Remove printf and add trd_gasCO2
[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"
8cde4af5 28
c04e3238 29#include "AliMagF.h"
8cde4af5 30
8cde4af5 31#include <TMath.h>
32#include <TMatrixD.h>
33#include <TGeoManager.h>
c04e3238 34
ea94c18b 35#include <Riostream.h>
36
78649106 37/// \cond CLASSIMP
c04e3238 38ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 39/// \endcond
c04e3238 40
41const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
4284483e 42const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 43const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 44const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
45const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 46
47 //__________________________________________________________________________
48Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
49{
50 /// Returns impact parameter at vertex in bending plane (cm),
51 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
52 /// using simple values for dipole magnetic field.
53 /// The sign of "BendingMomentum" is the sign of the charge.
54
55 if (bendingMomentum == 0.) return 1.e10;
56
57 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
58 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
59 Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
60 if (fgkField) fgkField->Field(x,b);
61 else {
62 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
63 exit(-1);
64 }
65 Double_t simpleBValue = (Double_t) b[0];
66
67 return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum);
68}
69
70 //__________________________________________________________________________
71Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
72{
73 /// Returns signed bending momentum in bending plane (GeV/c),
74 /// the sign being the sign of the charge for particles moving forward in Z,
75 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
76 /// using simple values for dipole magnetic field.
77
78 if (impactParam == 0.) return 1.e10;
79
80 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
81 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
82 Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
83 if (fgkField) fgkField->Field(x,b);
84 else {
85 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
86 exit(-1);
87 }
88 Double_t simpleBValue = (Double_t) b[0];
89
90 return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam);
91}
c04e3238 92
93 //__________________________________________________________________________
019df241 94void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
95{
96 /// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd".
97 /// On return, results from the extrapolation are updated in trackParam.
98
99 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
100
101 // Compute track parameters
102 Double_t dZ = zEnd - trackParam->GetZ();
103 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
104 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
105 trackParam->SetZ(zEnd);
106
107 // Update track parameters covariances if any
108 if (trackParam->CovariancesExist()) {
109 TMatrixD paramCov(trackParam->GetCovariances());
110 paramCov(0,0) += dZ * dZ * paramCov(1,1) + 2. * dZ * paramCov(0,1);
111 paramCov(0,1) += dZ * paramCov(1,1);
112 paramCov(1,0) = paramCov(0,1);
113 paramCov(2,2) += dZ * dZ * paramCov(3,3) + 2. * dZ * paramCov(2,3);
114 paramCov(2,3) += dZ * paramCov(3,3);
115 paramCov(3,2) = paramCov(2,3);
116 trackParam->SetCovariances(paramCov);
117 }
118
119}
120
121 //__________________________________________________________________________
c04e3238 122void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
123{
4284483e 124 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
125 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
126 if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
127 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
128}
129
130 //__________________________________________________________________________
131void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
132{
133 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 134 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
135 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
136 Double_t forwardBackward; // +1 if forward, -1 if backward
137 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
138 else forwardBackward = -1.0;
dade8580 139 Double_t v3[7], v3New[7]; // 7 in parameter ????
140 Int_t i3, stepNumber;
c04e3238 141 // For safety: return kTRUE or kFALSE ????
142 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 143 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 144 // sign of charge (sign of fInverseBendingMomentum if forward motion)
145 // must be changed if backward extrapolation
208f139e 146 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 147 // Extrapolation loop
148 stepNumber = 0;
208f139e 149 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 150 stepNumber++;
4284483e 151 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 152 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
c04e3238 153 // better use TArray ????
208f139e 154 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 155 }
208f139e 156 // check fgkMaxStepNumber ????
c04e3238 157 // Interpolation back to exact Z (2nd order)
158 // should be in function ???? using TArray ????
dade8580 159 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 160 if (TMath::Abs(dZ12) > 0) {
dade8580 161 Double_t dZ1i = zEnd - v3[2]; // 1-i
162 Double_t dZi2 = v3New[2] - zEnd; // i->2
163 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
164 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
165 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
166 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
167 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
168 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
169 v3[2] = zEnd; // Z
c04e3238 170 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
171 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
172 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 173 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 174 v3[3] = xPrimeI * v3[5]; // PX/PTOT
175 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 176 } else {
4284483e 177 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 178 }
4284483e 179 // Recover track parameters (charge back for forward motion)
dade8580 180 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 181}
182
183 //__________________________________________________________________________
4284483e 184void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
185{
186 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
187 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
188 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
189 Double_t forwardBackward; // +1 if forward, -1 if backward
190 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
191 else forwardBackward = -1.0;
192 // sign of charge (sign of fInverseBendingMomentum if forward motion)
193 // must be changed if backward extrapolation
194 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
195 Double_t v3[7], v3New[7];
196 Double_t dZ, step;
197 Int_t stepNumber = 0;
198
199 // Extrapolation loop (until within tolerance)
200 Double_t residue = zEnd - trackParam->GetZ();
201 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
202 dZ = zEnd - trackParam->GetZ();
203 // step lenght assuming linear trajectory
204 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
205 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
206 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
207 do { // reduce step lenght while zEnd oversteped
208 if (stepNumber > fgkMaxStepNumber) {
209 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
210 break;
211 }
212 stepNumber ++;
213 step = TMath::Abs(step);
214 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
215 residue = zEnd - v3New[2];
216 step *= dZ/(v3New[2]-trackParam->GetZ());
217 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
218 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
219 }
220
221 // terminate the extropolation with a straight line up to the exact "zEnd" value
222 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
223 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
224 trackParam->SetZ(zEnd);
225}
226
227 //__________________________________________________________________________
228void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 229{
dade8580 230 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 231 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
232 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 233 v3[0] = trackParam->GetNonBendingCoor(); // X
234 v3[1] = trackParam->GetBendingCoor(); // Y
235 v3[2] = trackParam->GetZ(); // Z
c04e3238 236 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
237 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 238 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
239 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
240 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
241 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 242}
243
244 //__________________________________________________________________________
dade8580 245void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 246{
dade8580 247 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 248 /// assumed to be calculated for forward motion in Z.
249 /// "InverseBendingMomentum" is signed with "charge".
dade8580 250 trackParam->SetNonBendingCoor(v3[0]); // X
251 trackParam->SetBendingCoor(v3[1]); // Y
252 trackParam->SetZ(v3[2]); // Z
253 Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]);
c04e3238 254 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 255 trackParam->SetBendingSlope(v3[4]/v3[5]);
256 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
c04e3238 257}
258
259 //__________________________________________________________________________
ea94c18b 260void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 261{
262 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
263 /// On return, results from the extrapolation are updated in trackParam.
264
265 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
266
ea94c18b 267 // No need to propagate the covariance matrix if it does not exist
268 if (!trackParam->CovariancesExist()) {
269 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
270 // Extrapolate track parameters to "zEnd"
271 ExtrapToZ(trackParam,zEnd);
272 return;
273 }
274
208f139e 275 // Save the actual track parameters
276 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 277 TMatrixD paramSave(trackParamSave.GetParameters());
278 Double_t zBegin = trackParamSave.GetZ();
279
280 // Get reference to the parameter covariance matrix
281 const TMatrixD& kParamCov = trackParam->GetCovariances();
208f139e 282
283 // Extrapolate track parameters to "zEnd"
284 ExtrapToZ(trackParam,zEnd);
208f139e 285
ea94c18b 286 // Get reference to the extrapolated parameters
287 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 288
289 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
290 TMatrixD jacob(5,5);
ea94c18b 291 jacob.Zero();
292 TMatrixD dParam(5,1);
208f139e 293 for (Int_t i=0; i<5; i++) {
294 // Skip jacobian calculation for parameters with no associated error
ea94c18b 295 if (kParamCov(i,i) == 0.) continue;
296
208f139e 297 // Small variation of parameter i only
298 for (Int_t j=0; j<5; j++) {
299 if (j==i) {
ea94c18b 300 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
301 if (j == 4) dParam(j,0) *= TMath::Sign(1.,-paramSave(4,0)); // variation always in the same direction
302 } else dParam(j,0) = 0.;
208f139e 303 }
ea94c18b 304
208f139e 305 // Set new parameters
ea94c18b 306 trackParamSave.SetParameters(paramSave);
307 trackParamSave.AddParameters(dParam);
308 trackParamSave.SetZ(zBegin);
309
208f139e 310 // Extrapolate new track parameters to "zEnd"
311 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 312
208f139e 313 // Calculate the jacobian
ea94c18b 314 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
315 jacobji *= 1. / dParam(i,0);
316 jacob.SetSub(0,i,jacobji);
208f139e 317 }
318
319 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 320 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
321 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
322 trackParam->SetCovariances(tmp2);
323
324 // Update the propagator if required
325 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 326
327}
328
329 //__________________________________________________________________________
c04e3238 330void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
331{
332 /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station"
333 /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut"
334 /// (index 0 and 1 for first and second chambers).
335 Double_t extZ[2], z1, z2;
336 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
337 // range of station to be checked ????
338 z1 = AliMUONConstants::DefaultChamberZ(2 * station);
339 z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1);
340 // First and second Z to extrapolate at
341 if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;}
342 else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;}
343 else {
208f139e 344 cout<<"E-AliMUONTrackExtrap::ExtrapToStation: Starting Z ("<<trackParamIn->GetZ()
c04e3238 345 <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
346 exit(-1);
347 }
348 extZ[i1] = z1;
349 extZ[i2] = z2;
350 // copy of track parameters
351 trackParamOut[i1] = *trackParamIn;
352 // first extrapolation
353 ExtrapToZ(&(trackParamOut[i1]),extZ[0]);
354 trackParamOut[i2] = trackParamOut[i1];
355 // second extrapolation
356 ExtrapToZ(&(trackParamOut[i2]),extZ[1]);
357 return;
358}
359
360 //__________________________________________________________________________
208f139e 361void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
362{
8cde4af5 363 /// Extrapolation to the vertex (at the z position "zVtx") without Branson and energy loss corrections.
208f139e 364 /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
365 /// Include multiple Coulomb scattering effects in trackParam covariances.
366
8cde4af5 367 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
368
208f139e 369 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
370 cout<<"W-AliMUONTrackExtrap::ExtrapToVertexUncorrected: Starting Z ("<<trackParam->GetZ()
371 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
372 exit(-1);
373 }
374
8cde4af5 375 // Check the vertex position relatively to the absorber
ea94c18b 376 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 377 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 378 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
379 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 380 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 381 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
382 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
383 else ExtrapToZ(trackParam,zVtx);
208f139e 384 return;
385 }
386
8cde4af5 387 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 388 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 389 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 390 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
391 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
392 else ExtrapToZ(trackParam,zVtx);
8cde4af5 393 return;
ea94c18b 394 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 395 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 396 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
208f139e 397 } else {
ea94c18b 398 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
399 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
208f139e 400 }
401
8cde4af5 402 // Then add MCS effect in absorber to the parameters covariances
403 AliMUONTrackParam trackParamIn(*trackParam);
ea94c18b 404 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
8cde4af5 405 Double_t trackXYZIn[3];
406 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
407 trackXYZIn[1] = trackParamIn.GetBendingCoor();
408 trackXYZIn[2] = trackParamIn.GetZ();
409 Double_t trackXYZOut[3];
410 trackXYZOut[0] = trackParam->GetNonBendingCoor();
411 trackXYZOut[1] = trackParam->GetBendingCoor();
412 trackXYZOut[2] = trackParam->GetZ();
413 Double_t pathLength = 0.;
414 Double_t f0 = 0.;
415 Double_t f1 = 0.;
416 Double_t f2 = 0.;
417 Double_t meanRho = 0.;
84f061ef 418 Double_t totalELoss = 0.;
419 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,trackParam->P(),pathLength,f0,f1,f2,meanRho,totalELoss);
8cde4af5 420 AddMCSEffectInAbsorber(trackParam,pathLength,f0,f1,f2);
208f139e 421
422 // finally go to the vertex
423 ExtrapToZCov(trackParam,zVtx);
424
425}
426
427 //__________________________________________________________________________
8cde4af5 428void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
429{
430 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
431 /// at the end of the front absorber using the absorber correction parameters
432
433 // absorber related covariance parameters
434 Double_t bendingSlope = param->GetBendingSlope();
435 Double_t nonBendingSlope = param->GetNonBendingSlope();
436 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
437 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
438 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
439 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
440 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
441 Double_t varSlop = alpha2 * f0;
442
ea94c18b 443 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 444 // Non bending plane
ea94c18b 445 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
446 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 447 // Bending plane
ea94c18b 448 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
449 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
450
451 // Set new covariances
452 param->SetCovariances(newParamCov);
8cde4af5 453
454}
455
456 //__________________________________________________________________________
84f061ef 457void AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal, Double_t &pathLength,
458 Double_t &f0, Double_t &f1, Double_t &f2, Double_t &meanRho, Double_t &totalELoss)
8cde4af5 459{
460 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
461 /// Calculated assuming a linear propagation between track positions trackXYZIn and trackXYZOut
462 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
463 // f0: 0th moment of z calculated with the inverse radiation-length distribution
464 // f1: 1st moment of z calculated with the inverse radiation-length distribution
465 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
466 // meanRho: average density of crossed material (g/cm3)
84f061ef 467 // totalELoss: total energy loss in absorber
8cde4af5 468
469 // Reset absorber's parameters
470 pathLength = 0.;
471 f0 = 0.;
472 f1 = 0.;
473 f2 = 0.;
474 meanRho = 0.;
84f061ef 475 totalELoss = 0.;
8cde4af5 476
477 // Check whether the geometry is available
478 if (!gGeoManager) {
479 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
480 return;
481 }
482
483 // Initialize starting point and direction
484 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
485 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
486 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
487 if (pathLength < TGeoShape::Tolerance()) return;
488 Double_t b[3];
489 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
490 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
491 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
492 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
493 if (!currentnode) {
494 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
495 return;
496 }
497
498 // loop over absorber slices and calculate absorber's parameters
499 Double_t rho = 0.; // material density (g/cm3)
500 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 501 Double_t atomicA = 0.; // A of material
502 Double_t atomicZ = 0.; // Z of material
8cde4af5 503 Double_t localPathLength = 0;
504 Double_t remainingPathLength = pathLength;
505 Double_t zB = trackXYZIn[2];
506 Double_t zE, dzB, dzE;
507 do {
508 // Get material properties
509 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
510 rho = material->GetDensity();
511 x0 = material->GetRadLen();
512 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
84f061ef 513 atomicA = material->GetA();
514 atomicZ = material->GetZ();
8cde4af5 515
516 // Get path length within this material
517 gGeoManager->FindNextBoundary(remainingPathLength);
518 localPathLength = gGeoManager->GetStep() + 1.e-6;
519 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
520 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
521 else {
522 currentnode = gGeoManager->Step();
523 if (!currentnode) {
524 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
525 f0 = f1 = f2 = meanRho = 0.;
526 return;
527 }
528 if (!gGeoManager->IsEntering()) {
529 // make another small step to try to enter in new absorber slice
530 gGeoManager->SetStep(0.001);
531 currentnode = gGeoManager->Step();
532 if (!gGeoManager->IsEntering() || !currentnode) {
533 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
534 f0 = f1 = f2 = meanRho = 0.;
535 return;
536 }
537 localPathLength += 0.001;
538 }
539 }
540
541 // calculate absorber's parameters
542 zE = b[2] * localPathLength + zB;
543 dzB = zB - trackXYZIn[2];
544 dzE = zE - trackXYZIn[2];
545 f0 += localPathLength / x0;
546 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
547 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
548 meanRho += localPathLength * rho;
84f061ef 549 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ);
8cde4af5 550
551 // prepare next step
552 zB = zE;
553 remainingPathLength -= localPathLength;
554 } while (remainingPathLength > TGeoShape::Tolerance());
555
556 meanRho /= pathLength;
557}
558
559 //__________________________________________________________________________
ea94c18b 560Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
561{
562 /// Return the angular dispersion square due to multiple Coulomb scattering
563 /// through a material of thickness "dZ" and of radiation length "x0"
564 /// assuming linear propagation and using the small angle approximation.
565
566 Double_t bendingSlope = param.GetBendingSlope();
567 Double_t nonBendingSlope = param.GetNonBendingSlope();
568 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
569 (1.0 + bendingSlope * bendingSlope) /
570 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
571 // Path length in the material
572 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
573 // relativistic velocity
574 Double_t velo = 1.;
575 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
576 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
577
578 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
579}
580
581 //__________________________________________________________________________
8cde4af5 582void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 583{
584 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
585 /// through a material of thickness "dZ" and of radiation length "x0"
586 /// assuming linear propagation and using the small angle approximation.
587
588 Double_t bendingSlope = param->GetBendingSlope();
589 Double_t nonBendingSlope = param->GetNonBendingSlope();
590 Double_t inverseTotalMomentum2 = param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum() *
591 (1.0 + bendingSlope * bendingSlope) /
592 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
593 // Path length in the material
594 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
595 Double_t pathLength2 = pathLength * pathLength;
596 // relativistic velocity
597 Double_t velo = 1.;
598 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
599 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
600 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
601
208f139e 602 Double_t varCoor = pathLength2 * theta02 / 3.;
603 Double_t varSlop = theta02;
604 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 605
606 // Add effects of multiple Coulomb scattering in track parameter covariances
607 TMatrixD newParamCov(param->GetCovariances());
208f139e 608 // Non bending plane
ea94c18b 609 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
610 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 611 // Bending plane
ea94c18b 612 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
613 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
208f139e 614
ea94c18b 615 // Set new covariances
616 param->SetCovariances(newParamCov);
208f139e 617}
618
619 //__________________________________________________________________________
fac70e25 620void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx,
621 Bool_t CorrectForMCS, Bool_t CorrectForEnergyLoss)
c04e3238 622{
623 /// Extrapolation to the vertex.
fac70e25 624 /// Returns the track parameters resulting from the extrapolation of the current TrackParam.
8cde4af5 625 /// Changes parameters according to Branson correction through the absorber and energy loss
c04e3238 626
8cde4af5 627 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 628
8cde4af5 629 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
fac70e25 630 cout<<"F-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
8cde4af5 631 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
632 exit(-1);
c04e3238 633 }
8cde4af5 634
fac70e25 635 // Check if correction required
636 if (!CorrectForMCS && !CorrectForEnergyLoss) {
637 ExtrapToZ(trackParam,zVtx);
638 return;
639 }
640
8cde4af5 641 // Check the vertex position relatively to the absorber
ea94c18b 642 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 643 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 644 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
645 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 646 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 647 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
8cde4af5 648 ExtrapToZ(trackParam,zVtx);
649 return;
650 }
651
652 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 653 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 654 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 655 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
8cde4af5 656 ExtrapToZ(trackParam,zVtx);
657 return;
ea94c18b 658 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 659 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 660 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 661 } else {
ea94c18b 662 ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 663 }
c04e3238 664
8cde4af5 665 // Get absorber correction parameters assuming linear propagation from vertex to the track position
666 Double_t trackXYZOut[3];
667 trackXYZOut[0] = trackParam->GetNonBendingCoor();
668 trackXYZOut[1] = trackParam->GetBendingCoor();
669 trackXYZOut[2] = trackParam->GetZ();
670 Double_t trackXYZIn[3];
ea94c18b 671 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
8cde4af5 672 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
673 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
84f061ef 674 Double_t pTot = trackParam->P();
8cde4af5 675 Double_t pathLength = 0.;
676 Double_t f0 = 0.;
677 Double_t f1 = 0.;
678 Double_t f2 = 0.;
679 Double_t meanRho = 0.;
84f061ef 680 Double_t deltaP = 0.;
681 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP);
8cde4af5 682
683 // Correct for half of energy loss
fac70e25 684 Double_t nonBendingSlope, bendingSlope;
84f061ef 685 Double_t charge = TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
fac70e25 686 if (CorrectForEnergyLoss) {
687 pTot += 0.5 * deltaP;
688 nonBendingSlope = trackParam->GetNonBendingSlope();
689 bendingSlope = trackParam->GetBendingSlope();
690 trackParam->SetInverseBendingMomentum(charge / pTot *
691 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
692 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
693 }
8cde4af5 694
fac70e25 695 if (CorrectForMCS) {
696 // Position of the Branson plane (spectro. (z<0))
697 Double_t zB = (f1>0.) ? trackXYZIn[2] - f2/f1 : 0.;
698
699 // Get track position in the Branson plane corrected for magnetic field effect
700 ExtrapToZ(trackParam,zVtx);
701 Double_t xB = trackParam->GetNonBendingCoor() + (zB - zVtx) * trackParam->GetNonBendingSlope();
702 Double_t yB = trackParam->GetBendingCoor() + (zB - zVtx) * trackParam->GetBendingSlope();
703
704 // Get track slopes corrected for multiple scattering (spectro. (z<0))
705 nonBendingSlope = (zB<0.) ? (xB - xVtx) / (zB - zVtx) : trackParam->GetNonBendingSlope();
706 bendingSlope = (zB<0.) ? (yB - yVtx) / (zB - zVtx) : trackParam->GetBendingSlope();
707
708 // Set track parameters at vertex
709 trackParam->SetNonBendingCoor(xVtx);
710 trackParam->SetBendingCoor(yVtx);
711 trackParam->SetZ(zVtx);
712 trackParam->SetNonBendingSlope(nonBendingSlope);
713 trackParam->SetBendingSlope(bendingSlope);
714 } else {
715 ExtrapToZ(trackParam,zVtx);
716 nonBendingSlope = trackParam->GetNonBendingSlope();
717 bendingSlope = trackParam->GetBendingSlope();
718 }
8cde4af5 719
720 // Correct for second half of energy loss
fac70e25 721 if (CorrectForEnergyLoss) pTot += 0.5 * deltaP;
8cde4af5 722
723 // Set track parameters at vertex
8cde4af5 724 trackParam->SetInverseBendingMomentum(charge / pTot *
fac70e25 725 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
726 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
727
728}
729
730 //__________________________________________________________________________
731Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
732{
733 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
734
735 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 736
fac70e25 737 // Check whether the geometry is available
738 if (!gGeoManager) {
739 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
740 return 0.;
741 }
742
743 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
744 Double_t trackXYZOut[3];
745 trackXYZOut[0] = trackParam->GetNonBendingCoor();
746 trackXYZOut[1] = trackParam->GetBendingCoor();
747 trackXYZOut[2] = trackParam->GetZ();
748 Double_t trackXYZIn[3];
749 trackXYZIn[0] = xVtx;
750 trackXYZIn[1] = yVtx;
751 trackXYZIn[2] = zVtx;
84f061ef 752 Double_t pTot = trackParam->P();
fac70e25 753 Double_t pathLength = 0.;
754 Double_t f0 = 0.;
755 Double_t f1 = 0.;
756 Double_t f2 = 0.;
757 Double_t meanRho = 0.;
84f061ef 758 Double_t totalELoss = 0.;
759 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss);
fac70e25 760
84f061ef 761 return totalELoss;
c04e3238 762}
763
764 //__________________________________________________________________________
84f061ef 765Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
c04e3238 766{
84f061ef 767 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
768 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
769 Double_t muMass = 0.105658369; // GeV
770 Double_t eMass = 0.510998918e-3; // GeV
771 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
772 Double_t i = 9.5e-9; // mean exitation energy per atomic Z (GeV)
8cde4af5 773 Double_t p2=pTotal*pTotal;
774 Double_t beta2=p2/(p2 + muMass*muMass);
8cde4af5 775
84f061ef 776 Double_t w = k * rho * pathLength * atomicZ / atomicA / beta2;
777
8cde4af5 778 if (beta2/(1-beta2)>3.5*3.5)
84f061ef 779 return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2);
8cde4af5 780
84f061ef 781 return w * (log(2.*eMass*beta2/(1-beta2)/(i*atomicZ)) - beta2);
c04e3238 782}
783
784 //__________________________________________________________________________
785void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
786{
71a2d3aa 787/// <pre>
c04e3238 788/// ******************************************************************
789/// * *
790/// * Performs the tracking of one step in a magnetic field *
791/// * The trajectory is assumed to be a helix in a constant field *
792/// * taken at the mid point of the step. *
793/// * Parameters: *
794/// * input *
795/// * STEP =arc length of the step asked *
796/// * VECT =input vector (position,direction cos and momentum) *
797/// * CHARGE= electric charge of the particle *
798/// * output *
799/// * VOUT = same as VECT after completion of the step *
800/// * *
2060b217 801/// * ==>Called by : USER, GUSWIM *
c04e3238 802/// * Author m.hansroul ********* *
803/// * modified s.egli, s.v.levonian *
804/// * modified v.perevoztchikov
805/// * *
806/// ******************************************************************
71a2d3aa 807/// </pre>
c04e3238 808
809// modif: everything in double precision
810
811 Double_t xyz[3], h[4], hxp[3];
812 Double_t h2xy, hp, rho, tet;
813 Double_t sint, sintt, tsint, cos1t;
814 Double_t f1, f2, f3, f4, f5, f6;
815
816 const Int_t kix = 0;
817 const Int_t kiy = 1;
818 const Int_t kiz = 2;
819 const Int_t kipx = 3;
820 const Int_t kipy = 4;
821 const Int_t kipz = 5;
822 const Int_t kipp = 6;
823
824 const Double_t kec = 2.9979251e-4;
825 //
826 // ------------------------------------------------------------------
827 //
828 // units are kgauss,centimeters,gev/c
829 //
830 vout[kipp] = vect[kipp];
831 if (TMath::Abs(charge) < 0.00001) {
832 for (Int_t i = 0; i < 3; i++) {
833 vout[i] = vect[i] + step * vect[i+3];
834 vout[i+3] = vect[i+3];
835 }
836 return;
837 }
838 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
839 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
840 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
841
842 //cmodif: call gufld (xyz, h) changed into:
843 GetField (xyz, h);
844
845 h2xy = h[0]*h[0] + h[1]*h[1];
846 h[3] = h[2]*h[2]+ h2xy;
847 if (h[3] < 1.e-12) {
848 for (Int_t i = 0; i < 3; i++) {
849 vout[i] = vect[i] + step * vect[i+3];
850 vout[i+3] = vect[i+3];
851 }
852 return;
853 }
854 if (h2xy < 1.e-12*h[3]) {
855 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
856 return;
857 }
858 h[3] = TMath::Sqrt(h[3]);
859 h[0] /= h[3];
860 h[1] /= h[3];
861 h[2] /= h[3];
862 h[3] *= kec;
863
864 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
865 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
866 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
867
868 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
869
870 rho = -charge*h[3]/vect[kipp];
871 tet = rho * step;
872
873 if (TMath::Abs(tet) > 0.15) {
874 sint = TMath::Sin(tet);
875 sintt = (sint/tet);
876 tsint = (tet-sint)/tet;
877 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
878 } else {
879 tsint = tet*tet/36.;
880 sintt = (1. - tsint);
881 sint = tet*sintt;
882 cos1t = 0.5*tet;
883 }
884
885 f1 = step * sintt;
886 f2 = step * cos1t;
887 f3 = step * tsint * hp;
888 f4 = -tet*cos1t;
889 f5 = sint;
890 f6 = tet * cos1t * hp;
891
892 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
893 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
894 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
895
896 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
897 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
898 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
899
900 return;
901}
902
903 //__________________________________________________________________________
904void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
905{
71a2d3aa 906/// <pre>
c04e3238 907/// ******************************************************************
908/// * *
909/// * Tracking routine in a constant field oriented *
910/// * along axis 3 *
911/// * Tracking is performed with a conventional *
912/// * helix step method *
913/// * *
2060b217 914/// * ==>Called by : USER, GUSWIM *
c04e3238 915/// * Authors R.Brun, M.Hansroul ********* *
916/// * Rewritten V.Perevoztchikov
917/// * *
918/// ******************************************************************
71a2d3aa 919/// </pre>
c04e3238 920
921 Double_t hxp[3];
922 Double_t h4, hp, rho, tet;
923 Double_t sint, sintt, tsint, cos1t;
924 Double_t f1, f2, f3, f4, f5, f6;
925
926 const Int_t kix = 0;
927 const Int_t kiy = 1;
928 const Int_t kiz = 2;
929 const Int_t kipx = 3;
930 const Int_t kipy = 4;
931 const Int_t kipz = 5;
932 const Int_t kipp = 6;
933
934 const Double_t kec = 2.9979251e-4;
935
936//
937// ------------------------------------------------------------------
938//
939// units are kgauss,centimeters,gev/c
940//
941 vout[kipp] = vect[kipp];
942 h4 = field * kec;
943
944 hxp[0] = - vect[kipy];
945 hxp[1] = + vect[kipx];
946
947 hp = vect[kipz];
948
949 rho = -h4/vect[kipp];
950 tet = rho * step;
951 if (TMath::Abs(tet) > 0.15) {
952 sint = TMath::Sin(tet);
953 sintt = (sint/tet);
954 tsint = (tet-sint)/tet;
955 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
956 } else {
957 tsint = tet*tet/36.;
958 sintt = (1. - tsint);
959 sint = tet*sintt;
960 cos1t = 0.5*tet;
961 }
962
963 f1 = step * sintt;
964 f2 = step * cos1t;
965 f3 = step * tsint * hp;
966 f4 = -tet*cos1t;
967 f5 = sint;
968 f6 = tet * cos1t * hp;
969
970 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
971 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
972 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
973
974 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
975 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
976 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
977
978 return;
979}
8cde4af5 980
c04e3238 981 //__________________________________________________________________________
982void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
983{
71a2d3aa 984/// <pre>
c04e3238 985/// ******************************************************************
986/// * *
987/// * Runge-Kutta method for tracking a particle through a magnetic *
988/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
989/// * Standards, procedure 25.5.20) *
990/// * *
991/// * Input parameters *
992/// * CHARGE Particle charge *
993/// * STEP Step size *
994/// * VECT Initial co-ords,direction cosines,momentum *
995/// * Output parameters *
996/// * VOUT Output co-ords,direction cosines,momentum *
997/// * User routine called *
998/// * CALL GUFLD(X,F) *
999/// * *
2060b217 1000/// * ==>Called by : USER, GUSWIM *
c04e3238 1001/// * Authors R.Brun, M.Hansroul ********* *
1002/// * V.Perevoztchikov (CUT STEP implementation) *
1003/// * *
1004/// * *
1005/// ******************************************************************
71a2d3aa 1006/// </pre>
c04e3238 1007
1008 Double_t h2, h4, f[4];
1009 Double_t xyzt[3], a, b, c, ph,ph2;
1010 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1011 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1012 Double_t est, at, bt, ct, cba;
1013 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1014
1015 Double_t x;
1016 Double_t y;
1017 Double_t z;
1018
1019 Double_t xt;
1020 Double_t yt;
1021 Double_t zt;
1022
1023 Double_t maxit = 1992;
1024 Double_t maxcut = 11;
1025
1026 const Double_t kdlt = 1e-4;
1027 const Double_t kdlt32 = kdlt/32.;
1028 const Double_t kthird = 1./3.;
1029 const Double_t khalf = 0.5;
1030 const Double_t kec = 2.9979251e-4;
1031
1032 const Double_t kpisqua = 9.86960440109;
1033 const Int_t kix = 0;
1034 const Int_t kiy = 1;
1035 const Int_t kiz = 2;
1036 const Int_t kipx = 3;
1037 const Int_t kipy = 4;
1038 const Int_t kipz = 5;
1039
1040 // *.
1041 // *. ------------------------------------------------------------------
1042 // *.
1043 // * this constant is for units cm,gev/c and kgauss
1044 // *
1045 Int_t iter = 0;
1046 Int_t ncut = 0;
1047 for(Int_t j = 0; j < 7; j++)
1048 vout[j] = vect[j];
1049
1050 Double_t pinv = kec * charge / vect[6];
1051 Double_t tl = 0.;
1052 Double_t h = step;
1053 Double_t rest;
1054
1055
1056 do {
1057 rest = step - tl;
1058 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1059 //cmodif: call gufld(vout,f) changed into:
1060
1061 GetField(vout,f);
1062
1063 // *
1064 // * start of integration
1065 // *
1066 x = vout[0];
1067 y = vout[1];
1068 z = vout[2];
1069 a = vout[3];
1070 b = vout[4];
1071 c = vout[5];
1072
1073 h2 = khalf * h;
1074 h4 = khalf * h2;
1075 ph = pinv * h;
1076 ph2 = khalf * ph;
1077 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1078 secys[0] = (c * f[0] - a * f[2]) * ph2;
1079 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1080 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1081 if (ang2 > kpisqua) break;
1082
1083 dxt = h2 * a + h4 * secxs[0];
1084 dyt = h2 * b + h4 * secys[0];
1085 dzt = h2 * c + h4 * seczs[0];
1086 xt = x + dxt;
1087 yt = y + dyt;
1088 zt = z + dzt;
1089 // *
1090 // * second intermediate point
1091 // *
1092
1093 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1094 if (est > h) {
1095 if (ncut++ > maxcut) break;
1096 h *= khalf;
1097 continue;
1098 }
1099
1100 xyzt[0] = xt;
1101 xyzt[1] = yt;
1102 xyzt[2] = zt;
1103
1104 //cmodif: call gufld(xyzt,f) changed into:
1105 GetField(xyzt,f);
1106
1107 at = a + secxs[0];
1108 bt = b + secys[0];
1109 ct = c + seczs[0];
1110
1111 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1112 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1113 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1114 at = a + secxs[1];
1115 bt = b + secys[1];
1116 ct = c + seczs[1];
1117 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1118 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1119 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1120 dxt = h * (a + secxs[2]);
1121 dyt = h * (b + secys[2]);
1122 dzt = h * (c + seczs[2]);
1123 xt = x + dxt;
1124 yt = y + dyt;
1125 zt = z + dzt;
1126 at = a + 2.*secxs[2];
1127 bt = b + 2.*secys[2];
1128 ct = c + 2.*seczs[2];
1129
1130 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1131 if (est > 2.*TMath::Abs(h)) {
1132 if (ncut++ > maxcut) break;
1133 h *= khalf;
1134 continue;
1135 }
1136
1137 xyzt[0] = xt;
1138 xyzt[1] = yt;
1139 xyzt[2] = zt;
1140
1141 //cmodif: call gufld(xyzt,f) changed into:
1142 GetField(xyzt,f);
1143
1144 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1145 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1146 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1147
1148 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1149 secys[3] = (ct*f[0] - at*f[2])* ph2;
1150 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1151 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1152 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1153 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1154
1155 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1156 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1157 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1158
1159 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1160 if (ncut++ > maxcut) break;
1161 h *= khalf;
1162 continue;
1163 }
1164
1165 ncut = 0;
1166 // * if too many iterations, go to helix
1167 if (iter++ > maxit) break;
1168
1169 tl += h;
1170 if (est < kdlt32)
1171 h *= 2.;
1172 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1173 vout[0] = x;
1174 vout[1] = y;
1175 vout[2] = z;
1176 vout[3] = cba*a;
1177 vout[4] = cba*b;
1178 vout[5] = cba*c;
1179 rest = step - tl;
1180 if (step < 0.) rest = -rest;
1181 if (rest < 1.e-5*TMath::Abs(step)) return;
1182
1183 } while(1);
1184
1185 // angle too big, use helix
1186
1187 f1 = f[0];
1188 f2 = f[1];
1189 f3 = f[2];
1190 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1191 rho = -f4*pinv;
1192 tet = rho * step;
1193
1194 hnorm = 1./f4;
1195 f1 = f1*hnorm;
1196 f2 = f2*hnorm;
1197 f3 = f3*hnorm;
1198
1199 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1200 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1201 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1202
1203 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1204
1205 rho1 = 1./rho;
1206 sint = TMath::Sin(tet);
1207 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1208
1209 g1 = sint*rho1;
1210 g2 = cost*rho1;
1211 g3 = (tet-sint) * hp*rho1;
1212 g4 = -cost;
1213 g5 = sint;
1214 g6 = cost * hp;
1215
1216 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1217 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1218 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1219
1220 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1221 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1222 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1223
1224 return;
1225}
8cde4af5 1226
c04e3238 1227//___________________________________________________________
1228 void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
1229{
1230 /// interface for arguments in double precision (Why ? ChF)
1231 Float_t x[3], b[3];
1232
1233 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
1234
1235 if (fgkField) fgkField->Field(x,b);
1236 else {
1237 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
1238 exit(-1);
1239 }
1240
1241 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
1242
1243 return;
1244}