Adding class description after ClassDef(..) where missing,
[u/mrichter/AliRoot.git] / MUON / AliMUONTrackExtrap.cxx
CommitLineData
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 //__________________________________________________________________________
019df241 100void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
101{
102 /// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd".
103 /// On return, results from the extrapolation are updated in trackParam.
104
105 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
106
107 // Compute track parameters
108 Double_t dZ = zEnd - trackParam->GetZ();
109 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
110 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
111 trackParam->SetZ(zEnd);
112
113 // Update track parameters covariances if any
114 if (trackParam->CovariancesExist()) {
115 TMatrixD paramCov(trackParam->GetCovariances());
116 paramCov(0,0) += dZ * dZ * paramCov(1,1) + 2. * dZ * paramCov(0,1);
117 paramCov(0,1) += dZ * paramCov(1,1);
118 paramCov(1,0) = paramCov(0,1);
119 paramCov(2,2) += dZ * dZ * paramCov(3,3) + 2. * dZ * paramCov(2,3);
120 paramCov(2,3) += dZ * paramCov(3,3);
121 paramCov(3,2) = paramCov(2,3);
122 trackParam->SetCovariances(paramCov);
123 }
124
125}
126
127 //__________________________________________________________________________
c04e3238 128void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
129{
4284483e 130 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
131 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
132 if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
133 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
134}
135
136 //__________________________________________________________________________
137void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
138{
139 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 140 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
141 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
142 Double_t forwardBackward; // +1 if forward, -1 if backward
143 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
144 else forwardBackward = -1.0;
dade8580 145 Double_t v3[7], v3New[7]; // 7 in parameter ????
146 Int_t i3, stepNumber;
c04e3238 147 // For safety: return kTRUE or kFALSE ????
148 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 149 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 150 // sign of charge (sign of fInverseBendingMomentum if forward motion)
151 // must be changed if backward extrapolation
208f139e 152 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 153 // Extrapolation loop
154 stepNumber = 0;
208f139e 155 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 156 stepNumber++;
4284483e 157 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 158 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
c04e3238 159 // better use TArray ????
208f139e 160 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 161 }
208f139e 162 // check fgkMaxStepNumber ????
c04e3238 163 // Interpolation back to exact Z (2nd order)
164 // should be in function ???? using TArray ????
dade8580 165 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 166 if (TMath::Abs(dZ12) > 0) {
dade8580 167 Double_t dZ1i = zEnd - v3[2]; // 1-i
168 Double_t dZi2 = v3New[2] - zEnd; // i->2
169 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
170 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
171 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
172 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
173 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
174 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
175 v3[2] = zEnd; // Z
c04e3238 176 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
177 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
178 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 179 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 180 v3[3] = xPrimeI * v3[5]; // PX/PTOT
181 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 182 } else {
4284483e 183 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 184 }
4284483e 185 // Recover track parameters (charge back for forward motion)
dade8580 186 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 187}
188
189 //__________________________________________________________________________
4284483e 190void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
191{
192 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
193 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
194 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
195 Double_t forwardBackward; // +1 if forward, -1 if backward
196 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
197 else forwardBackward = -1.0;
198 // sign of charge (sign of fInverseBendingMomentum if forward motion)
199 // must be changed if backward extrapolation
200 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
201 Double_t v3[7], v3New[7];
202 Double_t dZ, step;
203 Int_t stepNumber = 0;
204
205 // Extrapolation loop (until within tolerance)
206 Double_t residue = zEnd - trackParam->GetZ();
207 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
208 dZ = zEnd - trackParam->GetZ();
209 // step lenght assuming linear trajectory
210 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
211 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
212 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
213 do { // reduce step lenght while zEnd oversteped
214 if (stepNumber > fgkMaxStepNumber) {
215 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
216 break;
217 }
218 stepNumber ++;
219 step = TMath::Abs(step);
220 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
221 residue = zEnd - v3New[2];
222 step *= dZ/(v3New[2]-trackParam->GetZ());
223 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
224 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
225 }
226
227 // terminate the extropolation with a straight line up to the exact "zEnd" value
228 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
229 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
230 trackParam->SetZ(zEnd);
231}
232
233 //__________________________________________________________________________
234void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 235{
dade8580 236 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 237 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
238 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 239 v3[0] = trackParam->GetNonBendingCoor(); // X
240 v3[1] = trackParam->GetBendingCoor(); // Y
241 v3[2] = trackParam->GetZ(); // Z
c04e3238 242 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
243 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 244 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
245 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
246 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
247 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 248}
249
250 //__________________________________________________________________________
dade8580 251void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 252{
dade8580 253 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 254 /// assumed to be calculated for forward motion in Z.
255 /// "InverseBendingMomentum" is signed with "charge".
dade8580 256 trackParam->SetNonBendingCoor(v3[0]); // X
257 trackParam->SetBendingCoor(v3[1]); // Y
258 trackParam->SetZ(v3[2]); // Z
259 Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]);
c04e3238 260 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 261 trackParam->SetBendingSlope(v3[4]/v3[5]);
262 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
c04e3238 263}
264
265 //__________________________________________________________________________
ea94c18b 266void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 267{
268 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
269 /// On return, results from the extrapolation are updated in trackParam.
270
271 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
272
ea94c18b 273 // No need to propagate the covariance matrix if it does not exist
274 if (!trackParam->CovariancesExist()) {
275 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
276 // Extrapolate track parameters to "zEnd"
277 ExtrapToZ(trackParam,zEnd);
278 return;
279 }
280
208f139e 281 // Save the actual track parameters
282 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 283 TMatrixD paramSave(trackParamSave.GetParameters());
284 Double_t zBegin = trackParamSave.GetZ();
285
286 // Get reference to the parameter covariance matrix
287 const TMatrixD& kParamCov = trackParam->GetCovariances();
208f139e 288
289 // Extrapolate track parameters to "zEnd"
290 ExtrapToZ(trackParam,zEnd);
208f139e 291
ea94c18b 292 // Get reference to the extrapolated parameters
293 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 294
295 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
296 TMatrixD jacob(5,5);
ea94c18b 297 jacob.Zero();
298 TMatrixD dParam(5,1);
208f139e 299 for (Int_t i=0; i<5; i++) {
300 // Skip jacobian calculation for parameters with no associated error
ea94c18b 301 if (kParamCov(i,i) == 0.) continue;
302
208f139e 303 // Small variation of parameter i only
304 for (Int_t j=0; j<5; j++) {
305 if (j==i) {
ea94c18b 306 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
307 if (j == 4) dParam(j,0) *= TMath::Sign(1.,-paramSave(4,0)); // variation always in the same direction
308 } else dParam(j,0) = 0.;
208f139e 309 }
ea94c18b 310
208f139e 311 // Set new parameters
ea94c18b 312 trackParamSave.SetParameters(paramSave);
313 trackParamSave.AddParameters(dParam);
314 trackParamSave.SetZ(zBegin);
315
208f139e 316 // Extrapolate new track parameters to "zEnd"
317 ExtrapToZ(&trackParamSave,zEnd);
ea94c18b 318
208f139e 319 // Calculate the jacobian
ea94c18b 320 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
321 jacobji *= 1. / dParam(i,0);
322 jacob.SetSub(0,i,jacobji);
208f139e 323 }
324
325 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 326 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
327 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
328 trackParam->SetCovariances(tmp2);
329
330 // Update the propagator if required
331 if (updatePropagator) trackParam->UpdatePropagator(jacob);
208f139e 332
333}
334
335 //__________________________________________________________________________
c04e3238 336void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
337{
338 /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station"
339 /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut"
340 /// (index 0 and 1 for first and second chambers).
341 Double_t extZ[2], z1, z2;
342 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
343 // range of station to be checked ????
344 z1 = AliMUONConstants::DefaultChamberZ(2 * station);
345 z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1);
346 // First and second Z to extrapolate at
347 if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;}
348 else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;}
349 else {
208f139e 350 cout<<"E-AliMUONTrackExtrap::ExtrapToStation: Starting Z ("<<trackParamIn->GetZ()
c04e3238 351 <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
352 exit(-1);
353 }
354 extZ[i1] = z1;
355 extZ[i2] = z2;
356 // copy of track parameters
357 trackParamOut[i1] = *trackParamIn;
358 // first extrapolation
359 ExtrapToZ(&(trackParamOut[i1]),extZ[0]);
360 trackParamOut[i2] = trackParamOut[i1];
361 // second extrapolation
362 ExtrapToZ(&(trackParamOut[i2]),extZ[1]);
363 return;
364}
365
366 //__________________________________________________________________________
208f139e 367void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
368{
8cde4af5 369 /// Extrapolation to the vertex (at the z position "zVtx") without Branson and energy loss corrections.
208f139e 370 /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
371 /// Include multiple Coulomb scattering effects in trackParam covariances.
372
8cde4af5 373 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
374
208f139e 375 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
376 cout<<"W-AliMUONTrackExtrap::ExtrapToVertexUncorrected: Starting Z ("<<trackParam->GetZ()
377 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
378 exit(-1);
379 }
380
8cde4af5 381 // Check the vertex position relatively to the absorber
ea94c18b 382 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 383 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 384 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
385 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 386 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 387 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
388 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
389 else ExtrapToZ(trackParam,zVtx);
208f139e 390 return;
391 }
392
8cde4af5 393 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 394 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 395 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 396 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
397 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
398 else ExtrapToZ(trackParam,zVtx);
8cde4af5 399 return;
ea94c18b 400 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 401 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 402 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
208f139e 403 } else {
ea94c18b 404 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
405 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
208f139e 406 }
407
8cde4af5 408 // Then add MCS effect in absorber to the parameters covariances
409 AliMUONTrackParam trackParamIn(*trackParam);
ea94c18b 410 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
8cde4af5 411 Double_t trackXYZIn[3];
412 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
413 trackXYZIn[1] = trackParamIn.GetBendingCoor();
414 trackXYZIn[2] = trackParamIn.GetZ();
415 Double_t trackXYZOut[3];
416 trackXYZOut[0] = trackParam->GetNonBendingCoor();
417 trackXYZOut[1] = trackParam->GetBendingCoor();
418 trackXYZOut[2] = trackParam->GetZ();
419 Double_t pathLength = 0.;
420 Double_t f0 = 0.;
421 Double_t f1 = 0.;
422 Double_t f2 = 0.;
423 Double_t meanRho = 0.;
424 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
425 AddMCSEffectInAbsorber(trackParam,pathLength,f0,f1,f2);
208f139e 426
427 // finally go to the vertex
428 ExtrapToZCov(trackParam,zVtx);
429
430}
431
432 //__________________________________________________________________________
8cde4af5 433void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
434{
435 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
436 /// at the end of the front absorber using the absorber correction parameters
437
438 // absorber related covariance parameters
439 Double_t bendingSlope = param->GetBendingSlope();
440 Double_t nonBendingSlope = param->GetNonBendingSlope();
441 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
442 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
443 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
444 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
445 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
446 Double_t varSlop = alpha2 * f0;
447
ea94c18b 448 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 449 // Non bending plane
ea94c18b 450 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
451 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 452 // Bending plane
ea94c18b 453 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
454 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
455
456 // Set new covariances
457 param->SetCovariances(newParamCov);
8cde4af5 458
459}
460
461 //__________________________________________________________________________
462void AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t &pathLength,
463 Double_t &f0, Double_t &f1, Double_t &f2, Double_t &meanRho)
464{
465 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
466 /// Calculated assuming a linear propagation between track positions trackXYZIn and trackXYZOut
467 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
468 // f0: 0th moment of z calculated with the inverse radiation-length distribution
469 // f1: 1st moment of z calculated with the inverse radiation-length distribution
470 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
471 // meanRho: average density of crossed material (g/cm3)
472
473 // Reset absorber's parameters
474 pathLength = 0.;
475 f0 = 0.;
476 f1 = 0.;
477 f2 = 0.;
478 meanRho = 0.;
479
480 // Check whether the geometry is available
481 if (!gGeoManager) {
482 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
483 return;
484 }
485
486 // Initialize starting point and direction
487 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
488 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
489 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
490 if (pathLength < TGeoShape::Tolerance()) return;
491 Double_t b[3];
492 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
493 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
494 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
495 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
496 if (!currentnode) {
497 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
498 return;
499 }
500
501 // loop over absorber slices and calculate absorber's parameters
502 Double_t rho = 0.; // material density (g/cm3)
503 Double_t x0 = 0.; // radiation-length (cm-1)
504 Double_t localPathLength = 0;
505 Double_t remainingPathLength = pathLength;
506 Double_t zB = trackXYZIn[2];
507 Double_t zE, dzB, dzE;
508 do {
509 // Get material properties
510 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
511 rho = material->GetDensity();
512 x0 = material->GetRadLen();
513 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
514
515 // Get path length within this material
516 gGeoManager->FindNextBoundary(remainingPathLength);
517 localPathLength = gGeoManager->GetStep() + 1.e-6;
518 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
519 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
520 else {
521 currentnode = gGeoManager->Step();
522 if (!currentnode) {
523 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
524 f0 = f1 = f2 = meanRho = 0.;
525 return;
526 }
527 if (!gGeoManager->IsEntering()) {
528 // make another small step to try to enter in new absorber slice
529 gGeoManager->SetStep(0.001);
530 currentnode = gGeoManager->Step();
531 if (!gGeoManager->IsEntering() || !currentnode) {
532 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
533 f0 = f1 = f2 = meanRho = 0.;
534 return;
535 }
536 localPathLength += 0.001;
537 }
538 }
539
540 // calculate absorber's parameters
541 zE = b[2] * localPathLength + zB;
542 dzB = zB - trackXYZIn[2];
543 dzE = zE - trackXYZIn[2];
544 f0 += localPathLength / x0;
545 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
546 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
547 meanRho += localPathLength * rho;
548
549 // prepare next step
550 zB = zE;
551 remainingPathLength -= localPathLength;
552 } while (remainingPathLength > TGeoShape::Tolerance());
553
554 meanRho /= pathLength;
555}
556
557 //__________________________________________________________________________
ea94c18b 558Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
559{
560 /// Return the angular dispersion square due to multiple Coulomb scattering
561 /// through a material of thickness "dZ" and of radiation length "x0"
562 /// assuming linear propagation and using the small angle approximation.
563
564 Double_t bendingSlope = param.GetBendingSlope();
565 Double_t nonBendingSlope = param.GetNonBendingSlope();
566 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
567 (1.0 + bendingSlope * bendingSlope) /
568 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
569 // Path length in the material
570 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
571 // relativistic velocity
572 Double_t velo = 1.;
573 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
574 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
575
576 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
577}
578
579 //__________________________________________________________________________
8cde4af5 580void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 581{
582 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
583 /// through a material of thickness "dZ" and of radiation length "x0"
584 /// assuming linear propagation and using the small angle approximation.
585
586 Double_t bendingSlope = param->GetBendingSlope();
587 Double_t nonBendingSlope = param->GetNonBendingSlope();
588 Double_t inverseTotalMomentum2 = param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum() *
589 (1.0 + bendingSlope * bendingSlope) /
590 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
591 // Path length in the material
592 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
593 Double_t pathLength2 = pathLength * pathLength;
594 // relativistic velocity
595 Double_t velo = 1.;
596 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
597 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
598 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
599
208f139e 600 Double_t varCoor = pathLength2 * theta02 / 3.;
601 Double_t varSlop = theta02;
602 Double_t covCorrSlope = pathLength * theta02 / 2.;
ea94c18b 603
604 // Add effects of multiple Coulomb scattering in track parameter covariances
605 TMatrixD newParamCov(param->GetCovariances());
208f139e 606 // Non bending plane
ea94c18b 607 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
608 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 609 // Bending plane
ea94c18b 610 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
611 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
208f139e 612
ea94c18b 613 // Set new covariances
614 param->SetCovariances(newParamCov);
208f139e 615}
616
617 //__________________________________________________________________________
fac70e25 618void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx,
619 Bool_t CorrectForMCS, Bool_t CorrectForEnergyLoss)
c04e3238 620{
621 /// Extrapolation to the vertex.
fac70e25 622 /// Returns the track parameters resulting from the extrapolation of the current TrackParam.
8cde4af5 623 /// Changes parameters according to Branson correction through the absorber and energy loss
c04e3238 624
8cde4af5 625 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 626
8cde4af5 627 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
fac70e25 628 cout<<"F-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
8cde4af5 629 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
630 exit(-1);
c04e3238 631 }
8cde4af5 632
fac70e25 633 // Check if correction required
634 if (!CorrectForMCS && !CorrectForEnergyLoss) {
635 ExtrapToZ(trackParam,zVtx);
636 return;
637 }
638
8cde4af5 639 // Check the vertex position relatively to the absorber
ea94c18b 640 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 641 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 642 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
643 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 644 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
ea94c18b 645 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
8cde4af5 646 ExtrapToZ(trackParam,zVtx);
647 return;
648 }
649
650 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 651 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 652 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 653 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
8cde4af5 654 ExtrapToZ(trackParam,zVtx);
655 return;
ea94c18b 656 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 657 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
ea94c18b 658 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 659 } else {
ea94c18b 660 ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 661 }
c04e3238 662
8cde4af5 663 // Get absorber correction parameters assuming linear propagation from vertex to the track position
664 Double_t trackXYZOut[3];
665 trackXYZOut[0] = trackParam->GetNonBendingCoor();
666 trackXYZOut[1] = trackParam->GetBendingCoor();
667 trackXYZOut[2] = trackParam->GetZ();
668 Double_t trackXYZIn[3];
ea94c18b 669 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
8cde4af5 670 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
671 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
672 Double_t pathLength = 0.;
673 Double_t f0 = 0.;
674 Double_t f1 = 0.;
675 Double_t f2 = 0.;
676 Double_t meanRho = 0.;
677 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
c04e3238 678
8cde4af5 679 // Calculate energy loss
680 Double_t pTot = trackParam->P();
681 Double_t charge = TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
682 Double_t deltaP = TotalMomentumEnergyLoss(pTot,pathLength,meanRho);
683
684 // Correct for half of energy loss
fac70e25 685 Double_t nonBendingSlope, bendingSlope;
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;
752 Double_t pathLength = 0.;
753 Double_t f0 = 0.;
754 Double_t f1 = 0.;
755 Double_t f2 = 0.;
756 Double_t meanRho = 0.;
757 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
758
759 // Calculate energy loss
760 Double_t pTot = trackParam->P();
761 return TotalMomentumEnergyLoss(pTot,pathLength,meanRho);
c04e3238 762}
763
764 //__________________________________________________________________________
8cde4af5 765Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t pTotal, Double_t pathLength, Double_t rho)
c04e3238 766{
8cde4af5 767 /// Returns the total momentum energy loss in the front absorber
fac70e25 768 Double_t muMass = 0.105658369;
8cde4af5 769 Double_t p2=pTotal*pTotal;
770 Double_t beta2=p2/(p2 + muMass*muMass);
771 Double_t dE=ApproximateBetheBloch(beta2)*pathLength*rho;
772
773 return dE;
c04e3238 774}
775
776 //__________________________________________________________________________
71a2d3aa 777Double_t AliMUONTrackExtrap::ApproximateBetheBloch(Double_t beta2)
778{
779/// This is an approximation of the Bethe-Bloch formula with
780/// the density effect taken into account at beta*gamma > 3.5
781/// (the approximation is reasonable only for solid materials)
782
8cde4af5 783 if (beta2/(1-beta2)>3.5*3.5)
784 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
785
786 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
c04e3238 787}
788
789 //__________________________________________________________________________
790void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
791{
71a2d3aa 792/// <pre>
c04e3238 793/// ******************************************************************
794/// * *
795/// * Performs the tracking of one step in a magnetic field *
796/// * The trajectory is assumed to be a helix in a constant field *
797/// * taken at the mid point of the step. *
798/// * Parameters: *
799/// * input *
800/// * STEP =arc length of the step asked *
801/// * VECT =input vector (position,direction cos and momentum) *
802/// * CHARGE= electric charge of the particle *
803/// * output *
804/// * VOUT = same as VECT after completion of the step *
805/// * *
806/// * ==>Called by : <USER>, GUSWIM *
807/// * Author m.hansroul ********* *
808/// * modified s.egli, s.v.levonian *
809/// * modified v.perevoztchikov
810/// * *
811/// ******************************************************************
71a2d3aa 812/// </pre>
c04e3238 813
814// modif: everything in double precision
815
816 Double_t xyz[3], h[4], hxp[3];
817 Double_t h2xy, hp, rho, tet;
818 Double_t sint, sintt, tsint, cos1t;
819 Double_t f1, f2, f3, f4, f5, f6;
820
821 const Int_t kix = 0;
822 const Int_t kiy = 1;
823 const Int_t kiz = 2;
824 const Int_t kipx = 3;
825 const Int_t kipy = 4;
826 const Int_t kipz = 5;
827 const Int_t kipp = 6;
828
829 const Double_t kec = 2.9979251e-4;
830 //
831 // ------------------------------------------------------------------
832 //
833 // units are kgauss,centimeters,gev/c
834 //
835 vout[kipp] = vect[kipp];
836 if (TMath::Abs(charge) < 0.00001) {
837 for (Int_t i = 0; i < 3; i++) {
838 vout[i] = vect[i] + step * vect[i+3];
839 vout[i+3] = vect[i+3];
840 }
841 return;
842 }
843 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
844 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
845 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
846
847 //cmodif: call gufld (xyz, h) changed into:
848 GetField (xyz, h);
849
850 h2xy = h[0]*h[0] + h[1]*h[1];
851 h[3] = h[2]*h[2]+ h2xy;
852 if (h[3] < 1.e-12) {
853 for (Int_t i = 0; i < 3; i++) {
854 vout[i] = vect[i] + step * vect[i+3];
855 vout[i+3] = vect[i+3];
856 }
857 return;
858 }
859 if (h2xy < 1.e-12*h[3]) {
860 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
861 return;
862 }
863 h[3] = TMath::Sqrt(h[3]);
864 h[0] /= h[3];
865 h[1] /= h[3];
866 h[2] /= h[3];
867 h[3] *= kec;
868
869 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
870 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
871 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
872
873 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
874
875 rho = -charge*h[3]/vect[kipp];
876 tet = rho * step;
877
878 if (TMath::Abs(tet) > 0.15) {
879 sint = TMath::Sin(tet);
880 sintt = (sint/tet);
881 tsint = (tet-sint)/tet;
882 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
883 } else {
884 tsint = tet*tet/36.;
885 sintt = (1. - tsint);
886 sint = tet*sintt;
887 cos1t = 0.5*tet;
888 }
889
890 f1 = step * sintt;
891 f2 = step * cos1t;
892 f3 = step * tsint * hp;
893 f4 = -tet*cos1t;
894 f5 = sint;
895 f6 = tet * cos1t * hp;
896
897 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
898 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
899 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
900
901 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
902 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
903 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
904
905 return;
906}
907
908 //__________________________________________________________________________
909void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
910{
71a2d3aa 911/// <pre>
c04e3238 912/// ******************************************************************
913/// * *
914/// * Tracking routine in a constant field oriented *
915/// * along axis 3 *
916/// * Tracking is performed with a conventional *
917/// * helix step method *
918/// * *
919/// * ==>Called by : <USER>, GUSWIM *
920/// * Authors R.Brun, M.Hansroul ********* *
921/// * Rewritten V.Perevoztchikov
922/// * *
923/// ******************************************************************
71a2d3aa 924/// </pre>
c04e3238 925
926 Double_t hxp[3];
927 Double_t h4, hp, rho, tet;
928 Double_t sint, sintt, tsint, cos1t;
929 Double_t f1, f2, f3, f4, f5, f6;
930
931 const Int_t kix = 0;
932 const Int_t kiy = 1;
933 const Int_t kiz = 2;
934 const Int_t kipx = 3;
935 const Int_t kipy = 4;
936 const Int_t kipz = 5;
937 const Int_t kipp = 6;
938
939 const Double_t kec = 2.9979251e-4;
940
941//
942// ------------------------------------------------------------------
943//
944// units are kgauss,centimeters,gev/c
945//
946 vout[kipp] = vect[kipp];
947 h4 = field * kec;
948
949 hxp[0] = - vect[kipy];
950 hxp[1] = + vect[kipx];
951
952 hp = vect[kipz];
953
954 rho = -h4/vect[kipp];
955 tet = rho * step;
956 if (TMath::Abs(tet) > 0.15) {
957 sint = TMath::Sin(tet);
958 sintt = (sint/tet);
959 tsint = (tet-sint)/tet;
960 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
961 } else {
962 tsint = tet*tet/36.;
963 sintt = (1. - tsint);
964 sint = tet*sintt;
965 cos1t = 0.5*tet;
966 }
967
968 f1 = step * sintt;
969 f2 = step * cos1t;
970 f3 = step * tsint * hp;
971 f4 = -tet*cos1t;
972 f5 = sint;
973 f6 = tet * cos1t * hp;
974
975 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
976 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
977 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
978
979 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
980 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
981 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
982
983 return;
984}
8cde4af5 985
c04e3238 986 //__________________________________________________________________________
987void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
988{
71a2d3aa 989/// <pre>
c04e3238 990/// ******************************************************************
991/// * *
992/// * Runge-Kutta method for tracking a particle through a magnetic *
993/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
994/// * Standards, procedure 25.5.20) *
995/// * *
996/// * Input parameters *
997/// * CHARGE Particle charge *
998/// * STEP Step size *
999/// * VECT Initial co-ords,direction cosines,momentum *
1000/// * Output parameters *
1001/// * VOUT Output co-ords,direction cosines,momentum *
1002/// * User routine called *
1003/// * CALL GUFLD(X,F) *
1004/// * *
1005/// * ==>Called by : <USER>, GUSWIM *
1006/// * Authors R.Brun, M.Hansroul ********* *
1007/// * V.Perevoztchikov (CUT STEP implementation) *
1008/// * *
1009/// * *
1010/// ******************************************************************
71a2d3aa 1011/// </pre>
c04e3238 1012
1013 Double_t h2, h4, f[4];
1014 Double_t xyzt[3], a, b, c, ph,ph2;
1015 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1016 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1017 Double_t est, at, bt, ct, cba;
1018 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1019
1020 Double_t x;
1021 Double_t y;
1022 Double_t z;
1023
1024 Double_t xt;
1025 Double_t yt;
1026 Double_t zt;
1027
1028 Double_t maxit = 1992;
1029 Double_t maxcut = 11;
1030
1031 const Double_t kdlt = 1e-4;
1032 const Double_t kdlt32 = kdlt/32.;
1033 const Double_t kthird = 1./3.;
1034 const Double_t khalf = 0.5;
1035 const Double_t kec = 2.9979251e-4;
1036
1037 const Double_t kpisqua = 9.86960440109;
1038 const Int_t kix = 0;
1039 const Int_t kiy = 1;
1040 const Int_t kiz = 2;
1041 const Int_t kipx = 3;
1042 const Int_t kipy = 4;
1043 const Int_t kipz = 5;
1044
1045 // *.
1046 // *. ------------------------------------------------------------------
1047 // *.
1048 // * this constant is for units cm,gev/c and kgauss
1049 // *
1050 Int_t iter = 0;
1051 Int_t ncut = 0;
1052 for(Int_t j = 0; j < 7; j++)
1053 vout[j] = vect[j];
1054
1055 Double_t pinv = kec * charge / vect[6];
1056 Double_t tl = 0.;
1057 Double_t h = step;
1058 Double_t rest;
1059
1060
1061 do {
1062 rest = step - tl;
1063 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1064 //cmodif: call gufld(vout,f) changed into:
1065
1066 GetField(vout,f);
1067
1068 // *
1069 // * start of integration
1070 // *
1071 x = vout[0];
1072 y = vout[1];
1073 z = vout[2];
1074 a = vout[3];
1075 b = vout[4];
1076 c = vout[5];
1077
1078 h2 = khalf * h;
1079 h4 = khalf * h2;
1080 ph = pinv * h;
1081 ph2 = khalf * ph;
1082 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1083 secys[0] = (c * f[0] - a * f[2]) * ph2;
1084 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1085 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1086 if (ang2 > kpisqua) break;
1087
1088 dxt = h2 * a + h4 * secxs[0];
1089 dyt = h2 * b + h4 * secys[0];
1090 dzt = h2 * c + h4 * seczs[0];
1091 xt = x + dxt;
1092 yt = y + dyt;
1093 zt = z + dzt;
1094 // *
1095 // * second intermediate point
1096 // *
1097
1098 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1099 if (est > h) {
1100 if (ncut++ > maxcut) break;
1101 h *= khalf;
1102 continue;
1103 }
1104
1105 xyzt[0] = xt;
1106 xyzt[1] = yt;
1107 xyzt[2] = zt;
1108
1109 //cmodif: call gufld(xyzt,f) changed into:
1110 GetField(xyzt,f);
1111
1112 at = a + secxs[0];
1113 bt = b + secys[0];
1114 ct = c + seczs[0];
1115
1116 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1117 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1118 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1119 at = a + secxs[1];
1120 bt = b + secys[1];
1121 ct = c + seczs[1];
1122 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1123 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1124 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1125 dxt = h * (a + secxs[2]);
1126 dyt = h * (b + secys[2]);
1127 dzt = h * (c + seczs[2]);
1128 xt = x + dxt;
1129 yt = y + dyt;
1130 zt = z + dzt;
1131 at = a + 2.*secxs[2];
1132 bt = b + 2.*secys[2];
1133 ct = c + 2.*seczs[2];
1134
1135 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1136 if (est > 2.*TMath::Abs(h)) {
1137 if (ncut++ > maxcut) break;
1138 h *= khalf;
1139 continue;
1140 }
1141
1142 xyzt[0] = xt;
1143 xyzt[1] = yt;
1144 xyzt[2] = zt;
1145
1146 //cmodif: call gufld(xyzt,f) changed into:
1147 GetField(xyzt,f);
1148
1149 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1150 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1151 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1152
1153 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1154 secys[3] = (ct*f[0] - at*f[2])* ph2;
1155 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1156 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1157 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1158 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1159
1160 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1161 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1162 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1163
1164 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1165 if (ncut++ > maxcut) break;
1166 h *= khalf;
1167 continue;
1168 }
1169
1170 ncut = 0;
1171 // * if too many iterations, go to helix
1172 if (iter++ > maxit) break;
1173
1174 tl += h;
1175 if (est < kdlt32)
1176 h *= 2.;
1177 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1178 vout[0] = x;
1179 vout[1] = y;
1180 vout[2] = z;
1181 vout[3] = cba*a;
1182 vout[4] = cba*b;
1183 vout[5] = cba*c;
1184 rest = step - tl;
1185 if (step < 0.) rest = -rest;
1186 if (rest < 1.e-5*TMath::Abs(step)) return;
1187
1188 } while(1);
1189
1190 // angle too big, use helix
1191
1192 f1 = f[0];
1193 f2 = f[1];
1194 f3 = f[2];
1195 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1196 rho = -f4*pinv;
1197 tet = rho * step;
1198
1199 hnorm = 1./f4;
1200 f1 = f1*hnorm;
1201 f2 = f2*hnorm;
1202 f3 = f3*hnorm;
1203
1204 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1205 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1206 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1207
1208 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1209
1210 rho1 = 1./rho;
1211 sint = TMath::Sin(tet);
1212 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1213
1214 g1 = sint*rho1;
1215 g2 = cost*rho1;
1216 g3 = (tet-sint) * hp*rho1;
1217 g4 = -cost;
1218 g5 = sint;
1219 g6 = cost * hp;
1220
1221 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1222 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1223 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1224
1225 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1226 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1227 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1228
1229 return;
1230}
8cde4af5 1231
c04e3238 1232//___________________________________________________________
1233 void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
1234{
1235 /// interface for arguments in double precision (Why ? ChF)
1236 Float_t x[3], b[3];
1237
1238 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
1239
1240 if (fgkField) fgkField->Field(x,b);
1241 else {
1242 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
1243 exit(-1);
1244 }
1245
1246 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
1247
1248 return;
1249}