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AliESDtrack flags update during the TOF matching procedure. Now, (1) when a TPC/TRD...
[u/mrichter/AliRoot.git] / MUON / AliMUONTrackExtrap.cxx
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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 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
387 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
388 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
389 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
390
391 // Set MCS covariance matrix
ea94c18b 392 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 393 // Non bending plane
ea94c18b 394 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
395 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 396 // Bending plane
ea94c18b 397 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
398 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 399 // Inverse bending momentum (due to dependences with bending and non bending slopes)
400 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
401 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
402 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
403 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
404 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
ea94c18b 405
406 // Set new covariances
407 param->SetCovariances(newParamCov);
690d2205 408}
409
410//__________________________________________________________________________
411void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
412 Double_t xVtx, Double_t yVtx, Double_t zVtx,
413 Double_t errXVtx, Double_t errYVtx,
414 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
415{
416 /// Correct parameters and corresponding covariances using Branson correction
417 /// - input param are parameters and covariances at the end of absorber
418 /// - output param are parameters and covariances at vertex
419 /// Absorber correction parameters are supposed to be calculated at the current track z-position
420
421 // Position of the Branson plane (spectro. (z<0))
422 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
423
424 // Add MCS effects to current parameter covariances
425 AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2);
426
427 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
428 ExtrapToZCov(param,zVtx);
3fe6651e 429 LinearExtrapToZCov(param,zB);
690d2205 430
431 // compute track parameters at vertex
432 TMatrixD newParam(5,1);
433 newParam(0,0) = xVtx;
434 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
435 newParam(2,0) = yVtx;
436 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
437 newParam(4,0) = param->GetCharge() / param->P() *
438 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
439 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
440
441 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
442 TMatrixD paramCovP(param->GetCovariances());
443 Cov2CovP(param->GetParameters(),paramCovP);
444
445 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
446 TMatrixD paramCovVtx(5,5);
447 paramCovVtx.Zero();
448 paramCovVtx(0,0) = errXVtx * errXVtx;
449 paramCovVtx(1,1) = paramCovP(0,0);
450 paramCovVtx(2,2) = errYVtx * errYVtx;
451 paramCovVtx(3,3) = paramCovP(2,2);
452 paramCovVtx(4,4) = paramCovP(4,4);
453 paramCovVtx(1,3) = paramCovP(0,2);
454 paramCovVtx(3,1) = paramCovP(2,0);
455 paramCovVtx(1,4) = paramCovP(0,4);
456 paramCovVtx(4,1) = paramCovP(4,0);
457 paramCovVtx(3,4) = paramCovP(2,4);
458 paramCovVtx(4,3) = paramCovP(4,2);
459
460 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
461 TMatrixD jacob(5,5);
462 jacob.UnitMatrix();
463 jacob(1,0) = - 1. / (zB - zVtx);
464 jacob(1,1) = 1. / (zB - zVtx);
465 jacob(3,2) = - 1. / (zB - zVtx);
466 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 467
690d2205 468 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
469 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
470 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
471
472 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
473 CovP2Cov(newParam,newParamCov);
474
475 // Set parameters and covariances at vertex
476 param->SetParameters(newParam);
477 param->SetZ(zVtx);
478 param->SetCovariances(newParamCov);
8cde4af5 479}
480
690d2205 481//__________________________________________________________________________
482void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
483{
484 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
485
486 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
487 TMatrixD newParamCov(param->GetCovariances());
488 Cov2CovP(param->GetParameters(),newParamCov);
489
690d2205 490 // Compute new parameters corrected for energy loss
ecdf58c4 491 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
492 Double_t p = param->P();
493 Double_t e = TMath::Sqrt(p*p + muMass*muMass);
494 Double_t eCorr = e + eLoss;
495 Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
690d2205 496 Double_t nonBendingSlope = param->GetNonBendingSlope();
497 Double_t bendingSlope = param->GetBendingSlope();
ecdf58c4 498 param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
690d2205 499 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
500 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
501
ecdf58c4 502 // Add effects of energy loss fluctuation to covariances
503 newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
504
690d2205 505 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
506 CovP2Cov(param->GetParameters(),newParamCov);
507
508 // Set new parameter covariances
509 param->SetCovariances(newParamCov);
510}
511
512//__________________________________________________________________________
18abc511 513Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
514 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
515 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 516{
517 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 518 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 519 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
520 // f0: 0th moment of z calculated with the inverse radiation-length distribution
521 // f1: 1st moment of z calculated with the inverse radiation-length distribution
522 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
523 // meanRho: average density of crossed material (g/cm3)
84f061ef 524 // totalELoss: total energy loss in absorber
8cde4af5 525
526 // Reset absorber's parameters
527 pathLength = 0.;
528 f0 = 0.;
529 f1 = 0.;
530 f2 = 0.;
531 meanRho = 0.;
84f061ef 532 totalELoss = 0.;
690d2205 533 sigmaELoss2 = 0.;
8cde4af5 534
535 // Check whether the geometry is available
536 if (!gGeoManager) {
537 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 538 return kFALSE;
8cde4af5 539 }
540
541 // Initialize starting point and direction
542 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
543 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
544 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 545 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 546 Double_t b[3];
547 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
548 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
549 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
550 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
551 if (!currentnode) {
552 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 553 return kFALSE;
8cde4af5 554 }
555
556 // loop over absorber slices and calculate absorber's parameters
557 Double_t rho = 0.; // material density (g/cm3)
558 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 559 Double_t atomicA = 0.; // A of material
560 Double_t atomicZ = 0.; // Z of material
8cde4af5 561 Double_t localPathLength = 0;
562 Double_t remainingPathLength = pathLength;
563 Double_t zB = trackXYZIn[2];
564 Double_t zE, dzB, dzE;
565 do {
566 // Get material properties
567 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
568 rho = material->GetDensity();
569 x0 = material->GetRadLen();
570 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
84f061ef 571 atomicA = material->GetA();
572 atomicZ = material->GetZ();
8cde4af5 573
574 // Get path length within this material
575 gGeoManager->FindNextBoundary(remainingPathLength);
576 localPathLength = gGeoManager->GetStep() + 1.e-6;
577 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
578 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
579 else {
580 currentnode = gGeoManager->Step();
581 if (!currentnode) {
582 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 583 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
584 return kFALSE;
8cde4af5 585 }
586 if (!gGeoManager->IsEntering()) {
587 // make another small step to try to enter in new absorber slice
588 gGeoManager->SetStep(0.001);
589 currentnode = gGeoManager->Step();
590 if (!gGeoManager->IsEntering() || !currentnode) {
591 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 592 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
593 return kFALSE;
8cde4af5 594 }
595 localPathLength += 0.001;
596 }
597 }
598
599 // calculate absorber's parameters
600 zE = b[2] * localPathLength + zB;
601 dzB = zB - trackXYZIn[2];
602 dzE = zE - trackXYZIn[2];
603 f0 += localPathLength / x0;
604 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
605 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
606 meanRho += localPathLength * rho;
84f061ef 607 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ);
690d2205 608 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicA, atomicZ);
8cde4af5 609
610 // prepare next step
611 zB = zE;
612 remainingPathLength -= localPathLength;
613 } while (remainingPathLength > TGeoShape::Tolerance());
614
615 meanRho /= pathLength;
18abc511 616
617 return kTRUE;
8cde4af5 618}
619
690d2205 620//__________________________________________________________________________
ea94c18b 621Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
622{
623 /// Return the angular dispersion square due to multiple Coulomb scattering
624 /// through a material of thickness "dZ" and of radiation length "x0"
625 /// assuming linear propagation and using the small angle approximation.
626
627 Double_t bendingSlope = param.GetBendingSlope();
628 Double_t nonBendingSlope = param.GetNonBendingSlope();
629 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 630 (1.0 + bendingSlope * bendingSlope) /
631 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 632 // Path length in the material
633 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
634 // relativistic velocity
635 Double_t velo = 1.;
636 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
637 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
638
639 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
640}
641
690d2205 642//__________________________________________________________________________
8cde4af5 643void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 644{
645 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
646 /// through a material of thickness "dZ" and of radiation length "x0"
647 /// assuming linear propagation and using the small angle approximation.
648
649 Double_t bendingSlope = param->GetBendingSlope();
650 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 651 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
652 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
653 (1.0 + bendingSlope * bendingSlope) /
654 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 655 // Path length in the material
656 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
657 Double_t pathLength2 = pathLength * pathLength;
658 // relativistic velocity
659 Double_t velo = 1.;
660 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
661 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
662 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
663
208f139e 664 Double_t varCoor = pathLength2 * theta02 / 3.;
665 Double_t varSlop = theta02;
666 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 667
ecdf58c4 668 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
690d2205 669 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
670 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
671 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
672
673 // Set MCS covariance matrix
ea94c18b 674 TMatrixD newParamCov(param->GetCovariances());
208f139e 675 // Non bending plane
ea94c18b 676 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
677 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 678 // Bending plane
ea94c18b 679 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
680 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 681 // Inverse bending momentum (due to dependences with bending and non bending slopes)
682 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
683 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
684 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
685 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
686 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
208f139e 687
ea94c18b 688 // Set new covariances
689 param->SetCovariances(newParamCov);
c04e3238 690}
691
690d2205 692//__________________________________________________________________________
693void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
694 Double_t xVtx, Double_t yVtx, Double_t zVtx,
695 Double_t errXVtx, Double_t errYVtx,
696 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 697{
690d2205 698 /// Main method for extrapolation to the vertex:
699 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
700 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
701 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
702 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
703 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
704 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 705
8cde4af5 706 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 707
8cde4af5 708 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 709 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
710 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 711 return;
712 }
713
8cde4af5 714 // Check the vertex position relatively to the absorber
ea94c18b 715 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 716 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 717 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 718 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 719 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 720 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
721 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
722 else ExtrapToZ(trackParam,zVtx);
8cde4af5 723 return;
724 }
725
726 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 727 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 728 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 729 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
730 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
731 else ExtrapToZ(trackParam,zVtx);
8cde4af5 732 return;
ea94c18b 733 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 734 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 735 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 736 } else {
690d2205 737 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
738 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 739 }
c04e3238 740
690d2205 741 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 742 Double_t trackXYZOut[3];
743 trackXYZOut[0] = trackParam->GetNonBendingCoor();
744 trackXYZOut[1] = trackParam->GetBendingCoor();
745 trackXYZOut[2] = trackParam->GetZ();
746 Double_t trackXYZIn[3];
690d2205 747 if (correctForMCS) { // assume linear propagation until the vertex
748 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
749 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
750 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
751 } else {
752 AliMUONTrackParam trackParamIn(*trackParam);
753 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
754 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
755 trackXYZIn[1] = trackParamIn.GetBendingCoor();
756 trackXYZIn[2] = trackParamIn.GetZ();
757 }
84f061ef 758 Double_t pTot = trackParam->P();
ecdf58c4 759 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
760 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
18abc511 761 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
762 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
763 else ExtrapToZ(trackParam,zVtx);
764 return;
765 }
8cde4af5 766
690d2205 767 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
768 if (correctForMCS) {
fac70e25 769
690d2205 770 if (correctForEnergyLoss) {
771
772 // Correct for multiple scattering and energy loss
ecdf58c4 773 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 774 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
775 trackXYZIn[2], pathLength, f0, f1, f2);
ecdf58c4 776 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 777
778 } else {
779
780 // Correct for multiple scattering
781 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
782 trackXYZIn[2], pathLength, f0, f1, f2);
783 }
fac70e25 784
fac70e25 785 } else {
690d2205 786
787 if (correctForEnergyLoss) {
788
18abc511 789 // Correct for energy loss add multiple scattering dispersion in covariance matrix
ecdf58c4 790 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 791 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
792 ExtrapToZCov(trackParam, trackXYZIn[2]);
ecdf58c4 793 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 794 ExtrapToZCov(trackParam, zVtx);
795
796 } else {
797
18abc511 798 // add multiple scattering dispersion in covariance matrix
690d2205 799 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
800 ExtrapToZCov(trackParam, zVtx);
801
802 }
803
fac70e25 804 }
8cde4af5 805
fac70e25 806}
807
690d2205 808//__________________________________________________________________________
809void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
810 Double_t xVtx, Double_t yVtx, Double_t zVtx,
811 Double_t errXVtx, Double_t errYVtx)
812{
813 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
814 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
815 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
816}
817
818//__________________________________________________________________________
819void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
820 Double_t xVtx, Double_t yVtx, Double_t zVtx,
821 Double_t errXVtx, Double_t errYVtx)
822{
823 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
824 /// Add branson correction resolution to parameter covariances
825 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
826}
827
828//__________________________________________________________________________
829void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
830{
831 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
832 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
833 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
834}
835
836//__________________________________________________________________________
837void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
838{
839 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
840 /// Add dispersion due to multiple scattering to parameter covariances
841 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
842}
843
844//__________________________________________________________________________
fac70e25 845Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
846{
847 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
848
849 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 850
fac70e25 851 // Check whether the geometry is available
852 if (!gGeoManager) {
853 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
854 return 0.;
855 }
856
857 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
858 Double_t trackXYZOut[3];
859 trackXYZOut[0] = trackParam->GetNonBendingCoor();
860 trackXYZOut[1] = trackParam->GetBendingCoor();
861 trackXYZOut[2] = trackParam->GetZ();
862 Double_t trackXYZIn[3];
863 trackXYZIn[0] = xVtx;
864 trackXYZIn[1] = yVtx;
865 trackXYZIn[2] = zVtx;
84f061ef 866 Double_t pTot = trackParam->P();
18abc511 867 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 868 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 869
ecdf58c4 870 // total momentum corrected for energy loss
871 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
872 Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
873 Double_t eCorr = e + totalELoss;
874 Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
875
876 return pTotCorr - pTot;
c04e3238 877}
878
690d2205 879//__________________________________________________________________________
84f061ef 880Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
c04e3238 881{
84f061ef 882 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
883 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 884 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
84f061ef 885
ecdf58c4 886 // mean exitation energy (GeV)
887 Double_t i;
888 if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
889 else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
690d2205 890
ecdf58c4 891 return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZ/atomicA);
c04e3238 892}
893
690d2205 894//__________________________________________________________________________
895Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
896{
897 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
898 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 899 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
690d2205 900 //Double_t eMass = 0.510998918e-3; // GeV
901 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
902 Double_t p2=pTotal*pTotal;
903 Double_t beta2=p2/(p2 + muMass*muMass);
904
905 Double_t fwhm = 2. * k * rho * pathLength * atomicZ / atomicA / beta2; // FWHM of the energy loss Landau distribution
906 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
907
908 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
909
910 return sigma2;
911}
912
913//__________________________________________________________________________
914void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
915{
916 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
917 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
918
919 // charge * total momentum
920 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
921 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
922
923 // Jacobian of the opposite transformation
924 TMatrixD jacob(5,5);
925 jacob.UnitMatrix();
926 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
927 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
928 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
929 jacob(4,4) = - qPTot / param(4,0);
930
931 // compute covariances in new coordinate system
932 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
933 cov.Mult(jacob,tmp);
934}
935
936//__________________________________________________________________________
937void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
938{
939 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
940 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
941
942 // charge * total momentum
943 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
944 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
945
946 // Jacobian of the transformation
947 TMatrixD jacob(5,5);
948 jacob.UnitMatrix();
949 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
950 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
951 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
952 jacob(4,4) = - param(4,0) / qPTot;
953
954 // compute covariances in new coordinate system
955 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
956 covP.Mult(jacob,tmp);
957}
958
c04e3238 959 //__________________________________________________________________________
960void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
961{
71a2d3aa 962/// <pre>
c04e3238 963/// ******************************************************************
964/// * *
965/// * Performs the tracking of one step in a magnetic field *
966/// * The trajectory is assumed to be a helix in a constant field *
967/// * taken at the mid point of the step. *
968/// * Parameters: *
969/// * input *
970/// * STEP =arc length of the step asked *
971/// * VECT =input vector (position,direction cos and momentum) *
972/// * CHARGE= electric charge of the particle *
973/// * output *
974/// * VOUT = same as VECT after completion of the step *
975/// * *
2060b217 976/// * ==>Called by : USER, GUSWIM *
c04e3238 977/// * Author m.hansroul ********* *
978/// * modified s.egli, s.v.levonian *
979/// * modified v.perevoztchikov
980/// * *
981/// ******************************************************************
71a2d3aa 982/// </pre>
c04e3238 983
984// modif: everything in double precision
985
986 Double_t xyz[3], h[4], hxp[3];
987 Double_t h2xy, hp, rho, tet;
988 Double_t sint, sintt, tsint, cos1t;
989 Double_t f1, f2, f3, f4, f5, f6;
990
991 const Int_t kix = 0;
992 const Int_t kiy = 1;
993 const Int_t kiz = 2;
994 const Int_t kipx = 3;
995 const Int_t kipy = 4;
996 const Int_t kipz = 5;
997 const Int_t kipp = 6;
998
999 const Double_t kec = 2.9979251e-4;
1000 //
1001 // ------------------------------------------------------------------
1002 //
1003 // units are kgauss,centimeters,gev/c
1004 //
1005 vout[kipp] = vect[kipp];
1006 if (TMath::Abs(charge) < 0.00001) {
1007 for (Int_t i = 0; i < 3; i++) {
1008 vout[i] = vect[i] + step * vect[i+3];
1009 vout[i+3] = vect[i+3];
1010 }
1011 return;
1012 }
1013 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1014 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1015 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1016
1017 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 1018 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 1019
1020 h2xy = h[0]*h[0] + h[1]*h[1];
1021 h[3] = h[2]*h[2]+ h2xy;
1022 if (h[3] < 1.e-12) {
1023 for (Int_t i = 0; i < 3; i++) {
1024 vout[i] = vect[i] + step * vect[i+3];
1025 vout[i+3] = vect[i+3];
1026 }
1027 return;
1028 }
1029 if (h2xy < 1.e-12*h[3]) {
1030 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1031 return;
1032 }
1033 h[3] = TMath::Sqrt(h[3]);
1034 h[0] /= h[3];
1035 h[1] /= h[3];
1036 h[2] /= h[3];
1037 h[3] *= kec;
1038
1039 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1040 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1041 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1042
1043 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1044
1045 rho = -charge*h[3]/vect[kipp];
1046 tet = rho * step;
1047
1048 if (TMath::Abs(tet) > 0.15) {
1049 sint = TMath::Sin(tet);
1050 sintt = (sint/tet);
1051 tsint = (tet-sint)/tet;
1052 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1053 } else {
1054 tsint = tet*tet/36.;
1055 sintt = (1. - tsint);
1056 sint = tet*sintt;
1057 cos1t = 0.5*tet;
1058 }
1059
1060 f1 = step * sintt;
1061 f2 = step * cos1t;
1062 f3 = step * tsint * hp;
1063 f4 = -tet*cos1t;
1064 f5 = sint;
1065 f6 = tet * cos1t * hp;
1066
1067 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1068 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1069 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1070
1071 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1072 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1073 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1074
1075 return;
1076}
1077
1078 //__________________________________________________________________________
1079void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
1080{
71a2d3aa 1081/// <pre>
c04e3238 1082/// ******************************************************************
1083/// * *
1084/// * Tracking routine in a constant field oriented *
1085/// * along axis 3 *
1086/// * Tracking is performed with a conventional *
1087/// * helix step method *
1088/// * *
2060b217 1089/// * ==>Called by : USER, GUSWIM *
c04e3238 1090/// * Authors R.Brun, M.Hansroul ********* *
1091/// * Rewritten V.Perevoztchikov
1092/// * *
1093/// ******************************************************************
71a2d3aa 1094/// </pre>
c04e3238 1095
1096 Double_t hxp[3];
1097 Double_t h4, hp, rho, tet;
1098 Double_t sint, sintt, tsint, cos1t;
1099 Double_t f1, f2, f3, f4, f5, f6;
1100
1101 const Int_t kix = 0;
1102 const Int_t kiy = 1;
1103 const Int_t kiz = 2;
1104 const Int_t kipx = 3;
1105 const Int_t kipy = 4;
1106 const Int_t kipz = 5;
1107 const Int_t kipp = 6;
1108
1109 const Double_t kec = 2.9979251e-4;
1110
1111//
1112// ------------------------------------------------------------------
1113//
1114// units are kgauss,centimeters,gev/c
1115//
1116 vout[kipp] = vect[kipp];
1117 h4 = field * kec;
1118
1119 hxp[0] = - vect[kipy];
1120 hxp[1] = + vect[kipx];
1121
1122 hp = vect[kipz];
1123
1124 rho = -h4/vect[kipp];
1125 tet = rho * step;
1126 if (TMath::Abs(tet) > 0.15) {
1127 sint = TMath::Sin(tet);
1128 sintt = (sint/tet);
1129 tsint = (tet-sint)/tet;
1130 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1131 } else {
1132 tsint = tet*tet/36.;
1133 sintt = (1. - tsint);
1134 sint = tet*sintt;
1135 cos1t = 0.5*tet;
1136 }
1137
1138 f1 = step * sintt;
1139 f2 = step * cos1t;
1140 f3 = step * tsint * hp;
1141 f4 = -tet*cos1t;
1142 f5 = sint;
1143 f6 = tet * cos1t * hp;
1144
1145 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1146 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1147 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1148
1149 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1150 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1151 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1152
1153 return;
1154}
8cde4af5 1155
c04e3238 1156 //__________________________________________________________________________
1157void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
1158{
71a2d3aa 1159/// <pre>
c04e3238 1160/// ******************************************************************
1161/// * *
1162/// * Runge-Kutta method for tracking a particle through a magnetic *
1163/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1164/// * Standards, procedure 25.5.20) *
1165/// * *
1166/// * Input parameters *
1167/// * CHARGE Particle charge *
1168/// * STEP Step size *
1169/// * VECT Initial co-ords,direction cosines,momentum *
1170/// * Output parameters *
1171/// * VOUT Output co-ords,direction cosines,momentum *
1172/// * User routine called *
1173/// * CALL GUFLD(X,F) *
1174/// * *
2060b217 1175/// * ==>Called by : USER, GUSWIM *
c04e3238 1176/// * Authors R.Brun, M.Hansroul ********* *
1177/// * V.Perevoztchikov (CUT STEP implementation) *
1178/// * *
1179/// * *
1180/// ******************************************************************
71a2d3aa 1181/// </pre>
c04e3238 1182
1183 Double_t h2, h4, f[4];
1184 Double_t xyzt[3], a, b, c, ph,ph2;
1185 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1186 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1187 Double_t est, at, bt, ct, cba;
1188 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1189
1190 Double_t x;
1191 Double_t y;
1192 Double_t z;
1193
1194 Double_t xt;
1195 Double_t yt;
1196 Double_t zt;
1197
1198 Double_t maxit = 1992;
1199 Double_t maxcut = 11;
1200
1201 const Double_t kdlt = 1e-4;
1202 const Double_t kdlt32 = kdlt/32.;
1203 const Double_t kthird = 1./3.;
1204 const Double_t khalf = 0.5;
1205 const Double_t kec = 2.9979251e-4;
1206
1207 const Double_t kpisqua = 9.86960440109;
1208 const Int_t kix = 0;
1209 const Int_t kiy = 1;
1210 const Int_t kiz = 2;
1211 const Int_t kipx = 3;
1212 const Int_t kipy = 4;
1213 const Int_t kipz = 5;
1214
1215 // *.
1216 // *. ------------------------------------------------------------------
1217 // *.
1218 // * this constant is for units cm,gev/c and kgauss
1219 // *
1220 Int_t iter = 0;
1221 Int_t ncut = 0;
1222 for(Int_t j = 0; j < 7; j++)
1223 vout[j] = vect[j];
1224
1225 Double_t pinv = kec * charge / vect[6];
1226 Double_t tl = 0.;
1227 Double_t h = step;
1228 Double_t rest;
1229
1230
1231 do {
1232 rest = step - tl;
1233 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1234 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1235 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1236
1237 // *
1238 // * start of integration
1239 // *
1240 x = vout[0];
1241 y = vout[1];
1242 z = vout[2];
1243 a = vout[3];
1244 b = vout[4];
1245 c = vout[5];
1246
1247 h2 = khalf * h;
1248 h4 = khalf * h2;
1249 ph = pinv * h;
1250 ph2 = khalf * ph;
1251 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1252 secys[0] = (c * f[0] - a * f[2]) * ph2;
1253 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1254 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1255 if (ang2 > kpisqua) break;
1256
1257 dxt = h2 * a + h4 * secxs[0];
1258 dyt = h2 * b + h4 * secys[0];
1259 dzt = h2 * c + h4 * seczs[0];
1260 xt = x + dxt;
1261 yt = y + dyt;
1262 zt = z + dzt;
1263 // *
1264 // * second intermediate point
1265 // *
1266
1267 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1268 if (est > h) {
1269 if (ncut++ > maxcut) break;
1270 h *= khalf;
1271 continue;
1272 }
1273
1274 xyzt[0] = xt;
1275 xyzt[1] = yt;
1276 xyzt[2] = zt;
1277
1278 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1279 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1280
1281 at = a + secxs[0];
1282 bt = b + secys[0];
1283 ct = c + seczs[0];
1284
1285 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1286 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1287 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1288 at = a + secxs[1];
1289 bt = b + secys[1];
1290 ct = c + seczs[1];
1291 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1292 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1293 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1294 dxt = h * (a + secxs[2]);
1295 dyt = h * (b + secys[2]);
1296 dzt = h * (c + seczs[2]);
1297 xt = x + dxt;
1298 yt = y + dyt;
1299 zt = z + dzt;
1300 at = a + 2.*secxs[2];
1301 bt = b + 2.*secys[2];
1302 ct = c + 2.*seczs[2];
1303
1304 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1305 if (est > 2.*TMath::Abs(h)) {
1306 if (ncut++ > maxcut) break;
1307 h *= khalf;
1308 continue;
1309 }
1310
1311 xyzt[0] = xt;
1312 xyzt[1] = yt;
1313 xyzt[2] = zt;
1314
1315 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1316 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1317
1318 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1319 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1320 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1321
1322 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1323 secys[3] = (ct*f[0] - at*f[2])* ph2;
1324 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1325 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1326 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1327 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1328
1329 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1330 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1331 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1332
1333 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1334 if (ncut++ > maxcut) break;
1335 h *= khalf;
1336 continue;
1337 }
1338
1339 ncut = 0;
1340 // * if too many iterations, go to helix
1341 if (iter++ > maxit) break;
1342
1343 tl += h;
1344 if (est < kdlt32)
1345 h *= 2.;
1346 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1347 vout[0] = x;
1348 vout[1] = y;
1349 vout[2] = z;
1350 vout[3] = cba*a;
1351 vout[4] = cba*b;
1352 vout[5] = cba*c;
1353 rest = step - tl;
1354 if (step < 0.) rest = -rest;
1355 if (rest < 1.e-5*TMath::Abs(step)) return;
1356
1357 } while(1);
1358
1359 // angle too big, use helix
1360
1361 f1 = f[0];
1362 f2 = f[1];
1363 f3 = f[2];
1364 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1365 rho = -f4*pinv;
1366 tet = rho * step;
1367
1368 hnorm = 1./f4;
1369 f1 = f1*hnorm;
1370 f2 = f2*hnorm;
1371 f3 = f3*hnorm;
1372
1373 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1374 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1375 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1376
1377 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1378
1379 rho1 = 1./rho;
1380 sint = TMath::Sin(tet);
1381 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1382
1383 g1 = sint*rho1;
1384 g2 = cost*rho1;
1385 g3 = (tet-sint) * hp*rho1;
1386 g4 = -cost;
1387 g5 = sint;
1388 g6 = cost * hp;
1389
1390 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1391 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1392 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1393
1394 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1395 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1396 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1397
1398 return;
1399}
8cde4af5 1400