More robust raw-reader for HLT (Artur)
[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
18///////////////////////////////////////////////////
19//
20// Tools
21// for
22// track
23// extrapolation
24// in
25// ALICE
26// dimuon
27// spectrometer
28//
29///////////////////////////////////////////////////
30
c04e3238 31#include "AliMUONTrackExtrap.h"
32#include "AliMUONTrackParam.h"
33#include "AliMUONConstants.h"
8cde4af5 34
c04e3238 35#include "AliMagF.h"
8cde4af5 36
8cde4af5 37#include <TMath.h>
38#include <TMatrixD.h>
39#include <TGeoManager.h>
c04e3238 40
ea94c18b 41#include <Riostream.h>
42
78649106 43/// \cond CLASSIMP
c04e3238 44ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 45/// \endcond
c04e3238 46
47const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
4284483e 48const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 49const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 50const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
51const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 52
53 //__________________________________________________________________________
54Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
55{
56 /// Returns impact parameter at vertex in bending plane (cm),
57 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
58 /// using simple values for dipole magnetic field.
59 /// The sign of "BendingMomentum" is the sign of the charge.
60
61 if (bendingMomentum == 0.) return 1.e10;
62
63 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
64 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
65 Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
66 if (fgkField) fgkField->Field(x,b);
67 else {
68 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
69 exit(-1);
70 }
71 Double_t simpleBValue = (Double_t) b[0];
72
73 return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum);
74}
75
76 //__________________________________________________________________________
77Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
78{
79 /// Returns signed bending momentum in bending plane (GeV/c),
80 /// the sign being the sign of the charge for particles moving forward in Z,
81 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
82 /// using simple values for dipole magnetic field.
83
84 if (impactParam == 0.) return 1.e10;
85
86 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
87 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
88 Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
89 if (fgkField) fgkField->Field(x,b);
90 else {
91 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
92 exit(-1);
93 }
94 Double_t simpleBValue = (Double_t) b[0];
95
96 return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam);
97}
c04e3238 98
99 //__________________________________________________________________________
100void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
101{
4284483e 102 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
103 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
104 if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
105 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
106}
107
108 //__________________________________________________________________________
109void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
110{
111 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 112 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
113 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
114 Double_t forwardBackward; // +1 if forward, -1 if backward
115 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
116 else forwardBackward = -1.0;
dade8580 117 Double_t v3[7], v3New[7]; // 7 in parameter ????
118 Int_t i3, stepNumber;
c04e3238 119 // For safety: return kTRUE or kFALSE ????
120 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 121 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 122 // sign of charge (sign of fInverseBendingMomentum if forward motion)
123 // must be changed if backward extrapolation
208f139e 124 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 125 // Extrapolation loop
126 stepNumber = 0;
208f139e 127 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 128 stepNumber++;
4284483e 129 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 130 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
c04e3238 131 // better use TArray ????
208f139e 132 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 133 }
208f139e 134 // check fgkMaxStepNumber ????
c04e3238 135 // Interpolation back to exact Z (2nd order)
136 // should be in function ???? using TArray ????
dade8580 137 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 138 if (TMath::Abs(dZ12) > 0) {
dade8580 139 Double_t dZ1i = zEnd - v3[2]; // 1-i
140 Double_t dZi2 = v3New[2] - zEnd; // i->2
141 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
142 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
143 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
144 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
145 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
146 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
147 v3[2] = zEnd; // Z
c04e3238 148 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
149 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
150 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 151 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 152 v3[3] = xPrimeI * v3[5]; // PX/PTOT
153 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 154 } else {
4284483e 155 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 156 }
4284483e 157 // Recover track parameters (charge back for forward motion)
dade8580 158 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 159}
160
161 //__________________________________________________________________________
4284483e 162void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
163{
164 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
165 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
166 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
167 Double_t forwardBackward; // +1 if forward, -1 if backward
168 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
169 else forwardBackward = -1.0;
170 // sign of charge (sign of fInverseBendingMomentum if forward motion)
171 // must be changed if backward extrapolation
172 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
173 Double_t v3[7], v3New[7];
174 Double_t dZ, step;
175 Int_t stepNumber = 0;
176
177 // Extrapolation loop (until within tolerance)
178 Double_t residue = zEnd - trackParam->GetZ();
179 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
180 dZ = zEnd - trackParam->GetZ();
181 // step lenght assuming linear trajectory
182 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
183 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
184 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
185 do { // reduce step lenght while zEnd oversteped
186 if (stepNumber > fgkMaxStepNumber) {
187 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
188 break;
189 }
190 stepNumber ++;
191 step = TMath::Abs(step);
192 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
193 residue = zEnd - v3New[2];
194 step *= dZ/(v3New[2]-trackParam->GetZ());
195 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
196 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
197 }
198
199 // terminate the extropolation with a straight line up to the exact "zEnd" value
200 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
201 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
202 trackParam->SetZ(zEnd);
203}
204
205 //__________________________________________________________________________
206void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 207{
dade8580 208 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 209 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
210 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 211 v3[0] = trackParam->GetNonBendingCoor(); // X
212 v3[1] = trackParam->GetBendingCoor(); // Y
213 v3[2] = trackParam->GetZ(); // Z
c04e3238 214 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
215 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 216 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
217 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
218 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
219 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 220}
221
222 //__________________________________________________________________________
dade8580 223void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 224{
dade8580 225 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 226 /// assumed to be calculated for forward motion in Z.
227 /// "InverseBendingMomentum" is signed with "charge".
dade8580 228 trackParam->SetNonBendingCoor(v3[0]); // X
229 trackParam->SetBendingCoor(v3[1]); // Y
230 trackParam->SetZ(v3[2]); // Z
231 Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]);
c04e3238 232 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 233 trackParam->SetBendingSlope(v3[4]/v3[5]);
234 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
c04e3238 235}
236
237 //__________________________________________________________________________
ea94c18b 238void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 239{
240 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
241 /// On return, results from the extrapolation are updated in trackParam.
242
243 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
244
ea94c18b 245 // No need to propagate the covariance matrix if it does not exist
246 if (!trackParam->CovariancesExist()) {
247 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
248 // Extrapolate track parameters to "zEnd"
249 ExtrapToZ(trackParam,zEnd);
250 return;
251 }
252
208f139e 253 // Save the actual track parameters
254 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 255 TMatrixD paramSave(trackParamSave.GetParameters());
256 Double_t zBegin = trackParamSave.GetZ();
257
258 // Get reference to the parameter covariance matrix
259 const TMatrixD& kParamCov = trackParam->GetCovariances();
208f139e 260
261 // Extrapolate track parameters to "zEnd"
262 ExtrapToZ(trackParam,zEnd);
208f139e 263
ea94c18b 264 // Get reference to the extrapolated parameters
265 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 266
267 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
268 TMatrixD jacob(5,5);
ea94c18b 269 jacob.Zero();
270 TMatrixD dParam(5,1);
208f139e 271 for (Int_t i=0; i<5; i++) {
272 // Skip jacobian calculation for parameters with no associated error
ea94c18b 273 if (kParamCov(i,i) == 0.) continue;
274
208f139e 275 // Small variation of parameter i only
276 for (Int_t j=0; j<5; j++) {
277 if (j==i) {
ea94c18b 278 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
279 if (j == 4) dParam(j,0) *= TMath::Sign(1.,-paramSave(4,0)); // variation always in the same direction
280 } else dParam(j,0) = 0.;
208f139e 281 }
ea94c18b 282
208f139e 283 // Set new parameters
ea94c18b 284 trackParamSave.SetParameters(paramSave);
285 trackParamSave.AddParameters(dParam);
286 trackParamSave.SetZ(zBegin);
287
208f139e 288 // Extrapolate new track parameters to "zEnd"
289 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 290
208f139e 291 // Calculate the jacobian
ea94c18b 292 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
293 jacobji *= 1. / dParam(i,0);
294 jacob.SetSub(0,i,jacobji);
208f139e 295 }
296
297 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 298 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
299 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
300 trackParam->SetCovariances(tmp2);
301
302 // Update the propagator if required
303 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 304
305}
306
307 //__________________________________________________________________________
c04e3238 308void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
309{
310 /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station"
311 /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut"
312 /// (index 0 and 1 for first and second chambers).
313 Double_t extZ[2], z1, z2;
314 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
315 // range of station to be checked ????
316 z1 = AliMUONConstants::DefaultChamberZ(2 * station);
317 z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1);
318 // First and second Z to extrapolate at
319 if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;}
320 else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;}
321 else {
208f139e 322 cout<<"E-AliMUONTrackExtrap::ExtrapToStation: Starting Z ("<<trackParamIn->GetZ()
c04e3238 323 <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
324 exit(-1);
325 }
326 extZ[i1] = z1;
327 extZ[i2] = z2;
328 // copy of track parameters
329 trackParamOut[i1] = *trackParamIn;
330 // first extrapolation
331 ExtrapToZ(&(trackParamOut[i1]),extZ[0]);
332 trackParamOut[i2] = trackParamOut[i1];
333 // second extrapolation
334 ExtrapToZ(&(trackParamOut[i2]),extZ[1]);
335 return;
336}
337
338 //__________________________________________________________________________
208f139e 339void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
340{
8cde4af5 341 /// Extrapolation to the vertex (at the z position "zVtx") without Branson and energy loss corrections.
208f139e 342 /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
343 /// Include multiple Coulomb scattering effects in trackParam covariances.
344
8cde4af5 345 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
346
208f139e 347 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
348 cout<<"W-AliMUONTrackExtrap::ExtrapToVertexUncorrected: Starting Z ("<<trackParam->GetZ()
349 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
350 exit(-1);
351 }
352
8cde4af5 353 // Check the vertex position relatively to the absorber
ea94c18b 354 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 355 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 356 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
357 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 358 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 359 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
360 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
361 else ExtrapToZ(trackParam,zVtx);
208f139e 362 return;
363 }
364
8cde4af5 365 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 366 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 367 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 368 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
369 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
370 else ExtrapToZ(trackParam,zVtx);
8cde4af5 371 return;
ea94c18b 372 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 373 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 374 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
208f139e 375 } else {
ea94c18b 376 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
377 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
208f139e 378 }
379
8cde4af5 380 // Then add MCS effect in absorber to the parameters covariances
381 AliMUONTrackParam trackParamIn(*trackParam);
ea94c18b 382 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
8cde4af5 383 Double_t trackXYZIn[3];
384 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
385 trackXYZIn[1] = trackParamIn.GetBendingCoor();
386 trackXYZIn[2] = trackParamIn.GetZ();
387 Double_t trackXYZOut[3];
388 trackXYZOut[0] = trackParam->GetNonBendingCoor();
389 trackXYZOut[1] = trackParam->GetBendingCoor();
390 trackXYZOut[2] = trackParam->GetZ();
391 Double_t pathLength = 0.;
392 Double_t f0 = 0.;
393 Double_t f1 = 0.;
394 Double_t f2 = 0.;
395 Double_t meanRho = 0.;
396 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
397 AddMCSEffectInAbsorber(trackParam,pathLength,f0,f1,f2);
208f139e 398
399 // finally go to the vertex
400 ExtrapToZCov(trackParam,zVtx);
401
402}
403
404 //__________________________________________________________________________
8cde4af5 405void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
406{
407 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
408 /// at the end of the front absorber using the absorber correction parameters
409
410 // absorber related covariance parameters
411 Double_t bendingSlope = param->GetBendingSlope();
412 Double_t nonBendingSlope = param->GetNonBendingSlope();
413 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
414 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
415 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
416 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
417 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
418 Double_t varSlop = alpha2 * f0;
419
ea94c18b 420 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 421 // Non bending plane
ea94c18b 422 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
423 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 424 // Bending plane
ea94c18b 425 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
426 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
427
428 // Set new covariances
429 param->SetCovariances(newParamCov);
8cde4af5 430
431}
432
433 //__________________________________________________________________________
434void AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t &pathLength,
435 Double_t &f0, Double_t &f1, Double_t &f2, Double_t &meanRho)
436{
437 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
438 /// Calculated assuming a linear propagation between track positions trackXYZIn and trackXYZOut
439 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
440 // f0: 0th moment of z calculated with the inverse radiation-length distribution
441 // f1: 1st moment of z calculated with the inverse radiation-length distribution
442 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
443 // meanRho: average density of crossed material (g/cm3)
444
445 // Reset absorber's parameters
446 pathLength = 0.;
447 f0 = 0.;
448 f1 = 0.;
449 f2 = 0.;
450 meanRho = 0.;
451
452 // Check whether the geometry is available
453 if (!gGeoManager) {
454 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
455 return;
456 }
457
458 // Initialize starting point and direction
459 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
460 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
461 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
462 if (pathLength < TGeoShape::Tolerance()) return;
463 Double_t b[3];
464 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
465 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
466 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
467 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
468 if (!currentnode) {
469 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
470 return;
471 }
472
473 // loop over absorber slices and calculate absorber's parameters
474 Double_t rho = 0.; // material density (g/cm3)
475 Double_t x0 = 0.; // radiation-length (cm-1)
476 Double_t localPathLength = 0;
477 Double_t remainingPathLength = pathLength;
478 Double_t zB = trackXYZIn[2];
479 Double_t zE, dzB, dzE;
480 do {
481 // Get material properties
482 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
483 rho = material->GetDensity();
484 x0 = material->GetRadLen();
485 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
486
487 // Get path length within this material
488 gGeoManager->FindNextBoundary(remainingPathLength);
489 localPathLength = gGeoManager->GetStep() + 1.e-6;
490 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
491 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
492 else {
493 currentnode = gGeoManager->Step();
494 if (!currentnode) {
495 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
496 f0 = f1 = f2 = meanRho = 0.;
497 return;
498 }
499 if (!gGeoManager->IsEntering()) {
500 // make another small step to try to enter in new absorber slice
501 gGeoManager->SetStep(0.001);
502 currentnode = gGeoManager->Step();
503 if (!gGeoManager->IsEntering() || !currentnode) {
504 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
505 f0 = f1 = f2 = meanRho = 0.;
506 return;
507 }
508 localPathLength += 0.001;
509 }
510 }
511
512 // calculate absorber's parameters
513 zE = b[2] * localPathLength + zB;
514 dzB = zB - trackXYZIn[2];
515 dzE = zE - trackXYZIn[2];
516 f0 += localPathLength / x0;
517 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
518 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
519 meanRho += localPathLength * rho;
520
521 // prepare next step
522 zB = zE;
523 remainingPathLength -= localPathLength;
524 } while (remainingPathLength > TGeoShape::Tolerance());
525
526 meanRho /= pathLength;
527}
528
529 //__________________________________________________________________________
ea94c18b 530Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
531{
532 /// Return the angular dispersion square due to multiple Coulomb scattering
533 /// through a material of thickness "dZ" and of radiation length "x0"
534 /// assuming linear propagation and using the small angle approximation.
535
536 Double_t bendingSlope = param.GetBendingSlope();
537 Double_t nonBendingSlope = param.GetNonBendingSlope();
538 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
539 (1.0 + bendingSlope * bendingSlope) /
540 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
541 // Path length in the material
542 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
543 // relativistic velocity
544 Double_t velo = 1.;
545 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
546 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
547
548 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
549}
550
551 //__________________________________________________________________________
8cde4af5 552void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 553{
554 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
555 /// through a material of thickness "dZ" and of radiation length "x0"
556 /// assuming linear propagation and using the small angle approximation.
557
558 Double_t bendingSlope = param->GetBendingSlope();
559 Double_t nonBendingSlope = param->GetNonBendingSlope();
560 Double_t inverseTotalMomentum2 = param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum() *
561 (1.0 + bendingSlope * bendingSlope) /
562 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
563 // Path length in the material
564 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
565 Double_t pathLength2 = pathLength * pathLength;
566 // relativistic velocity
567 Double_t velo = 1.;
568 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
569 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
570 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
571
208f139e 572 Double_t varCoor = pathLength2 * theta02 / 3.;
573 Double_t varSlop = theta02;
574 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 575
576 // Add effects of multiple Coulomb scattering in track parameter covariances
577 TMatrixD newParamCov(param->GetCovariances());
208f139e 578 // Non bending plane
ea94c18b 579 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
580 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 581 // Bending plane
ea94c18b 582 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
583 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
208f139e 584
ea94c18b 585 // Set new covariances
586 param->SetCovariances(newParamCov);
208f139e 587}
588
589 //__________________________________________________________________________
fac70e25 590void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx,
591 Bool_t CorrectForMCS, Bool_t CorrectForEnergyLoss)
c04e3238 592{
593 /// Extrapolation to the vertex.
fac70e25 594 /// Returns the track parameters resulting from the extrapolation of the current TrackParam.
8cde4af5 595 /// Changes parameters according to Branson correction through the absorber and energy loss
c04e3238 596
8cde4af5 597 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 598
8cde4af5 599 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
fac70e25 600 cout<<"F-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
8cde4af5 601 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
602 exit(-1);
c04e3238 603 }
8cde4af5 604
fac70e25 605 // Check if correction required
606 if (!CorrectForMCS && !CorrectForEnergyLoss) {
607 ExtrapToZ(trackParam,zVtx);
608 return;
609 }
610
8cde4af5 611 // Check the vertex position relatively to the absorber
ea94c18b 612 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 613 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 614 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
615 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 616 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 617 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
8cde4af5 618 ExtrapToZ(trackParam,zVtx);
619 return;
620 }
621
622 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 623 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 624 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 625 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
8cde4af5 626 ExtrapToZ(trackParam,zVtx);
627 return;
ea94c18b 628 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 629 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 630 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 631 } else {
ea94c18b 632 ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 633 }
c04e3238 634
8cde4af5 635 // Get absorber correction parameters assuming linear propagation from vertex to the track position
636 Double_t trackXYZOut[3];
637 trackXYZOut[0] = trackParam->GetNonBendingCoor();
638 trackXYZOut[1] = trackParam->GetBendingCoor();
639 trackXYZOut[2] = trackParam->GetZ();
640 Double_t trackXYZIn[3];
ea94c18b 641 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
8cde4af5 642 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
643 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
644 Double_t pathLength = 0.;
645 Double_t f0 = 0.;
646 Double_t f1 = 0.;
647 Double_t f2 = 0.;
648 Double_t meanRho = 0.;
649 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
c04e3238 650
8cde4af5 651 // Calculate energy loss
652 Double_t pTot = trackParam->P();
653 Double_t charge = TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
654 Double_t deltaP = TotalMomentumEnergyLoss(pTot,pathLength,meanRho);
655
656 // Correct for half of energy loss
fac70e25 657 Double_t nonBendingSlope, bendingSlope;
658 if (CorrectForEnergyLoss) {
659 pTot += 0.5 * deltaP;
660 nonBendingSlope = trackParam->GetNonBendingSlope();
661 bendingSlope = trackParam->GetBendingSlope();
662 trackParam->SetInverseBendingMomentum(charge / pTot *
663 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
664 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
665 }
8cde4af5 666
fac70e25 667 if (CorrectForMCS) {
668 // Position of the Branson plane (spectro. (z<0))
669 Double_t zB = (f1>0.) ? trackXYZIn[2] - f2/f1 : 0.;
670
671 // Get track position in the Branson plane corrected for magnetic field effect
672 ExtrapToZ(trackParam,zVtx);
673 Double_t xB = trackParam->GetNonBendingCoor() + (zB - zVtx) * trackParam->GetNonBendingSlope();
674 Double_t yB = trackParam->GetBendingCoor() + (zB - zVtx) * trackParam->GetBendingSlope();
675
676 // Get track slopes corrected for multiple scattering (spectro. (z<0))
677 nonBendingSlope = (zB<0.) ? (xB - xVtx) / (zB - zVtx) : trackParam->GetNonBendingSlope();
678 bendingSlope = (zB<0.) ? (yB - yVtx) / (zB - zVtx) : trackParam->GetBendingSlope();
679
680 // Set track parameters at vertex
681 trackParam->SetNonBendingCoor(xVtx);
682 trackParam->SetBendingCoor(yVtx);
683 trackParam->SetZ(zVtx);
684 trackParam->SetNonBendingSlope(nonBendingSlope);
685 trackParam->SetBendingSlope(bendingSlope);
686 } else {
687 ExtrapToZ(trackParam,zVtx);
688 nonBendingSlope = trackParam->GetNonBendingSlope();
689 bendingSlope = trackParam->GetBendingSlope();
690 }
8cde4af5 691
692 // Correct for second half of energy loss
fac70e25 693 if (CorrectForEnergyLoss) pTot += 0.5 * deltaP;
8cde4af5 694
695 // Set track parameters at vertex
8cde4af5 696 trackParam->SetInverseBendingMomentum(charge / pTot *
fac70e25 697 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
698 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
699
700}
701
702 //__________________________________________________________________________
703Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
704{
705 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
706
707 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 708
fac70e25 709 // Check whether the geometry is available
710 if (!gGeoManager) {
711 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
712 return 0.;
713 }
714
715 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
716 Double_t trackXYZOut[3];
717 trackXYZOut[0] = trackParam->GetNonBendingCoor();
718 trackXYZOut[1] = trackParam->GetBendingCoor();
719 trackXYZOut[2] = trackParam->GetZ();
720 Double_t trackXYZIn[3];
721 trackXYZIn[0] = xVtx;
722 trackXYZIn[1] = yVtx;
723 trackXYZIn[2] = zVtx;
724 Double_t pathLength = 0.;
725 Double_t f0 = 0.;
726 Double_t f1 = 0.;
727 Double_t f2 = 0.;
728 Double_t meanRho = 0.;
729 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
730
731 // Calculate energy loss
732 Double_t pTot = trackParam->P();
733 return TotalMomentumEnergyLoss(pTot,pathLength,meanRho);
c04e3238 734}
735
736 //__________________________________________________________________________
8cde4af5 737Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t pTotal, Double_t pathLength, Double_t rho)
c04e3238 738{
8cde4af5 739 /// Returns the total momentum energy loss in the front absorber
fac70e25 740 Double_t muMass = 0.105658369;
8cde4af5 741 Double_t p2=pTotal*pTotal;
742 Double_t beta2=p2/(p2 + muMass*muMass);
743 Double_t dE=ApproximateBetheBloch(beta2)*pathLength*rho;
744
745 return dE;
c04e3238 746}
747
748 //__________________________________________________________________________
71a2d3aa 749Double_t AliMUONTrackExtrap::ApproximateBetheBloch(Double_t beta2)
750{
751/// This is an approximation of the Bethe-Bloch formula with
752/// the density effect taken into account at beta*gamma > 3.5
753/// (the approximation is reasonable only for solid materials)
754
8cde4af5 755 if (beta2/(1-beta2)>3.5*3.5)
756 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
757
758 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
c04e3238 759}
760
761 //__________________________________________________________________________
762void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
763{
71a2d3aa 764/// <pre>
c04e3238 765/// ******************************************************************
766/// * *
767/// * Performs the tracking of one step in a magnetic field *
768/// * The trajectory is assumed to be a helix in a constant field *
769/// * taken at the mid point of the step. *
770/// * Parameters: *
771/// * input *
772/// * STEP =arc length of the step asked *
773/// * VECT =input vector (position,direction cos and momentum) *
774/// * CHARGE= electric charge of the particle *
775/// * output *
776/// * VOUT = same as VECT after completion of the step *
777/// * *
778/// * ==>Called by : <USER>, GUSWIM *
779/// * Author m.hansroul ********* *
780/// * modified s.egli, s.v.levonian *
781/// * modified v.perevoztchikov
782/// * *
783/// ******************************************************************
71a2d3aa 784/// </pre>
c04e3238 785
786// modif: everything in double precision
787
788 Double_t xyz[3], h[4], hxp[3];
789 Double_t h2xy, hp, rho, tet;
790 Double_t sint, sintt, tsint, cos1t;
791 Double_t f1, f2, f3, f4, f5, f6;
792
793 const Int_t kix = 0;
794 const Int_t kiy = 1;
795 const Int_t kiz = 2;
796 const Int_t kipx = 3;
797 const Int_t kipy = 4;
798 const Int_t kipz = 5;
799 const Int_t kipp = 6;
800
801 const Double_t kec = 2.9979251e-4;
802 //
803 // ------------------------------------------------------------------
804 //
805 // units are kgauss,centimeters,gev/c
806 //
807 vout[kipp] = vect[kipp];
808 if (TMath::Abs(charge) < 0.00001) {
809 for (Int_t i = 0; i < 3; i++) {
810 vout[i] = vect[i] + step * vect[i+3];
811 vout[i+3] = vect[i+3];
812 }
813 return;
814 }
815 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
816 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
817 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
818
819 //cmodif: call gufld (xyz, h) changed into:
820 GetField (xyz, h);
821
822 h2xy = h[0]*h[0] + h[1]*h[1];
823 h[3] = h[2]*h[2]+ h2xy;
824 if (h[3] < 1.e-12) {
825 for (Int_t i = 0; i < 3; i++) {
826 vout[i] = vect[i] + step * vect[i+3];
827 vout[i+3] = vect[i+3];
828 }
829 return;
830 }
831 if (h2xy < 1.e-12*h[3]) {
832 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
833 return;
834 }
835 h[3] = TMath::Sqrt(h[3]);
836 h[0] /= h[3];
837 h[1] /= h[3];
838 h[2] /= h[3];
839 h[3] *= kec;
840
841 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
842 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
843 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
844
845 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
846
847 rho = -charge*h[3]/vect[kipp];
848 tet = rho * step;
849
850 if (TMath::Abs(tet) > 0.15) {
851 sint = TMath::Sin(tet);
852 sintt = (sint/tet);
853 tsint = (tet-sint)/tet;
854 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
855 } else {
856 tsint = tet*tet/36.;
857 sintt = (1. - tsint);
858 sint = tet*sintt;
859 cos1t = 0.5*tet;
860 }
861
862 f1 = step * sintt;
863 f2 = step * cos1t;
864 f3 = step * tsint * hp;
865 f4 = -tet*cos1t;
866 f5 = sint;
867 f6 = tet * cos1t * hp;
868
869 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
870 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
871 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
872
873 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
874 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
875 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
876
877 return;
878}
879
880 //__________________________________________________________________________
881void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
882{
71a2d3aa 883/// <pre>
c04e3238 884/// ******************************************************************
885/// * *
886/// * Tracking routine in a constant field oriented *
887/// * along axis 3 *
888/// * Tracking is performed with a conventional *
889/// * helix step method *
890/// * *
891/// * ==>Called by : <USER>, GUSWIM *
892/// * Authors R.Brun, M.Hansroul ********* *
893/// * Rewritten V.Perevoztchikov
894/// * *
895/// ******************************************************************
71a2d3aa 896/// </pre>
c04e3238 897
898 Double_t hxp[3];
899 Double_t h4, hp, rho, tet;
900 Double_t sint, sintt, tsint, cos1t;
901 Double_t f1, f2, f3, f4, f5, f6;
902
903 const Int_t kix = 0;
904 const Int_t kiy = 1;
905 const Int_t kiz = 2;
906 const Int_t kipx = 3;
907 const Int_t kipy = 4;
908 const Int_t kipz = 5;
909 const Int_t kipp = 6;
910
911 const Double_t kec = 2.9979251e-4;
912
913//
914// ------------------------------------------------------------------
915//
916// units are kgauss,centimeters,gev/c
917//
918 vout[kipp] = vect[kipp];
919 h4 = field * kec;
920
921 hxp[0] = - vect[kipy];
922 hxp[1] = + vect[kipx];
923
924 hp = vect[kipz];
925
926 rho = -h4/vect[kipp];
927 tet = rho * step;
928 if (TMath::Abs(tet) > 0.15) {
929 sint = TMath::Sin(tet);
930 sintt = (sint/tet);
931 tsint = (tet-sint)/tet;
932 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
933 } else {
934 tsint = tet*tet/36.;
935 sintt = (1. - tsint);
936 sint = tet*sintt;
937 cos1t = 0.5*tet;
938 }
939
940 f1 = step * sintt;
941 f2 = step * cos1t;
942 f3 = step * tsint * hp;
943 f4 = -tet*cos1t;
944 f5 = sint;
945 f6 = tet * cos1t * hp;
946
947 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
948 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
949 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
950
951 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
952 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
953 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
954
955 return;
956}
8cde4af5 957
c04e3238 958 //__________________________________________________________________________
959void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
960{
71a2d3aa 961/// <pre>
c04e3238 962/// ******************************************************************
963/// * *
964/// * Runge-Kutta method for tracking a particle through a magnetic *
965/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
966/// * Standards, procedure 25.5.20) *
967/// * *
968/// * Input parameters *
969/// * CHARGE Particle charge *
970/// * STEP Step size *
971/// * VECT Initial co-ords,direction cosines,momentum *
972/// * Output parameters *
973/// * VOUT Output co-ords,direction cosines,momentum *
974/// * User routine called *
975/// * CALL GUFLD(X,F) *
976/// * *
977/// * ==>Called by : <USER>, GUSWIM *
978/// * Authors R.Brun, M.Hansroul ********* *
979/// * V.Perevoztchikov (CUT STEP implementation) *
980/// * *
981/// * *
982/// ******************************************************************
71a2d3aa 983/// </pre>
c04e3238 984
985 Double_t h2, h4, f[4];
986 Double_t xyzt[3], a, b, c, ph,ph2;
987 Double_t secxs[4],secys[4],seczs[4],hxp[3];
988 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
989 Double_t est, at, bt, ct, cba;
990 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
991
992 Double_t x;
993 Double_t y;
994 Double_t z;
995
996 Double_t xt;
997 Double_t yt;
998 Double_t zt;
999
1000 Double_t maxit = 1992;
1001 Double_t maxcut = 11;
1002
1003 const Double_t kdlt = 1e-4;
1004 const Double_t kdlt32 = kdlt/32.;
1005 const Double_t kthird = 1./3.;
1006 const Double_t khalf = 0.5;
1007 const Double_t kec = 2.9979251e-4;
1008
1009 const Double_t kpisqua = 9.86960440109;
1010 const Int_t kix = 0;
1011 const Int_t kiy = 1;
1012 const Int_t kiz = 2;
1013 const Int_t kipx = 3;
1014 const Int_t kipy = 4;
1015 const Int_t kipz = 5;
1016
1017 // *.
1018 // *. ------------------------------------------------------------------
1019 // *.
1020 // * this constant is for units cm,gev/c and kgauss
1021 // *
1022 Int_t iter = 0;
1023 Int_t ncut = 0;
1024 for(Int_t j = 0; j < 7; j++)
1025 vout[j] = vect[j];
1026
1027 Double_t pinv = kec * charge / vect[6];
1028 Double_t tl = 0.;
1029 Double_t h = step;
1030 Double_t rest;
1031
1032
1033 do {
1034 rest = step - tl;
1035 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1036 //cmodif: call gufld(vout,f) changed into:
1037
1038 GetField(vout,f);
1039
1040 // *
1041 // * start of integration
1042 // *
1043 x = vout[0];
1044 y = vout[1];
1045 z = vout[2];
1046 a = vout[3];
1047 b = vout[4];
1048 c = vout[5];
1049
1050 h2 = khalf * h;
1051 h4 = khalf * h2;
1052 ph = pinv * h;
1053 ph2 = khalf * ph;
1054 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1055 secys[0] = (c * f[0] - a * f[2]) * ph2;
1056 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1057 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1058 if (ang2 > kpisqua) break;
1059
1060 dxt = h2 * a + h4 * secxs[0];
1061 dyt = h2 * b + h4 * secys[0];
1062 dzt = h2 * c + h4 * seczs[0];
1063 xt = x + dxt;
1064 yt = y + dyt;
1065 zt = z + dzt;
1066 // *
1067 // * second intermediate point
1068 // *
1069
1070 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1071 if (est > h) {
1072 if (ncut++ > maxcut) break;
1073 h *= khalf;
1074 continue;
1075 }
1076
1077 xyzt[0] = xt;
1078 xyzt[1] = yt;
1079 xyzt[2] = zt;
1080
1081 //cmodif: call gufld(xyzt,f) changed into:
1082 GetField(xyzt,f);
1083
1084 at = a + secxs[0];
1085 bt = b + secys[0];
1086 ct = c + seczs[0];
1087
1088 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1089 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1090 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1091 at = a + secxs[1];
1092 bt = b + secys[1];
1093 ct = c + seczs[1];
1094 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1095 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1096 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1097 dxt = h * (a + secxs[2]);
1098 dyt = h * (b + secys[2]);
1099 dzt = h * (c + seczs[2]);
1100 xt = x + dxt;
1101 yt = y + dyt;
1102 zt = z + dzt;
1103 at = a + 2.*secxs[2];
1104 bt = b + 2.*secys[2];
1105 ct = c + 2.*seczs[2];
1106
1107 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1108 if (est > 2.*TMath::Abs(h)) {
1109 if (ncut++ > maxcut) break;
1110 h *= khalf;
1111 continue;
1112 }
1113
1114 xyzt[0] = xt;
1115 xyzt[1] = yt;
1116 xyzt[2] = zt;
1117
1118 //cmodif: call gufld(xyzt,f) changed into:
1119 GetField(xyzt,f);
1120
1121 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1122 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1123 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1124
1125 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1126 secys[3] = (ct*f[0] - at*f[2])* ph2;
1127 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1128 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1129 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1130 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1131
1132 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1133 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1134 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1135
1136 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1137 if (ncut++ > maxcut) break;
1138 h *= khalf;
1139 continue;
1140 }
1141
1142 ncut = 0;
1143 // * if too many iterations, go to helix
1144 if (iter++ > maxit) break;
1145
1146 tl += h;
1147 if (est < kdlt32)
1148 h *= 2.;
1149 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1150 vout[0] = x;
1151 vout[1] = y;
1152 vout[2] = z;
1153 vout[3] = cba*a;
1154 vout[4] = cba*b;
1155 vout[5] = cba*c;
1156 rest = step - tl;
1157 if (step < 0.) rest = -rest;
1158 if (rest < 1.e-5*TMath::Abs(step)) return;
1159
1160 } while(1);
1161
1162 // angle too big, use helix
1163
1164 f1 = f[0];
1165 f2 = f[1];
1166 f3 = f[2];
1167 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1168 rho = -f4*pinv;
1169 tet = rho * step;
1170
1171 hnorm = 1./f4;
1172 f1 = f1*hnorm;
1173 f2 = f2*hnorm;
1174 f3 = f3*hnorm;
1175
1176 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1177 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1178 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1179
1180 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1181
1182 rho1 = 1./rho;
1183 sint = TMath::Sin(tet);
1184 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1185
1186 g1 = sint*rho1;
1187 g2 = cost*rho1;
1188 g3 = (tet-sint) * hp*rho1;
1189 g4 = -cost;
1190 g5 = sint;
1191 g6 = cost * hp;
1192
1193 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1194 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1195 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1196
1197 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1198 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1199 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1200
1201 return;
1202}
8cde4af5 1203
c04e3238 1204//___________________________________________________________
1205 void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
1206{
1207 /// interface for arguments in double precision (Why ? ChF)
1208 Float_t x[3], b[3];
1209
1210 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
1211
1212 if (fgkField) fgkField->Field(x,b);
1213 else {
1214 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
1215 exit(-1);
1216 }
1217
1218 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
1219
1220 return;
1221}