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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"
8cde4af5 29
ecdf58c4 30#include "AliMagF.h"
31#include "AliExternalTrackParam.h"
8cde4af5 32
f7a1cc68 33#include <TGeoGlobalMagField.h>
8cde4af5 34#include <TGeoManager.h>
f7a1cc68 35#include <TMath.h>
ecdf58c4 36#include <TDatabasePDG.h>
c04e3238 37
ea94c18b 38#include <Riostream.h>
39
78649106 40/// \cond CLASSIMP
c04e3238 41ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 42/// \endcond
c04e3238 43
9f093251 44const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
45const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
46 Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
47 Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
4284483e 48const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 49const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 50const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
51const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 52
9f093251 53//__________________________________________________________________________
f7a1cc68 54void AliMUONTrackExtrap::SetField()
9f093251 55{
cddcc1f3 56 /// set field on/off flag;
57 /// set field at the centre of the dipole
f7a1cc68 58 const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
59 Double_t b[3] = {0.,0.,0.};
60 TGeoGlobalMagField::Instance()->Field(x,b);
61 fgSimpleBValue = b[0];
62 fgFieldON = fgSimpleBValue ? kTRUE : kFALSE;
9f093251 63
64}
65
690d2205 66//__________________________________________________________________________
208f139e 67Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
68{
69 /// Returns impact parameter at vertex in bending plane (cm),
70 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
71 /// using simple values for dipole magnetic field.
72 /// The sign of "BendingMomentum" is the sign of the charge.
73
74 if (bendingMomentum == 0.) return 1.e10;
75
6b191dea 76 const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
9f093251 77
78 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
208f139e 79}
80
690d2205 81//__________________________________________________________________________
9bdbee64 82Double_t
83AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
208f139e 84{
85 /// Returns signed bending momentum in bending plane (GeV/c),
86 /// the sign being the sign of the charge for particles moving forward in Z,
87 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
88 /// using simple values for dipole magnetic field.
89
90 if (impactParam == 0.) return 1.e10;
91
9f093251 92 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
93
9bdbee64 94 if (fgFieldON)
95 {
96 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
97 }
98 else
99 {
100 return AliMUONConstants::GetMostProbBendingMomentum();
101 }
019df241 102}
103
690d2205 104//__________________________________________________________________________
3fe6651e 105void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
019df241 106{
3fe6651e 107 /// Track parameters linearly extrapolated to the plane at "zEnd".
019df241 108 /// On return, results from the extrapolation are updated in trackParam.
109
110 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
111
112 // Compute track parameters
113 Double_t dZ = zEnd - trackParam->GetZ();
114 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
115 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
116 trackParam->SetZ(zEnd);
3fe6651e 117}
118
119//__________________________________________________________________________
120void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
121{
122 /// Track parameters and their covariances linearly extrapolated to the plane at "zEnd".
123 /// On return, results from the extrapolation are updated in trackParam.
019df241 124
3fe6651e 125 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
126
127 // No need to propagate the covariance matrix if it does not exist
128 if (!trackParam->CovariancesExist()) {
129 cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
130 // Extrapolate linearly track parameters to "zEnd"
131 LinearExtrapToZ(trackParam,zEnd);
132 return;
019df241 133 }
134
3fe6651e 135 // Compute track parameters
136 Double_t dZ = zEnd - trackParam->GetZ();
137 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
138 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
139 trackParam->SetZ(zEnd);
140
141 // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
142 TMatrixD jacob(5,5);
143 jacob.UnitMatrix();
144 jacob(0,1) = dZ;
145 jacob(2,3) = dZ;
146
147 // Extrapolate track parameter covariances to "zEnd"
148 TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
149 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
150 trackParam->SetCovariances(tmp2);
151
152 // Update the propagator if required
153 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 154}
c04e3238 155
690d2205 156//__________________________________________________________________________
c04e3238 157void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
158{
4284483e 159 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
160 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
9f093251 161 if (!fgFieldON) AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
162 else if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
4284483e 163 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
164}
165
690d2205 166//__________________________________________________________________________
4284483e 167void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
168{
169 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 170 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
171 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
172 Double_t forwardBackward; // +1 if forward, -1 if backward
173 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
174 else forwardBackward = -1.0;
dade8580 175 Double_t v3[7], v3New[7]; // 7 in parameter ????
176 Int_t i3, stepNumber;
c04e3238 177 // For safety: return kTRUE or kFALSE ????
178 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 179 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 180 // sign of charge (sign of fInverseBendingMomentum if forward motion)
181 // must be changed if backward extrapolation
208f139e 182 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 183 // Extrapolation loop
184 stepNumber = 0;
208f139e 185 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 186 stepNumber++;
4284483e 187 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 188 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 189 // better use TArray ????
208f139e 190 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 191 }
208f139e 192 // check fgkMaxStepNumber ????
c04e3238 193 // Interpolation back to exact Z (2nd order)
194 // should be in function ???? using TArray ????
dade8580 195 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 196 if (TMath::Abs(dZ12) > 0) {
dade8580 197 Double_t dZ1i = zEnd - v3[2]; // 1-i
198 Double_t dZi2 = v3New[2] - zEnd; // i->2
199 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
200 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
201 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
202 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
203 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
204 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
205 v3[2] = zEnd; // Z
c04e3238 206 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
207 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
208 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 209 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 210 v3[3] = xPrimeI * v3[5]; // PX/PTOT
211 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 212 } else {
4284483e 213 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 214 }
4284483e 215 // Recover track parameters (charge back for forward motion)
dade8580 216 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 217}
218
690d2205 219//__________________________________________________________________________
4284483e 220void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
221{
222 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
223 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
224 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
225 Double_t forwardBackward; // +1 if forward, -1 if backward
226 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
227 else forwardBackward = -1.0;
228 // sign of charge (sign of fInverseBendingMomentum if forward motion)
229 // must be changed if backward extrapolation
230 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
231 Double_t v3[7], v3New[7];
232 Double_t dZ, step;
233 Int_t stepNumber = 0;
234
235 // Extrapolation loop (until within tolerance)
236 Double_t residue = zEnd - trackParam->GetZ();
237 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
238 dZ = zEnd - trackParam->GetZ();
239 // step lenght assuming linear trajectory
240 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 241 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 242 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
243 do { // reduce step lenght while zEnd oversteped
244 if (stepNumber > fgkMaxStepNumber) {
245 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
246 break;
247 }
248 stepNumber ++;
249 step = TMath::Abs(step);
250 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
251 residue = zEnd - v3New[2];
252 step *= dZ/(v3New[2]-trackParam->GetZ());
253 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
254 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
255 }
256
257 // terminate the extropolation with a straight line up to the exact "zEnd" value
258 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
259 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
260 trackParam->SetZ(zEnd);
261}
262
690d2205 263//__________________________________________________________________________
4284483e 264void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 265{
dade8580 266 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 267 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
268 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 269 v3[0] = trackParam->GetNonBendingCoor(); // X
270 v3[1] = trackParam->GetBendingCoor(); // Y
271 v3[2] = trackParam->GetZ(); // Z
c04e3238 272 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
273 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 274 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
275 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
276 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
277 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 278}
279
690d2205 280//__________________________________________________________________________
dade8580 281void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 282{
dade8580 283 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 284 /// assumed to be calculated for forward motion in Z.
285 /// "InverseBendingMomentum" is signed with "charge".
dade8580 286 trackParam->SetNonBendingCoor(v3[0]); // X
287 trackParam->SetBendingCoor(v3[1]); // Y
288 trackParam->SetZ(v3[2]); // Z
60e55aee 289 Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
c04e3238 290 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 291 trackParam->SetBendingSlope(v3[4]/v3[5]);
292 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
208f139e 293}
294
690d2205 295//__________________________________________________________________________
ea94c18b 296void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 297{
298 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
299 /// On return, results from the extrapolation are updated in trackParam.
300
301 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
302
9f093251 303 if (!fgFieldON) { // linear extrapolation if no magnetic field
3fe6651e 304 AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
9f093251 305 return;
306 }
307
ea94c18b 308 // No need to propagate the covariance matrix if it does not exist
309 if (!trackParam->CovariancesExist()) {
310 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
311 // Extrapolate track parameters to "zEnd"
312 ExtrapToZ(trackParam,zEnd);
313 return;
314 }
315
208f139e 316 // Save the actual track parameters
317 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 318 TMatrixD paramSave(trackParamSave.GetParameters());
319 Double_t zBegin = trackParamSave.GetZ();
320
321 // Get reference to the parameter covariance matrix
322 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 323
208f139e 324 // Extrapolate track parameters to "zEnd"
325 ExtrapToZ(trackParam,zEnd);
208f139e 326
ea94c18b 327 // Get reference to the extrapolated parameters
328 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 329
330 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
331 TMatrixD jacob(5,5);
ea94c18b 332 jacob.Zero();
333 TMatrixD dParam(5,1);
6b191dea 334 Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
208f139e 335 for (Int_t i=0; i<5; i++) {
336 // Skip jacobian calculation for parameters with no associated error
18abc511 337 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 338
208f139e 339 // Small variation of parameter i only
340 for (Int_t j=0; j<5; j++) {
341 if (j==i) {
ea94c18b 342 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
6b191dea 343 dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
ea94c18b 344 } else dParam(j,0) = 0.;
208f139e 345 }
ea94c18b 346
208f139e 347 // Set new parameters
ea94c18b 348 trackParamSave.SetParameters(paramSave);
349 trackParamSave.AddParameters(dParam);
350 trackParamSave.SetZ(zBegin);
351
208f139e 352 // Extrapolate new track parameters to "zEnd"
353 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 354
208f139e 355 // Calculate the jacobian
ea94c18b 356 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
357 jacobji *= 1. / dParam(i,0);
358 jacob.SetSub(0,i,jacobji);
208f139e 359 }
360
361 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 362 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
363 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
364 trackParam->SetCovariances(tmp2);
365
366 // Update the propagator if required
367 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 368}
369
690d2205 370//__________________________________________________________________________
8cde4af5 371void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
372{
373 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
690d2205 374 /// The absorber correction parameters are supposed to be calculated at the current track z-position
8cde4af5 375
376 // absorber related covariance parameters
377 Double_t bendingSlope = param->GetBendingSlope();
378 Double_t nonBendingSlope = param->GetNonBendingSlope();
379 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
380 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 381 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
8cde4af5 382 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
383 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
384 Double_t varSlop = alpha2 * f0;
385
690d2205 386 // Set MCS covariance matrix
ea94c18b 387 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 388 // Non bending plane
ea94c18b 389 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
390 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 391 // Bending plane
ea94c18b 392 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
393 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 394
395 // Set momentum related covariances if B!=0
396 if (fgFieldON) {
397 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
398 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
399 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
400 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
401 // Inverse bending momentum (due to dependences with bending and non bending slopes)
402 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
403 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
404 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
405 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
406 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
407 }
ea94c18b 408
409 // Set new covariances
410 param->SetCovariances(newParamCov);
690d2205 411}
412
413//__________________________________________________________________________
414void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
415 Double_t xVtx, Double_t yVtx, Double_t zVtx,
416 Double_t errXVtx, Double_t errYVtx,
417 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
418{
419 /// Correct parameters and corresponding covariances using Branson correction
420 /// - input param are parameters and covariances at the end of absorber
421 /// - output param are parameters and covariances at vertex
422 /// Absorber correction parameters are supposed to be calculated at the current track z-position
423
424 // Position of the Branson plane (spectro. (z<0))
425 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
426
427 // Add MCS effects to current parameter covariances
428 AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2);
429
430 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
431 ExtrapToZCov(param,zVtx);
3fe6651e 432 LinearExtrapToZCov(param,zB);
690d2205 433
434 // compute track parameters at vertex
435 TMatrixD newParam(5,1);
436 newParam(0,0) = xVtx;
437 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
438 newParam(2,0) = yVtx;
439 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
440 newParam(4,0) = param->GetCharge() / param->P() *
441 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
442 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
443
444 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
445 TMatrixD paramCovP(param->GetCovariances());
446 Cov2CovP(param->GetParameters(),paramCovP);
447
448 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
449 TMatrixD paramCovVtx(5,5);
450 paramCovVtx.Zero();
451 paramCovVtx(0,0) = errXVtx * errXVtx;
452 paramCovVtx(1,1) = paramCovP(0,0);
453 paramCovVtx(2,2) = errYVtx * errYVtx;
454 paramCovVtx(3,3) = paramCovP(2,2);
455 paramCovVtx(4,4) = paramCovP(4,4);
456 paramCovVtx(1,3) = paramCovP(0,2);
457 paramCovVtx(3,1) = paramCovP(2,0);
458 paramCovVtx(1,4) = paramCovP(0,4);
459 paramCovVtx(4,1) = paramCovP(4,0);
460 paramCovVtx(3,4) = paramCovP(2,4);
461 paramCovVtx(4,3) = paramCovP(4,2);
462
463 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
464 TMatrixD jacob(5,5);
465 jacob.UnitMatrix();
466 jacob(1,0) = - 1. / (zB - zVtx);
467 jacob(1,1) = 1. / (zB - zVtx);
468 jacob(3,2) = - 1. / (zB - zVtx);
469 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 470
690d2205 471 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
472 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
473 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
474
475 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
476 CovP2Cov(newParam,newParamCov);
477
478 // Set parameters and covariances at vertex
479 param->SetParameters(newParam);
480 param->SetZ(zVtx);
481 param->SetCovariances(newParamCov);
8cde4af5 482}
483
690d2205 484//__________________________________________________________________________
485void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
486{
487 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
488
489 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
490 TMatrixD newParamCov(param->GetCovariances());
491 Cov2CovP(param->GetParameters(),newParamCov);
492
690d2205 493 // Compute new parameters corrected for energy loss
ecdf58c4 494 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
495 Double_t p = param->P();
496 Double_t e = TMath::Sqrt(p*p + muMass*muMass);
497 Double_t eCorr = e + eLoss;
498 Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
690d2205 499 Double_t nonBendingSlope = param->GetNonBendingSlope();
500 Double_t bendingSlope = param->GetBendingSlope();
ecdf58c4 501 param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
690d2205 502 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
503 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
504
ecdf58c4 505 // Add effects of energy loss fluctuation to covariances
506 newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
507
690d2205 508 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
509 CovP2Cov(param->GetParameters(),newParamCov);
510
511 // Set new parameter covariances
512 param->SetCovariances(newParamCov);
513}
514
515//__________________________________________________________________________
18abc511 516Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
517 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
518 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 519{
520 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 521 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 522 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
523 // f0: 0th moment of z calculated with the inverse radiation-length distribution
524 // f1: 1st moment of z calculated with the inverse radiation-length distribution
525 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
526 // meanRho: average density of crossed material (g/cm3)
84f061ef 527 // totalELoss: total energy loss in absorber
8cde4af5 528
529 // Reset absorber's parameters
530 pathLength = 0.;
531 f0 = 0.;
532 f1 = 0.;
533 f2 = 0.;
534 meanRho = 0.;
84f061ef 535 totalELoss = 0.;
690d2205 536 sigmaELoss2 = 0.;
8cde4af5 537
538 // Check whether the geometry is available
539 if (!gGeoManager) {
540 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 541 return kFALSE;
8cde4af5 542 }
543
544 // Initialize starting point and direction
545 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
546 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
547 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 548 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 549 Double_t b[3];
550 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
551 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
552 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
553 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
554 if (!currentnode) {
555 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 556 return kFALSE;
8cde4af5 557 }
558
559 // loop over absorber slices and calculate absorber's parameters
560 Double_t rho = 0.; // material density (g/cm3)
561 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 562 Double_t atomicA = 0.; // A of material
563 Double_t atomicZ = 0.; // Z of material
8cde4af5 564 Double_t localPathLength = 0;
565 Double_t remainingPathLength = pathLength;
566 Double_t zB = trackXYZIn[2];
567 Double_t zE, dzB, dzE;
568 do {
569 // Get material properties
570 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
571 rho = material->GetDensity();
572 x0 = material->GetRadLen();
573 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
84f061ef 574 atomicA = material->GetA();
575 atomicZ = material->GetZ();
8cde4af5 576
577 // Get path length within this material
578 gGeoManager->FindNextBoundary(remainingPathLength);
579 localPathLength = gGeoManager->GetStep() + 1.e-6;
580 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
581 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
582 else {
583 currentnode = gGeoManager->Step();
584 if (!currentnode) {
585 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 586 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
587 return kFALSE;
8cde4af5 588 }
589 if (!gGeoManager->IsEntering()) {
590 // make another small step to try to enter in new absorber slice
591 gGeoManager->SetStep(0.001);
592 currentnode = gGeoManager->Step();
593 if (!gGeoManager->IsEntering() || !currentnode) {
594 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 595 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
596 return kFALSE;
8cde4af5 597 }
598 localPathLength += 0.001;
599 }
600 }
601
602 // calculate absorber's parameters
603 zE = b[2] * localPathLength + zB;
604 dzB = zB - trackXYZIn[2];
605 dzE = zE - trackXYZIn[2];
606 f0 += localPathLength / x0;
607 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
608 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
609 meanRho += localPathLength * rho;
84f061ef 610 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ);
690d2205 611 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicA, atomicZ);
8cde4af5 612
613 // prepare next step
614 zB = zE;
615 remainingPathLength -= localPathLength;
616 } while (remainingPathLength > TGeoShape::Tolerance());
617
618 meanRho /= pathLength;
18abc511 619
620 return kTRUE;
8cde4af5 621}
622
690d2205 623//__________________________________________________________________________
ea94c18b 624Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
625{
626 /// Return the angular dispersion square due to multiple Coulomb scattering
627 /// through a material of thickness "dZ" and of radiation length "x0"
628 /// assuming linear propagation and using the small angle approximation.
629
630 Double_t bendingSlope = param.GetBendingSlope();
631 Double_t nonBendingSlope = param.GetNonBendingSlope();
632 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 633 (1.0 + bendingSlope * bendingSlope) /
634 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 635 // Path length in the material
636 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
637 // relativistic velocity
638 Double_t velo = 1.;
639 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
640 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
641
642 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
643}
644
690d2205 645//__________________________________________________________________________
8cde4af5 646void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 647{
648 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
649 /// through a material of thickness "dZ" and of radiation length "x0"
650 /// assuming linear propagation and using the small angle approximation.
651
652 Double_t bendingSlope = param->GetBendingSlope();
653 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 654 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
655 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
656 (1.0 + bendingSlope * bendingSlope) /
657 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 658 // Path length in the material
659 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
660 Double_t pathLength2 = pathLength * pathLength;
661 // relativistic velocity
662 Double_t velo = 1.;
663 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
664 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
665 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
666
208f139e 667 Double_t varCoor = pathLength2 * theta02 / 3.;
668 Double_t varSlop = theta02;
669 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 670
690d2205 671 // Set MCS covariance matrix
ea94c18b 672 TMatrixD newParamCov(param->GetCovariances());
208f139e 673 // Non bending plane
ea94c18b 674 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
675 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 676 // Bending plane
ea94c18b 677 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
678 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 679
680 // Set momentum related covariances if B!=0
681 if (fgFieldON) {
682 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
683 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
684 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
685 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
686 // Inverse bending momentum (due to dependences with bending and non bending slopes)
687 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
688 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
689 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
690 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
691 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
692 }
208f139e 693
ea94c18b 694 // Set new covariances
695 param->SetCovariances(newParamCov);
c04e3238 696}
697
690d2205 698//__________________________________________________________________________
699void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
700 Double_t xVtx, Double_t yVtx, Double_t zVtx,
701 Double_t errXVtx, Double_t errYVtx,
702 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 703{
690d2205 704 /// Main method for extrapolation to the vertex:
705 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
706 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
707 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
708 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
709 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
710 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 711
8cde4af5 712 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 713
8cde4af5 714 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 715 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
716 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 717 return;
718 }
719
8cde4af5 720 // Check the vertex position relatively to the absorber
ea94c18b 721 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 722 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 723 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 724 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 725 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 726 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
727 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
728 else ExtrapToZ(trackParam,zVtx);
8cde4af5 729 return;
730 }
731
732 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 733 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 734 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 735 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
736 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
737 else ExtrapToZ(trackParam,zVtx);
8cde4af5 738 return;
ea94c18b 739 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 740 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 741 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 742 } else {
690d2205 743 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
744 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 745 }
c04e3238 746
690d2205 747 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 748 Double_t trackXYZOut[3];
749 trackXYZOut[0] = trackParam->GetNonBendingCoor();
750 trackXYZOut[1] = trackParam->GetBendingCoor();
751 trackXYZOut[2] = trackParam->GetZ();
752 Double_t trackXYZIn[3];
690d2205 753 if (correctForMCS) { // assume linear propagation until the vertex
754 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
755 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
756 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
757 } else {
758 AliMUONTrackParam trackParamIn(*trackParam);
759 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
760 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
761 trackXYZIn[1] = trackParamIn.GetBendingCoor();
762 trackXYZIn[2] = trackParamIn.GetZ();
763 }
84f061ef 764 Double_t pTot = trackParam->P();
ecdf58c4 765 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
766 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
18abc511 767 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
768 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
769 else ExtrapToZ(trackParam,zVtx);
770 return;
771 }
8cde4af5 772
690d2205 773 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
774 if (correctForMCS) {
fac70e25 775
690d2205 776 if (correctForEnergyLoss) {
777
778 // Correct for multiple scattering and energy loss
ecdf58c4 779 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 780 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
781 trackXYZIn[2], pathLength, f0, f1, f2);
ecdf58c4 782 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 783
784 } else {
785
786 // Correct for multiple scattering
787 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
788 trackXYZIn[2], pathLength, f0, f1, f2);
789 }
fac70e25 790
fac70e25 791 } else {
690d2205 792
793 if (correctForEnergyLoss) {
794
18abc511 795 // Correct for energy loss add multiple scattering dispersion in covariance matrix
ecdf58c4 796 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 797 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
798 ExtrapToZCov(trackParam, trackXYZIn[2]);
ecdf58c4 799 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 800 ExtrapToZCov(trackParam, zVtx);
801
802 } else {
803
18abc511 804 // add multiple scattering dispersion in covariance matrix
690d2205 805 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
806 ExtrapToZCov(trackParam, zVtx);
807
808 }
809
fac70e25 810 }
8cde4af5 811
fac70e25 812}
813
690d2205 814//__________________________________________________________________________
815void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
816 Double_t xVtx, Double_t yVtx, Double_t zVtx,
817 Double_t errXVtx, Double_t errYVtx)
818{
819 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
820 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
821 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
822}
823
824//__________________________________________________________________________
825void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
826 Double_t xVtx, Double_t yVtx, Double_t zVtx,
827 Double_t errXVtx, Double_t errYVtx)
828{
829 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
830 /// Add branson correction resolution to parameter covariances
831 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
832}
833
834//__________________________________________________________________________
835void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
836{
837 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
838 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
839 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
840}
841
842//__________________________________________________________________________
843void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
844{
845 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
846 /// Add dispersion due to multiple scattering to parameter covariances
847 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
848}
849
850//__________________________________________________________________________
fac70e25 851Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
852{
853 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
854
855 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 856
fac70e25 857 // Check whether the geometry is available
858 if (!gGeoManager) {
859 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
860 return 0.;
861 }
862
863 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
864 Double_t trackXYZOut[3];
865 trackXYZOut[0] = trackParam->GetNonBendingCoor();
866 trackXYZOut[1] = trackParam->GetBendingCoor();
867 trackXYZOut[2] = trackParam->GetZ();
868 Double_t trackXYZIn[3];
869 trackXYZIn[0] = xVtx;
870 trackXYZIn[1] = yVtx;
871 trackXYZIn[2] = zVtx;
84f061ef 872 Double_t pTot = trackParam->P();
18abc511 873 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 874 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 875
ecdf58c4 876 // total momentum corrected for energy loss
877 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
878 Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
879 Double_t eCorr = e + totalELoss;
880 Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
881
882 return pTotCorr - pTot;
c04e3238 883}
884
690d2205 885//__________________________________________________________________________
84f061ef 886Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
c04e3238 887{
84f061ef 888 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
889 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 890 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
84f061ef 891
ecdf58c4 892 // mean exitation energy (GeV)
893 Double_t i;
894 if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
895 else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
690d2205 896
ecdf58c4 897 return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZ/atomicA);
c04e3238 898}
899
690d2205 900//__________________________________________________________________________
901Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
902{
903 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
904 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 905 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
690d2205 906 //Double_t eMass = 0.510998918e-3; // GeV
907 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
908 Double_t p2=pTotal*pTotal;
909 Double_t beta2=p2/(p2 + muMass*muMass);
910
911 Double_t fwhm = 2. * k * rho * pathLength * atomicZ / atomicA / beta2; // FWHM of the energy loss Landau distribution
912 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
913
914 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
915
916 return sigma2;
917}
918
919//__________________________________________________________________________
920void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
921{
922 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
923 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
924
925 // charge * total momentum
926 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
927 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
928
929 // Jacobian of the opposite transformation
930 TMatrixD jacob(5,5);
931 jacob.UnitMatrix();
932 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
933 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
934 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
935 jacob(4,4) = - qPTot / param(4,0);
936
937 // compute covariances in new coordinate system
938 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
939 cov.Mult(jacob,tmp);
940}
941
942//__________________________________________________________________________
943void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
944{
945 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
946 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
947
948 // charge * total momentum
949 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
950 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
951
952 // Jacobian of the transformation
953 TMatrixD jacob(5,5);
954 jacob.UnitMatrix();
955 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
956 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
957 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
958 jacob(4,4) = - param(4,0) / qPTot;
959
960 // compute covariances in new coordinate system
961 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
962 covP.Mult(jacob,tmp);
963}
964
c04e3238 965 //__________________________________________________________________________
966void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
967{
71a2d3aa 968/// <pre>
c04e3238 969/// ******************************************************************
970/// * *
971/// * Performs the tracking of one step in a magnetic field *
972/// * The trajectory is assumed to be a helix in a constant field *
973/// * taken at the mid point of the step. *
974/// * Parameters: *
975/// * input *
976/// * STEP =arc length of the step asked *
977/// * VECT =input vector (position,direction cos and momentum) *
978/// * CHARGE= electric charge of the particle *
979/// * output *
980/// * VOUT = same as VECT after completion of the step *
981/// * *
2060b217 982/// * ==>Called by : USER, GUSWIM *
c04e3238 983/// * Author m.hansroul ********* *
984/// * modified s.egli, s.v.levonian *
985/// * modified v.perevoztchikov
986/// * *
987/// ******************************************************************
71a2d3aa 988/// </pre>
c04e3238 989
990// modif: everything in double precision
991
992 Double_t xyz[3], h[4], hxp[3];
993 Double_t h2xy, hp, rho, tet;
994 Double_t sint, sintt, tsint, cos1t;
995 Double_t f1, f2, f3, f4, f5, f6;
996
997 const Int_t kix = 0;
998 const Int_t kiy = 1;
999 const Int_t kiz = 2;
1000 const Int_t kipx = 3;
1001 const Int_t kipy = 4;
1002 const Int_t kipz = 5;
1003 const Int_t kipp = 6;
1004
1005 const Double_t kec = 2.9979251e-4;
1006 //
1007 // ------------------------------------------------------------------
1008 //
1009 // units are kgauss,centimeters,gev/c
1010 //
1011 vout[kipp] = vect[kipp];
1012 if (TMath::Abs(charge) < 0.00001) {
1013 for (Int_t i = 0; i < 3; i++) {
1014 vout[i] = vect[i] + step * vect[i+3];
1015 vout[i+3] = vect[i+3];
1016 }
1017 return;
1018 }
1019 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1020 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1021 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1022
1023 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 1024 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 1025
1026 h2xy = h[0]*h[0] + h[1]*h[1];
1027 h[3] = h[2]*h[2]+ h2xy;
1028 if (h[3] < 1.e-12) {
1029 for (Int_t i = 0; i < 3; i++) {
1030 vout[i] = vect[i] + step * vect[i+3];
1031 vout[i+3] = vect[i+3];
1032 }
1033 return;
1034 }
1035 if (h2xy < 1.e-12*h[3]) {
1036 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1037 return;
1038 }
1039 h[3] = TMath::Sqrt(h[3]);
1040 h[0] /= h[3];
1041 h[1] /= h[3];
1042 h[2] /= h[3];
1043 h[3] *= kec;
1044
1045 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1046 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1047 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1048
1049 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1050
1051 rho = -charge*h[3]/vect[kipp];
1052 tet = rho * step;
1053
1054 if (TMath::Abs(tet) > 0.15) {
1055 sint = TMath::Sin(tet);
1056 sintt = (sint/tet);
1057 tsint = (tet-sint)/tet;
1058 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1059 } else {
1060 tsint = tet*tet/36.;
1061 sintt = (1. - tsint);
1062 sint = tet*sintt;
1063 cos1t = 0.5*tet;
1064 }
1065
1066 f1 = step * sintt;
1067 f2 = step * cos1t;
1068 f3 = step * tsint * hp;
1069 f4 = -tet*cos1t;
1070 f5 = sint;
1071 f6 = tet * cos1t * hp;
1072
1073 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1074 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1075 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1076
1077 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1078 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1079 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1080
1081 return;
1082}
1083
1084 //__________________________________________________________________________
1085void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
1086{
71a2d3aa 1087/// <pre>
c04e3238 1088/// ******************************************************************
1089/// * *
1090/// * Tracking routine in a constant field oriented *
1091/// * along axis 3 *
1092/// * Tracking is performed with a conventional *
1093/// * helix step method *
1094/// * *
2060b217 1095/// * ==>Called by : USER, GUSWIM *
c04e3238 1096/// * Authors R.Brun, M.Hansroul ********* *
1097/// * Rewritten V.Perevoztchikov
1098/// * *
1099/// ******************************************************************
71a2d3aa 1100/// </pre>
c04e3238 1101
1102 Double_t hxp[3];
1103 Double_t h4, hp, rho, tet;
1104 Double_t sint, sintt, tsint, cos1t;
1105 Double_t f1, f2, f3, f4, f5, f6;
1106
1107 const Int_t kix = 0;
1108 const Int_t kiy = 1;
1109 const Int_t kiz = 2;
1110 const Int_t kipx = 3;
1111 const Int_t kipy = 4;
1112 const Int_t kipz = 5;
1113 const Int_t kipp = 6;
1114
1115 const Double_t kec = 2.9979251e-4;
1116
1117//
1118// ------------------------------------------------------------------
1119//
1120// units are kgauss,centimeters,gev/c
1121//
1122 vout[kipp] = vect[kipp];
1123 h4 = field * kec;
1124
1125 hxp[0] = - vect[kipy];
1126 hxp[1] = + vect[kipx];
1127
1128 hp = vect[kipz];
1129
1130 rho = -h4/vect[kipp];
1131 tet = rho * step;
1132 if (TMath::Abs(tet) > 0.15) {
1133 sint = TMath::Sin(tet);
1134 sintt = (sint/tet);
1135 tsint = (tet-sint)/tet;
1136 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1137 } else {
1138 tsint = tet*tet/36.;
1139 sintt = (1. - tsint);
1140 sint = tet*sintt;
1141 cos1t = 0.5*tet;
1142 }
1143
1144 f1 = step * sintt;
1145 f2 = step * cos1t;
1146 f3 = step * tsint * hp;
1147 f4 = -tet*cos1t;
1148 f5 = sint;
1149 f6 = tet * cos1t * hp;
1150
1151 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1152 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1153 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1154
1155 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1156 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1157 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1158
1159 return;
1160}
8cde4af5 1161
c04e3238 1162 //__________________________________________________________________________
1163void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
1164{
71a2d3aa 1165/// <pre>
c04e3238 1166/// ******************************************************************
1167/// * *
1168/// * Runge-Kutta method for tracking a particle through a magnetic *
1169/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1170/// * Standards, procedure 25.5.20) *
1171/// * *
1172/// * Input parameters *
1173/// * CHARGE Particle charge *
1174/// * STEP Step size *
1175/// * VECT Initial co-ords,direction cosines,momentum *
1176/// * Output parameters *
1177/// * VOUT Output co-ords,direction cosines,momentum *
1178/// * User routine called *
1179/// * CALL GUFLD(X,F) *
1180/// * *
2060b217 1181/// * ==>Called by : USER, GUSWIM *
c04e3238 1182/// * Authors R.Brun, M.Hansroul ********* *
1183/// * V.Perevoztchikov (CUT STEP implementation) *
1184/// * *
1185/// * *
1186/// ******************************************************************
71a2d3aa 1187/// </pre>
c04e3238 1188
1189 Double_t h2, h4, f[4];
1190 Double_t xyzt[3], a, b, c, ph,ph2;
1191 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1192 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1193 Double_t est, at, bt, ct, cba;
1194 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1195
1196 Double_t x;
1197 Double_t y;
1198 Double_t z;
1199
1200 Double_t xt;
1201 Double_t yt;
1202 Double_t zt;
1203
1204 Double_t maxit = 1992;
1205 Double_t maxcut = 11;
1206
1207 const Double_t kdlt = 1e-4;
1208 const Double_t kdlt32 = kdlt/32.;
1209 const Double_t kthird = 1./3.;
1210 const Double_t khalf = 0.5;
1211 const Double_t kec = 2.9979251e-4;
1212
1213 const Double_t kpisqua = 9.86960440109;
1214 const Int_t kix = 0;
1215 const Int_t kiy = 1;
1216 const Int_t kiz = 2;
1217 const Int_t kipx = 3;
1218 const Int_t kipy = 4;
1219 const Int_t kipz = 5;
1220
1221 // *.
1222 // *. ------------------------------------------------------------------
1223 // *.
1224 // * this constant is for units cm,gev/c and kgauss
1225 // *
1226 Int_t iter = 0;
1227 Int_t ncut = 0;
1228 for(Int_t j = 0; j < 7; j++)
1229 vout[j] = vect[j];
1230
1231 Double_t pinv = kec * charge / vect[6];
1232 Double_t tl = 0.;
1233 Double_t h = step;
1234 Double_t rest;
1235
1236
1237 do {
1238 rest = step - tl;
1239 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1240 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1241 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1242
1243 // *
1244 // * start of integration
1245 // *
1246 x = vout[0];
1247 y = vout[1];
1248 z = vout[2];
1249 a = vout[3];
1250 b = vout[4];
1251 c = vout[5];
1252
1253 h2 = khalf * h;
1254 h4 = khalf * h2;
1255 ph = pinv * h;
1256 ph2 = khalf * ph;
1257 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1258 secys[0] = (c * f[0] - a * f[2]) * ph2;
1259 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1260 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1261 if (ang2 > kpisqua) break;
1262
1263 dxt = h2 * a + h4 * secxs[0];
1264 dyt = h2 * b + h4 * secys[0];
1265 dzt = h2 * c + h4 * seczs[0];
1266 xt = x + dxt;
1267 yt = y + dyt;
1268 zt = z + dzt;
1269 // *
1270 // * second intermediate point
1271 // *
1272
1273 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1274 if (est > h) {
1275 if (ncut++ > maxcut) break;
1276 h *= khalf;
1277 continue;
1278 }
1279
1280 xyzt[0] = xt;
1281 xyzt[1] = yt;
1282 xyzt[2] = zt;
1283
1284 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1285 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1286
1287 at = a + secxs[0];
1288 bt = b + secys[0];
1289 ct = c + seczs[0];
1290
1291 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1292 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1293 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1294 at = a + secxs[1];
1295 bt = b + secys[1];
1296 ct = c + seczs[1];
1297 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1298 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1299 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1300 dxt = h * (a + secxs[2]);
1301 dyt = h * (b + secys[2]);
1302 dzt = h * (c + seczs[2]);
1303 xt = x + dxt;
1304 yt = y + dyt;
1305 zt = z + dzt;
1306 at = a + 2.*secxs[2];
1307 bt = b + 2.*secys[2];
1308 ct = c + 2.*seczs[2];
1309
1310 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1311 if (est > 2.*TMath::Abs(h)) {
1312 if (ncut++ > maxcut) break;
1313 h *= khalf;
1314 continue;
1315 }
1316
1317 xyzt[0] = xt;
1318 xyzt[1] = yt;
1319 xyzt[2] = zt;
1320
1321 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1322 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1323
1324 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1325 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1326 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1327
1328 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1329 secys[3] = (ct*f[0] - at*f[2])* ph2;
1330 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1331 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1332 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1333 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1334
1335 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1336 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1337 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1338
1339 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1340 if (ncut++ > maxcut) break;
1341 h *= khalf;
1342 continue;
1343 }
1344
1345 ncut = 0;
1346 // * if too many iterations, go to helix
1347 if (iter++ > maxit) break;
1348
1349 tl += h;
1350 if (est < kdlt32)
1351 h *= 2.;
1352 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1353 vout[0] = x;
1354 vout[1] = y;
1355 vout[2] = z;
1356 vout[3] = cba*a;
1357 vout[4] = cba*b;
1358 vout[5] = cba*c;
1359 rest = step - tl;
1360 if (step < 0.) rest = -rest;
1361 if (rest < 1.e-5*TMath::Abs(step)) return;
1362
1363 } while(1);
1364
1365 // angle too big, use helix
1366
1367 f1 = f[0];
1368 f2 = f[1];
1369 f3 = f[2];
1370 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1371 rho = -f4*pinv;
1372 tet = rho * step;
1373
1374 hnorm = 1./f4;
1375 f1 = f1*hnorm;
1376 f2 = f2*hnorm;
1377 f3 = f3*hnorm;
1378
1379 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1380 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1381 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1382
1383 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1384
1385 rho1 = 1./rho;
1386 sint = TMath::Sin(tet);
1387 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1388
1389 g1 = sint*rho1;
1390 g2 = cost*rho1;
1391 g3 = (tet-sint) * hp*rho1;
1392 g4 = -cost;
1393 g5 = sint;
1394 g6 = cost * hp;
1395
1396 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1397 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1398 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1399
1400 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1401 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1402 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1403
1404 return;
1405}
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