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-- modified cut analysis for Pb-Pb
[u/mrichter/AliRoot.git] / MUON / AliMUONTrackExtrap.cxx
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c04e3238 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
56316147 18//-----------------------------------------------------------------------------
19// Class AliMUONTrackExtrap
20// ------------------------
21// Tools for track extrapolation in ALICE dimuon spectrometer
22// Author: Philippe Pillot
23//-----------------------------------------------------------------------------
c04e3238 24
c04e3238 25#include "AliMUONTrackExtrap.h"
26#include "AliMUONTrackParam.h"
27#include "AliMUONConstants.h"
0e894e58 28#include "AliMUONReconstructor.h"
8cde4af5 29
ecdf58c4 30#include "AliMagF.h"
31#include "AliExternalTrackParam.h"
8cde4af5 32
f7a1cc68 33#include <TGeoGlobalMagField.h>
8cde4af5 34#include <TGeoManager.h>
f7a1cc68 35#include <TMath.h>
ecdf58c4 36#include <TDatabasePDG.h>
c04e3238 37
ea94c18b 38#include <Riostream.h>
39
78649106 40/// \cond CLASSIMP
c04e3238 41ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 42/// \endcond
c04e3238 43
9f093251 44const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
45const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
46 Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
47 Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
4284483e 48const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 49const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 50const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
51const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 52
9f093251 53//__________________________________________________________________________
f7a1cc68 54void AliMUONTrackExtrap::SetField()
9f093251 55{
cddcc1f3 56 /// set field on/off flag;
57 /// set field at the centre of the dipole
f7a1cc68 58 const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
59 Double_t b[3] = {0.,0.,0.};
60 TGeoGlobalMagField::Instance()->Field(x,b);
61 fgSimpleBValue = b[0];
ade4e6f9 62 fgFieldON = (TMath::Abs(fgSimpleBValue) > 1.e-10) ? kTRUE : kFALSE;
9f093251 63
64}
65
690d2205 66//__________________________________________________________________________
208f139e 67Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
68{
69 /// Returns impact parameter at vertex in bending plane (cm),
70 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
71 /// using simple values for dipole magnetic field.
72 /// The sign of "BendingMomentum" is the sign of the charge.
73
74 if (bendingMomentum == 0.) return 1.e10;
75
6b191dea 76 const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
9f093251 77
78 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
208f139e 79}
80
690d2205 81//__________________________________________________________________________
9bdbee64 82Double_t
83AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
208f139e 84{
85 /// Returns signed bending momentum in bending plane (GeV/c),
86 /// the sign being the sign of the charge for particles moving forward in Z,
87 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
88 /// using simple values for dipole magnetic field.
89
90 if (impactParam == 0.) return 1.e10;
91
9f093251 92 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
93
9bdbee64 94 if (fgFieldON)
95 {
96 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
97 }
98 else
99 {
100 return AliMUONConstants::GetMostProbBendingMomentum();
101 }
019df241 102}
103
690d2205 104//__________________________________________________________________________
3fe6651e 105void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
019df241 106{
3fe6651e 107 /// Track parameters linearly extrapolated to the plane at "zEnd".
019df241 108 /// On return, results from the extrapolation are updated in trackParam.
109
110 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
111
112 // Compute track parameters
113 Double_t dZ = zEnd - trackParam->GetZ();
114 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
115 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
116 trackParam->SetZ(zEnd);
3fe6651e 117}
118
119//__________________________________________________________________________
120void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
121{
122 /// Track parameters and their covariances linearly extrapolated to the plane at "zEnd".
123 /// On return, results from the extrapolation are updated in trackParam.
019df241 124
3fe6651e 125 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
126
127 // No need to propagate the covariance matrix if it does not exist
128 if (!trackParam->CovariancesExist()) {
129 cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
130 // Extrapolate linearly track parameters to "zEnd"
131 LinearExtrapToZ(trackParam,zEnd);
132 return;
019df241 133 }
134
3fe6651e 135 // Compute track parameters
136 Double_t dZ = zEnd - trackParam->GetZ();
137 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
138 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
139 trackParam->SetZ(zEnd);
140
141 // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
142 TMatrixD jacob(5,5);
143 jacob.UnitMatrix();
144 jacob(0,1) = dZ;
145 jacob(2,3) = dZ;
146
147 // Extrapolate track parameter covariances to "zEnd"
148 TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
149 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
150 trackParam->SetCovariances(tmp2);
151
152 // Update the propagator if required
153 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 154}
c04e3238 155
690d2205 156//__________________________________________________________________________
4ea3f013 157Bool_t AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
c04e3238 158{
4284483e 159 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
160 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 161 if (!fgFieldON) {
162 AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
163 return kTRUE;
164 }
165 else if (fgkUseHelix) return AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
166 else return AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
4284483e 167}
168
690d2205 169//__________________________________________________________________________
4ea3f013 170Bool_t AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
4284483e 171{
172 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 173 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 174 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
c04e3238 175 Double_t forwardBackward; // +1 if forward, -1 if backward
176 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
177 else forwardBackward = -1.0;
dade8580 178 Double_t v3[7], v3New[7]; // 7 in parameter ????
179 Int_t i3, stepNumber;
c04e3238 180 // For safety: return kTRUE or kFALSE ????
181 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 182 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 183 // sign of charge (sign of fInverseBendingMomentum if forward motion)
184 // must be changed if backward extrapolation
208f139e 185 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 186 // Extrapolation loop
187 stepNumber = 0;
208f139e 188 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 189 stepNumber++;
4284483e 190 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 191 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 192 // better use TArray ????
208f139e 193 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 194 }
208f139e 195 // check fgkMaxStepNumber ????
c04e3238 196 // Interpolation back to exact Z (2nd order)
197 // should be in function ???? using TArray ????
dade8580 198 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 199 if (TMath::Abs(dZ12) > 0) {
dade8580 200 Double_t dZ1i = zEnd - v3[2]; // 1-i
201 Double_t dZi2 = v3New[2] - zEnd; // i->2
202 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
203 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
204 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
205 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
206 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
207 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
208 v3[2] = zEnd; // Z
c04e3238 209 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
210 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
211 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 212 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 213 v3[3] = xPrimeI * v3[5]; // PX/PTOT
214 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 215 } else {
4284483e 216 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 217 }
4284483e 218 // Recover track parameters (charge back for forward motion)
dade8580 219 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
4ea3f013 220 return kTRUE;
c04e3238 221}
222
690d2205 223//__________________________________________________________________________
4ea3f013 224Bool_t AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
4284483e 225{
226 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
227 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 228 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
4284483e 229 Double_t forwardBackward; // +1 if forward, -1 if backward
230 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
231 else forwardBackward = -1.0;
232 // sign of charge (sign of fInverseBendingMomentum if forward motion)
233 // must be changed if backward extrapolation
234 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
235 Double_t v3[7], v3New[7];
236 Double_t dZ, step;
237 Int_t stepNumber = 0;
238
4ea3f013 239 // Extrapolation loop (until within tolerance or the track turn around)
4284483e 240 Double_t residue = zEnd - trackParam->GetZ();
4ea3f013 241 Bool_t uturn = kFALSE;
ade4e6f9 242 Bool_t trackingFailed = kFALSE;
4ea3f013 243 Bool_t tooManyStep = kFALSE;
4284483e 244 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
4ea3f013 245
4284483e 246 dZ = zEnd - trackParam->GetZ();
247 // step lenght assuming linear trajectory
248 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 249 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 250 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
4ea3f013 251
4284483e 252 do { // reduce step lenght while zEnd oversteped
253 if (stepNumber > fgkMaxStepNumber) {
254 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
4ea3f013 255 tooManyStep = kTRUE;
4284483e 256 break;
257 }
258 stepNumber ++;
259 step = TMath::Abs(step);
ade4e6f9 260 if (!AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New)) {
261 trackingFailed = kTRUE;
262 break;
263 }
4284483e 264 residue = zEnd - v3New[2];
265 step *= dZ/(v3New[2]-trackParam->GetZ());
266 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
4ea3f013 267
ade4e6f9 268 if (trackingFailed) break;
269 else if (v3New[5]*v3[5] < 0) { // the track turned around
4ea3f013 270 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl;
271 uturn = kTRUE;
272 break;
273 } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
274
4284483e 275 }
276
277 // terminate the extropolation with a straight line up to the exact "zEnd" value
ade4e6f9 278 if (trackingFailed || uturn) {
4ea3f013 279
280 // track ends +-100 meters away in the bending direction
281 dZ = zEnd - v3[2];
282 Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ;
283 Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
284 Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope());
285 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope);
286 trackParam->SetNonBendingSlope(nonBendingSlope);
287 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope);
288 trackParam->SetBendingSlope(bendingSlope);
289 trackParam->SetZ(zEnd);
290
291 return kFALSE;
292
293 } else {
294
295 // track extrapolated normally
296 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
297 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
298 trackParam->SetZ(zEnd);
299
300 return !tooManyStep;
301
302 }
303
4284483e 304}
305
690d2205 306//__________________________________________________________________________
4284483e 307void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 308{
dade8580 309 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 310 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
311 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 312 v3[0] = trackParam->GetNonBendingCoor(); // X
313 v3[1] = trackParam->GetBendingCoor(); // Y
314 v3[2] = trackParam->GetZ(); // Z
c04e3238 315 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
316 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 317 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
318 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
319 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
320 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 321}
322
690d2205 323//__________________________________________________________________________
dade8580 324void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 325{
dade8580 326 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 327 /// assumed to be calculated for forward motion in Z.
328 /// "InverseBendingMomentum" is signed with "charge".
dade8580 329 trackParam->SetNonBendingCoor(v3[0]); // X
330 trackParam->SetBendingCoor(v3[1]); // Y
331 trackParam->SetZ(v3[2]); // Z
60e55aee 332 Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
c04e3238 333 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 334 trackParam->SetBendingSlope(v3[4]/v3[5]);
335 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
208f139e 336}
337
690d2205 338//__________________________________________________________________________
4ea3f013 339Bool_t AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 340{
341 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
342 /// On return, results from the extrapolation are updated in trackParam.
343
4ea3f013 344 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z
208f139e 345
9f093251 346 if (!fgFieldON) { // linear extrapolation if no magnetic field
3fe6651e 347 AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
4ea3f013 348 return kTRUE;
9f093251 349 }
350
ea94c18b 351 // No need to propagate the covariance matrix if it does not exist
352 if (!trackParam->CovariancesExist()) {
353 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
354 // Extrapolate track parameters to "zEnd"
4ea3f013 355 return ExtrapToZ(trackParam,zEnd);
ea94c18b 356 }
357
208f139e 358 // Save the actual track parameters
359 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 360 TMatrixD paramSave(trackParamSave.GetParameters());
361 Double_t zBegin = trackParamSave.GetZ();
362
363 // Get reference to the parameter covariance matrix
364 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 365
208f139e 366 // Extrapolate track parameters to "zEnd"
4ea3f013 367 // Do not update the covariance matrix if the extrapolation failed
368 if (!ExtrapToZ(trackParam,zEnd)) return kFALSE;
208f139e 369
ea94c18b 370 // Get reference to the extrapolated parameters
371 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 372
373 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
4ea3f013 374 Bool_t extrapStatus = kTRUE;
208f139e 375 TMatrixD jacob(5,5);
ea94c18b 376 jacob.Zero();
377 TMatrixD dParam(5,1);
6b191dea 378 Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
208f139e 379 for (Int_t i=0; i<5; i++) {
380 // Skip jacobian calculation for parameters with no associated error
18abc511 381 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 382
208f139e 383 // Small variation of parameter i only
384 for (Int_t j=0; j<5; j++) {
385 if (j==i) {
ea94c18b 386 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
6b191dea 387 dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
ea94c18b 388 } else dParam(j,0) = 0.;
208f139e 389 }
ea94c18b 390
208f139e 391 // Set new parameters
ea94c18b 392 trackParamSave.SetParameters(paramSave);
393 trackParamSave.AddParameters(dParam);
394 trackParamSave.SetZ(zBegin);
395
208f139e 396 // Extrapolate new track parameters to "zEnd"
4ea3f013 397 if (!ExtrapToZ(&trackParamSave,zEnd)) {
398 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl;
399 extrapStatus = kFALSE;
400 }
ea94c18b 401
208f139e 402 // Calculate the jacobian
ea94c18b 403 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
404 jacobji *= 1. / dParam(i,0);
405 jacob.SetSub(0,i,jacobji);
208f139e 406 }
407
408 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 409 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
410 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
411 trackParam->SetCovariances(tmp2);
412
413 // Update the propagator if required
414 if (updatePropagator) trackParam->UpdatePropagator(jacob);
4ea3f013 415
416 return extrapStatus;
208f139e 417}
418
690d2205 419//__________________________________________________________________________
37a615ac 420void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
8cde4af5 421{
422 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 423 /// signedPathLength must have the sign of (zOut - zIn) where all other parameters are assumed to be given at zOut.
8cde4af5 424
425 // absorber related covariance parameters
426 Double_t bendingSlope = param->GetBendingSlope();
427 Double_t nonBendingSlope = param->GetNonBendingSlope();
428 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
429 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 430 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
37a615ac 431 Double_t pathLength = TMath::Abs(signedPathLength);
8cde4af5 432 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
37a615ac 433 Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1);
8cde4af5 434 Double_t varSlop = alpha2 * f0;
435
690d2205 436 // Set MCS covariance matrix
ea94c18b 437 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 438 // Non bending plane
ea94c18b 439 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
440 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 441 // Bending plane
ea94c18b 442 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
443 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 444
445 // Set momentum related covariances if B!=0
446 if (fgFieldON) {
447 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
448 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
449 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
450 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
451 // Inverse bending momentum (due to dependences with bending and non bending slopes)
452 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
453 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
454 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
455 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
456 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
457 }
ea94c18b 458
459 // Set new covariances
460 param->SetCovariances(newParamCov);
690d2205 461}
462
463//__________________________________________________________________________
464void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
465 Double_t xVtx, Double_t yVtx, Double_t zVtx,
466 Double_t errXVtx, Double_t errYVtx,
467 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
468{
469 /// Correct parameters and corresponding covariances using Branson correction
470 /// - input param are parameters and covariances at the end of absorber
471 /// - output param are parameters and covariances at vertex
472 /// Absorber correction parameters are supposed to be calculated at the current track z-position
473
474 // Position of the Branson plane (spectro. (z<0))
475 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
476
37a615ac 477 // Add MCS effects to current parameter covariances (spectro. (z<0))
478 AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2);
690d2205 479
480 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
481 ExtrapToZCov(param,zVtx);
3fe6651e 482 LinearExtrapToZCov(param,zB);
690d2205 483
484 // compute track parameters at vertex
485 TMatrixD newParam(5,1);
486 newParam(0,0) = xVtx;
487 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
488 newParam(2,0) = yVtx;
489 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
490 newParam(4,0) = param->GetCharge() / param->P() *
491 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
492 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
493
494 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
495 TMatrixD paramCovP(param->GetCovariances());
496 Cov2CovP(param->GetParameters(),paramCovP);
497
498 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
499 TMatrixD paramCovVtx(5,5);
500 paramCovVtx.Zero();
501 paramCovVtx(0,0) = errXVtx * errXVtx;
502 paramCovVtx(1,1) = paramCovP(0,0);
503 paramCovVtx(2,2) = errYVtx * errYVtx;
504 paramCovVtx(3,3) = paramCovP(2,2);
505 paramCovVtx(4,4) = paramCovP(4,4);
506 paramCovVtx(1,3) = paramCovP(0,2);
507 paramCovVtx(3,1) = paramCovP(2,0);
508 paramCovVtx(1,4) = paramCovP(0,4);
509 paramCovVtx(4,1) = paramCovP(4,0);
510 paramCovVtx(3,4) = paramCovP(2,4);
511 paramCovVtx(4,3) = paramCovP(4,2);
512
513 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
514 TMatrixD jacob(5,5);
515 jacob.UnitMatrix();
516 jacob(1,0) = - 1. / (zB - zVtx);
517 jacob(1,1) = 1. / (zB - zVtx);
518 jacob(3,2) = - 1. / (zB - zVtx);
519 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 520
690d2205 521 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
522 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
523 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
524
525 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
526 CovP2Cov(newParam,newParamCov);
527
528 // Set parameters and covariances at vertex
529 param->SetParameters(newParam);
530 param->SetZ(zVtx);
531 param->SetCovariances(newParamCov);
8cde4af5 532}
533
690d2205 534//__________________________________________________________________________
535void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
536{
537 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
538
539 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
540 TMatrixD newParamCov(param->GetCovariances());
541 Cov2CovP(param->GetParameters(),newParamCov);
542
690d2205 543 // Compute new parameters corrected for energy loss
ecdf58c4 544 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
545 Double_t p = param->P();
546 Double_t e = TMath::Sqrt(p*p + muMass*muMass);
547 Double_t eCorr = e + eLoss;
548 Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
690d2205 549 Double_t nonBendingSlope = param->GetNonBendingSlope();
550 Double_t bendingSlope = param->GetBendingSlope();
ecdf58c4 551 param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
690d2205 552 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
553 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
554
ecdf58c4 555 // Add effects of energy loss fluctuation to covariances
556 newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
557
690d2205 558 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
559 CovP2Cov(param->GetParameters(),newParamCov);
560
561 // Set new parameter covariances
562 param->SetCovariances(newParamCov);
563}
564
565//__________________________________________________________________________
18abc511 566Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
567 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
568 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 569{
570 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 571 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 572 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
573 // f0: 0th moment of z calculated with the inverse radiation-length distribution
574 // f1: 1st moment of z calculated with the inverse radiation-length distribution
575 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
576 // meanRho: average density of crossed material (g/cm3)
84f061ef 577 // totalELoss: total energy loss in absorber
8cde4af5 578
579 // Reset absorber's parameters
580 pathLength = 0.;
581 f0 = 0.;
582 f1 = 0.;
583 f2 = 0.;
584 meanRho = 0.;
84f061ef 585 totalELoss = 0.;
690d2205 586 sigmaELoss2 = 0.;
8cde4af5 587
588 // Check whether the geometry is available
589 if (!gGeoManager) {
590 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 591 return kFALSE;
8cde4af5 592 }
593
594 // Initialize starting point and direction
595 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
596 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
597 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 598 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 599 Double_t b[3];
600 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
601 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
602 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
603 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
604 if (!currentnode) {
605 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 606 return kFALSE;
8cde4af5 607 }
608
609 // loop over absorber slices and calculate absorber's parameters
610 Double_t rho = 0.; // material density (g/cm3)
611 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 612 Double_t atomicA = 0.; // A of material
613 Double_t atomicZ = 0.; // Z of material
fa5e35be 614 Double_t atomicZoverA = 0.; // Z/A of material
8cde4af5 615 Double_t localPathLength = 0;
616 Double_t remainingPathLength = pathLength;
617 Double_t zB = trackXYZIn[2];
618 Double_t zE, dzB, dzE;
619 do {
620 // Get material properties
621 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
622 rho = material->GetDensity();
623 x0 = material->GetRadLen();
84f061ef 624 atomicA = material->GetA();
625 atomicZ = material->GetZ();
fa5e35be 626 if(material->IsMixture()){
627 TGeoMixture * mixture = (TGeoMixture*)material;
628 atomicZoverA = 0.;
629 Double_t sum = 0.;
630 for (Int_t iel=0;iel<mixture->GetNelements();iel++){
631 sum += mixture->GetWmixt()[iel];
632 atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
633 }
634 atomicZoverA/=sum;
635 }
636 else atomicZoverA = atomicZ/atomicA;
8cde4af5 637
638 // Get path length within this material
639 gGeoManager->FindNextBoundary(remainingPathLength);
640 localPathLength = gGeoManager->GetStep() + 1.e-6;
641 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
642 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
643 else {
644 currentnode = gGeoManager->Step();
645 if (!currentnode) {
646 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 647 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
648 return kFALSE;
8cde4af5 649 }
650 if (!gGeoManager->IsEntering()) {
651 // make another small step to try to enter in new absorber slice
652 gGeoManager->SetStep(0.001);
653 currentnode = gGeoManager->Step();
654 if (!gGeoManager->IsEntering() || !currentnode) {
655 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 656 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
657 return kFALSE;
8cde4af5 658 }
659 localPathLength += 0.001;
660 }
661 }
662
663 // calculate absorber's parameters
664 zE = b[2] * localPathLength + zB;
665 dzB = zB - trackXYZIn[2];
666 dzE = zE - trackXYZIn[2];
667 f0 += localPathLength / x0;
668 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
669 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
670 meanRho += localPathLength * rho;
fa5e35be 671 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
672 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicZoverA);
8cde4af5 673
674 // prepare next step
675 zB = zE;
676 remainingPathLength -= localPathLength;
677 } while (remainingPathLength > TGeoShape::Tolerance());
678
679 meanRho /= pathLength;
18abc511 680
681 return kTRUE;
8cde4af5 682}
683
690d2205 684//__________________________________________________________________________
ea94c18b 685Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
686{
687 /// Return the angular dispersion square due to multiple Coulomb scattering
688 /// through a material of thickness "dZ" and of radiation length "x0"
689 /// assuming linear propagation and using the small angle approximation.
690
691 Double_t bendingSlope = param.GetBendingSlope();
692 Double_t nonBendingSlope = param.GetNonBendingSlope();
693 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 694 (1.0 + bendingSlope * bendingSlope) /
695 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 696 // Path length in the material
697 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
698 // relativistic velocity
699 Double_t velo = 1.;
700 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
701 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
702
703 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
704}
705
690d2205 706//__________________________________________________________________________
8cde4af5 707void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 708{
709 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 710 /// through a material of thickness "Abs(dZ)" and of radiation length "x0"
208f139e 711 /// assuming linear propagation and using the small angle approximation.
37a615ac 712 /// dZ = zOut - zIn (sign is important) and "param" is assumed to be given zOut.
713 /// If x0 <= 0., assume dZ = pathLength/x0 and consider the material thickness as negligible.
208f139e 714
715 Double_t bendingSlope = param->GetBendingSlope();
716 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 717 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
718 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
719 (1.0 + bendingSlope * bendingSlope) /
720 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 721 // Path length in the material
37a615ac 722 Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
723 Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength);
208f139e 724 // relativistic velocity
725 Double_t velo = 1.;
726 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
37a615ac 727 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
728 theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
208f139e 729
37a615ac 730 Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
208f139e 731 Double_t varSlop = theta02;
37a615ac 732 Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.;
ea94c18b 733
690d2205 734 // Set MCS covariance matrix
ea94c18b 735 TMatrixD newParamCov(param->GetCovariances());
208f139e 736 // Non bending plane
ea94c18b 737 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
738 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 739 // Bending plane
ea94c18b 740 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
741 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 742
743 // Set momentum related covariances if B!=0
744 if (fgFieldON) {
745 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
746 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
747 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
748 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
749 // Inverse bending momentum (due to dependences with bending and non bending slopes)
750 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
751 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
752 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
753 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
754 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
755 }
208f139e 756
ea94c18b 757 // Set new covariances
758 param->SetCovariances(newParamCov);
c04e3238 759}
760
690d2205 761//__________________________________________________________________________
762void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
763 Double_t xVtx, Double_t yVtx, Double_t zVtx,
764 Double_t errXVtx, Double_t errYVtx,
765 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 766{
690d2205 767 /// Main method for extrapolation to the vertex:
768 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
769 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
770 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
771 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
772 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
773 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 774
8cde4af5 775 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 776
8cde4af5 777 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 778 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
779 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 780 return;
781 }
782
8cde4af5 783 // Check the vertex position relatively to the absorber
ea94c18b 784 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 785 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 786 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 787 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 788 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 789 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
790 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
791 else ExtrapToZ(trackParam,zVtx);
8cde4af5 792 return;
793 }
794
795 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 796 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 797 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 798 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
799 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
800 else ExtrapToZ(trackParam,zVtx);
8cde4af5 801 return;
ea94c18b 802 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 803 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 804 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 805 } else {
690d2205 806 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
807 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 808 }
c04e3238 809
690d2205 810 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 811 Double_t trackXYZOut[3];
812 trackXYZOut[0] = trackParam->GetNonBendingCoor();
813 trackXYZOut[1] = trackParam->GetBendingCoor();
814 trackXYZOut[2] = trackParam->GetZ();
815 Double_t trackXYZIn[3];
690d2205 816 if (correctForMCS) { // assume linear propagation until the vertex
817 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
818 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
819 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
820 } else {
821 AliMUONTrackParam trackParamIn(*trackParam);
822 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
823 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
824 trackXYZIn[1] = trackParamIn.GetBendingCoor();
825 trackXYZIn[2] = trackParamIn.GetZ();
826 }
84f061ef 827 Double_t pTot = trackParam->P();
ecdf58c4 828 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
829 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
18abc511 830 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
831 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
832 else ExtrapToZ(trackParam,zVtx);
833 return;
834 }
8cde4af5 835
690d2205 836 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
837 if (correctForMCS) {
fac70e25 838
690d2205 839 if (correctForEnergyLoss) {
840
841 // Correct for multiple scattering and energy loss
ecdf58c4 842 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 843 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
844 trackXYZIn[2], pathLength, f0, f1, f2);
ecdf58c4 845 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 846
847 } else {
848
849 // Correct for multiple scattering
850 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
851 trackXYZIn[2], pathLength, f0, f1, f2);
852 }
fac70e25 853
fac70e25 854 } else {
690d2205 855
856 if (correctForEnergyLoss) {
857
18abc511 858 // Correct for energy loss add multiple scattering dispersion in covariance matrix
ecdf58c4 859 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
37a615ac 860 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 861 ExtrapToZCov(trackParam, trackXYZIn[2]);
ecdf58c4 862 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 863 ExtrapToZCov(trackParam, zVtx);
864
865 } else {
866
18abc511 867 // add multiple scattering dispersion in covariance matrix
37a615ac 868 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 869 ExtrapToZCov(trackParam, zVtx);
870
871 }
872
fac70e25 873 }
8cde4af5 874
fac70e25 875}
876
690d2205 877//__________________________________________________________________________
878void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
879 Double_t xVtx, Double_t yVtx, Double_t zVtx,
880 Double_t errXVtx, Double_t errYVtx)
881{
882 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
883 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
884 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
885}
886
887//__________________________________________________________________________
888void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
889 Double_t xVtx, Double_t yVtx, Double_t zVtx,
890 Double_t errXVtx, Double_t errYVtx)
891{
892 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
893 /// Add branson correction resolution to parameter covariances
894 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
895}
896
897//__________________________________________________________________________
898void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
899{
900 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
901 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
902 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
903}
904
905//__________________________________________________________________________
906void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
907{
908 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
909 /// Add dispersion due to multiple scattering to parameter covariances
910 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
911}
912
913//__________________________________________________________________________
fac70e25 914Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
915{
916 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
917
918 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 919
fac70e25 920 // Check whether the geometry is available
921 if (!gGeoManager) {
922 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
923 return 0.;
924 }
925
926 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
927 Double_t trackXYZOut[3];
928 trackXYZOut[0] = trackParam->GetNonBendingCoor();
929 trackXYZOut[1] = trackParam->GetBendingCoor();
930 trackXYZOut[2] = trackParam->GetZ();
931 Double_t trackXYZIn[3];
932 trackXYZIn[0] = xVtx;
933 trackXYZIn[1] = yVtx;
934 trackXYZIn[2] = zVtx;
84f061ef 935 Double_t pTot = trackParam->P();
18abc511 936 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 937 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 938
ecdf58c4 939 // total momentum corrected for energy loss
940 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
941 Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
942 Double_t eCorr = e + totalELoss;
943 Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
944
945 return pTotCorr - pTot;
c04e3238 946}
947
690d2205 948//__________________________________________________________________________
fa5e35be 949Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
c04e3238 950{
84f061ef 951 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
952 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 953 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
84f061ef 954
ecdf58c4 955 // mean exitation energy (GeV)
956 Double_t i;
957 if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
958 else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
690d2205 959
fa5e35be 960 return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
c04e3238 961}
962
690d2205 963//__________________________________________________________________________
fa5e35be 964Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
690d2205 965{
966 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
967 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 968 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
690d2205 969 //Double_t eMass = 0.510998918e-3; // GeV
970 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
971 Double_t p2=pTotal*pTotal;
972 Double_t beta2=p2/(p2 + muMass*muMass);
973
fa5e35be 974 Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
690d2205 975 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
976
977 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
978
979 return sigma2;
980}
981
982//__________________________________________________________________________
983void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
984{
985 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
986 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
987
988 // charge * total momentum
989 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
990 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
991
992 // Jacobian of the opposite transformation
993 TMatrixD jacob(5,5);
994 jacob.UnitMatrix();
995 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
996 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
997 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
998 jacob(4,4) = - qPTot / param(4,0);
999
1000 // compute covariances in new coordinate system
1001 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
1002 cov.Mult(jacob,tmp);
1003}
1004
1005//__________________________________________________________________________
1006void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
1007{
1008 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
1009 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
1010
1011 // charge * total momentum
1012 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
1013 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
1014
1015 // Jacobian of the transformation
1016 TMatrixD jacob(5,5);
1017 jacob.UnitMatrix();
1018 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1019 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
1020 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1021 jacob(4,4) = - param(4,0) / qPTot;
1022
1023 // compute covariances in new coordinate system
1024 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
1025 covP.Mult(jacob,tmp);
1026}
1027
c04e3238 1028 //__________________________________________________________________________
57e2ad1a 1029void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
c04e3238 1030{
71a2d3aa 1031/// <pre>
c04e3238 1032/// ******************************************************************
1033/// * *
1034/// * Performs the tracking of one step in a magnetic field *
1035/// * The trajectory is assumed to be a helix in a constant field *
1036/// * taken at the mid point of the step. *
1037/// * Parameters: *
1038/// * input *
1039/// * STEP =arc length of the step asked *
1040/// * VECT =input vector (position,direction cos and momentum) *
1041/// * CHARGE= electric charge of the particle *
1042/// * output *
1043/// * VOUT = same as VECT after completion of the step *
1044/// * *
2060b217 1045/// * ==>Called by : USER, GUSWIM *
c04e3238 1046/// * Author m.hansroul ********* *
1047/// * modified s.egli, s.v.levonian *
1048/// * modified v.perevoztchikov
1049/// * *
1050/// ******************************************************************
71a2d3aa 1051/// </pre>
c04e3238 1052
1053// modif: everything in double precision
1054
1055 Double_t xyz[3], h[4], hxp[3];
1056 Double_t h2xy, hp, rho, tet;
1057 Double_t sint, sintt, tsint, cos1t;
1058 Double_t f1, f2, f3, f4, f5, f6;
1059
1060 const Int_t kix = 0;
1061 const Int_t kiy = 1;
1062 const Int_t kiz = 2;
1063 const Int_t kipx = 3;
1064 const Int_t kipy = 4;
1065 const Int_t kipz = 5;
1066 const Int_t kipp = 6;
1067
1068 const Double_t kec = 2.9979251e-4;
1069 //
1070 // ------------------------------------------------------------------
1071 //
1072 // units are kgauss,centimeters,gev/c
1073 //
1074 vout[kipp] = vect[kipp];
1075 if (TMath::Abs(charge) < 0.00001) {
1076 for (Int_t i = 0; i < 3; i++) {
1077 vout[i] = vect[i] + step * vect[i+3];
1078 vout[i+3] = vect[i+3];
1079 }
1080 return;
1081 }
1082 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1083 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1084 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1085
1086 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 1087 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 1088
1089 h2xy = h[0]*h[0] + h[1]*h[1];
1090 h[3] = h[2]*h[2]+ h2xy;
1091 if (h[3] < 1.e-12) {
1092 for (Int_t i = 0; i < 3; i++) {
1093 vout[i] = vect[i] + step * vect[i+3];
1094 vout[i+3] = vect[i+3];
1095 }
1096 return;
1097 }
1098 if (h2xy < 1.e-12*h[3]) {
1099 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1100 return;
1101 }
1102 h[3] = TMath::Sqrt(h[3]);
1103 h[0] /= h[3];
1104 h[1] /= h[3];
1105 h[2] /= h[3];
1106 h[3] *= kec;
1107
1108 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1109 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1110 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1111
1112 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1113
1114 rho = -charge*h[3]/vect[kipp];
1115 tet = rho * step;
1116
1117 if (TMath::Abs(tet) > 0.15) {
1118 sint = TMath::Sin(tet);
1119 sintt = (sint/tet);
1120 tsint = (tet-sint)/tet;
1121 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1122 } else {
1123 tsint = tet*tet/36.;
1124 sintt = (1. - tsint);
1125 sint = tet*sintt;
1126 cos1t = 0.5*tet;
1127 }
1128
1129 f1 = step * sintt;
1130 f2 = step * cos1t;
1131 f3 = step * tsint * hp;
1132 f4 = -tet*cos1t;
1133 f5 = sint;
1134 f6 = tet * cos1t * hp;
1135
1136 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1137 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1138 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1139
1140 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1141 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1142 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1143
1144 return;
1145}
1146
1147 //__________________________________________________________________________
57e2ad1a 1148void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
c04e3238 1149{
71a2d3aa 1150/// <pre>
c04e3238 1151/// ******************************************************************
1152/// * *
1153/// * Tracking routine in a constant field oriented *
1154/// * along axis 3 *
1155/// * Tracking is performed with a conventional *
1156/// * helix step method *
1157/// * *
2060b217 1158/// * ==>Called by : USER, GUSWIM *
c04e3238 1159/// * Authors R.Brun, M.Hansroul ********* *
1160/// * Rewritten V.Perevoztchikov
1161/// * *
1162/// ******************************************************************
71a2d3aa 1163/// </pre>
c04e3238 1164
1165 Double_t hxp[3];
1166 Double_t h4, hp, rho, tet;
1167 Double_t sint, sintt, tsint, cos1t;
1168 Double_t f1, f2, f3, f4, f5, f6;
1169
1170 const Int_t kix = 0;
1171 const Int_t kiy = 1;
1172 const Int_t kiz = 2;
1173 const Int_t kipx = 3;
1174 const Int_t kipy = 4;
1175 const Int_t kipz = 5;
1176 const Int_t kipp = 6;
1177
1178 const Double_t kec = 2.9979251e-4;
1179
1180//
1181// ------------------------------------------------------------------
1182//
1183// units are kgauss,centimeters,gev/c
1184//
1185 vout[kipp] = vect[kipp];
1186 h4 = field * kec;
1187
1188 hxp[0] = - vect[kipy];
1189 hxp[1] = + vect[kipx];
1190
1191 hp = vect[kipz];
1192
1193 rho = -h4/vect[kipp];
1194 tet = rho * step;
1195 if (TMath::Abs(tet) > 0.15) {
1196 sint = TMath::Sin(tet);
1197 sintt = (sint/tet);
1198 tsint = (tet-sint)/tet;
1199 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1200 } else {
1201 tsint = tet*tet/36.;
1202 sintt = (1. - tsint);
1203 sint = tet*sintt;
1204 cos1t = 0.5*tet;
1205 }
1206
1207 f1 = step * sintt;
1208 f2 = step * cos1t;
1209 f3 = step * tsint * hp;
1210 f4 = -tet*cos1t;
1211 f5 = sint;
1212 f6 = tet * cos1t * hp;
1213
1214 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1215 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1216 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1217
1218 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1219 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1220 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1221
1222 return;
1223}
8cde4af5 1224
c04e3238 1225 //__________________________________________________________________________
57e2ad1a 1226Bool_t AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t* vect, Double_t* vout)
c04e3238 1227{
71a2d3aa 1228/// <pre>
c04e3238 1229/// ******************************************************************
1230/// * *
1231/// * Runge-Kutta method for tracking a particle through a magnetic *
1232/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1233/// * Standards, procedure 25.5.20) *
1234/// * *
1235/// * Input parameters *
1236/// * CHARGE Particle charge *
1237/// * STEP Step size *
1238/// * VECT Initial co-ords,direction cosines,momentum *
1239/// * Output parameters *
1240/// * VOUT Output co-ords,direction cosines,momentum *
1241/// * User routine called *
1242/// * CALL GUFLD(X,F) *
1243/// * *
2060b217 1244/// * ==>Called by : USER, GUSWIM *
c04e3238 1245/// * Authors R.Brun, M.Hansroul ********* *
1246/// * V.Perevoztchikov (CUT STEP implementation) *
1247/// * *
1248/// * *
1249/// ******************************************************************
71a2d3aa 1250/// </pre>
c04e3238 1251
1252 Double_t h2, h4, f[4];
d373bcbe 1253 Double_t xyzt[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
1254 Double_t a, b, c, ph,ph2;
c04e3238 1255 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1256 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1257 Double_t est, at, bt, ct, cba;
1258 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1259
1260 Double_t x;
1261 Double_t y;
1262 Double_t z;
1263
1264 Double_t xt;
1265 Double_t yt;
1266 Double_t zt;
1267
1268 Double_t maxit = 1992;
1269 Double_t maxcut = 11;
1270
1271 const Double_t kdlt = 1e-4;
1272 const Double_t kdlt32 = kdlt/32.;
1273 const Double_t kthird = 1./3.;
1274 const Double_t khalf = 0.5;
1275 const Double_t kec = 2.9979251e-4;
1276
1277 const Double_t kpisqua = 9.86960440109;
1278 const Int_t kix = 0;
1279 const Int_t kiy = 1;
1280 const Int_t kiz = 2;
1281 const Int_t kipx = 3;
1282 const Int_t kipy = 4;
1283 const Int_t kipz = 5;
1284
1285 // *.
1286 // *. ------------------------------------------------------------------
1287 // *.
1288 // * this constant is for units cm,gev/c and kgauss
1289 // *
1290 Int_t iter = 0;
1291 Int_t ncut = 0;
1292 for(Int_t j = 0; j < 7; j++)
1293 vout[j] = vect[j];
1294
1295 Double_t pinv = kec * charge / vect[6];
1296 Double_t tl = 0.;
1297 Double_t h = step;
1298 Double_t rest;
1299
1300
1301 do {
1302 rest = step - tl;
1303 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1304 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1305 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1306
1307 // *
1308 // * start of integration
1309 // *
1310 x = vout[0];
1311 y = vout[1];
1312 z = vout[2];
1313 a = vout[3];
1314 b = vout[4];
1315 c = vout[5];
1316
1317 h2 = khalf * h;
1318 h4 = khalf * h2;
1319 ph = pinv * h;
1320 ph2 = khalf * ph;
1321 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1322 secys[0] = (c * f[0] - a * f[2]) * ph2;
1323 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1324 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1325 if (ang2 > kpisqua) break;
1326
1327 dxt = h2 * a + h4 * secxs[0];
1328 dyt = h2 * b + h4 * secys[0];
1329 dzt = h2 * c + h4 * seczs[0];
1330 xt = x + dxt;
1331 yt = y + dyt;
1332 zt = z + dzt;
1333 // *
1334 // * second intermediate point
1335 // *
1336
1337 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1338 if (est > h) {
1339 if (ncut++ > maxcut) break;
1340 h *= khalf;
1341 continue;
1342 }
1343
1344 xyzt[0] = xt;
1345 xyzt[1] = yt;
1346 xyzt[2] = zt;
1347
1348 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1349 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1350
1351 at = a + secxs[0];
1352 bt = b + secys[0];
1353 ct = c + seczs[0];
1354
1355 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1356 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1357 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1358 at = a + secxs[1];
1359 bt = b + secys[1];
1360 ct = c + seczs[1];
1361 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1362 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1363 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1364 dxt = h * (a + secxs[2]);
1365 dyt = h * (b + secys[2]);
1366 dzt = h * (c + seczs[2]);
1367 xt = x + dxt;
1368 yt = y + dyt;
1369 zt = z + dzt;
1370 at = a + 2.*secxs[2];
1371 bt = b + 2.*secys[2];
1372 ct = c + 2.*seczs[2];
1373
1374 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1375 if (est > 2.*TMath::Abs(h)) {
1376 if (ncut++ > maxcut) break;
1377 h *= khalf;
1378 continue;
1379 }
1380
1381 xyzt[0] = xt;
1382 xyzt[1] = yt;
1383 xyzt[2] = zt;
1384
1385 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1386 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1387
1388 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1389 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1390 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1391
1392 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1393 secys[3] = (ct*f[0] - at*f[2])* ph2;
1394 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1395 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1396 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1397 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1398
1399 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1400 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1401 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1402
1403 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1404 if (ncut++ > maxcut) break;
1405 h *= khalf;
1406 continue;
1407 }
1408
1409 ncut = 0;
1410 // * if too many iterations, go to helix
1411 if (iter++ > maxit) break;
1412
1413 tl += h;
1414 if (est < kdlt32)
1415 h *= 2.;
1416 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1417 vout[0] = x;
1418 vout[1] = y;
1419 vout[2] = z;
1420 vout[3] = cba*a;
1421 vout[4] = cba*b;
1422 vout[5] = cba*c;
1423 rest = step - tl;
1424 if (step < 0.) rest = -rest;
ade4e6f9 1425 if (rest < 1.e-5*TMath::Abs(step)) return kTRUE;
c04e3238 1426
1427 } while(1);
1428
1429 // angle too big, use helix
ade4e6f9 1430 cout<<"W-AliMUONTrackExtrap::ExtrapOneStepRungekutta: Ruge-Kutta failed: switch to helix"<<endl;
c04e3238 1431
1432 f1 = f[0];
1433 f2 = f[1];
1434 f3 = f[2];
1435 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
ade4e6f9 1436 if (f4 < 1.e-10) {
1437 cout<<"E-AliMUONTrackExtrap::ExtrapOneStepRungekutta: magnetic field at (";
1438 cout<<xyzt[0]<<", "<<xyzt[1]<<", "<<xyzt[2]<<") = "<<f4<<": giving up"<<endl;
1439 return kFALSE;
1440 }
c04e3238 1441 rho = -f4*pinv;
1442 tet = rho * step;
1443
1444 hnorm = 1./f4;
1445 f1 = f1*hnorm;
1446 f2 = f2*hnorm;
1447 f3 = f3*hnorm;
1448
1449 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1450 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1451 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1452
1453 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1454
1455 rho1 = 1./rho;
1456 sint = TMath::Sin(tet);
1457 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1458
1459 g1 = sint*rho1;
1460 g2 = cost*rho1;
1461 g3 = (tet-sint) * hp*rho1;
1462 g4 = -cost;
1463 g5 = sint;
1464 g6 = cost * hp;
1465
1466 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1467 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1468 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1469
1470 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1471 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1472 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1473
ade4e6f9 1474 return kTRUE;
c04e3238 1475}
8cde4af5 1476