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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
c04e3238 30#include "AliMagF.h"
8cde4af5 31
f7a1cc68 32#include <TGeoGlobalMagField.h>
8cde4af5 33#include <TGeoManager.h>
f7a1cc68 34#include <TMath.h>
c04e3238 35
ea94c18b 36#include <Riostream.h>
37
78649106 38/// \cond CLASSIMP
c04e3238 39ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 40/// \endcond
c04e3238 41
9f093251 42const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
43const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
44 Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
45 Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
4284483e 46const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 47const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 48const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
49const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 50
9f093251 51//__________________________________________________________________________
f7a1cc68 52void AliMUONTrackExtrap::SetField()
9f093251 53{
f7a1cc68 54 // set field on/off flag
9f093251 55 // set field at the centre of the dipole
f7a1cc68 56 const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
57 Double_t b[3] = {0.,0.,0.};
58 TGeoGlobalMagField::Instance()->Field(x,b);
59 fgSimpleBValue = b[0];
60 fgFieldON = fgSimpleBValue ? kTRUE : kFALSE;
9f093251 61
62}
63
690d2205 64//__________________________________________________________________________
208f139e 65Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
66{
67 /// Returns impact parameter at vertex in bending plane (cm),
68 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
69 /// using simple values for dipole magnetic field.
70 /// The sign of "BendingMomentum" is the sign of the charge.
71
72 if (bendingMomentum == 0.) return 1.e10;
73
6b191dea 74 const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
9f093251 75
76 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
208f139e 77}
78
690d2205 79//__________________________________________________________________________
9bdbee64 80Double_t
81AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
208f139e 82{
83 /// Returns signed bending momentum in bending plane (GeV/c),
84 /// the sign being the sign of the charge for particles moving forward in Z,
85 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
86 /// using simple values for dipole magnetic field.
87
88 if (impactParam == 0.) return 1.e10;
89
9f093251 90 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
91
9bdbee64 92 if (fgFieldON)
93 {
94 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
95 }
96 else
97 {
98 return AliMUONConstants::GetMostProbBendingMomentum();
99 }
019df241 100}
101
690d2205 102//__________________________________________________________________________
9f093251 103void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
019df241 104{
105 /// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd".
106 /// On return, results from the extrapolation are updated in trackParam.
107
108 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
109
110 // Compute track parameters
111 Double_t dZ = zEnd - trackParam->GetZ();
112 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
113 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
114 trackParam->SetZ(zEnd);
115
116 // Update track parameters covariances if any
117 if (trackParam->CovariancesExist()) {
118 TMatrixD paramCov(trackParam->GetCovariances());
119 paramCov(0,0) += dZ * dZ * paramCov(1,1) + 2. * dZ * paramCov(0,1);
120 paramCov(0,1) += dZ * paramCov(1,1);
121 paramCov(1,0) = paramCov(0,1);
122 paramCov(2,2) += dZ * dZ * paramCov(3,3) + 2. * dZ * paramCov(2,3);
123 paramCov(2,3) += dZ * paramCov(3,3);
124 paramCov(3,2) = paramCov(2,3);
125 trackParam->SetCovariances(paramCov);
9f093251 126
127 // Update the propagator if required
128 if (updatePropagator) {
129 TMatrixD jacob(5,5);
130 jacob.UnitMatrix();
131 jacob(0,1) = dZ;
132 jacob(2,3) = dZ;
133 trackParam->UpdatePropagator(jacob);
134 }
135
019df241 136 }
137
208f139e 138}
c04e3238 139
690d2205 140//__________________________________________________________________________
c04e3238 141void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
142{
4284483e 143 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
144 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
9f093251 145 if (!fgFieldON) AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
146 else if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
4284483e 147 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
148}
149
690d2205 150//__________________________________________________________________________
4284483e 151void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
152{
153 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 154 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
155 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
156 Double_t forwardBackward; // +1 if forward, -1 if backward
157 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
158 else forwardBackward = -1.0;
dade8580 159 Double_t v3[7], v3New[7]; // 7 in parameter ????
160 Int_t i3, stepNumber;
c04e3238 161 // For safety: return kTRUE or kFALSE ????
162 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 163 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 164 // sign of charge (sign of fInverseBendingMomentum if forward motion)
165 // must be changed if backward extrapolation
208f139e 166 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 167 // Extrapolation loop
168 stepNumber = 0;
208f139e 169 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 170 stepNumber++;
4284483e 171 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 172 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 173 // better use TArray ????
208f139e 174 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 175 }
208f139e 176 // check fgkMaxStepNumber ????
c04e3238 177 // Interpolation back to exact Z (2nd order)
178 // should be in function ???? using TArray ????
dade8580 179 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 180 if (TMath::Abs(dZ12) > 0) {
dade8580 181 Double_t dZ1i = zEnd - v3[2]; // 1-i
182 Double_t dZi2 = v3New[2] - zEnd; // i->2
183 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
184 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
185 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
186 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
187 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
188 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
189 v3[2] = zEnd; // Z
c04e3238 190 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
191 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
192 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 193 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 194 v3[3] = xPrimeI * v3[5]; // PX/PTOT
195 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 196 } else {
4284483e 197 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 198 }
4284483e 199 // Recover track parameters (charge back for forward motion)
dade8580 200 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 201}
202
690d2205 203//__________________________________________________________________________
4284483e 204void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
205{
206 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
207 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
208 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
209 Double_t forwardBackward; // +1 if forward, -1 if backward
210 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
211 else forwardBackward = -1.0;
212 // sign of charge (sign of fInverseBendingMomentum if forward motion)
213 // must be changed if backward extrapolation
214 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
215 Double_t v3[7], v3New[7];
216 Double_t dZ, step;
217 Int_t stepNumber = 0;
218
219 // Extrapolation loop (until within tolerance)
220 Double_t residue = zEnd - trackParam->GetZ();
221 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
222 dZ = zEnd - trackParam->GetZ();
223 // step lenght assuming linear trajectory
224 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 225 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 226 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
227 do { // reduce step lenght while zEnd oversteped
228 if (stepNumber > fgkMaxStepNumber) {
229 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
230 break;
231 }
232 stepNumber ++;
233 step = TMath::Abs(step);
234 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
235 residue = zEnd - v3New[2];
236 step *= dZ/(v3New[2]-trackParam->GetZ());
237 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
238 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
239 }
240
241 // terminate the extropolation with a straight line up to the exact "zEnd" value
242 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
243 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
244 trackParam->SetZ(zEnd);
245}
246
690d2205 247//__________________________________________________________________________
4284483e 248void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 249{
dade8580 250 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 251 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
252 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 253 v3[0] = trackParam->GetNonBendingCoor(); // X
254 v3[1] = trackParam->GetBendingCoor(); // Y
255 v3[2] = trackParam->GetZ(); // Z
c04e3238 256 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
257 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 258 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
259 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
260 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
261 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 262}
263
690d2205 264//__________________________________________________________________________
dade8580 265void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 266{
dade8580 267 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 268 /// assumed to be calculated for forward motion in Z.
269 /// "InverseBendingMomentum" is signed with "charge".
dade8580 270 trackParam->SetNonBendingCoor(v3[0]); // X
271 trackParam->SetBendingCoor(v3[1]); // Y
272 trackParam->SetZ(v3[2]); // Z
60e55aee 273 Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
c04e3238 274 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 275 trackParam->SetBendingSlope(v3[4]/v3[5]);
276 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
208f139e 277}
278
690d2205 279//__________________________________________________________________________
ea94c18b 280void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 281{
282 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
283 /// On return, results from the extrapolation are updated in trackParam.
284
285 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
286
9f093251 287 if (!fgFieldON) { // linear extrapolation if no magnetic field
288 AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd,updatePropagator);
289 return;
290 }
291
ea94c18b 292 // No need to propagate the covariance matrix if it does not exist
293 if (!trackParam->CovariancesExist()) {
294 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
295 // Extrapolate track parameters to "zEnd"
296 ExtrapToZ(trackParam,zEnd);
297 return;
298 }
299
208f139e 300 // Save the actual track parameters
301 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 302 TMatrixD paramSave(trackParamSave.GetParameters());
303 Double_t zBegin = trackParamSave.GetZ();
304
305 // Get reference to the parameter covariance matrix
306 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 307
208f139e 308 // Extrapolate track parameters to "zEnd"
309 ExtrapToZ(trackParam,zEnd);
208f139e 310
ea94c18b 311 // Get reference to the extrapolated parameters
312 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 313
314 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
315 TMatrixD jacob(5,5);
ea94c18b 316 jacob.Zero();
317 TMatrixD dParam(5,1);
6b191dea 318 Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
208f139e 319 for (Int_t i=0; i<5; i++) {
320 // Skip jacobian calculation for parameters with no associated error
18abc511 321 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 322
208f139e 323 // Small variation of parameter i only
324 for (Int_t j=0; j<5; j++) {
325 if (j==i) {
ea94c18b 326 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
6b191dea 327 dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
ea94c18b 328 } else dParam(j,0) = 0.;
208f139e 329 }
ea94c18b 330
208f139e 331 // Set new parameters
ea94c18b 332 trackParamSave.SetParameters(paramSave);
333 trackParamSave.AddParameters(dParam);
334 trackParamSave.SetZ(zBegin);
335
208f139e 336 // Extrapolate new track parameters to "zEnd"
337 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 338
208f139e 339 // Calculate the jacobian
ea94c18b 340 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
341 jacobji *= 1. / dParam(i,0);
342 jacob.SetSub(0,i,jacobji);
208f139e 343 }
344
345 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 346 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
347 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
348 trackParam->SetCovariances(tmp2);
349
350 // Update the propagator if required
351 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 352}
353
690d2205 354//__________________________________________________________________________
8cde4af5 355void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
356{
357 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
690d2205 358 /// The absorber correction parameters are supposed to be calculated at the current track z-position
8cde4af5 359
360 // absorber related covariance parameters
361 Double_t bendingSlope = param->GetBendingSlope();
362 Double_t nonBendingSlope = param->GetNonBendingSlope();
363 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
364 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 365 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
8cde4af5 366 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
367 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
368 Double_t varSlop = alpha2 * f0;
369
690d2205 370 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
371 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
372 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
373 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
374
375 // Set MCS covariance matrix
ea94c18b 376 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 377 // Non bending plane
ea94c18b 378 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
379 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 380 // Bending plane
ea94c18b 381 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
382 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 383 // Inverse bending momentum (due to dependences with bending and non bending slopes)
384 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
385 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
386 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
387 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
388 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
ea94c18b 389
390 // Set new covariances
391 param->SetCovariances(newParamCov);
690d2205 392}
393
394//__________________________________________________________________________
395void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
396 Double_t xVtx, Double_t yVtx, Double_t zVtx,
397 Double_t errXVtx, Double_t errYVtx,
398 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
399{
400 /// Correct parameters and corresponding covariances using Branson correction
401 /// - input param are parameters and covariances at the end of absorber
402 /// - output param are parameters and covariances at vertex
403 /// Absorber correction parameters are supposed to be calculated at the current track z-position
404
405 // Position of the Branson plane (spectro. (z<0))
406 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
407
408 // Add MCS effects to current parameter covariances
409 AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2);
410
411 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
412 ExtrapToZCov(param,zVtx);
413 LinearExtrapToZ(param,zB);
414
415 // compute track parameters at vertex
416 TMatrixD newParam(5,1);
417 newParam(0,0) = xVtx;
418 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
419 newParam(2,0) = yVtx;
420 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
421 newParam(4,0) = param->GetCharge() / param->P() *
422 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
423 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
424
425 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
426 TMatrixD paramCovP(param->GetCovariances());
427 Cov2CovP(param->GetParameters(),paramCovP);
428
429 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
430 TMatrixD paramCovVtx(5,5);
431 paramCovVtx.Zero();
432 paramCovVtx(0,0) = errXVtx * errXVtx;
433 paramCovVtx(1,1) = paramCovP(0,0);
434 paramCovVtx(2,2) = errYVtx * errYVtx;
435 paramCovVtx(3,3) = paramCovP(2,2);
436 paramCovVtx(4,4) = paramCovP(4,4);
437 paramCovVtx(1,3) = paramCovP(0,2);
438 paramCovVtx(3,1) = paramCovP(2,0);
439 paramCovVtx(1,4) = paramCovP(0,4);
440 paramCovVtx(4,1) = paramCovP(4,0);
441 paramCovVtx(3,4) = paramCovP(2,4);
442 paramCovVtx(4,3) = paramCovP(4,2);
443
444 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
445 TMatrixD jacob(5,5);
446 jacob.UnitMatrix();
447 jacob(1,0) = - 1. / (zB - zVtx);
448 jacob(1,1) = 1. / (zB - zVtx);
449 jacob(3,2) = - 1. / (zB - zVtx);
450 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 451
690d2205 452 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
453 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
454 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
455
456 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
457 CovP2Cov(newParam,newParamCov);
458
459 // Set parameters and covariances at vertex
460 param->SetParameters(newParam);
461 param->SetZ(zVtx);
462 param->SetCovariances(newParamCov);
8cde4af5 463}
464
690d2205 465//__________________________________________________________________________
466void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
467{
468 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
469
470 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
471 TMatrixD newParamCov(param->GetCovariances());
472 Cov2CovP(param->GetParameters(),newParamCov);
473
474 // Add effects of energy loss fluctuation to covariances
475 newParamCov(4,4) += sigmaELoss2;
476
477 // Compute new parameters corrected for energy loss
478 Double_t nonBendingSlope = param->GetNonBendingSlope();
479 Double_t bendingSlope = param->GetBendingSlope();
480 param->SetInverseBendingMomentum(param->GetCharge() / (param->P() + eLoss) *
481 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
482 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
483
484 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
485 CovP2Cov(param->GetParameters(),newParamCov);
486
487 // Set new parameter covariances
488 param->SetCovariances(newParamCov);
489}
490
491//__________________________________________________________________________
18abc511 492Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
493 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
494 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 495{
496 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 497 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 498 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
499 // f0: 0th moment of z calculated with the inverse radiation-length distribution
500 // f1: 1st moment of z calculated with the inverse radiation-length distribution
501 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
502 // meanRho: average density of crossed material (g/cm3)
84f061ef 503 // totalELoss: total energy loss in absorber
8cde4af5 504
505 // Reset absorber's parameters
506 pathLength = 0.;
507 f0 = 0.;
508 f1 = 0.;
509 f2 = 0.;
510 meanRho = 0.;
84f061ef 511 totalELoss = 0.;
690d2205 512 sigmaELoss2 = 0.;
8cde4af5 513
514 // Check whether the geometry is available
515 if (!gGeoManager) {
516 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 517 return kFALSE;
8cde4af5 518 }
519
520 // Initialize starting point and direction
521 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
522 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
523 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 524 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 525 Double_t b[3];
526 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
527 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
528 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
529 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
530 if (!currentnode) {
531 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 532 return kFALSE;
8cde4af5 533 }
534
535 // loop over absorber slices and calculate absorber's parameters
536 Double_t rho = 0.; // material density (g/cm3)
537 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 538 Double_t atomicA = 0.; // A of material
539 Double_t atomicZ = 0.; // Z of material
8cde4af5 540 Double_t localPathLength = 0;
541 Double_t remainingPathLength = pathLength;
542 Double_t zB = trackXYZIn[2];
543 Double_t zE, dzB, dzE;
544 do {
545 // Get material properties
546 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
547 rho = material->GetDensity();
548 x0 = material->GetRadLen();
549 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
84f061ef 550 atomicA = material->GetA();
551 atomicZ = material->GetZ();
8cde4af5 552
553 // Get path length within this material
554 gGeoManager->FindNextBoundary(remainingPathLength);
555 localPathLength = gGeoManager->GetStep() + 1.e-6;
556 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
557 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
558 else {
559 currentnode = gGeoManager->Step();
560 if (!currentnode) {
561 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 562 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
563 return kFALSE;
8cde4af5 564 }
565 if (!gGeoManager->IsEntering()) {
566 // make another small step to try to enter in new absorber slice
567 gGeoManager->SetStep(0.001);
568 currentnode = gGeoManager->Step();
569 if (!gGeoManager->IsEntering() || !currentnode) {
570 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 571 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
572 return kFALSE;
8cde4af5 573 }
574 localPathLength += 0.001;
575 }
576 }
577
578 // calculate absorber's parameters
579 zE = b[2] * localPathLength + zB;
580 dzB = zB - trackXYZIn[2];
581 dzE = zE - trackXYZIn[2];
582 f0 += localPathLength / x0;
583 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
584 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
585 meanRho += localPathLength * rho;
84f061ef 586 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ);
690d2205 587 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicA, atomicZ);
8cde4af5 588
589 // prepare next step
590 zB = zE;
591 remainingPathLength -= localPathLength;
592 } while (remainingPathLength > TGeoShape::Tolerance());
593
594 meanRho /= pathLength;
18abc511 595
596 return kTRUE;
8cde4af5 597}
598
690d2205 599//__________________________________________________________________________
ea94c18b 600Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
601{
602 /// Return the angular dispersion square due to multiple Coulomb scattering
603 /// through a material of thickness "dZ" and of radiation length "x0"
604 /// assuming linear propagation and using the small angle approximation.
605
606 Double_t bendingSlope = param.GetBendingSlope();
607 Double_t nonBendingSlope = param.GetNonBendingSlope();
608 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 609 (1.0 + bendingSlope * bendingSlope) /
610 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 611 // Path length in the material
612 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
613 // relativistic velocity
614 Double_t velo = 1.;
615 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
616 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
617
618 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
619}
620
690d2205 621//__________________________________________________________________________
8cde4af5 622void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 623{
624 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
625 /// through a material of thickness "dZ" and of radiation length "x0"
626 /// assuming linear propagation and using the small angle approximation.
627
628 Double_t bendingSlope = param->GetBendingSlope();
629 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 630 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
631 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
632 (1.0 + bendingSlope * bendingSlope) /
633 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 634 // Path length in the material
635 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
636 Double_t pathLength2 = pathLength * pathLength;
637 // relativistic velocity
638 Double_t velo = 1.;
639 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
640 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
641 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
642
208f139e 643 Double_t varCoor = pathLength2 * theta02 / 3.;
644 Double_t varSlop = theta02;
645 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 646
690d2205 647 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
648 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
649 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
650 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
651
652 // Set MCS covariance matrix
ea94c18b 653 TMatrixD newParamCov(param->GetCovariances());
208f139e 654 // Non bending plane
ea94c18b 655 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
656 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 657 // Bending plane
ea94c18b 658 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
659 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
690d2205 660 // Inverse bending momentum (due to dependences with bending and non bending slopes)
661 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
662 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
663 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
664 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
665 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
208f139e 666
ea94c18b 667 // Set new covariances
668 param->SetCovariances(newParamCov);
c04e3238 669}
670
690d2205 671//__________________________________________________________________________
672void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
673 Double_t xVtx, Double_t yVtx, Double_t zVtx,
674 Double_t errXVtx, Double_t errYVtx,
675 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 676{
690d2205 677 /// Main method for extrapolation to the vertex:
678 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
679 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
680 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
681 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
682 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
683 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 684
8cde4af5 685 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 686
8cde4af5 687 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 688 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
689 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 690 return;
691 }
692
8cde4af5 693 // Check the vertex position relatively to the absorber
ea94c18b 694 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 695 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 696 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 697 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 698 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 699 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
700 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
701 else ExtrapToZ(trackParam,zVtx);
8cde4af5 702 return;
703 }
704
705 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 706 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 707 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 708 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
709 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
710 else ExtrapToZ(trackParam,zVtx);
8cde4af5 711 return;
ea94c18b 712 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 713 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 714 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 715 } else {
690d2205 716 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
717 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 718 }
c04e3238 719
690d2205 720 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 721 Double_t trackXYZOut[3];
722 trackXYZOut[0] = trackParam->GetNonBendingCoor();
723 trackXYZOut[1] = trackParam->GetBendingCoor();
724 trackXYZOut[2] = trackParam->GetZ();
725 Double_t trackXYZIn[3];
690d2205 726 if (correctForMCS) { // assume linear propagation until the vertex
727 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
728 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
729 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
730 } else {
731 AliMUONTrackParam trackParamIn(*trackParam);
732 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
733 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
734 trackXYZIn[1] = trackParamIn.GetBendingCoor();
735 trackXYZIn[2] = trackParamIn.GetZ();
736 }
84f061ef 737 Double_t pTot = trackParam->P();
18abc511 738 Double_t pathLength, f0, f1, f2, meanRho, deltaP, sigmaDeltaP2;
739 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP,sigmaDeltaP2)) {
740 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
741 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
742 else ExtrapToZ(trackParam,zVtx);
743 return;
744 }
8cde4af5 745
690d2205 746 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
747 if (correctForMCS) {
fac70e25 748
690d2205 749 if (correctForEnergyLoss) {
750
751 // Correct for multiple scattering and energy loss
752 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
753 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
754 trackXYZIn[2], pathLength, f0, f1, f2);
755 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
756
757 } else {
758
759 // Correct for multiple scattering
760 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
761 trackXYZIn[2], pathLength, f0, f1, f2);
762 }
fac70e25 763
fac70e25 764 } else {
690d2205 765
766 if (correctForEnergyLoss) {
767
18abc511 768 // Correct for energy loss add multiple scattering dispersion in covariance matrix
690d2205 769 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
770 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
771 ExtrapToZCov(trackParam, trackXYZIn[2]);
772 CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
773 ExtrapToZCov(trackParam, zVtx);
774
775 } else {
776
18abc511 777 // add multiple scattering dispersion in covariance matrix
690d2205 778 AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
779 ExtrapToZCov(trackParam, zVtx);
780
781 }
782
fac70e25 783 }
8cde4af5 784
fac70e25 785}
786
690d2205 787//__________________________________________________________________________
788void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
789 Double_t xVtx, Double_t yVtx, Double_t zVtx,
790 Double_t errXVtx, Double_t errYVtx)
791{
792 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
793 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
794 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
795}
796
797//__________________________________________________________________________
798void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
799 Double_t xVtx, Double_t yVtx, Double_t zVtx,
800 Double_t errXVtx, Double_t errYVtx)
801{
802 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
803 /// Add branson correction resolution to parameter covariances
804 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
805}
806
807//__________________________________________________________________________
808void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
809{
810 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
811 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
812 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
813}
814
815//__________________________________________________________________________
816void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
817{
818 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
819 /// Add dispersion due to multiple scattering to parameter covariances
820 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
821}
822
823//__________________________________________________________________________
fac70e25 824Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
825{
826 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
827
828 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 829
fac70e25 830 // Check whether the geometry is available
831 if (!gGeoManager) {
832 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
833 return 0.;
834 }
835
836 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
837 Double_t trackXYZOut[3];
838 trackXYZOut[0] = trackParam->GetNonBendingCoor();
839 trackXYZOut[1] = trackParam->GetBendingCoor();
840 trackXYZOut[2] = trackParam->GetZ();
841 Double_t trackXYZIn[3];
842 trackXYZIn[0] = xVtx;
843 trackXYZIn[1] = yVtx;
844 trackXYZIn[2] = zVtx;
84f061ef 845 Double_t pTot = trackParam->P();
18abc511 846 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 847 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 848
84f061ef 849 return totalELoss;
c04e3238 850}
851
690d2205 852//__________________________________________________________________________
84f061ef 853Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
c04e3238 854{
84f061ef 855 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
856 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
857 Double_t muMass = 0.105658369; // GeV
858 Double_t eMass = 0.510998918e-3; // GeV
859 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
860 Double_t i = 9.5e-9; // mean exitation energy per atomic Z (GeV)
8cde4af5 861 Double_t p2=pTotal*pTotal;
862 Double_t beta2=p2/(p2 + muMass*muMass);
8cde4af5 863
84f061ef 864 Double_t w = k * rho * pathLength * atomicZ / atomicA / beta2;
865
8cde4af5 866 if (beta2/(1-beta2)>3.5*3.5)
690d2205 867 return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2);
868
84f061ef 869 return w * (log(2.*eMass*beta2/(1-beta2)/(i*atomicZ)) - beta2);
c04e3238 870}
871
690d2205 872//__________________________________________________________________________
873Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
874{
875 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
876 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
877 Double_t muMass = 0.105658369; // GeV
878 //Double_t eMass = 0.510998918e-3; // GeV
879 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
880 Double_t p2=pTotal*pTotal;
881 Double_t beta2=p2/(p2 + muMass*muMass);
882
883 Double_t fwhm = 2. * k * rho * pathLength * atomicZ / atomicA / beta2; // FWHM of the energy loss Landau distribution
884 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
885
886 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
887
888 return sigma2;
889}
890
891//__________________________________________________________________________
892void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
893{
894 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
895 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
896
897 // charge * total momentum
898 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
899 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
900
901 // Jacobian of the opposite transformation
902 TMatrixD jacob(5,5);
903 jacob.UnitMatrix();
904 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
905 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
906 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
907 jacob(4,4) = - qPTot / param(4,0);
908
909 // compute covariances in new coordinate system
910 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
911 cov.Mult(jacob,tmp);
912}
913
914//__________________________________________________________________________
915void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
916{
917 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
918 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
919
920 // charge * total momentum
921 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
922 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
923
924 // Jacobian of the transformation
925 TMatrixD jacob(5,5);
926 jacob.UnitMatrix();
927 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
928 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
929 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
930 jacob(4,4) = - param(4,0) / qPTot;
931
932 // compute covariances in new coordinate system
933 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
934 covP.Mult(jacob,tmp);
935}
936
c04e3238 937 //__________________________________________________________________________
938void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
939{
71a2d3aa 940/// <pre>
c04e3238 941/// ******************************************************************
942/// * *
943/// * Performs the tracking of one step in a magnetic field *
944/// * The trajectory is assumed to be a helix in a constant field *
945/// * taken at the mid point of the step. *
946/// * Parameters: *
947/// * input *
948/// * STEP =arc length of the step asked *
949/// * VECT =input vector (position,direction cos and momentum) *
950/// * CHARGE= electric charge of the particle *
951/// * output *
952/// * VOUT = same as VECT after completion of the step *
953/// * *
2060b217 954/// * ==>Called by : USER, GUSWIM *
c04e3238 955/// * Author m.hansroul ********* *
956/// * modified s.egli, s.v.levonian *
957/// * modified v.perevoztchikov
958/// * *
959/// ******************************************************************
71a2d3aa 960/// </pre>
c04e3238 961
962// modif: everything in double precision
963
964 Double_t xyz[3], h[4], hxp[3];
965 Double_t h2xy, hp, rho, tet;
966 Double_t sint, sintt, tsint, cos1t;
967 Double_t f1, f2, f3, f4, f5, f6;
968
969 const Int_t kix = 0;
970 const Int_t kiy = 1;
971 const Int_t kiz = 2;
972 const Int_t kipx = 3;
973 const Int_t kipy = 4;
974 const Int_t kipz = 5;
975 const Int_t kipp = 6;
976
977 const Double_t kec = 2.9979251e-4;
978 //
979 // ------------------------------------------------------------------
980 //
981 // units are kgauss,centimeters,gev/c
982 //
983 vout[kipp] = vect[kipp];
984 if (TMath::Abs(charge) < 0.00001) {
985 for (Int_t i = 0; i < 3; i++) {
986 vout[i] = vect[i] + step * vect[i+3];
987 vout[i+3] = vect[i+3];
988 }
989 return;
990 }
991 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
992 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
993 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
994
995 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 996 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 997
998 h2xy = h[0]*h[0] + h[1]*h[1];
999 h[3] = h[2]*h[2]+ h2xy;
1000 if (h[3] < 1.e-12) {
1001 for (Int_t i = 0; i < 3; i++) {
1002 vout[i] = vect[i] + step * vect[i+3];
1003 vout[i+3] = vect[i+3];
1004 }
1005 return;
1006 }
1007 if (h2xy < 1.e-12*h[3]) {
1008 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1009 return;
1010 }
1011 h[3] = TMath::Sqrt(h[3]);
1012 h[0] /= h[3];
1013 h[1] /= h[3];
1014 h[2] /= h[3];
1015 h[3] *= kec;
1016
1017 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1018 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1019 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1020
1021 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1022
1023 rho = -charge*h[3]/vect[kipp];
1024 tet = rho * step;
1025
1026 if (TMath::Abs(tet) > 0.15) {
1027 sint = TMath::Sin(tet);
1028 sintt = (sint/tet);
1029 tsint = (tet-sint)/tet;
1030 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1031 } else {
1032 tsint = tet*tet/36.;
1033 sintt = (1. - tsint);
1034 sint = tet*sintt;
1035 cos1t = 0.5*tet;
1036 }
1037
1038 f1 = step * sintt;
1039 f2 = step * cos1t;
1040 f3 = step * tsint * hp;
1041 f4 = -tet*cos1t;
1042 f5 = sint;
1043 f6 = tet * cos1t * hp;
1044
1045 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1046 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1047 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1048
1049 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1050 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1051 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1052
1053 return;
1054}
1055
1056 //__________________________________________________________________________
1057void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
1058{
71a2d3aa 1059/// <pre>
c04e3238 1060/// ******************************************************************
1061/// * *
1062/// * Tracking routine in a constant field oriented *
1063/// * along axis 3 *
1064/// * Tracking is performed with a conventional *
1065/// * helix step method *
1066/// * *
2060b217 1067/// * ==>Called by : USER, GUSWIM *
c04e3238 1068/// * Authors R.Brun, M.Hansroul ********* *
1069/// * Rewritten V.Perevoztchikov
1070/// * *
1071/// ******************************************************************
71a2d3aa 1072/// </pre>
c04e3238 1073
1074 Double_t hxp[3];
1075 Double_t h4, hp, rho, tet;
1076 Double_t sint, sintt, tsint, cos1t;
1077 Double_t f1, f2, f3, f4, f5, f6;
1078
1079 const Int_t kix = 0;
1080 const Int_t kiy = 1;
1081 const Int_t kiz = 2;
1082 const Int_t kipx = 3;
1083 const Int_t kipy = 4;
1084 const Int_t kipz = 5;
1085 const Int_t kipp = 6;
1086
1087 const Double_t kec = 2.9979251e-4;
1088
1089//
1090// ------------------------------------------------------------------
1091//
1092// units are kgauss,centimeters,gev/c
1093//
1094 vout[kipp] = vect[kipp];
1095 h4 = field * kec;
1096
1097 hxp[0] = - vect[kipy];
1098 hxp[1] = + vect[kipx];
1099
1100 hp = vect[kipz];
1101
1102 rho = -h4/vect[kipp];
1103 tet = rho * step;
1104 if (TMath::Abs(tet) > 0.15) {
1105 sint = TMath::Sin(tet);
1106 sintt = (sint/tet);
1107 tsint = (tet-sint)/tet;
1108 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1109 } else {
1110 tsint = tet*tet/36.;
1111 sintt = (1. - tsint);
1112 sint = tet*sintt;
1113 cos1t = 0.5*tet;
1114 }
1115
1116 f1 = step * sintt;
1117 f2 = step * cos1t;
1118 f3 = step * tsint * hp;
1119 f4 = -tet*cos1t;
1120 f5 = sint;
1121 f6 = tet * cos1t * hp;
1122
1123 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1124 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1125 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1126
1127 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1128 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1129 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1130
1131 return;
1132}
8cde4af5 1133
c04e3238 1134 //__________________________________________________________________________
1135void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
1136{
71a2d3aa 1137/// <pre>
c04e3238 1138/// ******************************************************************
1139/// * *
1140/// * Runge-Kutta method for tracking a particle through a magnetic *
1141/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1142/// * Standards, procedure 25.5.20) *
1143/// * *
1144/// * Input parameters *
1145/// * CHARGE Particle charge *
1146/// * STEP Step size *
1147/// * VECT Initial co-ords,direction cosines,momentum *
1148/// * Output parameters *
1149/// * VOUT Output co-ords,direction cosines,momentum *
1150/// * User routine called *
1151/// * CALL GUFLD(X,F) *
1152/// * *
2060b217 1153/// * ==>Called by : USER, GUSWIM *
c04e3238 1154/// * Authors R.Brun, M.Hansroul ********* *
1155/// * V.Perevoztchikov (CUT STEP implementation) *
1156/// * *
1157/// * *
1158/// ******************************************************************
71a2d3aa 1159/// </pre>
c04e3238 1160
1161 Double_t h2, h4, f[4];
1162 Double_t xyzt[3], a, b, c, ph,ph2;
1163 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1164 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1165 Double_t est, at, bt, ct, cba;
1166 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1167
1168 Double_t x;
1169 Double_t y;
1170 Double_t z;
1171
1172 Double_t xt;
1173 Double_t yt;
1174 Double_t zt;
1175
1176 Double_t maxit = 1992;
1177 Double_t maxcut = 11;
1178
1179 const Double_t kdlt = 1e-4;
1180 const Double_t kdlt32 = kdlt/32.;
1181 const Double_t kthird = 1./3.;
1182 const Double_t khalf = 0.5;
1183 const Double_t kec = 2.9979251e-4;
1184
1185 const Double_t kpisqua = 9.86960440109;
1186 const Int_t kix = 0;
1187 const Int_t kiy = 1;
1188 const Int_t kiz = 2;
1189 const Int_t kipx = 3;
1190 const Int_t kipy = 4;
1191 const Int_t kipz = 5;
1192
1193 // *.
1194 // *. ------------------------------------------------------------------
1195 // *.
1196 // * this constant is for units cm,gev/c and kgauss
1197 // *
1198 Int_t iter = 0;
1199 Int_t ncut = 0;
1200 for(Int_t j = 0; j < 7; j++)
1201 vout[j] = vect[j];
1202
1203 Double_t pinv = kec * charge / vect[6];
1204 Double_t tl = 0.;
1205 Double_t h = step;
1206 Double_t rest;
1207
1208
1209 do {
1210 rest = step - tl;
1211 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1212 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1213 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1214
1215 // *
1216 // * start of integration
1217 // *
1218 x = vout[0];
1219 y = vout[1];
1220 z = vout[2];
1221 a = vout[3];
1222 b = vout[4];
1223 c = vout[5];
1224
1225 h2 = khalf * h;
1226 h4 = khalf * h2;
1227 ph = pinv * h;
1228 ph2 = khalf * ph;
1229 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1230 secys[0] = (c * f[0] - a * f[2]) * ph2;
1231 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1232 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1233 if (ang2 > kpisqua) break;
1234
1235 dxt = h2 * a + h4 * secxs[0];
1236 dyt = h2 * b + h4 * secys[0];
1237 dzt = h2 * c + h4 * seczs[0];
1238 xt = x + dxt;
1239 yt = y + dyt;
1240 zt = z + dzt;
1241 // *
1242 // * second intermediate point
1243 // *
1244
1245 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1246 if (est > h) {
1247 if (ncut++ > maxcut) break;
1248 h *= khalf;
1249 continue;
1250 }
1251
1252 xyzt[0] = xt;
1253 xyzt[1] = yt;
1254 xyzt[2] = zt;
1255
1256 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1257 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1258
1259 at = a + secxs[0];
1260 bt = b + secys[0];
1261 ct = c + seczs[0];
1262
1263 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1264 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1265 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1266 at = a + secxs[1];
1267 bt = b + secys[1];
1268 ct = c + seczs[1];
1269 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1270 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1271 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1272 dxt = h * (a + secxs[2]);
1273 dyt = h * (b + secys[2]);
1274 dzt = h * (c + seczs[2]);
1275 xt = x + dxt;
1276 yt = y + dyt;
1277 zt = z + dzt;
1278 at = a + 2.*secxs[2];
1279 bt = b + 2.*secys[2];
1280 ct = c + 2.*seczs[2];
1281
1282 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1283 if (est > 2.*TMath::Abs(h)) {
1284 if (ncut++ > maxcut) break;
1285 h *= khalf;
1286 continue;
1287 }
1288
1289 xyzt[0] = xt;
1290 xyzt[1] = yt;
1291 xyzt[2] = zt;
1292
1293 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1294 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1295
1296 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1297 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1298 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1299
1300 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1301 secys[3] = (ct*f[0] - at*f[2])* ph2;
1302 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1303 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1304 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1305 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1306
1307 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1308 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1309 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1310
1311 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1312 if (ncut++ > maxcut) break;
1313 h *= khalf;
1314 continue;
1315 }
1316
1317 ncut = 0;
1318 // * if too many iterations, go to helix
1319 if (iter++ > maxit) break;
1320
1321 tl += h;
1322 if (est < kdlt32)
1323 h *= 2.;
1324 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1325 vout[0] = x;
1326 vout[1] = y;
1327 vout[2] = z;
1328 vout[3] = cba*a;
1329 vout[4] = cba*b;
1330 vout[5] = cba*c;
1331 rest = step - tl;
1332 if (step < 0.) rest = -rest;
1333 if (rest < 1.e-5*TMath::Abs(step)) return;
1334
1335 } while(1);
1336
1337 // angle too big, use helix
1338
1339 f1 = f[0];
1340 f2 = f[1];
1341 f3 = f[2];
1342 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1343 rho = -f4*pinv;
1344 tet = rho * step;
1345
1346 hnorm = 1./f4;
1347 f1 = f1*hnorm;
1348 f2 = f2*hnorm;
1349 f3 = f3*hnorm;
1350
1351 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1352 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1353 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1354
1355 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1356
1357 rho1 = 1./rho;
1358 sint = TMath::Sin(tet);
1359 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1360
1361 g1 = sint*rho1;
1362 g2 = cost*rho1;
1363 g3 = (tet-sint) * hp*rho1;
1364 g4 = -cost;
1365 g5 = sint;
1366 g6 = cost * hp;
1367
1368 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1369 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1370 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1371
1372 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1373 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1374 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1375
1376 return;
1377}
8cde4af5 1378