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Restoring backward compatibility of the SSD calibration objects + output of the SSD...
[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"
29#include "AliMUONRecoParam.h"
8cde4af5 30
c04e3238 31#include "AliMagF.h"
8cde4af5 32
8cde4af5 33#include <TMath.h>
8cde4af5 34#include <TGeoManager.h>
c04e3238 35
ea94c18b 36#include <Riostream.h>
37
78649106 38/// \cond CLASSIMP
c04e3238 39ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 40/// \endcond
c04e3238 41
42const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
9f093251 43const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
44const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
45 Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
46 Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
4284483e 47const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 48const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 49const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
50const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 51
9f093251 52//__________________________________________________________________________
53void AliMUONTrackExtrap::SetField(const AliMagF* magField)
54{
55 /// set magnetic field
56
57 // set field map
58 fgkField = magField;
59 if (!fgkField) {
60 cout<<"E-AliMUONTrackExtrap::SetField: fgkField = 0x0"<<endl;
61 return;
62 }
63
64 // set field on/off flag
65 fgFieldON = (fgkField->Factor() == 0.) ? kFALSE : kTRUE;
66
67 // set field at the centre of the dipole
68 if (fgFieldON) {
69 Float_t b[3] = {0.,0.,0.}, x[3] = {50.,50.,(Float_t) fgkSimpleBPosition};
70 fgkField->Field(x,b);
71 fgSimpleBValue = (Double_t) b[0];
72 } else fgSimpleBValue = 0.;
73
74}
75
690d2205 76//__________________________________________________________________________
208f139e 77Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
78{
79 /// Returns impact parameter at vertex in bending plane (cm),
80 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
81 /// using simple values for dipole magnetic field.
82 /// The sign of "BendingMomentum" is the sign of the charge.
83
84 if (bendingMomentum == 0.) return 1.e10;
85
9f093251 86 if (!fgkField) {
208f139e 87 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
88 exit(-1);
89 }
208f139e 90
9f093251 91 const Double_t kCorrectionFactor = 0.9; // impact parameter is 10% overestimated
92
93 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
208f139e 94}
95
690d2205 96//__________________________________________________________________________
9bdbee64 97Double_t
98AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
208f139e 99{
100 /// Returns signed bending momentum in bending plane (GeV/c),
101 /// the sign being the sign of the charge for particles moving forward in Z,
102 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
103 /// using simple values for dipole magnetic field.
104
105 if (impactParam == 0.) return 1.e10;
106
9f093251 107 if (!fgkField) {
208f139e 108 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
109 exit(-1);
110 }
208f139e 111
9f093251 112 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
113
9bdbee64 114 if (fgFieldON)
115 {
116 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
117 }
118 else
119 {
120 return AliMUONConstants::GetMostProbBendingMomentum();
121 }
019df241 122}
123
690d2205 124//__________________________________________________________________________
9f093251 125void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
019df241 126{
127 /// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd".
128 /// On return, results from the extrapolation are updated in trackParam.
129
130 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
131
132 // Compute track parameters
133 Double_t dZ = zEnd - trackParam->GetZ();
134 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
135 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
136 trackParam->SetZ(zEnd);
137
138 // Update track parameters covariances if any
139 if (trackParam->CovariancesExist()) {
140 TMatrixD paramCov(trackParam->GetCovariances());
141 paramCov(0,0) += dZ * dZ * paramCov(1,1) + 2. * dZ * paramCov(0,1);
142 paramCov(0,1) += dZ * paramCov(1,1);
143 paramCov(1,0) = paramCov(0,1);
144 paramCov(2,2) += dZ * dZ * paramCov(3,3) + 2. * dZ * paramCov(2,3);
145 paramCov(2,3) += dZ * paramCov(3,3);
146 paramCov(3,2) = paramCov(2,3);
147 trackParam->SetCovariances(paramCov);
9f093251 148
149 // Update the propagator if required
150 if (updatePropagator) {
151 TMatrixD jacob(5,5);
152 jacob.UnitMatrix();
153 jacob(0,1) = dZ;
154 jacob(2,3) = dZ;
155 trackParam->UpdatePropagator(jacob);
156 }
157
019df241 158 }
159
208f139e 160}
c04e3238 161
690d2205 162//__________________________________________________________________________
c04e3238 163void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
164{
4284483e 165 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
166 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
9f093251 167 if (!fgFieldON) AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
168 else if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
4284483e 169 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
170}
171
690d2205 172//__________________________________________________________________________
4284483e 173void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
174{
175 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 176 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
177 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
178 Double_t forwardBackward; // +1 if forward, -1 if backward
179 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
180 else forwardBackward = -1.0;
dade8580 181 Double_t v3[7], v3New[7]; // 7 in parameter ????
182 Int_t i3, stepNumber;
c04e3238 183 // For safety: return kTRUE or kFALSE ????
184 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 185 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 186 // sign of charge (sign of fInverseBendingMomentum if forward motion)
187 // must be changed if backward extrapolation
208f139e 188 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 189 // Extrapolation loop
190 stepNumber = 0;
208f139e 191 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 192 stepNumber++;
4284483e 193 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 194 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 195 // better use TArray ????
208f139e 196 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 197 }
208f139e 198 // check fgkMaxStepNumber ????
c04e3238 199 // Interpolation back to exact Z (2nd order)
200 // should be in function ???? using TArray ????
dade8580 201 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 202 if (TMath::Abs(dZ12) > 0) {
dade8580 203 Double_t dZ1i = zEnd - v3[2]; // 1-i
204 Double_t dZi2 = v3New[2] - zEnd; // i->2
205 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
206 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
207 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
208 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
209 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
210 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
211 v3[2] = zEnd; // Z
c04e3238 212 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
213 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
214 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 215 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 216 v3[3] = xPrimeI * v3[5]; // PX/PTOT
217 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 218 } else {
4284483e 219 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 220 }
4284483e 221 // Recover track parameters (charge back for forward motion)
dade8580 222 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 223}
224
690d2205 225//__________________________________________________________________________
4284483e 226void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
227{
228 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
229 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
230 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
231 Double_t forwardBackward; // +1 if forward, -1 if backward
232 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
233 else forwardBackward = -1.0;
234 // sign of charge (sign of fInverseBendingMomentum if forward motion)
235 // must be changed if backward extrapolation
236 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
237 Double_t v3[7], v3New[7];
238 Double_t dZ, step;
239 Int_t stepNumber = 0;
240
241 // Extrapolation loop (until within tolerance)
242 Double_t residue = zEnd - trackParam->GetZ();
243 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
244 dZ = zEnd - trackParam->GetZ();
245 // step lenght assuming linear trajectory
246 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 247 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 248 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
249 do { // reduce step lenght while zEnd oversteped
250 if (stepNumber > fgkMaxStepNumber) {
251 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
252 break;
253 }
254 stepNumber ++;
255 step = TMath::Abs(step);
256 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
257 residue = zEnd - v3New[2];
258 step *= dZ/(v3New[2]-trackParam->GetZ());
259 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
260 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
261 }
262
263 // terminate the extropolation with a straight line up to the exact "zEnd" value
264 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
265 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
266 trackParam->SetZ(zEnd);
267}
268
690d2205 269//__________________________________________________________________________
4284483e 270void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 271{
dade8580 272 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 273 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
274 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 275 v3[0] = trackParam->GetNonBendingCoor(); // X
276 v3[1] = trackParam->GetBendingCoor(); // Y
277 v3[2] = trackParam->GetZ(); // Z
c04e3238 278 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
279 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 280 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
281 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
282 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
283 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 284}
285
690d2205 286//__________________________________________________________________________
dade8580 287void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 288{
dade8580 289 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 290 /// assumed to be calculated for forward motion in Z.
291 /// "InverseBendingMomentum" is signed with "charge".
dade8580 292 trackParam->SetNonBendingCoor(v3[0]); // X
293 trackParam->SetBendingCoor(v3[1]); // Y
294 trackParam->SetZ(v3[2]); // Z
295 Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]);
c04e3238 296 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 297 trackParam->SetBendingSlope(v3[4]/v3[5]);
298 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
208f139e 299}
300
690d2205 301//__________________________________________________________________________
ea94c18b 302void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 303{
304 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
305 /// On return, results from the extrapolation are updated in trackParam.
306
307 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
308
9f093251 309 if (!fgFieldON) { // linear extrapolation if no magnetic field
310 AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd,updatePropagator);
311 return;
312 }
313
ea94c18b 314 // No need to propagate the covariance matrix if it does not exist
315 if (!trackParam->CovariancesExist()) {
316 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
317 // Extrapolate track parameters to "zEnd"
318 ExtrapToZ(trackParam,zEnd);
319 return;
320 }
321
208f139e 322 // Save the actual track parameters
323 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 324 TMatrixD paramSave(trackParamSave.GetParameters());
325 Double_t zBegin = trackParamSave.GetZ();
326
327 // Get reference to the parameter covariance matrix
328 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 329
208f139e 330 // Extrapolate track parameters to "zEnd"
331 ExtrapToZ(trackParam,zEnd);
208f139e 332
ea94c18b 333 // Get reference to the extrapolated parameters
334 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 335
336 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
337 TMatrixD jacob(5,5);
ea94c18b 338 jacob.Zero();
339 TMatrixD dParam(5,1);
208f139e 340 for (Int_t i=0; i<5; i++) {
341 // Skip jacobian calculation for parameters with no associated error
18abc511 342 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 343
208f139e 344 // Small variation of parameter i only
345 for (Int_t j=0; j<5; j++) {
346 if (j==i) {
ea94c18b 347 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
348 if (j == 4) dParam(j,0) *= TMath::Sign(1.,-paramSave(4,0)); // variation always in the same direction
349 } else dParam(j,0) = 0.;
208f139e 350 }
ea94c18b 351
208f139e 352 // Set new parameters
ea94c18b 353 trackParamSave.SetParameters(paramSave);
354 trackParamSave.AddParameters(dParam);
355 trackParamSave.SetZ(zBegin);
356
208f139e 357 // Extrapolate new track parameters to "zEnd"
358 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 359
208f139e 360 // Calculate the jacobian
ea94c18b 361 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
362 jacobji *= 1. / dParam(i,0);
363 jacob.SetSub(0,i,jacobji);
208f139e 364 }
365
366 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 367 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
368 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
369 trackParam->SetCovariances(tmp2);
370
371 // Update the propagator if required
372 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 373}
374
690d2205 375//__________________________________________________________________________
8cde4af5 376void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
377{
378 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
690d2205 379 /// The absorber correction parameters are supposed to be calculated at the current track z-position
8cde4af5 380
381 // absorber related covariance parameters
382 Double_t bendingSlope = param->GetBendingSlope();
383 Double_t nonBendingSlope = param->GetNonBendingSlope();
384 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
385 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 386 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
8cde4af5 387 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
388 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
389 Double_t varSlop = alpha2 * f0;
390
690d2205 391 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
392 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
393 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
394 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
395
396 // Set MCS covariance matrix
ea94c18b 397 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 398 // Non bending plane
ea94c18b 399 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
400 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 401 // Bending plane
ea94c18b 402 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
403 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 404 // Inverse bending momentum (due to dependences with bending and non bending slopes)
405 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
406 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
407 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
408 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
409 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
ea94c18b 410
411 // Set new covariances
412 param->SetCovariances(newParamCov);
690d2205 413}
414
415//__________________________________________________________________________
416void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
417 Double_t xVtx, Double_t yVtx, Double_t zVtx,
418 Double_t errXVtx, Double_t errYVtx,
419 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
420{
421 /// Correct parameters and corresponding covariances using Branson correction
422 /// - input param are parameters and covariances at the end of absorber
423 /// - output param are parameters and covariances at vertex
424 /// Absorber correction parameters are supposed to be calculated at the current track z-position
425
426 // Position of the Branson plane (spectro. (z<0))
427 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
428
429 // Add MCS effects to current parameter covariances
430 AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2);
431
432 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
433 ExtrapToZCov(param,zVtx);
434 LinearExtrapToZ(param,zB);
435
436 // compute track parameters at vertex
437 TMatrixD newParam(5,1);
438 newParam(0,0) = xVtx;
439 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
440 newParam(2,0) = yVtx;
441 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
442 newParam(4,0) = param->GetCharge() / param->P() *
443 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
444 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
445
446 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
447 TMatrixD paramCovP(param->GetCovariances());
448 Cov2CovP(param->GetParameters(),paramCovP);
449
450 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
451 TMatrixD paramCovVtx(5,5);
452 paramCovVtx.Zero();
453 paramCovVtx(0,0) = errXVtx * errXVtx;
454 paramCovVtx(1,1) = paramCovP(0,0);
455 paramCovVtx(2,2) = errYVtx * errYVtx;
456 paramCovVtx(3,3) = paramCovP(2,2);
457 paramCovVtx(4,4) = paramCovP(4,4);
458 paramCovVtx(1,3) = paramCovP(0,2);
459 paramCovVtx(3,1) = paramCovP(2,0);
460 paramCovVtx(1,4) = paramCovP(0,4);
461 paramCovVtx(4,1) = paramCovP(4,0);
462 paramCovVtx(3,4) = paramCovP(2,4);
463 paramCovVtx(4,3) = paramCovP(4,2);
464
465 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
466 TMatrixD jacob(5,5);
467 jacob.UnitMatrix();
468 jacob(1,0) = - 1. / (zB - zVtx);
469 jacob(1,1) = 1. / (zB - zVtx);
470 jacob(3,2) = - 1. / (zB - zVtx);
471 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 472
690d2205 473 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
474 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
475 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
476
477 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
478 CovP2Cov(newParam,newParamCov);
479
480 // Set parameters and covariances at vertex
481 param->SetParameters(newParam);
482 param->SetZ(zVtx);
483 param->SetCovariances(newParamCov);
8cde4af5 484}
485
690d2205 486//__________________________________________________________________________
487void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
488{
489 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
490
491 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
492 TMatrixD newParamCov(param->GetCovariances());
493 Cov2CovP(param->GetParameters(),newParamCov);
494
495 // Add effects of energy loss fluctuation to covariances
496 newParamCov(4,4) += sigmaELoss2;
497
498 // Compute new parameters corrected for energy loss
499 Double_t nonBendingSlope = param->GetNonBendingSlope();
500 Double_t bendingSlope = param->GetBendingSlope();
501 param->SetInverseBendingMomentum(param->GetCharge() / (param->P() + eLoss) *
502 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
503 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
504
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
690d2205 668 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
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();
18abc511 759 Double_t pathLength, f0, f1, f2, meanRho, deltaP, sigmaDeltaP2;
760 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP,sigmaDeltaP2)) {
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
773 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
774 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
775 trackXYZIn[2], pathLength, f0, f1, f2);
776 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
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
690d2205 790 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
791 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
792 ExtrapToZCov(trackParam, trackXYZIn[2]);
793 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
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
84f061ef 870 return totalELoss;
c04e3238 871}
872
690d2205 873//__________________________________________________________________________
84f061ef 874Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
c04e3238 875{
84f061ef 876 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
877 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
878 Double_t muMass = 0.105658369; // GeV
879 Double_t eMass = 0.510998918e-3; // GeV
880 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
881 Double_t i = 9.5e-9; // mean exitation energy per atomic Z (GeV)
8cde4af5 882 Double_t p2=pTotal*pTotal;
883 Double_t beta2=p2/(p2 + muMass*muMass);
8cde4af5 884
84f061ef 885 Double_t w = k * rho * pathLength * atomicZ / atomicA / beta2;
886
8cde4af5 887 if (beta2/(1-beta2)>3.5*3.5)
690d2205 888 return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2);
889
84f061ef 890 return w * (log(2.*eMass*beta2/(1-beta2)/(i*atomicZ)) - beta2);
c04e3238 891}
892
690d2205 893//__________________________________________________________________________
894Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
895{
896 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
897 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
898 Double_t muMass = 0.105658369; // GeV
899 //Double_t eMass = 0.510998918e-3; // GeV
900 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
901 Double_t p2=pTotal*pTotal;
902 Double_t beta2=p2/(p2 + muMass*muMass);
903
904 Double_t fwhm = 2. * k * rho * pathLength * atomicZ / atomicA / beta2; // FWHM of the energy loss Landau distribution
905 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
906
907 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
908
909 return sigma2;
910}
911
912//__________________________________________________________________________
913void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
914{
915 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
916 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
917
918 // charge * total momentum
919 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
920 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
921
922 // Jacobian of the opposite transformation
923 TMatrixD jacob(5,5);
924 jacob.UnitMatrix();
925 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
926 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
927 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
928 jacob(4,4) = - qPTot / param(4,0);
929
930 // compute covariances in new coordinate system
931 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
932 cov.Mult(jacob,tmp);
933}
934
935//__________________________________________________________________________
936void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
937{
938 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
939 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
940
941 // charge * total momentum
942 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
943 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
944
945 // Jacobian of the transformation
946 TMatrixD jacob(5,5);
947 jacob.UnitMatrix();
948 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
949 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
950 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
951 jacob(4,4) = - param(4,0) / qPTot;
952
953 // compute covariances in new coordinate system
954 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
955 covP.Mult(jacob,tmp);
956}
957
c04e3238 958 //__________________________________________________________________________
959void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
960{
71a2d3aa 961/// <pre>
c04e3238 962/// ******************************************************************
963/// * *
964/// * Performs the tracking of one step in a magnetic field *
965/// * The trajectory is assumed to be a helix in a constant field *
966/// * taken at the mid point of the step. *
967/// * Parameters: *
968/// * input *
969/// * STEP =arc length of the step asked *
970/// * VECT =input vector (position,direction cos and momentum) *
971/// * CHARGE= electric charge of the particle *
972/// * output *
973/// * VOUT = same as VECT after completion of the step *
974/// * *
2060b217 975/// * ==>Called by : USER, GUSWIM *
c04e3238 976/// * Author m.hansroul ********* *
977/// * modified s.egli, s.v.levonian *
978/// * modified v.perevoztchikov
979/// * *
980/// ******************************************************************
71a2d3aa 981/// </pre>
c04e3238 982
983// modif: everything in double precision
984
985 Double_t xyz[3], h[4], hxp[3];
986 Double_t h2xy, hp, rho, tet;
987 Double_t sint, sintt, tsint, cos1t;
988 Double_t f1, f2, f3, f4, f5, f6;
989
990 const Int_t kix = 0;
991 const Int_t kiy = 1;
992 const Int_t kiz = 2;
993 const Int_t kipx = 3;
994 const Int_t kipy = 4;
995 const Int_t kipz = 5;
996 const Int_t kipp = 6;
997
998 const Double_t kec = 2.9979251e-4;
999 //
1000 // ------------------------------------------------------------------
1001 //
1002 // units are kgauss,centimeters,gev/c
1003 //
1004 vout[kipp] = vect[kipp];
1005 if (TMath::Abs(charge) < 0.00001) {
1006 for (Int_t i = 0; i < 3; i++) {
1007 vout[i] = vect[i] + step * vect[i+3];
1008 vout[i+3] = vect[i+3];
1009 }
1010 return;
1011 }
1012 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1013 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1014 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1015
1016 //cmodif: call gufld (xyz, h) changed into:
1017 GetField (xyz, h);
1018
1019 h2xy = h[0]*h[0] + h[1]*h[1];
1020 h[3] = h[2]*h[2]+ h2xy;
1021 if (h[3] < 1.e-12) {
1022 for (Int_t i = 0; i < 3; i++) {
1023 vout[i] = vect[i] + step * vect[i+3];
1024 vout[i+3] = vect[i+3];
1025 }
1026 return;
1027 }
1028 if (h2xy < 1.e-12*h[3]) {
1029 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1030 return;
1031 }
1032 h[3] = TMath::Sqrt(h[3]);
1033 h[0] /= h[3];
1034 h[1] /= h[3];
1035 h[2] /= h[3];
1036 h[3] *= kec;
1037
1038 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1039 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1040 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1041
1042 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1043
1044 rho = -charge*h[3]/vect[kipp];
1045 tet = rho * step;
1046
1047 if (TMath::Abs(tet) > 0.15) {
1048 sint = TMath::Sin(tet);
1049 sintt = (sint/tet);
1050 tsint = (tet-sint)/tet;
1051 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1052 } else {
1053 tsint = tet*tet/36.;
1054 sintt = (1. - tsint);
1055 sint = tet*sintt;
1056 cos1t = 0.5*tet;
1057 }
1058
1059 f1 = step * sintt;
1060 f2 = step * cos1t;
1061 f3 = step * tsint * hp;
1062 f4 = -tet*cos1t;
1063 f5 = sint;
1064 f6 = tet * cos1t * hp;
1065
1066 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1067 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1068 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1069
1070 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1071 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1072 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1073
1074 return;
1075}
1076
1077 //__________________________________________________________________________
1078void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
1079{
71a2d3aa 1080/// <pre>
c04e3238 1081/// ******************************************************************
1082/// * *
1083/// * Tracking routine in a constant field oriented *
1084/// * along axis 3 *
1085/// * Tracking is performed with a conventional *
1086/// * helix step method *
1087/// * *
2060b217 1088/// * ==>Called by : USER, GUSWIM *
c04e3238 1089/// * Authors R.Brun, M.Hansroul ********* *
1090/// * Rewritten V.Perevoztchikov
1091/// * *
1092/// ******************************************************************
71a2d3aa 1093/// </pre>
c04e3238 1094
1095 Double_t hxp[3];
1096 Double_t h4, hp, rho, tet;
1097 Double_t sint, sintt, tsint, cos1t;
1098 Double_t f1, f2, f3, f4, f5, f6;
1099
1100 const Int_t kix = 0;
1101 const Int_t kiy = 1;
1102 const Int_t kiz = 2;
1103 const Int_t kipx = 3;
1104 const Int_t kipy = 4;
1105 const Int_t kipz = 5;
1106 const Int_t kipp = 6;
1107
1108 const Double_t kec = 2.9979251e-4;
1109
1110//
1111// ------------------------------------------------------------------
1112//
1113// units are kgauss,centimeters,gev/c
1114//
1115 vout[kipp] = vect[kipp];
1116 h4 = field * kec;
1117
1118 hxp[0] = - vect[kipy];
1119 hxp[1] = + vect[kipx];
1120
1121 hp = vect[kipz];
1122
1123 rho = -h4/vect[kipp];
1124 tet = rho * step;
1125 if (TMath::Abs(tet) > 0.15) {
1126 sint = TMath::Sin(tet);
1127 sintt = (sint/tet);
1128 tsint = (tet-sint)/tet;
1129 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1130 } else {
1131 tsint = tet*tet/36.;
1132 sintt = (1. - tsint);
1133 sint = tet*sintt;
1134 cos1t = 0.5*tet;
1135 }
1136
1137 f1 = step * sintt;
1138 f2 = step * cos1t;
1139 f3 = step * tsint * hp;
1140 f4 = -tet*cos1t;
1141 f5 = sint;
1142 f6 = tet * cos1t * hp;
1143
1144 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1145 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1146 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1147
1148 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1149 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1150 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1151
1152 return;
1153}
8cde4af5 1154
c04e3238 1155 //__________________________________________________________________________
1156void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
1157{
71a2d3aa 1158/// <pre>
c04e3238 1159/// ******************************************************************
1160/// * *
1161/// * Runge-Kutta method for tracking a particle through a magnetic *
1162/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1163/// * Standards, procedure 25.5.20) *
1164/// * *
1165/// * Input parameters *
1166/// * CHARGE Particle charge *
1167/// * STEP Step size *
1168/// * VECT Initial co-ords,direction cosines,momentum *
1169/// * Output parameters *
1170/// * VOUT Output co-ords,direction cosines,momentum *
1171/// * User routine called *
1172/// * CALL GUFLD(X,F) *
1173/// * *
2060b217 1174/// * ==>Called by : USER, GUSWIM *
c04e3238 1175/// * Authors R.Brun, M.Hansroul ********* *
1176/// * V.Perevoztchikov (CUT STEP implementation) *
1177/// * *
1178/// * *
1179/// ******************************************************************
71a2d3aa 1180/// </pre>
c04e3238 1181
1182 Double_t h2, h4, f[4];
1183 Double_t xyzt[3], a, b, c, ph,ph2;
1184 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1185 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1186 Double_t est, at, bt, ct, cba;
1187 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1188
1189 Double_t x;
1190 Double_t y;
1191 Double_t z;
1192
1193 Double_t xt;
1194 Double_t yt;
1195 Double_t zt;
1196
1197 Double_t maxit = 1992;
1198 Double_t maxcut = 11;
1199
1200 const Double_t kdlt = 1e-4;
1201 const Double_t kdlt32 = kdlt/32.;
1202 const Double_t kthird = 1./3.;
1203 const Double_t khalf = 0.5;
1204 const Double_t kec = 2.9979251e-4;
1205
1206 const Double_t kpisqua = 9.86960440109;
1207 const Int_t kix = 0;
1208 const Int_t kiy = 1;
1209 const Int_t kiz = 2;
1210 const Int_t kipx = 3;
1211 const Int_t kipy = 4;
1212 const Int_t kipz = 5;
1213
1214 // *.
1215 // *. ------------------------------------------------------------------
1216 // *.
1217 // * this constant is for units cm,gev/c and kgauss
1218 // *
1219 Int_t iter = 0;
1220 Int_t ncut = 0;
1221 for(Int_t j = 0; j < 7; j++)
1222 vout[j] = vect[j];
1223
1224 Double_t pinv = kec * charge / vect[6];
1225 Double_t tl = 0.;
1226 Double_t h = step;
1227 Double_t rest;
1228
1229
1230 do {
1231 rest = step - tl;
1232 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1233 //cmodif: call gufld(vout,f) changed into:
1234
1235 GetField(vout,f);
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:
1279 GetField(xyzt,f);
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:
1316 GetField(xyzt,f);
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
c04e3238 1401//___________________________________________________________
690d2205 1402void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
c04e3238 1403{
1404 /// interface for arguments in double precision (Why ? ChF)
1405 Float_t x[3], b[3];
690d2205 1406
c04e3238 1407 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
690d2205 1408
c04e3238 1409 if (fgkField) fgkField->Field(x,b);
1410 else {
1411 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
1412 exit(-1);
1413 }
1414
1415 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
690d2205 1416
c04e3238 1417 return;
1418}