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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
9f093251 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
690d2205 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 }
019df241 104}
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);
208f139e 156}
c04e3238 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]);
208f139e 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;
619 Double_t zB = trackXYZIn[2];
620 Double_t zE, dzB, dzE;
621 do {
622 // Get material properties
623 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
624 rho = material->GetDensity();
625 x0 = material->GetRadLen();
84f061ef 626 atomicA = material->GetA();
627 atomicZ = material->GetZ();
fa5e35be 628 if(material->IsMixture()){
629 TGeoMixture * mixture = (TGeoMixture*)material;
630 atomicZoverA = 0.;
631 Double_t sum = 0.;
632 for (Int_t iel=0;iel<mixture->GetNelements();iel++){
633 sum += mixture->GetWmixt()[iel];
634 atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
635 }
636 atomicZoverA/=sum;
637 }
638 else atomicZoverA = atomicZ/atomicA;
8cde4af5 639
640 // Get path length within this material
641 gGeoManager->FindNextBoundary(remainingPathLength);
642 localPathLength = gGeoManager->GetStep() + 1.e-6;
643 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
644 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
645 else {
646 currentnode = gGeoManager->Step();
647 if (!currentnode) {
648 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 649 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
650 return kFALSE;
8cde4af5 651 }
652 if (!gGeoManager->IsEntering()) {
653 // make another small step to try to enter in new absorber slice
654 gGeoManager->SetStep(0.001);
655 currentnode = gGeoManager->Step();
656 if (!gGeoManager->IsEntering() || !currentnode) {
657 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 658 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
659 return kFALSE;
8cde4af5 660 }
661 localPathLength += 0.001;
662 }
663 }
664
665 // calculate absorber's parameters
666 zE = b[2] * localPathLength + zB;
667 dzB = zB - trackXYZIn[2];
668 dzE = zE - trackXYZIn[2];
669 f0 += localPathLength / x0;
670 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
671 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
672 meanRho += localPathLength * rho;
fa5e35be 673 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
674 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicZoverA);
8cde4af5 675
676 // prepare next step
677 zB = zE;
678 remainingPathLength -= localPathLength;
679 } while (remainingPathLength > TGeoShape::Tolerance());
680
681 meanRho /= pathLength;
18abc511 682
683 return kTRUE;
8cde4af5 684}
685
690d2205 686//__________________________________________________________________________
ea94c18b 687Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
688{
689 /// Return the angular dispersion square due to multiple Coulomb scattering
690 /// through a material of thickness "dZ" and of radiation length "x0"
691 /// assuming linear propagation and using the small angle approximation.
692
693 Double_t bendingSlope = param.GetBendingSlope();
694 Double_t nonBendingSlope = param.GetNonBendingSlope();
695 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 696 (1.0 + bendingSlope * bendingSlope) /
697 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 698 // Path length in the material
699 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
700 // relativistic velocity
701 Double_t velo = 1.;
702 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
703 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
704
705 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
706}
707
690d2205 708//__________________________________________________________________________
8cde4af5 709void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 710{
711 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 712 /// through a material of thickness "Abs(dZ)" and of radiation length "x0"
208f139e 713 /// assuming linear propagation and using the small angle approximation.
37a615ac 714 /// dZ = zOut - zIn (sign is important) and "param" is assumed to be given zOut.
715 /// If x0 <= 0., assume dZ = pathLength/x0 and consider the material thickness as negligible.
208f139e 716
717 Double_t bendingSlope = param->GetBendingSlope();
718 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 719 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
720 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
721 (1.0 + bendingSlope * bendingSlope) /
722 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 723 // Path length in the material
37a615ac 724 Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
725 Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength);
208f139e 726 // relativistic velocity
727 Double_t velo = 1.;
728 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
37a615ac 729 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
730 theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
208f139e 731
37a615ac 732 Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
208f139e 733 Double_t varSlop = theta02;
37a615ac 734 Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.;
ea94c18b 735
690d2205 736 // Set MCS covariance matrix
ea94c18b 737 TMatrixD newParamCov(param->GetCovariances());
208f139e 738 // Non bending plane
ea94c18b 739 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
740 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 741 // Bending plane
ea94c18b 742 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
743 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 744
745 // Set momentum related covariances if B!=0
746 if (fgFieldON) {
747 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
748 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
749 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
750 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
751 // Inverse bending momentum (due to dependences with bending and non bending slopes)
752 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
753 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
754 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
755 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
756 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
757 }
208f139e 758
ea94c18b 759 // Set new covariances
760 param->SetCovariances(newParamCov);
c04e3238 761}
762
690d2205 763//__________________________________________________________________________
764void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
765 Double_t xVtx, Double_t yVtx, Double_t zVtx,
766 Double_t errXVtx, Double_t errYVtx,
767 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 768{
690d2205 769 /// Main method for extrapolation to the vertex:
770 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
771 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
772 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
773 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
774 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
775 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 776
8cde4af5 777 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 778
8cde4af5 779 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 780 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
781 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 782 return;
783 }
784
8cde4af5 785 // Check the vertex position relatively to the absorber
ea94c18b 786 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 787 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 788 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 789 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 790 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 791 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
792 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
793 else ExtrapToZ(trackParam,zVtx);
8cde4af5 794 return;
795 }
796
797 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 798 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 799 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 800 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
801 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
802 else ExtrapToZ(trackParam,zVtx);
8cde4af5 803 return;
ea94c18b 804 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 805 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 806 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 807 } else {
690d2205 808 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
809 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 810 }
c04e3238 811
690d2205 812 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 813 Double_t trackXYZOut[3];
814 trackXYZOut[0] = trackParam->GetNonBendingCoor();
815 trackXYZOut[1] = trackParam->GetBendingCoor();
816 trackXYZOut[2] = trackParam->GetZ();
817 Double_t trackXYZIn[3];
690d2205 818 if (correctForMCS) { // assume linear propagation until the vertex
819 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
820 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
821 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
822 } else {
823 AliMUONTrackParam trackParamIn(*trackParam);
824 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
825 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
826 trackXYZIn[1] = trackParamIn.GetBendingCoor();
827 trackXYZIn[2] = trackParamIn.GetZ();
828 }
84f061ef 829 Double_t pTot = trackParam->P();
ecdf58c4 830 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
831 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
18abc511 832 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
833 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
834 else ExtrapToZ(trackParam,zVtx);
835 return;
836 }
8cde4af5 837
690d2205 838 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
839 if (correctForMCS) {
fac70e25 840
690d2205 841 if (correctForEnergyLoss) {
842
843 // Correct for multiple scattering and energy loss
ecdf58c4 844 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 845 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
846 trackXYZIn[2], pathLength, f0, f1, f2);
ecdf58c4 847 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 848
849 } else {
850
851 // Correct for multiple scattering
852 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
853 trackXYZIn[2], pathLength, f0, f1, f2);
854 }
fac70e25 855
fac70e25 856 } else {
690d2205 857
858 if (correctForEnergyLoss) {
859
18abc511 860 // Correct for energy loss add multiple scattering dispersion in covariance matrix
ecdf58c4 861 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
37a615ac 862 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 863 ExtrapToZCov(trackParam, trackXYZIn[2]);
ecdf58c4 864 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 865 ExtrapToZCov(trackParam, zVtx);
866
867 } else {
868
18abc511 869 // add multiple scattering dispersion in covariance matrix
37a615ac 870 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 871 ExtrapToZCov(trackParam, zVtx);
872
873 }
874
fac70e25 875 }
8cde4af5 876
fac70e25 877}
878
690d2205 879//__________________________________________________________________________
880void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
881 Double_t xVtx, Double_t yVtx, Double_t zVtx,
882 Double_t errXVtx, Double_t errYVtx)
883{
884 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
885 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
886 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
887}
888
889//__________________________________________________________________________
890void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
891 Double_t xVtx, Double_t yVtx, Double_t zVtx,
892 Double_t errXVtx, Double_t errYVtx)
893{
894 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
895 /// Add branson correction resolution to parameter covariances
896 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
897}
898
899//__________________________________________________________________________
900void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
901{
902 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
903 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
904 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
905}
906
907//__________________________________________________________________________
908void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
909{
910 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
911 /// Add dispersion due to multiple scattering to parameter covariances
912 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
913}
914
915//__________________________________________________________________________
fac70e25 916Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
917{
918 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
919
920 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 921
fac70e25 922 // Check whether the geometry is available
923 if (!gGeoManager) {
924 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
925 return 0.;
926 }
927
928 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
929 Double_t trackXYZOut[3];
930 trackXYZOut[0] = trackParam->GetNonBendingCoor();
931 trackXYZOut[1] = trackParam->GetBendingCoor();
932 trackXYZOut[2] = trackParam->GetZ();
933 Double_t trackXYZIn[3];
934 trackXYZIn[0] = xVtx;
935 trackXYZIn[1] = yVtx;
936 trackXYZIn[2] = zVtx;
84f061ef 937 Double_t pTot = trackParam->P();
18abc511 938 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 939 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 940
ecdf58c4 941 // total momentum corrected for energy loss
942 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
943 Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
944 Double_t eCorr = e + totalELoss;
945 Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
946
947 return pTotCorr - pTot;
c04e3238 948}
949
690d2205 950//__________________________________________________________________________
fa5e35be 951Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
c04e3238 952{
84f061ef 953 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
954 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 955 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
84f061ef 956
ecdf58c4 957 // mean exitation energy (GeV)
958 Double_t i;
959 if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
960 else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
690d2205 961
fa5e35be 962 return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
c04e3238 963}
964
690d2205 965//__________________________________________________________________________
fa5e35be 966Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
690d2205 967{
968 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
969 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 970 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
690d2205 971 //Double_t eMass = 0.510998918e-3; // GeV
972 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
973 Double_t p2=pTotal*pTotal;
974 Double_t beta2=p2/(p2 + muMass*muMass);
975
fa5e35be 976 Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
690d2205 977 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
978
979 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
980
981 return sigma2;
982}
983
984//__________________________________________________________________________
985void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
986{
987 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
988 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
989
990 // charge * total momentum
991 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
992 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
993
994 // Jacobian of the opposite transformation
995 TMatrixD jacob(5,5);
996 jacob.UnitMatrix();
997 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
998 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
999 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1000 jacob(4,4) = - qPTot / param(4,0);
1001
1002 // compute covariances in new coordinate system
1003 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
1004 cov.Mult(jacob,tmp);
1005}
1006
1007//__________________________________________________________________________
1008void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
1009{
1010 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
1011 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
1012
1013 // charge * total momentum
1014 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
1015 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
1016
1017 // Jacobian of the transformation
1018 TMatrixD jacob(5,5);
1019 jacob.UnitMatrix();
1020 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1021 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
1022 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1023 jacob(4,4) = - param(4,0) / qPTot;
1024
1025 // compute covariances in new coordinate system
1026 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
1027 covP.Mult(jacob,tmp);
1028}
1029
c04e3238 1030 //__________________________________________________________________________
57e2ad1a 1031void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
c04e3238 1032{
71a2d3aa 1033/// <pre>
c04e3238 1034/// ******************************************************************
1035/// * *
1036/// * Performs the tracking of one step in a magnetic field *
1037/// * The trajectory is assumed to be a helix in a constant field *
1038/// * taken at the mid point of the step. *
1039/// * Parameters: *
1040/// * input *
1041/// * STEP =arc length of the step asked *
1042/// * VECT =input vector (position,direction cos and momentum) *
1043/// * CHARGE= electric charge of the particle *
1044/// * output *
1045/// * VOUT = same as VECT after completion of the step *
1046/// * *
2060b217 1047/// * ==>Called by : USER, GUSWIM *
c04e3238 1048/// * Author m.hansroul ********* *
1049/// * modified s.egli, s.v.levonian *
1050/// * modified v.perevoztchikov
1051/// * *
1052/// ******************************************************************
71a2d3aa 1053/// </pre>
c04e3238 1054
1055// modif: everything in double precision
1056
1057 Double_t xyz[3], h[4], hxp[3];
1058 Double_t h2xy, hp, rho, tet;
1059 Double_t sint, sintt, tsint, cos1t;
1060 Double_t f1, f2, f3, f4, f5, f6;
1061
1062 const Int_t kix = 0;
1063 const Int_t kiy = 1;
1064 const Int_t kiz = 2;
1065 const Int_t kipx = 3;
1066 const Int_t kipy = 4;
1067 const Int_t kipz = 5;
1068 const Int_t kipp = 6;
1069
1070 const Double_t kec = 2.9979251e-4;
1071 //
1072 // ------------------------------------------------------------------
1073 //
1074 // units are kgauss,centimeters,gev/c
1075 //
1076 vout[kipp] = vect[kipp];
1077 if (TMath::Abs(charge) < 0.00001) {
1078 for (Int_t i = 0; i < 3; i++) {
1079 vout[i] = vect[i] + step * vect[i+3];
1080 vout[i+3] = vect[i+3];
1081 }
1082 return;
1083 }
1084 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1085 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1086 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1087
1088 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 1089 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 1090
1091 h2xy = h[0]*h[0] + h[1]*h[1];
1092 h[3] = h[2]*h[2]+ h2xy;
1093 if (h[3] < 1.e-12) {
1094 for (Int_t i = 0; i < 3; i++) {
1095 vout[i] = vect[i] + step * vect[i+3];
1096 vout[i+3] = vect[i+3];
1097 }
1098 return;
1099 }
1100 if (h2xy < 1.e-12*h[3]) {
1101 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1102 return;
1103 }
1104 h[3] = TMath::Sqrt(h[3]);
1105 h[0] /= h[3];
1106 h[1] /= h[3];
1107 h[2] /= h[3];
1108 h[3] *= kec;
1109
1110 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1111 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1112 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1113
1114 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1115
1116 rho = -charge*h[3]/vect[kipp];
1117 tet = rho * step;
1118
1119 if (TMath::Abs(tet) > 0.15) {
1120 sint = TMath::Sin(tet);
1121 sintt = (sint/tet);
1122 tsint = (tet-sint)/tet;
1123 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1124 } else {
1125 tsint = tet*tet/36.;
1126 sintt = (1. - tsint);
1127 sint = tet*sintt;
1128 cos1t = 0.5*tet;
1129 }
1130
1131 f1 = step * sintt;
1132 f2 = step * cos1t;
1133 f3 = step * tsint * hp;
1134 f4 = -tet*cos1t;
1135 f5 = sint;
1136 f6 = tet * cos1t * hp;
1137
1138 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1139 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1140 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1141
1142 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1143 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1144 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1145
1146 return;
1147}
1148
1149 //__________________________________________________________________________
57e2ad1a 1150void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
c04e3238 1151{
71a2d3aa 1152/// <pre>
c04e3238 1153/// ******************************************************************
1154/// * *
1155/// * Tracking routine in a constant field oriented *
1156/// * along axis 3 *
1157/// * Tracking is performed with a conventional *
1158/// * helix step method *
1159/// * *
2060b217 1160/// * ==>Called by : USER, GUSWIM *
c04e3238 1161/// * Authors R.Brun, M.Hansroul ********* *
1162/// * Rewritten V.Perevoztchikov
1163/// * *
1164/// ******************************************************************
71a2d3aa 1165/// </pre>
c04e3238 1166
1167 Double_t hxp[3];
1168 Double_t h4, hp, rho, tet;
1169 Double_t sint, sintt, tsint, cos1t;
1170 Double_t f1, f2, f3, f4, f5, f6;
1171
1172 const Int_t kix = 0;
1173 const Int_t kiy = 1;
1174 const Int_t kiz = 2;
1175 const Int_t kipx = 3;
1176 const Int_t kipy = 4;
1177 const Int_t kipz = 5;
1178 const Int_t kipp = 6;
1179
1180 const Double_t kec = 2.9979251e-4;
1181
1182//
1183// ------------------------------------------------------------------
1184//
1185// units are kgauss,centimeters,gev/c
1186//
1187 vout[kipp] = vect[kipp];
1188 h4 = field * kec;
1189
1190 hxp[0] = - vect[kipy];
1191 hxp[1] = + vect[kipx];
1192
1193 hp = vect[kipz];
1194
1195 rho = -h4/vect[kipp];
1196 tet = rho * step;
1197 if (TMath::Abs(tet) > 0.15) {
1198 sint = TMath::Sin(tet);
1199 sintt = (sint/tet);
1200 tsint = (tet-sint)/tet;
1201 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1202 } else {
1203 tsint = tet*tet/36.;
1204 sintt = (1. - tsint);
1205 sint = tet*sintt;
1206 cos1t = 0.5*tet;
1207 }
1208
1209 f1 = step * sintt;
1210 f2 = step * cos1t;
1211 f3 = step * tsint * hp;
1212 f4 = -tet*cos1t;
1213 f5 = sint;
1214 f6 = tet * cos1t * hp;
1215
1216 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1217 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1218 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1219
1220 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1221 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1222 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1223
1224 return;
1225}
8cde4af5 1226
c04e3238 1227 //__________________________________________________________________________
57e2ad1a 1228Bool_t AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t* vect, Double_t* vout)
c04e3238 1229{
71a2d3aa 1230/// <pre>
c04e3238 1231/// ******************************************************************
1232/// * *
1233/// * Runge-Kutta method for tracking a particle through a magnetic *
1234/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1235/// * Standards, procedure 25.5.20) *
1236/// * *
1237/// * Input parameters *
1238/// * CHARGE Particle charge *
1239/// * STEP Step size *
1240/// * VECT Initial co-ords,direction cosines,momentum *
1241/// * Output parameters *
1242/// * VOUT Output co-ords,direction cosines,momentum *
1243/// * User routine called *
1244/// * CALL GUFLD(X,F) *
1245/// * *
2060b217 1246/// * ==>Called by : USER, GUSWIM *
c04e3238 1247/// * Authors R.Brun, M.Hansroul ********* *
1248/// * V.Perevoztchikov (CUT STEP implementation) *
1249/// * *
1250/// * *
1251/// ******************************************************************
71a2d3aa 1252/// </pre>
c04e3238 1253
1254 Double_t h2, h4, f[4];
d373bcbe 1255 Double_t xyzt[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
1256 Double_t a, b, c, ph,ph2;
c04e3238 1257 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1258 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1259 Double_t est, at, bt, ct, cba;
1260 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1261
1262 Double_t x;
1263 Double_t y;
1264 Double_t z;
1265
1266 Double_t xt;
1267 Double_t yt;
1268 Double_t zt;
1269
1270 Double_t maxit = 1992;
1271 Double_t maxcut = 11;
1272
1273 const Double_t kdlt = 1e-4;
1274 const Double_t kdlt32 = kdlt/32.;
1275 const Double_t kthird = 1./3.;
1276 const Double_t khalf = 0.5;
1277 const Double_t kec = 2.9979251e-4;
1278
1279 const Double_t kpisqua = 9.86960440109;
1280 const Int_t kix = 0;
1281 const Int_t kiy = 1;
1282 const Int_t kiz = 2;
1283 const Int_t kipx = 3;
1284 const Int_t kipy = 4;
1285 const Int_t kipz = 5;
1286
1287 // *.
1288 // *. ------------------------------------------------------------------
1289 // *.
1290 // * this constant is for units cm,gev/c and kgauss
1291 // *
1292 Int_t iter = 0;
1293 Int_t ncut = 0;
1294 for(Int_t j = 0; j < 7; j++)
1295 vout[j] = vect[j];
1296
1297 Double_t pinv = kec * charge / vect[6];
1298 Double_t tl = 0.;
1299 Double_t h = step;
1300 Double_t rest;
1301
1302
1303 do {
1304 rest = step - tl;
1305 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1306 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1307 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1308
1309 // *
1310 // * start of integration
1311 // *
1312 x = vout[0];
1313 y = vout[1];
1314 z = vout[2];
1315 a = vout[3];
1316 b = vout[4];
1317 c = vout[5];
1318
1319 h2 = khalf * h;
1320 h4 = khalf * h2;
1321 ph = pinv * h;
1322 ph2 = khalf * ph;
1323 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1324 secys[0] = (c * f[0] - a * f[2]) * ph2;
1325 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1326 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1327 if (ang2 > kpisqua) break;
1328
1329 dxt = h2 * a + h4 * secxs[0];
1330 dyt = h2 * b + h4 * secys[0];
1331 dzt = h2 * c + h4 * seczs[0];
1332 xt = x + dxt;
1333 yt = y + dyt;
1334 zt = z + dzt;
1335 // *
1336 // * second intermediate point
1337 // *
1338
1339 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1340 if (est > h) {
1341 if (ncut++ > maxcut) break;
1342 h *= khalf;
1343 continue;
1344 }
1345
1346 xyzt[0] = xt;
1347 xyzt[1] = yt;
1348 xyzt[2] = zt;
1349
1350 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1351 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1352
1353 at = a + secxs[0];
1354 bt = b + secys[0];
1355 ct = c + seczs[0];
1356
1357 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1358 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1359 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1360 at = a + secxs[1];
1361 bt = b + secys[1];
1362 ct = c + seczs[1];
1363 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1364 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1365 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1366 dxt = h * (a + secxs[2]);
1367 dyt = h * (b + secys[2]);
1368 dzt = h * (c + seczs[2]);
1369 xt = x + dxt;
1370 yt = y + dyt;
1371 zt = z + dzt;
1372 at = a + 2.*secxs[2];
1373 bt = b + 2.*secys[2];
1374 ct = c + 2.*seczs[2];
1375
1376 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1377 if (est > 2.*TMath::Abs(h)) {
1378 if (ncut++ > maxcut) break;
1379 h *= khalf;
1380 continue;
1381 }
1382
1383 xyzt[0] = xt;
1384 xyzt[1] = yt;
1385 xyzt[2] = zt;
1386
1387 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1388 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1389
1390 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1391 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1392 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1393
1394 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1395 secys[3] = (ct*f[0] - at*f[2])* ph2;
1396 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1397 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1398 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1399 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1400
1401 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1402 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1403 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1404
1405 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1406 if (ncut++ > maxcut) break;
1407 h *= khalf;
1408 continue;
1409 }
1410
1411 ncut = 0;
1412 // * if too many iterations, go to helix
1413 if (iter++ > maxit) break;
1414
1415 tl += h;
1416 if (est < kdlt32)
1417 h *= 2.;
1418 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1419 vout[0] = x;
1420 vout[1] = y;
1421 vout[2] = z;
1422 vout[3] = cba*a;
1423 vout[4] = cba*b;
1424 vout[5] = cba*c;
1425 rest = step - tl;
1426 if (step < 0.) rest = -rest;
ade4e6f9 1427 if (rest < 1.e-5*TMath::Abs(step)) return kTRUE;
c04e3238 1428
1429 } while(1);
1430
1431 // angle too big, use helix
ade4e6f9 1432 cout<<"W-AliMUONTrackExtrap::ExtrapOneStepRungekutta: Ruge-Kutta failed: switch to helix"<<endl;
c04e3238 1433
1434 f1 = f[0];
1435 f2 = f[1];
1436 f3 = f[2];
1437 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
ade4e6f9 1438 if (f4 < 1.e-10) {
1439 cout<<"E-AliMUONTrackExtrap::ExtrapOneStepRungekutta: magnetic field at (";
1440 cout<<xyzt[0]<<", "<<xyzt[1]<<", "<<xyzt[2]<<") = "<<f4<<": giving up"<<endl;
1441 return kFALSE;
1442 }
c04e3238 1443 rho = -f4*pinv;
1444 tet = rho * step;
1445
1446 hnorm = 1./f4;
1447 f1 = f1*hnorm;
1448 f2 = f2*hnorm;
1449 f3 = f3*hnorm;
1450
1451 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1452 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1453 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1454
1455 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1456
1457 rho1 = 1./rho;
1458 sint = TMath::Sin(tet);
1459 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1460
1461 g1 = sint*rho1;
1462 g2 = cost*rho1;
1463 g3 = (tet-sint) * hp*rho1;
1464 g4 = -cost;
1465 g5 = sint;
1466 g6 = cost * hp;
1467
1468 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1469 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1470 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1471
1472 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1473 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1474 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1475
ade4e6f9 1476 return kTRUE;
c04e3238 1477}
8cde4af5 1478