Update HFE v2 analyses
[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
cdd730d0 40using std::endl;
41using std::cout;
78649106 42/// \cond CLASSIMP
c04e3238 43ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 44/// \endcond
c04e3238 45
9f093251 46const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
47const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
48 Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
49 Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
4284483e 50const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 51const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 52const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
53const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 54
690d2205 55//__________________________________________________________________________
f7a1cc68 56void AliMUONTrackExtrap::SetField()
9f093251 57{
cddcc1f3 58 /// set field on/off flag;
59 /// set field at the centre of the dipole
f7a1cc68 60 const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
61 Double_t b[3] = {0.,0.,0.};
62 TGeoGlobalMagField::Instance()->Field(x,b);
63 fgSimpleBValue = b[0];
ade4e6f9 64 fgFieldON = (TMath::Abs(fgSimpleBValue) > 1.e-10) ? kTRUE : kFALSE;
9f093251 65
66}
67
68//__________________________________________________________________________
208f139e 69Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
70{
71 /// Returns impact parameter at vertex in bending plane (cm),
72 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
73 /// using simple values for dipole magnetic field.
74 /// The sign of "BendingMomentum" is the sign of the charge.
75
76 if (bendingMomentum == 0.) return 1.e10;
77
6b191dea 78 const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
9f093251 79
80 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
208f139e 81}
82
690d2205 83//__________________________________________________________________________
9bdbee64 84Double_t
85AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
208f139e 86{
87 /// Returns signed bending momentum in bending plane (GeV/c),
88 /// the sign being the sign of the charge for particles moving forward in Z,
89 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
90 /// using simple values for dipole magnetic field.
91
92 if (impactParam == 0.) return 1.e10;
93
9f093251 94 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
95
9bdbee64 96 if (fgFieldON)
97 {
98 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
99 }
100 else
101 {
102 return AliMUONConstants::GetMostProbBendingMomentum();
103 }
208f139e 104}
c04e3238 105
690d2205 106//__________________________________________________________________________
3fe6651e 107void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
019df241 108{
3fe6651e 109 /// Track parameters linearly extrapolated to the plane at "zEnd".
019df241 110 /// On return, results from the extrapolation are updated in trackParam.
111
112 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
113
114 // Compute track parameters
115 Double_t dZ = zEnd - trackParam->GetZ();
116 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
117 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
118 trackParam->SetZ(zEnd);
3fe6651e 119}
120
121//__________________________________________________________________________
122void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
123{
124 /// Track parameters and their covariances linearly extrapolated to the plane at "zEnd".
125 /// On return, results from the extrapolation are updated in trackParam.
019df241 126
3fe6651e 127 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
128
129 // No need to propagate the covariance matrix if it does not exist
130 if (!trackParam->CovariancesExist()) {
131 cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
132 // Extrapolate linearly track parameters to "zEnd"
133 LinearExtrapToZ(trackParam,zEnd);
134 return;
019df241 135 }
136
3fe6651e 137 // Compute track parameters
138 Double_t dZ = zEnd - trackParam->GetZ();
139 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
140 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
141 trackParam->SetZ(zEnd);
142
143 // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
144 TMatrixD jacob(5,5);
145 jacob.UnitMatrix();
146 jacob(0,1) = dZ;
147 jacob(2,3) = dZ;
148
149 // Extrapolate track parameter covariances to "zEnd"
150 TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
151 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
152 trackParam->SetCovariances(tmp2);
153
154 // Update the propagator if required
155 if (updatePropagator) trackParam->UpdatePropagator(jacob);
019df241 156}
157
690d2205 158//__________________________________________________________________________
4ea3f013 159Bool_t AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
c04e3238 160{
4284483e 161 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
162 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 163 if (!fgFieldON) {
164 AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
165 return kTRUE;
166 }
167 else if (fgkUseHelix) return AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
168 else return AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
4284483e 169}
170
690d2205 171//__________________________________________________________________________
4ea3f013 172Bool_t AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
4284483e 173{
174 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 175 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 176 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
c04e3238 177 Double_t forwardBackward; // +1 if forward, -1 if backward
178 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
179 else forwardBackward = -1.0;
dade8580 180 Double_t v3[7], v3New[7]; // 7 in parameter ????
181 Int_t i3, stepNumber;
c04e3238 182 // For safety: return kTRUE or kFALSE ????
183 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 184 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 185 // sign of charge (sign of fInverseBendingMomentum if forward motion)
186 // must be changed if backward extrapolation
208f139e 187 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 188 // Extrapolation loop
189 stepNumber = 0;
208f139e 190 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 191 stepNumber++;
4284483e 192 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 193 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 194 // better use TArray ????
208f139e 195 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 196 }
208f139e 197 // check fgkMaxStepNumber ????
c04e3238 198 // Interpolation back to exact Z (2nd order)
199 // should be in function ???? using TArray ????
dade8580 200 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 201 if (TMath::Abs(dZ12) > 0) {
dade8580 202 Double_t dZ1i = zEnd - v3[2]; // 1-i
203 Double_t dZi2 = v3New[2] - zEnd; // i->2
204 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
205 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
206 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
207 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
208 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
209 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
210 v3[2] = zEnd; // Z
c04e3238 211 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
212 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
213 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 214 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 215 v3[3] = xPrimeI * v3[5]; // PX/PTOT
216 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 217 } else {
4284483e 218 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 219 }
4284483e 220 // Recover track parameters (charge back for forward motion)
dade8580 221 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
4ea3f013 222 return kTRUE;
c04e3238 223}
224
690d2205 225//__________________________________________________________________________
4ea3f013 226Bool_t AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
4284483e 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.
4ea3f013 230 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
4284483e 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
4ea3f013 241 // Extrapolation loop (until within tolerance or the track turn around)
4284483e 242 Double_t residue = zEnd - trackParam->GetZ();
4ea3f013 243 Bool_t uturn = kFALSE;
ade4e6f9 244 Bool_t trackingFailed = kFALSE;
4ea3f013 245 Bool_t tooManyStep = kFALSE;
4284483e 246 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
4ea3f013 247
4284483e 248 dZ = zEnd - trackParam->GetZ();
249 // step lenght assuming linear trajectory
250 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 251 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 252 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
4ea3f013 253
4284483e 254 do { // reduce step lenght while zEnd oversteped
255 if (stepNumber > fgkMaxStepNumber) {
256 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
4ea3f013 257 tooManyStep = kTRUE;
4284483e 258 break;
259 }
260 stepNumber ++;
261 step = TMath::Abs(step);
ade4e6f9 262 if (!AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New)) {
263 trackingFailed = kTRUE;
264 break;
265 }
4284483e 266 residue = zEnd - v3New[2];
267 step *= dZ/(v3New[2]-trackParam->GetZ());
268 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
4ea3f013 269
ade4e6f9 270 if (trackingFailed) break;
271 else if (v3New[5]*v3[5] < 0) { // the track turned around
4ea3f013 272 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl;
273 uturn = kTRUE;
274 break;
275 } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
276
4284483e 277 }
278
279 // terminate the extropolation with a straight line up to the exact "zEnd" value
ade4e6f9 280 if (trackingFailed || uturn) {
4ea3f013 281
282 // track ends +-100 meters away in the bending direction
283 dZ = zEnd - v3[2];
284 Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ;
285 Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
286 Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope());
287 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope);
288 trackParam->SetNonBendingSlope(nonBendingSlope);
289 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope);
290 trackParam->SetBendingSlope(bendingSlope);
291 trackParam->SetZ(zEnd);
292
293 return kFALSE;
294
295 } else {
296
297 // track extrapolated normally
298 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
299 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
300 trackParam->SetZ(zEnd);
301
302 return !tooManyStep;
303
304 }
305
4284483e 306}
307
690d2205 308//__________________________________________________________________________
4284483e 309void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 310{
dade8580 311 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 312 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
313 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 314 v3[0] = trackParam->GetNonBendingCoor(); // X
315 v3[1] = trackParam->GetBendingCoor(); // Y
316 v3[2] = trackParam->GetZ(); // Z
c04e3238 317 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
318 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 319 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
320 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
321 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
322 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 323}
324
690d2205 325//__________________________________________________________________________
dade8580 326void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 327{
dade8580 328 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 329 /// assumed to be calculated for forward motion in Z.
330 /// "InverseBendingMomentum" is signed with "charge".
dade8580 331 trackParam->SetNonBendingCoor(v3[0]); // X
332 trackParam->SetBendingCoor(v3[1]); // Y
333 trackParam->SetZ(v3[2]); // Z
60e55aee 334 Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
c04e3238 335 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 336 trackParam->SetBendingSlope(v3[4]/v3[5]);
337 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
c04e3238 338}
339
690d2205 340//__________________________________________________________________________
4ea3f013 341Bool_t AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 342{
343 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
344 /// On return, results from the extrapolation are updated in trackParam.
345
4ea3f013 346 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z
208f139e 347
9f093251 348 if (!fgFieldON) { // linear extrapolation if no magnetic field
3fe6651e 349 AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
4ea3f013 350 return kTRUE;
9f093251 351 }
352
ea94c18b 353 // No need to propagate the covariance matrix if it does not exist
354 if (!trackParam->CovariancesExist()) {
355 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
356 // Extrapolate track parameters to "zEnd"
4ea3f013 357 return ExtrapToZ(trackParam,zEnd);
ea94c18b 358 }
359
208f139e 360 // Save the actual track parameters
361 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 362 TMatrixD paramSave(trackParamSave.GetParameters());
363 Double_t zBegin = trackParamSave.GetZ();
364
365 // Get reference to the parameter covariance matrix
366 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 367
208f139e 368 // Extrapolate track parameters to "zEnd"
4ea3f013 369 // Do not update the covariance matrix if the extrapolation failed
370 if (!ExtrapToZ(trackParam,zEnd)) return kFALSE;
208f139e 371
ea94c18b 372 // Get reference to the extrapolated parameters
373 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 374
375 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
4ea3f013 376 Bool_t extrapStatus = kTRUE;
208f139e 377 TMatrixD jacob(5,5);
ea94c18b 378 jacob.Zero();
379 TMatrixD dParam(5,1);
6b191dea 380 Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
208f139e 381 for (Int_t i=0; i<5; i++) {
382 // Skip jacobian calculation for parameters with no associated error
18abc511 383 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 384
208f139e 385 // Small variation of parameter i only
386 for (Int_t j=0; j<5; j++) {
387 if (j==i) {
ea94c18b 388 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
6b191dea 389 dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
ea94c18b 390 } else dParam(j,0) = 0.;
208f139e 391 }
ea94c18b 392
208f139e 393 // Set new parameters
ea94c18b 394 trackParamSave.SetParameters(paramSave);
395 trackParamSave.AddParameters(dParam);
396 trackParamSave.SetZ(zBegin);
397
208f139e 398 // Extrapolate new track parameters to "zEnd"
4ea3f013 399 if (!ExtrapToZ(&trackParamSave,zEnd)) {
400 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl;
401 extrapStatus = kFALSE;
402 }
ea94c18b 403
208f139e 404 // Calculate the jacobian
ea94c18b 405 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
406 jacobji *= 1. / dParam(i,0);
407 jacob.SetSub(0,i,jacobji);
208f139e 408 }
409
410 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 411 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
412 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
413 trackParam->SetCovariances(tmp2);
414
415 // Update the propagator if required
416 if (updatePropagator) trackParam->UpdatePropagator(jacob);
4ea3f013 417
418 return extrapStatus;
208f139e 419}
420
690d2205 421//__________________________________________________________________________
37a615ac 422void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
8cde4af5 423{
424 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 425 /// signedPathLength must have the sign of (zOut - zIn) where all other parameters are assumed to be given at zOut.
8cde4af5 426
427 // absorber related covariance parameters
428 Double_t bendingSlope = param->GetBendingSlope();
429 Double_t nonBendingSlope = param->GetNonBendingSlope();
430 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
431 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 432 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
37a615ac 433 Double_t pathLength = TMath::Abs(signedPathLength);
8cde4af5 434 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
37a615ac 435 Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1);
8cde4af5 436 Double_t varSlop = alpha2 * f0;
437
690d2205 438 // Set MCS covariance matrix
ea94c18b 439 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 440 // Non bending plane
ea94c18b 441 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
442 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 443 // Bending plane
ea94c18b 444 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
445 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 446
447 // Set momentum related covariances if B!=0
448 if (fgFieldON) {
449 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
450 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
451 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
452 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
453 // Inverse bending momentum (due to dependences with bending and non bending slopes)
454 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
455 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
456 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
457 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
458 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
459 }
ea94c18b 460
461 // Set new covariances
462 param->SetCovariances(newParamCov);
690d2205 463}
464
465//__________________________________________________________________________
466void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
467 Double_t xVtx, Double_t yVtx, Double_t zVtx,
468 Double_t errXVtx, Double_t errYVtx,
469 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
470{
471 /// Correct parameters and corresponding covariances using Branson correction
472 /// - input param are parameters and covariances at the end of absorber
473 /// - output param are parameters and covariances at vertex
474 /// Absorber correction parameters are supposed to be calculated at the current track z-position
475
476 // Position of the Branson plane (spectro. (z<0))
477 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
478
37a615ac 479 // Add MCS effects to current parameter covariances (spectro. (z<0))
480 AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2);
690d2205 481
482 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
483 ExtrapToZCov(param,zVtx);
3fe6651e 484 LinearExtrapToZCov(param,zB);
690d2205 485
486 // compute track parameters at vertex
487 TMatrixD newParam(5,1);
488 newParam(0,0) = xVtx;
489 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
490 newParam(2,0) = yVtx;
491 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
492 newParam(4,0) = param->GetCharge() / param->P() *
493 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
494 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
495
496 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
497 TMatrixD paramCovP(param->GetCovariances());
498 Cov2CovP(param->GetParameters(),paramCovP);
499
500 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
501 TMatrixD paramCovVtx(5,5);
502 paramCovVtx.Zero();
503 paramCovVtx(0,0) = errXVtx * errXVtx;
504 paramCovVtx(1,1) = paramCovP(0,0);
505 paramCovVtx(2,2) = errYVtx * errYVtx;
506 paramCovVtx(3,3) = paramCovP(2,2);
507 paramCovVtx(4,4) = paramCovP(4,4);
508 paramCovVtx(1,3) = paramCovP(0,2);
509 paramCovVtx(3,1) = paramCovP(2,0);
510 paramCovVtx(1,4) = paramCovP(0,4);
511 paramCovVtx(4,1) = paramCovP(4,0);
512 paramCovVtx(3,4) = paramCovP(2,4);
513 paramCovVtx(4,3) = paramCovP(4,2);
514
515 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
516 TMatrixD jacob(5,5);
517 jacob.UnitMatrix();
518 jacob(1,0) = - 1. / (zB - zVtx);
519 jacob(1,1) = 1. / (zB - zVtx);
520 jacob(3,2) = - 1. / (zB - zVtx);
521 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 522
690d2205 523 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
524 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
525 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
526
527 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
528 CovP2Cov(newParam,newParamCov);
529
530 // Set parameters and covariances at vertex
531 param->SetParameters(newParam);
532 param->SetZ(zVtx);
533 param->SetCovariances(newParamCov);
8cde4af5 534}
535
690d2205 536//__________________________________________________________________________
537void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
538{
539 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
540
541 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
542 TMatrixD newParamCov(param->GetCovariances());
543 Cov2CovP(param->GetParameters(),newParamCov);
544
690d2205 545 // Compute new parameters corrected for energy loss
ecdf58c4 546 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
547 Double_t p = param->P();
548 Double_t e = TMath::Sqrt(p*p + muMass*muMass);
549 Double_t eCorr = e + eLoss;
550 Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
690d2205 551 Double_t nonBendingSlope = param->GetNonBendingSlope();
552 Double_t bendingSlope = param->GetBendingSlope();
ecdf58c4 553 param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
690d2205 554 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
555 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
556
ecdf58c4 557 // Add effects of energy loss fluctuation to covariances
558 newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
559
690d2205 560 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
561 CovP2Cov(param->GetParameters(),newParamCov);
562
563 // Set new parameter covariances
564 param->SetCovariances(newParamCov);
565}
566
567//__________________________________________________________________________
18abc511 568Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
569 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
570 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 571{
572 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 573 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 574 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
575 // f0: 0th moment of z calculated with the inverse radiation-length distribution
576 // f1: 1st moment of z calculated with the inverse radiation-length distribution
577 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
578 // meanRho: average density of crossed material (g/cm3)
84f061ef 579 // totalELoss: total energy loss in absorber
8cde4af5 580
581 // Reset absorber's parameters
582 pathLength = 0.;
583 f0 = 0.;
584 f1 = 0.;
585 f2 = 0.;
586 meanRho = 0.;
84f061ef 587 totalELoss = 0.;
690d2205 588 sigmaELoss2 = 0.;
8cde4af5 589
590 // Check whether the geometry is available
591 if (!gGeoManager) {
592 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 593 return kFALSE;
8cde4af5 594 }
595
596 // Initialize starting point and direction
597 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
598 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
599 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 600 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 601 Double_t b[3];
602 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
603 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
604 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
605 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
606 if (!currentnode) {
607 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 608 return kFALSE;
8cde4af5 609 }
610
611 // loop over absorber slices and calculate absorber's parameters
612 Double_t rho = 0.; // material density (g/cm3)
613 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 614 Double_t atomicA = 0.; // A of material
615 Double_t atomicZ = 0.; // Z of material
fa5e35be 616 Double_t atomicZoverA = 0.; // Z/A of material
8cde4af5 617 Double_t localPathLength = 0;
618 Double_t remainingPathLength = pathLength;
00d38895 619 Double_t sigmaELoss = 0.;
8cde4af5 620 Double_t zB = trackXYZIn[2];
621 Double_t zE, dzB, dzE;
622 do {
623 // Get material properties
624 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
625 rho = material->GetDensity();
626 x0 = material->GetRadLen();
84f061ef 627 atomicA = material->GetA();
628 atomicZ = material->GetZ();
fa5e35be 629 if(material->IsMixture()){
630 TGeoMixture * mixture = (TGeoMixture*)material;
631 atomicZoverA = 0.;
632 Double_t sum = 0.;
633 for (Int_t iel=0;iel<mixture->GetNelements();iel++){
634 sum += mixture->GetWmixt()[iel];
635 atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
636 }
637 atomicZoverA/=sum;
638 }
639 else atomicZoverA = atomicZ/atomicA;
8cde4af5 640
641 // Get path length within this material
642 gGeoManager->FindNextBoundary(remainingPathLength);
643 localPathLength = gGeoManager->GetStep() + 1.e-6;
644 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
645 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
646 else {
647 currentnode = gGeoManager->Step();
648 if (!currentnode) {
649 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 650 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
651 return kFALSE;
8cde4af5 652 }
653 if (!gGeoManager->IsEntering()) {
654 // make another small step to try to enter in new absorber slice
655 gGeoManager->SetStep(0.001);
656 currentnode = gGeoManager->Step();
657 if (!gGeoManager->IsEntering() || !currentnode) {
658 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 659 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
660 return kFALSE;
8cde4af5 661 }
662 localPathLength += 0.001;
663 }
664 }
665
666 // calculate absorber's parameters
667 zE = b[2] * localPathLength + zB;
668 dzB = zB - trackXYZIn[2];
669 dzE = zE - trackXYZIn[2];
670 f0 += localPathLength / x0;
671 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
672 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
673 meanRho += localPathLength * rho;
fa5e35be 674 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
00d38895 675 sigmaELoss += EnergyLossFluctuation(pTotal, localPathLength, rho, atomicZoverA);
8cde4af5 676
677 // prepare next step
678 zB = zE;
679 remainingPathLength -= localPathLength;
680 } while (remainingPathLength > TGeoShape::Tolerance());
681
682 meanRho /= pathLength;
00d38895 683 sigmaELoss2 = sigmaELoss*sigmaELoss;
18abc511 684
685 return kTRUE;
8cde4af5 686}
687
690d2205 688//__________________________________________________________________________
ea94c18b 689Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
690{
691 /// Return the angular dispersion square due to multiple Coulomb scattering
692 /// through a material of thickness "dZ" and of radiation length "x0"
693 /// assuming linear propagation and using the small angle approximation.
694
695 Double_t bendingSlope = param.GetBendingSlope();
696 Double_t nonBendingSlope = param.GetNonBendingSlope();
697 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 698 (1.0 + bendingSlope * bendingSlope) /
699 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 700 // Path length in the material
701 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
702 // relativistic velocity
703 Double_t velo = 1.;
704 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
705 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
706
707 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
708}
709
690d2205 710//__________________________________________________________________________
8cde4af5 711void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 712{
713 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 714 /// through a material of thickness "Abs(dZ)" and of radiation length "x0"
208f139e 715 /// assuming linear propagation and using the small angle approximation.
37a615ac 716 /// dZ = zOut - zIn (sign is important) and "param" is assumed to be given zOut.
717 /// If x0 <= 0., assume dZ = pathLength/x0 and consider the material thickness as negligible.
208f139e 718
719 Double_t bendingSlope = param->GetBendingSlope();
720 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 721 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
722 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
723 (1.0 + bendingSlope * bendingSlope) /
724 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 725 // Path length in the material
37a615ac 726 Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
727 Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength);
208f139e 728 // relativistic velocity
729 Double_t velo = 1.;
730 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
37a615ac 731 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
732 theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
208f139e 733
37a615ac 734 Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
208f139e 735 Double_t varSlop = theta02;
37a615ac 736 Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.;
ea94c18b 737
690d2205 738 // Set MCS covariance matrix
ea94c18b 739 TMatrixD newParamCov(param->GetCovariances());
208f139e 740 // Non bending plane
ea94c18b 741 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
742 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 743 // Bending plane
ea94c18b 744 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
745 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 746
747 // Set momentum related covariances if B!=0
748 if (fgFieldON) {
749 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
750 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
751 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
752 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
753 // Inverse bending momentum (due to dependences with bending and non bending slopes)
754 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
755 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
756 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
757 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
758 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
759 }
208f139e 760
ea94c18b 761 // Set new covariances
762 param->SetCovariances(newParamCov);
208f139e 763}
764
690d2205 765//__________________________________________________________________________
766void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
767 Double_t xVtx, Double_t yVtx, Double_t zVtx,
768 Double_t errXVtx, Double_t errYVtx,
769 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 770{
690d2205 771 /// Main method for extrapolation to the vertex:
772 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
773 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
774 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
775 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
776 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
777 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 778
8cde4af5 779 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 780
8cde4af5 781 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 782 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
783 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 784 return;
785 }
786
8cde4af5 787 // Check the vertex position relatively to the absorber
ea94c18b 788 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 789 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 790 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 791 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 792 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 793 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
794 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
795 else ExtrapToZ(trackParam,zVtx);
8cde4af5 796 return;
797 }
798
799 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 800 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 801 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 802 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
803 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
804 else ExtrapToZ(trackParam,zVtx);
8cde4af5 805 return;
ea94c18b 806 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 807 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 808 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 809 } else {
690d2205 810 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
811 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 812 }
c04e3238 813
690d2205 814 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 815 Double_t trackXYZOut[3];
816 trackXYZOut[0] = trackParam->GetNonBendingCoor();
817 trackXYZOut[1] = trackParam->GetBendingCoor();
818 trackXYZOut[2] = trackParam->GetZ();
819 Double_t trackXYZIn[3];
690d2205 820 if (correctForMCS) { // assume linear propagation until the vertex
821 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
822 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
823 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
824 } else {
825 AliMUONTrackParam trackParamIn(*trackParam);
826 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
827 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
828 trackXYZIn[1] = trackParamIn.GetBendingCoor();
829 trackXYZIn[2] = trackParamIn.GetZ();
830 }
84f061ef 831 Double_t pTot = trackParam->P();
ecdf58c4 832 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
833 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
18abc511 834 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
835 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
836 else ExtrapToZ(trackParam,zVtx);
837 return;
838 }
8cde4af5 839
690d2205 840 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
841 if (correctForMCS) {
fac70e25 842
690d2205 843 if (correctForEnergyLoss) {
844
845 // Correct for multiple scattering and energy loss
ecdf58c4 846 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 847 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
848 trackXYZIn[2], pathLength, f0, f1, f2);
ecdf58c4 849 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 850
851 } else {
852
853 // Correct for multiple scattering
854 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
855 trackXYZIn[2], pathLength, f0, f1, f2);
856 }
fac70e25 857
fac70e25 858 } else {
690d2205 859
860 if (correctForEnergyLoss) {
861
18abc511 862 // Correct for energy loss add multiple scattering dispersion in covariance matrix
ecdf58c4 863 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
37a615ac 864 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 865 ExtrapToZCov(trackParam, trackXYZIn[2]);
ecdf58c4 866 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 867 ExtrapToZCov(trackParam, zVtx);
868
869 } else {
870
18abc511 871 // add multiple scattering dispersion in covariance matrix
37a615ac 872 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 873 ExtrapToZCov(trackParam, zVtx);
874
875 }
876
fac70e25 877 }
8cde4af5 878
fac70e25 879}
880
690d2205 881//__________________________________________________________________________
882void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
883 Double_t xVtx, Double_t yVtx, Double_t zVtx,
884 Double_t errXVtx, Double_t errYVtx)
885{
886 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
887 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
888 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
889}
890
891//__________________________________________________________________________
892void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
893 Double_t xVtx, Double_t yVtx, Double_t zVtx,
894 Double_t errXVtx, Double_t errYVtx)
895{
896 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
897 /// Add branson correction resolution to parameter covariances
898 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
899}
900
901//__________________________________________________________________________
902void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
903{
904 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
905 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
906 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
907}
908
909//__________________________________________________________________________
910void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
911{
912 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
913 /// Add dispersion due to multiple scattering to parameter covariances
914 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
915}
916
917//__________________________________________________________________________
fac70e25 918Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
919{
920 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
921
922 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 923
fac70e25 924 // Check whether the geometry is available
925 if (!gGeoManager) {
926 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
927 return 0.;
928 }
929
930 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
931 Double_t trackXYZOut[3];
932 trackXYZOut[0] = trackParam->GetNonBendingCoor();
933 trackXYZOut[1] = trackParam->GetBendingCoor();
934 trackXYZOut[2] = trackParam->GetZ();
935 Double_t trackXYZIn[3];
936 trackXYZIn[0] = xVtx;
937 trackXYZIn[1] = yVtx;
938 trackXYZIn[2] = zVtx;
84f061ef 939 Double_t pTot = trackParam->P();
18abc511 940 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 941 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 942
ecdf58c4 943 // total momentum corrected for energy loss
944 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
945 Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
946 Double_t eCorr = e + totalELoss;
947 Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
948
949 return pTotCorr - pTot;
c04e3238 950}
951
690d2205 952//__________________________________________________________________________
fa5e35be 953Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
c04e3238 954{
84f061ef 955 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
956 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 957 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
84f061ef 958
ecdf58c4 959 // mean exitation energy (GeV)
960 Double_t i;
961 if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
962 else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
690d2205 963
fa5e35be 964 return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
c04e3238 965}
966
690d2205 967//__________________________________________________________________________
00d38895 968Double_t AliMUONTrackExtrap::EnergyLossFluctuation(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
690d2205 969{
970 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
971 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 972 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
690d2205 973 //Double_t eMass = 0.510998918e-3; // GeV
974 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
975 Double_t p2=pTotal*pTotal;
976 Double_t beta2=p2/(p2 + muMass*muMass);
977
fa5e35be 978 Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
00d38895 979 Double_t sigma = fwhm / TMath::Sqrt(8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
690d2205 980
981 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
982
00d38895 983 return sigma;
690d2205 984}
985
986//__________________________________________________________________________
987void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
988{
989 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
990 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
991
992 // charge * total momentum
993 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
994 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
995
996 // Jacobian of the opposite transformation
997 TMatrixD jacob(5,5);
998 jacob.UnitMatrix();
999 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1000 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
1001 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1002 jacob(4,4) = - qPTot / param(4,0);
1003
1004 // compute covariances in new coordinate system
1005 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
1006 cov.Mult(jacob,tmp);
1007}
1008
1009//__________________________________________________________________________
1010void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
1011{
1012 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
1013 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
1014
1015 // charge * total momentum
1016 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
1017 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
1018
1019 // Jacobian of the transformation
1020 TMatrixD jacob(5,5);
1021 jacob.UnitMatrix();
1022 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1023 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
1024 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1025 jacob(4,4) = - param(4,0) / qPTot;
1026
1027 // compute covariances in new coordinate system
1028 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
1029 covP.Mult(jacob,tmp);
1030}
1031
c04e3238 1032 //__________________________________________________________________________
57e2ad1a 1033void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
c04e3238 1034{
71a2d3aa 1035/// <pre>
c04e3238 1036/// ******************************************************************
1037/// * *
1038/// * Performs the tracking of one step in a magnetic field *
1039/// * The trajectory is assumed to be a helix in a constant field *
1040/// * taken at the mid point of the step. *
1041/// * Parameters: *
1042/// * input *
1043/// * STEP =arc length of the step asked *
1044/// * VECT =input vector (position,direction cos and momentum) *
1045/// * CHARGE= electric charge of the particle *
1046/// * output *
1047/// * VOUT = same as VECT after completion of the step *
1048/// * *
2060b217 1049/// * ==>Called by : USER, GUSWIM *
c04e3238 1050/// * Author m.hansroul ********* *
1051/// * modified s.egli, s.v.levonian *
1052/// * modified v.perevoztchikov
1053/// * *
1054/// ******************************************************************
71a2d3aa 1055/// </pre>
c04e3238 1056
1057// modif: everything in double precision
1058
1059 Double_t xyz[3], h[4], hxp[3];
1060 Double_t h2xy, hp, rho, tet;
1061 Double_t sint, sintt, tsint, cos1t;
1062 Double_t f1, f2, f3, f4, f5, f6;
1063
1064 const Int_t kix = 0;
1065 const Int_t kiy = 1;
1066 const Int_t kiz = 2;
1067 const Int_t kipx = 3;
1068 const Int_t kipy = 4;
1069 const Int_t kipz = 5;
1070 const Int_t kipp = 6;
1071
1072 const Double_t kec = 2.9979251e-4;
1073 //
1074 // ------------------------------------------------------------------
1075 //
1076 // units are kgauss,centimeters,gev/c
1077 //
1078 vout[kipp] = vect[kipp];
1079 if (TMath::Abs(charge) < 0.00001) {
1080 for (Int_t i = 0; i < 3; i++) {
1081 vout[i] = vect[i] + step * vect[i+3];
1082 vout[i+3] = vect[i+3];
1083 }
1084 return;
1085 }
1086 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1087 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1088 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1089
1090 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 1091 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 1092
1093 h2xy = h[0]*h[0] + h[1]*h[1];
1094 h[3] = h[2]*h[2]+ h2xy;
1095 if (h[3] < 1.e-12) {
1096 for (Int_t i = 0; i < 3; i++) {
1097 vout[i] = vect[i] + step * vect[i+3];
1098 vout[i+3] = vect[i+3];
1099 }
1100 return;
1101 }
1102 if (h2xy < 1.e-12*h[3]) {
1103 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1104 return;
1105 }
1106 h[3] = TMath::Sqrt(h[3]);
1107 h[0] /= h[3];
1108 h[1] /= h[3];
1109 h[2] /= h[3];
1110 h[3] *= kec;
1111
1112 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1113 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1114 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1115
1116 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1117
1118 rho = -charge*h[3]/vect[kipp];
1119 tet = rho * step;
1120
1121 if (TMath::Abs(tet) > 0.15) {
1122 sint = TMath::Sin(tet);
1123 sintt = (sint/tet);
1124 tsint = (tet-sint)/tet;
1125 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1126 } else {
1127 tsint = tet*tet/36.;
1128 sintt = (1. - tsint);
1129 sint = tet*sintt;
1130 cos1t = 0.5*tet;
1131 }
1132
1133 f1 = step * sintt;
1134 f2 = step * cos1t;
1135 f3 = step * tsint * hp;
1136 f4 = -tet*cos1t;
1137 f5 = sint;
1138 f6 = tet * cos1t * hp;
1139
1140 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1141 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1142 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1143
1144 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1145 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1146 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1147
1148 return;
1149}
1150
1151 //__________________________________________________________________________
57e2ad1a 1152void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
c04e3238 1153{
71a2d3aa 1154/// <pre>
c04e3238 1155/// ******************************************************************
1156/// * *
1157/// * Tracking routine in a constant field oriented *
1158/// * along axis 3 *
1159/// * Tracking is performed with a conventional *
1160/// * helix step method *
1161/// * *
2060b217 1162/// * ==>Called by : USER, GUSWIM *
c04e3238 1163/// * Authors R.Brun, M.Hansroul ********* *
1164/// * Rewritten V.Perevoztchikov
1165/// * *
1166/// ******************************************************************
71a2d3aa 1167/// </pre>
c04e3238 1168
1169 Double_t hxp[3];
1170 Double_t h4, hp, rho, tet;
1171 Double_t sint, sintt, tsint, cos1t;
1172 Double_t f1, f2, f3, f4, f5, f6;
1173
1174 const Int_t kix = 0;
1175 const Int_t kiy = 1;
1176 const Int_t kiz = 2;
1177 const Int_t kipx = 3;
1178 const Int_t kipy = 4;
1179 const Int_t kipz = 5;
1180 const Int_t kipp = 6;
1181
1182 const Double_t kec = 2.9979251e-4;
1183
1184//
1185// ------------------------------------------------------------------
1186//
1187// units are kgauss,centimeters,gev/c
1188//
1189 vout[kipp] = vect[kipp];
1190 h4 = field * kec;
1191
1192 hxp[0] = - vect[kipy];
1193 hxp[1] = + vect[kipx];
1194
1195 hp = vect[kipz];
1196
1197 rho = -h4/vect[kipp];
1198 tet = rho * step;
1199 if (TMath::Abs(tet) > 0.15) {
1200 sint = TMath::Sin(tet);
1201 sintt = (sint/tet);
1202 tsint = (tet-sint)/tet;
1203 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1204 } else {
1205 tsint = tet*tet/36.;
1206 sintt = (1. - tsint);
1207 sint = tet*sintt;
1208 cos1t = 0.5*tet;
1209 }
1210
1211 f1 = step * sintt;
1212 f2 = step * cos1t;
1213 f3 = step * tsint * hp;
1214 f4 = -tet*cos1t;
1215 f5 = sint;
1216 f6 = tet * cos1t * hp;
1217
1218 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1219 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1220 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1221
1222 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1223 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1224 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1225
1226 return;
1227}
8cde4af5 1228
c04e3238 1229 //__________________________________________________________________________
57e2ad1a 1230Bool_t AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t* vect, Double_t* vout)
c04e3238 1231{
71a2d3aa 1232/// <pre>
c04e3238 1233/// ******************************************************************
1234/// * *
1235/// * Runge-Kutta method for tracking a particle through a magnetic *
1236/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1237/// * Standards, procedure 25.5.20) *
1238/// * *
1239/// * Input parameters *
1240/// * CHARGE Particle charge *
1241/// * STEP Step size *
1242/// * VECT Initial co-ords,direction cosines,momentum *
1243/// * Output parameters *
1244/// * VOUT Output co-ords,direction cosines,momentum *
1245/// * User routine called *
1246/// * CALL GUFLD(X,F) *
1247/// * *
2060b217 1248/// * ==>Called by : USER, GUSWIM *
c04e3238 1249/// * Authors R.Brun, M.Hansroul ********* *
1250/// * V.Perevoztchikov (CUT STEP implementation) *
1251/// * *
1252/// * *
1253/// ******************************************************************
71a2d3aa 1254/// </pre>
c04e3238 1255
1256 Double_t h2, h4, f[4];
d373bcbe 1257 Double_t xyzt[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
1258 Double_t a, b, c, ph,ph2;
c04e3238 1259 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1260 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1261 Double_t est, at, bt, ct, cba;
1262 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1263
1264 Double_t x;
1265 Double_t y;
1266 Double_t z;
1267
1268 Double_t xt;
1269 Double_t yt;
1270 Double_t zt;
1271
1272 Double_t maxit = 1992;
1273 Double_t maxcut = 11;
1274
1275 const Double_t kdlt = 1e-4;
1276 const Double_t kdlt32 = kdlt/32.;
1277 const Double_t kthird = 1./3.;
1278 const Double_t khalf = 0.5;
1279 const Double_t kec = 2.9979251e-4;
1280
1281 const Double_t kpisqua = 9.86960440109;
1282 const Int_t kix = 0;
1283 const Int_t kiy = 1;
1284 const Int_t kiz = 2;
1285 const Int_t kipx = 3;
1286 const Int_t kipy = 4;
1287 const Int_t kipz = 5;
1288
1289 // *.
1290 // *. ------------------------------------------------------------------
1291 // *.
1292 // * this constant is for units cm,gev/c and kgauss
1293 // *
1294 Int_t iter = 0;
1295 Int_t ncut = 0;
1296 for(Int_t j = 0; j < 7; j++)
1297 vout[j] = vect[j];
1298
1299 Double_t pinv = kec * charge / vect[6];
1300 Double_t tl = 0.;
1301 Double_t h = step;
1302 Double_t rest;
1303
1304
1305 do {
1306 rest = step - tl;
1307 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1308 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1309 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1310
1311 // *
1312 // * start of integration
1313 // *
1314 x = vout[0];
1315 y = vout[1];
1316 z = vout[2];
1317 a = vout[3];
1318 b = vout[4];
1319 c = vout[5];
1320
1321 h2 = khalf * h;
1322 h4 = khalf * h2;
1323 ph = pinv * h;
1324 ph2 = khalf * ph;
1325 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1326 secys[0] = (c * f[0] - a * f[2]) * ph2;
1327 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1328 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1329 if (ang2 > kpisqua) break;
1330
1331 dxt = h2 * a + h4 * secxs[0];
1332 dyt = h2 * b + h4 * secys[0];
1333 dzt = h2 * c + h4 * seczs[0];
1334 xt = x + dxt;
1335 yt = y + dyt;
1336 zt = z + dzt;
1337 // *
1338 // * second intermediate point
1339 // *
1340
1341 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1342 if (est > h) {
1343 if (ncut++ > maxcut) break;
1344 h *= khalf;
1345 continue;
1346 }
1347
1348 xyzt[0] = xt;
1349 xyzt[1] = yt;
1350 xyzt[2] = zt;
1351
1352 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1353 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1354
1355 at = a + secxs[0];
1356 bt = b + secys[0];
1357 ct = c + seczs[0];
1358
1359 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1360 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1361 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1362 at = a + secxs[1];
1363 bt = b + secys[1];
1364 ct = c + seczs[1];
1365 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1366 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1367 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1368 dxt = h * (a + secxs[2]);
1369 dyt = h * (b + secys[2]);
1370 dzt = h * (c + seczs[2]);
1371 xt = x + dxt;
1372 yt = y + dyt;
1373 zt = z + dzt;
1374 at = a + 2.*secxs[2];
1375 bt = b + 2.*secys[2];
1376 ct = c + 2.*seczs[2];
1377
1378 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1379 if (est > 2.*TMath::Abs(h)) {
1380 if (ncut++ > maxcut) break;
1381 h *= khalf;
1382 continue;
1383 }
1384
1385 xyzt[0] = xt;
1386 xyzt[1] = yt;
1387 xyzt[2] = zt;
1388
1389 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1390 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1391
1392 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1393 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1394 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1395
1396 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1397 secys[3] = (ct*f[0] - at*f[2])* ph2;
1398 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1399 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1400 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1401 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1402
1403 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1404 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1405 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1406
1407 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1408 if (ncut++ > maxcut) break;
1409 h *= khalf;
1410 continue;
1411 }
1412
1413 ncut = 0;
1414 // * if too many iterations, go to helix
1415 if (iter++ > maxit) break;
1416
1417 tl += h;
1418 if (est < kdlt32)
1419 h *= 2.;
1420 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1421 vout[0] = x;
1422 vout[1] = y;
1423 vout[2] = z;
1424 vout[3] = cba*a;
1425 vout[4] = cba*b;
1426 vout[5] = cba*c;
1427 rest = step - tl;
1428 if (step < 0.) rest = -rest;
ade4e6f9 1429 if (rest < 1.e-5*TMath::Abs(step)) return kTRUE;
c04e3238 1430
1431 } while(1);
1432
1433 // angle too big, use helix
ade4e6f9 1434 cout<<"W-AliMUONTrackExtrap::ExtrapOneStepRungekutta: Ruge-Kutta failed: switch to helix"<<endl;
c04e3238 1435
1436 f1 = f[0];
1437 f2 = f[1];
1438 f3 = f[2];
1439 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
ade4e6f9 1440 if (f4 < 1.e-10) {
1441 cout<<"E-AliMUONTrackExtrap::ExtrapOneStepRungekutta: magnetic field at (";
1442 cout<<xyzt[0]<<", "<<xyzt[1]<<", "<<xyzt[2]<<") = "<<f4<<": giving up"<<endl;
1443 return kFALSE;
1444 }
c04e3238 1445 rho = -f4*pinv;
1446 tet = rho * step;
1447
1448 hnorm = 1./f4;
1449 f1 = f1*hnorm;
1450 f2 = f2*hnorm;
1451 f3 = f3*hnorm;
1452
1453 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1454 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1455 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1456
1457 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1458
1459 rho1 = 1./rho;
1460 sint = TMath::Sin(tet);
1461 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1462
1463 g1 = sint*rho1;
1464 g2 = cost*rho1;
1465 g3 = (tet-sint) * hp*rho1;
1466 g4 = -cost;
1467 g5 = sint;
1468 g6 = cost * hp;
1469
1470 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1471 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1472 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1473
1474 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1475 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1476 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1477
ade4e6f9 1478 return kTRUE;
c04e3238 1479}
8cde4af5 1480