Extrapolate new track parameters to "zEnd"
312 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 313
208f139e 314 // Calculate the jacobian
ea94c18b 315 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
316 jacobji *= 1. / dParam(i,0);
317 jacob.SetSub(0,i,jacobji);
208f139e 318 }
319
320 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 321 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
322 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
323 trackParam->SetCovariances(tmp2);
324
325 // Update the propagator if required
326 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 327}
328
690d2205 329//__________________________________________________________________________
8cde4af5 330void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
331{
332 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
690d2205 333 /// The absorber correction parameters are supposed to be calculated at the current track z-position
8cde4af5 334
335 // absorber related covariance parameters
336 Double_t bendingSlope = param->GetBendingSlope();
337 Double_t nonBendingSlope = param->GetNonBendingSlope();
338 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
339 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 340 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
8cde4af5 341 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
342 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
343 Double_t varSlop = alpha2 * f0;
344
690d2205 345 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
346 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
347 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
348 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
349
350 // Set MCS covariance matrix
ea94c18b 351 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 352 // Non bending plane
ea94c18b 353 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
354 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 355 // Bending plane
ea94c18b 356 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
357 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 358 // Inverse bending momentum (due to dependences with bending and non bending slopes)
359 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
360 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
361 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
362 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
363 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
ea94c18b 364
365 // Set new covariances
366 param->SetCovariances(newParamCov);
690d2205 367}
368
369//__________________________________________________________________________
370void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
371 Double_t xVtx, Double_t yVtx, Double_t zVtx,
372 Double_t errXVtx, Double_t errYVtx,
373 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
374{
375 /// Correct parameters and corresponding covariances using Branson correction
376 /// - input param are parameters and covariances at the end of absorber
377 /// - output param are parameters and covariances at vertex
378 /// Absorber correction parameters are supposed to be calculated at the current track z-position
379
380 // Position of the Branson plane (spectro. (z<0))
381 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
382
383 // Add MCS effects to current parameter covariances
384 AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2);
385
386 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
387 ExtrapToZCov(param,zVtx);
388 LinearExtrapToZ(param,zB);
389
390 // compute track parameters at vertex
391 TMatrixD newParam(5,1);
392 newParam(0,0) = xVtx;
393 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
394 newParam(2,0) = yVtx;
395 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
396 newParam(4,0) = param->GetCharge() / param->P() *
397 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
398 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
399
400 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
401 TMatrixD paramCovP(param->GetCovariances());
402 Cov2CovP(param->GetParameters(),paramCovP);
403
404 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
405 TMatrixD paramCovVtx(5,5);
406 paramCovVtx.Zero();
407 paramCovVtx(0,0) = errXVtx * errXVtx;
408 paramCovVtx(1,1) = paramCovP(0,0);
409 paramCovVtx(2,2) = errYVtx * errYVtx;
410 paramCovVtx(3,3) = paramCovP(2,2);
411 paramCovVtx(4,4) = paramCovP(4,4);
412 paramCovVtx(1,3) = paramCovP(0,2);
413 paramCovVtx(3,1) = paramCovP(2,0);
414 paramCovVtx(1,4) = paramCovP(0,4);
415 paramCovVtx(4,1) = paramCovP(4,0);
416 paramCovVtx(3,4) = paramCovP(2,4);
417 paramCovVtx(4,3) = paramCovP(4,2);
418
419 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
420 TMatrixD jacob(5,5);
421 jacob.UnitMatrix();
422 jacob(1,0) = - 1. / (zB - zVtx);
423 jacob(1,1) = 1. / (zB - zVtx);
424 jacob(3,2) = - 1. / (zB - zVtx);
425 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 426
690d2205 427 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
428 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
429 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
430
431 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
432 CovP2Cov(newParam,newParamCov);
433
434 // Set parameters and covariances at vertex
435 param->SetParameters(newParam);
436 param->SetZ(zVtx);
437 param->SetCovariances(newParamCov);
8cde4af5 438}
439
690d2205 440//__________________________________________________________________________
441void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
442{
443 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
444
445 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
446 TMatrixD newParamCov(param->GetCovariances());
447 Cov2CovP(param->GetParameters(),newParamCov);
448
449 // Add effects of energy loss fluctuation to covariances
450 newParamCov(4,4) += sigmaELoss2;
451
452 // Compute new parameters corrected for energy loss
453 Double_t nonBendingSlope = param->GetNonBendingSlope();
454 Double_t bendingSlope = param->GetBendingSlope();
455 param->SetInverseBendingMomentum(param->GetCharge() / (param->P() + eLoss) *
456 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
457 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
458
459 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
460 CovP2Cov(param->GetParameters(),newParamCov);
461
462 // Set new parameter covariances
463 param->SetCovariances(newParamCov);
464}
465
466//__________________________________________________________________________
18abc511 467Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
468 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
469 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 470{
471 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 472 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 473 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
474 // f0: 0th moment of z calculated with the inverse radiation-length distribution
475 // f1: 1st moment of z calculated with the inverse radiation-length distribution
476 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
477 // meanRho: average density of crossed material (g/cm3)
84f061ef 478 // totalELoss: total energy loss in absorber
8cde4af5 479
480 // Reset absorber's parameters
481 pathLength = 0.;
482 f0 = 0.;
483 f1 = 0.;
484 f2 = 0.;
485 meanRho = 0.;
84f061ef 486 totalELoss = 0.;
690d2205 487 sigmaELoss2 = 0.;
8cde4af5 488
489 // Check whether the geometry is available
490 if (!gGeoManager) {
491 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 492 return kFALSE;
8cde4af5 493 }
494
495 // Initialize starting point and direction
496 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
497 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
498 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 499 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 500 Double_t b[3];
501 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
502 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
503 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
504 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
505 if (!currentnode) {
506 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 507 return kFALSE;
8cde4af5 508 }
509
510 // loop over absorber slices and calculate absorber's parameters
511 Double_t rho = 0.; // material density (g/cm3)
512 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 513 Double_t atomicA = 0.; // A of material
514 Double_t atomicZ = 0.; // Z of material
8cde4af5 515 Double_t localPathLength = 0;
516 Double_t remainingPathLength = pathLength;
517 Double_t zB = trackXYZIn[2];
518 Double_t zE, dzB, dzE;
519 do {
520 // Get material properties
521 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
522 rho = material->GetDensity();
523 x0 = material->GetRadLen();
524 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
84f061ef 525 atomicA = material->GetA();
526 atomicZ = material->GetZ();
8cde4af5 527
528 // Get path length within this material
529 gGeoManager->FindNextBoundary(remainingPathLength);
530 localPathLength = gGeoManager->GetStep() + 1.e-6;
531 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
532 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
533 else {
534 currentnode = gGeoManager->Step();
535 if (!currentnode) {
536 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 537 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
538 return kFALSE;
8cde4af5 539 }
540 if (!gGeoManager->IsEntering()) {
541 // make another small step to try to enter in new absorber slice
542 gGeoManager->SetStep(0.001);
543 currentnode = gGeoManager->Step();
544 if (!gGeoManager->IsEntering() || !currentnode) {
545 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 546 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
547 return kFALSE;
8cde4af5 548 }
549 localPathLength += 0.001;
550 }
551 }
552
553 // calculate absorber's parameters
554 zE = b[2] * localPathLength + zB;
555 dzB = zB - trackXYZIn[2];
556 dzE = zE - trackXYZIn[2];
557 f0 += localPathLength / x0;
558 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
559 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
560 meanRho += localPathLength * rho;
84f061ef 561 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ);
690d2205 562 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicA, atomicZ);
8cde4af5 563
564 // prepare next step
565 zB = zE;
566 remainingPathLength -= localPathLength;
567 } while (remainingPathLength > TGeoShape::Tolerance());
568
569 meanRho /= pathLength;
18abc511 570
571 return kTRUE;
8cde4af5 572}
573
690d2205 574//__________________________________________________________________________
ea94c18b 575Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
576{
577 /// Return the angular dispersion square due to multiple Coulomb scattering
578 /// through a material of thickness "dZ" and of radiation length "x0"
579 /// assuming linear propagation and using the small angle approximation.
580
581 Double_t bendingSlope = param.GetBendingSlope();
582 Double_t nonBendingSlope = param.GetNonBendingSlope();
583 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 584 (1.0 + bendingSlope * bendingSlope) /
585 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 586 // Path length in the material
587 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
588 // relativistic velocity
589 Double_t velo = 1.;
590 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
591 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
592
593 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
594}
595
690d2205 596//__________________________________________________________________________
8cde4af5 597void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 598{
599 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
600 /// through a material of thickness "dZ" and of radiation length "x0"
601 /// assuming linear propagation and using the small angle approximation.
602
603 Double_t bendingSlope = param->GetBendingSlope();
604 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 605 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
606 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
607 (1.0 + bendingSlope * bendingSlope) /
608 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 609 // Path length in the material
610 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
611 Double_t pathLength2 = pathLength * pathLength;
612 // relativistic velocity
613 Double_t velo = 1.;
614 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
615 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
616 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
617
208f139e 618 Double_t varCoor = pathLength2 * theta02 / 3.;
619 Double_t varSlop = theta02;
620 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 621
690d2205 622 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
623 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
624 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
625 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
626
627 // Set MCS covariance matrix
ea94c18b 628 TMatrixD newParamCov(param->GetCovariances());
208f139e 629 // Non bending plane
ea94c18b 630 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
631 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 632 // Bending plane
ea94c18b 633 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
634 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 635 // Inverse bending momentum (due to dependences with bending and non bending slopes)
636 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
637 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
638 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
639 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
640 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
208f139e 641
ea94c18b 642 // Set new covariances
643 param->SetCovariances(newParamCov);
c04e3238 644}
645
690d2205 646//__________________________________________________________________________
647void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
648 Double_t xVtx, Double_t yVtx, Double_t zVtx,
649 Double_t errXVtx, Double_t errYVtx,
650 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 651{
690d2205 652 /// Main method for extrapolation to the vertex:
653 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
654 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
655 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
656 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
657 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
658 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 659
8cde4af5 660 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 661
8cde4af5 662 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 663 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
664 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 665 return;
666 }
667
8cde4af5 668 // Check the vertex position relatively to the absorber
ea94c18b 669 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 670 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 671 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 672 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 673 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 674 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
675 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
676 else ExtrapToZ(trackParam,zVtx);
8cde4af5 677 return;
678 }
679
680 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 681 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 682 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 683 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
684 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
685 else ExtrapToZ(trackParam,zVtx);
8cde4af5 686 return;
ea94c18b 687 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 688 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 689 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 690 } else {
690d2205 691 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
692 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 693 }
c04e3238 694
690d2205 695 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 696 Double_t trackXYZOut[3];
697 trackXYZOut[0] = trackParam->GetNonBendingCoor();
698 trackXYZOut[1] = trackParam->GetBendingCoor();
699 trackXYZOut[2] = trackParam->GetZ();
700 Double_t trackXYZIn[3];
690d2205 701 if (correctForMCS) { // assume linear propagation until the vertex
702 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
703 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
704 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
705 } else {
706 AliMUONTrackParam trackParamIn(*trackParam);
707 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
708 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
709 trackXYZIn[1] = trackParamIn.GetBendingCoor();
710 trackXYZIn[2] = trackParamIn.GetZ();
711 }
84f061ef 712 Double_t pTot = trackParam->P();
18abc511 713 Double_t pathLength, f0, f1, f2, meanRho, deltaP, sigmaDeltaP2;
714 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP,sigmaDeltaP2)) {
715 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
716 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
717 else ExtrapToZ(trackParam,zVtx);
718 return;
719 }
8cde4af5 720
690d2205 721 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
722 if (correctForMCS) {
fac70e25 723
690d2205 724 if (correctForEnergyLoss) {
725
726 // Correct for multiple scattering and energy loss
727 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
728 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
729 trackXYZIn[2], pathLength, f0, f1, f2);
730 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
731
732 } else {
733
734 // Correct for multiple scattering
735 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
736 trackXYZIn[2], pathLength, f0, f1, f2);
737 }
fac70e25 738
fac70e25 739 } else {
690d2205 740
741 if (correctForEnergyLoss) {
742
18abc511 743 // Correct for energy loss add multiple scattering dispersion in covariance matrix
690d2205 744 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
745 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
746 ExtrapToZCov(trackParam, trackXYZIn[2]);
747 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
748 ExtrapToZCov(trackParam, zVtx);
749
750 } else {
751
18abc511 752 // add multiple scattering dispersion in covariance matrix
690d2205 753 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
754 ExtrapToZCov(trackParam, zVtx);
755
756 }
757
fac70e25 758 }
8cde4af5 759
fac70e25 760}
761
690d2205 762//__________________________________________________________________________
763void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
764 Double_t xVtx, Double_t yVtx, Double_t zVtx,
765 Double_t errXVtx, Double_t errYVtx)
766{
767 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
768 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
769 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
770}
771
772//__________________________________________________________________________
773void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
774 Double_t xVtx, Double_t yVtx, Double_t zVtx,
775 Double_t errXVtx, Double_t errYVtx)
776{
777 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
778 /// Add branson correction resolution to parameter covariances
779 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
780}
781
782//__________________________________________________________________________
783void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
784{
785 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
786 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
787 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
788}
789
790//__________________________________________________________________________
791void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
792{
793 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
794 /// Add dispersion due to multiple scattering to parameter covariances
795 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
796}
797
798//__________________________________________________________________________
fac70e25 799Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
800{
801 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
802
803 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 804
fac70e25 805 // Check whether the geometry is available
806 if (!gGeoManager) {
807 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
808 return 0.;
809 }
810
811 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
812 Double_t trackXYZOut[3];
813 trackXYZOut[0] = trackParam->GetNonBendingCoor();
814 trackXYZOut[1] = trackParam->GetBendingCoor();
815 trackXYZOut[2] = trackParam->GetZ();
816 Double_t trackXYZIn[3];
817 trackXYZIn[0] = xVtx;
818 trackXYZIn[1] = yVtx;
819 trackXYZIn[2] = zVtx;
84f061ef 820 Double_t pTot = trackParam->P();
18abc511 821 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 822 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 823
84f061ef 824 return totalELoss;
c04e3238 825}
826
690d2205 827//__________________________________________________________________________
84f061ef 828Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
c04e3238 829{
84f061ef 830 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
831 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
832 Double_t muMass = 0.105658369; // GeV
833 Double_t eMass = 0.510998918e-3; // GeV
834 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
835 Double_t i = 9.5e-9; // mean exitation energy per atomic Z (GeV)
8cde4af5 836 Double_t p2=pTotal*pTotal;
837 Double_t beta2=p2/(p2 + muMass*muMass);
8cde4af5 838
84f061ef 839 Double_t w = k * rho * pathLength * atomicZ / atomicA / beta2;
840
8cde4af5 841 if (beta2/(1-beta2)>3.5*3.5)
690d2205 842 return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2);
843
84f061ef 844 return w * (log(2.*eMass*beta2/(1-beta2)/(i*atomicZ)) - beta2);
c04e3238 845}
846
690d2205 847//__________________________________________________________________________
848Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
849{
850 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
851 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
852 Double_t muMass = 0.105658369; // GeV
853 //Double_t eMass = 0.510998918e-3; // GeV
854 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
855 Double_t p2=pTotal*pTotal;
856 Double_t beta2=p2/(p2 + muMass*muMass);
857
858 Double_t fwhm = 2. * k * rho * pathLength * atomicZ / atomicA / beta2; // FWHM of the energy loss Landau distribution
859 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
860
861 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
862
863 return sigma2;
864}
865
866//__________________________________________________________________________
867void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
868{
869 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
870 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
871
872 // charge * total momentum
873 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
874 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
875
876 // Jacobian of the opposite transformation
877 TMatrixD jacob(5,5);
878 jacob.UnitMatrix();
879 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
880 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
881 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
882 jacob(4,4) = - qPTot / param(4,0);
883
884 // compute covariances in new coordinate system
885 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
886 cov.Mult(jacob,tmp);
887}
888
889//__________________________________________________________________________
890void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
891{
892 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
893 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
894
895 // charge * total momentum
896 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
897 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
898
899 // Jacobian of the transformation
900 TMatrixD jacob(5,5);
901 jacob.UnitMatrix();
902 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
903 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
904 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
905 jacob(4,4) = - param(4,0) / qPTot;
906
907 // compute covariances in new coordinate system
908 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
909 covP.Mult(jacob,tmp);
910}
911
c04e3238 912 //__________________________________________________________________________
913void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
914{
71a2d3aa 915/// <pre>
c04e3238 916/// ******************************************************************
917/// * *
918/// * Performs the tracking of one step in a magnetic field *
919/// * The trajectory is assumed to be a helix in a constant field *
920/// * taken at the mid point of the step. *
921/// * Parameters: *
922/// * input *
923/// * STEP =arc length of the step asked *
924/// * VECT =input vector (position,direction cos and momentum) *
925/// * CHARGE= electric charge of the particle *
926/// * output *
927/// * VOUT = same as VECT after completion of the step *
928/// * *
2060b217 929/// * ==>Called by : USER, GUSWIM *
c04e3238 930/// * Author m.hansroul ********* *
931/// * modified s.egli, s.v.levonian *
932/// * modified v.perevoztchikov
933/// * *
934/// ******************************************************************
71a2d3aa 935/// </pre>
c04e3238 936
937// modif: everything in double precision
938
939 Double_t xyz[3], h[4], hxp[3];
940 Double_t h2xy, hp, rho, tet;
941 Double_t sint, sintt, tsint, cos1t;
942 Double_t f1, f2, f3, f4, f5, f6;
943
944 const Int_t kix = 0;
945 const Int_t kiy = 1;
946 const Int_t kiz = 2;
947 const Int_t kipx = 3;
948 const Int_t kipy = 4;
949 const Int_t kipz = 5;
950 const Int_t kipp = 6;
951
952 const Double_t kec = 2.9979251e-4;
953 //
954 // ------------------------------------------------------------------
955 //
956 // units are kgauss,centimeters,gev/c
957 //
958 vout[kipp] = vect[kipp];
959 if (TMath::Abs(charge) < 0.00001) {
960 for (Int_t i = 0; i < 3; i++) {
961 vout[i] = vect[i] + step * vect[i+3];
962 vout[i+3] = vect[i+3];
963 }
964 return;
965 }
966 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
967 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
968 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
969
970 //cmodif: call gufld (xyz, h) changed into:
971 GetField (xyz, h);
972
973 h2xy = h[0]*h[0] + h[1]*h[1];
974 h[3] = h[2]*h[2]+ h2xy;
975 if (h[3] < 1.e-12) {
976 for (Int_t i = 0; i < 3; i++) {
977 vout[i] = vect[i] + step * vect[i+3];
978 vout[i+3] = vect[i+3];
979 }
980 return;
981 }
982 if (h2xy < 1.e-12*h[3]) {
983 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
984 return;
985 }
986 h[3] = TMath::Sqrt(h[3]);
987 h[0] /= h[3];
988 h[1] /= h[3];
989 h[2] /= h[3];
990 h[3] *= kec;
991
992 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
993 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
994 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
995
996 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
997
998 rho = -charge*h[3]/vect[kipp];
999 tet = rho * step;
1000
1001 if (TMath::Abs(tet) > 0.15) {
1002 sint = TMath::Sin(tet);
1003 sintt = (sint/tet);
1004 tsint = (tet-sint)/tet;
1005 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1006 } else {
1007 tsint = tet*tet/36.;
1008 sintt = (1. - tsint);
1009 sint = tet*sintt;
1010 cos1t = 0.5*tet;
1011 }
1012
1013 f1 = step * sintt;
1014 f2 = step * cos1t;
1015 f3 = step * tsint * hp;
1016 f4 = -tet*cos1t;
1017 f5 = sint;
1018 f6 = tet * cos1t * hp;
1019
1020 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1021 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1022 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1023
1024 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1025 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1026 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1027
1028 return;
1029}
1030
1031 //__________________________________________________________________________
1032void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
1033{
71a2d3aa 1034/// <pre>
c04e3238 1035/// ******************************************************************
1036/// * *
1037/// * Tracking routine in a constant field oriented *
1038/// * along axis 3 *
1039/// * Tracking is performed with a conventional *
1040/// * helix step method *
1041/// * *
2060b217 1042/// * ==>Called by : USER, GUSWIM *
c04e3238 1043/// * Authors R.Brun, M.Hansroul ********* *
1044/// * Rewritten V.Perevoztchikov
1045/// * *
1046/// ******************************************************************
71a2d3aa 1047/// </pre>
c04e3238 1048
1049 Double_t hxp[3];
1050 Double_t h4, hp, rho, tet;
1051 Double_t sint, sintt, tsint, cos1t;
1052 Double_t f1, f2, f3, f4, f5, f6;
1053
1054 const Int_t kix = 0;
1055 const Int_t kiy = 1;
1056 const Int_t kiz = 2;
1057 const Int_t kipx = 3;
1058 const Int_t kipy = 4;
1059 const Int_t kipz = 5;
1060 const Int_t kipp = 6;
1061
1062 const Double_t kec = 2.9979251e-4;
1063
1064//
1065// ------------------------------------------------------------------
1066//
1067// units are kgauss,centimeters,gev/c
1068//
1069 vout[kipp] = vect[kipp];
1070 h4 = field * kec;
1071
1072 hxp[0] = - vect[kipy];
1073 hxp[1] = + vect[kipx];
1074
1075 hp = vect[kipz];
1076
1077 rho = -h4/vect[kipp];
1078 tet = rho * step;
1079 if (TMath::Abs(tet) > 0.15) {
1080 sint = TMath::Sin(tet);
1081 sintt = (sint/tet);
1082 tsint = (tet-sint)/tet;
1083 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1084 } else {
1085 tsint = tet*tet/36.;
1086 sintt = (1. - tsint);
1087 sint = tet*sintt;
1088 cos1t = 0.5*tet;
1089 }
1090
1091 f1 = step * sintt;
1092 f2 = step * cos1t;
1093 f3 = step * tsint * hp;
1094 f4 = -tet*cos1t;
1095 f5 = sint;
1096 f6 = tet * cos1t * hp;
1097
1098 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1099 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1100 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1101
1102 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1103 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1104 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1105
1106 return;
1107}
8cde4af5 1108
c04e3238 1109 //__________________________________________________________________________
1110void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
1111{
71a2d3aa 1112/// <pre>
c04e3238 1113/// ******************************************************************
1114/// * *
1115/// * Runge-Kutta method for tracking a particle through a magnetic *
1116/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1117/// * Standards, procedure 25.5.20) *
1118/// * *
1119/// * Input parameters *
1120/// * CHARGE Particle charge *
1121/// * STEP Step size *
1122/// * VECT Initial co-ords,direction cosines,momentum *
1123/// * Output parameters *
1124/// * VOUT Output co-ords,direction cosines,momentum *
1125/// * User routine called *
1126/// * CALL GUFLD(X,F) *
1127/// * *
2060b217 1128/// * ==>Called by : USER, GUSWIM *
c04e3238 1129/// * Authors R.Brun, M.Hansroul ********* *
1130/// * V.Perevoztchikov (CUT STEP implementation) *
1131/// * *
1132/// * *
1133/// ******************************************************************
71a2d3aa 1134/// </pre>
c04e3238 1135
1136 Double_t h2, h4, f[4];
1137 Double_t xyzt[3], a, b, c, ph,ph2;
1138 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1139 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1140 Double_t est, at, bt, ct, cba;
1141 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1142
1143 Double_t x;
1144 Double_t y;
1145 Double_t z;
1146
1147 Double_t xt;
1148 Double_t yt;
1149 Double_t zt;
1150
1151 Double_t maxit = 1992;
1152 Double_t maxcut = 11;
1153
1154 const Double_t kdlt = 1e-4;
1155 const Double_t kdlt32 = kdlt/32.;
1156 const Double_t kthird = 1./3.;
1157 const Double_t khalf = 0.5;
1158 const Double_t kec = 2.9979251e-4;
1159
1160 const Double_t kpisqua = 9.86960440109;
1161 const Int_t kix = 0;
1162 const Int_t kiy = 1;
1163 const Int_t kiz = 2;
1164 const Int_t kipx = 3;
1165 const Int_t kipy = 4;
1166 const Int_t kipz = 5;
1167
1168 // *.
1169 // *. ------------------------------------------------------------------
1170 // *.
1171 // * this constant is for units cm,gev/c and kgauss
1172 // *
1173 Int_t iter = 0;
1174 Int_t ncut = 0;
1175 for(Int_t j = 0; j < 7; j++)
1176 vout[j] = vect[j];
1177
1178 Double_t pinv = kec * charge / vect[6];
1179 Double_t tl = 0.;
1180 Double_t h = step;
1181 Double_t rest;
1182
1183
1184 do {
1185 rest = step - tl;
1186 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1187 //cmodif: call gufld(vout,f) changed into:
1188
1189 GetField(vout,f);
1190
1191 // *
1192 // * start of integration
1193 // *
1194 x = vout[0];
1195 y = vout[1];
1196 z = vout[2];
1197 a = vout[3];
1198 b = vout[4];
1199 c = vout[5];
1200
1201 h2 = khalf * h;
1202 h4 = khalf * h2;
1203 ph = pinv * h;
1204 ph2 = khalf * ph;
1205 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1206 secys[0] = (c * f[0] - a * f[2]) * ph2;
1207 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1208 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1209 if (ang2 > kpisqua) break;
1210
1211 dxt = h2 * a + h4 * secxs[0];
1212 dyt = h2 * b + h4 * secys[0];
1213 dzt = h2 * c + h4 * seczs[0];
1214 xt = x + dxt;
1215 yt = y + dyt;
1216 zt = z + dzt;
1217 // *
1218 // * second intermediate point
1219 // *
1220
1221 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1222 if (est > h) {
1223 if (ncut++ > maxcut) break;
1224 h *= khalf;
1225 continue;
1226 }
1227
1228 xyzt[0] = xt;
1229 xyzt[1] = yt;
1230 xyzt[2] = zt;
1231
1232 //cmodif: call gufld(xyzt,f) changed into:
1233 GetField(xyzt,f);
1234
1235 at = a + secxs[0];
1236 bt = b + secys[0];
1237 ct = c + seczs[0];
1238
1239 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1240 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1241 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1242 at = a + secxs[1];
1243 bt = b + secys[1];
1244 ct = c + seczs[1];
1245 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1246 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1247 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1248 dxt = h * (a + secxs[2]);
1249 dyt = h * (b + secys[2]);
1250 dzt = h * (c + seczs[2]);
1251 xt = x + dxt;
1252 yt = y + dyt;
1253 zt = z + dzt;
1254 at = a + 2.*secxs[2];
1255 bt = b + 2.*secys[2];
1256 ct = c + 2.*seczs[2];
1257
1258 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1259 if (est > 2.*TMath::Abs(h)) {
1260 if (ncut++ > maxcut) break;
1261 h *= khalf;
1262 continue;
1263 }
1264
1265 xyzt[0] = xt;
1266 xyzt[1] = yt;
1267 xyzt[2] = zt;
1268
1269 //cmodif: call gufld(xyzt,f) changed into:
1270 GetField(xyzt,f);
1271
1272 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1273 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1274 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1275
1276 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1277 secys[3] = (ct*f[0] - at*f[2])* ph2;
1278 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1279 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1280 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1281 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1282
1283 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1284 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1285 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1286
1287 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1288 if (ncut++ > maxcut) break;
1289 h *= khalf;
1290 continue;
1291 }
1292
1293 ncut = 0;
1294 // * if too many iterations, go to helix
1295 if (iter++ > maxit) break;
1296
1297 tl += h;
1298 if (est < kdlt32)
1299 h *= 2.;
1300 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1301 vout[0] = x;
1302 vout[1] = y;
1303 vout[2] = z;
1304 vout[3] = cba*a;
1305 vout[4] = cba*b;
1306 vout[5] = cba*c;
1307 rest = step - tl;
1308 if (step < 0.) rest = -rest;
1309 if (rest < 1.e-5*TMath::Abs(step)) return;
1310
1311 } while(1);
1312
1313 // angle too big, use helix
1314
1315 f1 = f[0];
1316 f2 = f[1];
1317 f3 = f[2];
1318 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1319 rho = -f4*pinv;
1320 tet = rho * step;
1321
1322 hnorm = 1./f4;
1323 f1 = f1*hnorm;
1324 f2 = f2*hnorm;
1325 f3 = f3*hnorm;
1326
1327 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1328 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1329 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1330
1331 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1332
1333 rho1 = 1./rho;
1334 sint = TMath::Sin(tet);
1335 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1336
1337 g1 = sint*rho1;
1338 g2 = cost*rho1;
1339 g3 = (tet-sint) * hp*rho1;
1340 g4 = -cost;
1341 g5 = sint;
1342 g6 = cost * hp;
1343
1344 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1345 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1346 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1347
1348 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1349 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1350 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1351
1352 return;
1353}
8cde4af5 1354
c04e3238 1355//___________________________________________________________
690d2205 1356void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
c04e3238 1357{
1358 /// interface for arguments in double precision (Why ? ChF)
1359 Float_t x[3], b[3];
690d2205 1360
c04e3238 1361 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
690d2205 1362
c04e3238 1363 if (fgkField) fgkField->Field(x,b);
1364 else {
1365 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
1366 exit(-1);
1367 }
1368
1369 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
690d2205 1370
c04e3238 1371 return;
1372}