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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
37#include <Riostream.h>
38#include <TMath.h>
39#include <TMatrixD.h>
40#include <TGeoManager.h>
c04e3238 41
78649106 42/// \cond CLASSIMP
c04e3238 43ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 44/// \endcond
c04e3238 45
46const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
4284483e 47const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 48const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 49const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
50const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 51
52 //__________________________________________________________________________
53Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
54{
55 /// Returns impact parameter at vertex in bending plane (cm),
56 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
57 /// using simple values for dipole magnetic field.
58 /// The sign of "BendingMomentum" is the sign of the charge.
59
60 if (bendingMomentum == 0.) return 1.e10;
61
62 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
63 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
64 Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
65 if (fgkField) fgkField->Field(x,b);
66 else {
67 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
68 exit(-1);
69 }
70 Double_t simpleBValue = (Double_t) b[0];
71
72 return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum);
73}
74
75 //__________________________________________________________________________
76Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
77{
78 /// Returns signed bending momentum in bending plane (GeV/c),
79 /// the sign being the sign of the charge for particles moving forward in Z,
80 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
81 /// using simple values for dipole magnetic field.
82
83 if (impactParam == 0.) return 1.e10;
84
85 Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
86 Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
87 Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
88 if (fgkField) fgkField->Field(x,b);
89 else {
90 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
91 exit(-1);
92 }
93 Double_t simpleBValue = (Double_t) b[0];
94
95 return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam);
96}
c04e3238 97
98 //__________________________________________________________________________
99void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
100{
4284483e 101 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
102 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
103 if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
104 else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
105}
106
107 //__________________________________________________________________________
108void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
109{
110 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 111 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
112 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
113 Double_t forwardBackward; // +1 if forward, -1 if backward
114 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
115 else forwardBackward = -1.0;
dade8580 116 Double_t v3[7], v3New[7]; // 7 in parameter ????
117 Int_t i3, stepNumber;
c04e3238 118 // For safety: return kTRUE or kFALSE ????
119 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 120 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 121 // sign of charge (sign of fInverseBendingMomentum if forward motion)
122 // must be changed if backward extrapolation
208f139e 123 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 124 // Extrapolation loop
125 stepNumber = 0;
208f139e 126 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 127 stepNumber++;
4284483e 128 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 129 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
c04e3238 130 // better use TArray ????
208f139e 131 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 132 }
208f139e 133 // check fgkMaxStepNumber ????
c04e3238 134 // Interpolation back to exact Z (2nd order)
135 // should be in function ???? using TArray ????
dade8580 136 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 137 if (TMath::Abs(dZ12) > 0) {
dade8580 138 Double_t dZ1i = zEnd - v3[2]; // 1-i
139 Double_t dZi2 = v3New[2] - zEnd; // i->2
140 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
141 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
142 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
143 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
144 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
145 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
146 v3[2] = zEnd; // Z
c04e3238 147 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
148 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
149 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 150 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 151 v3[3] = xPrimeI * v3[5]; // PX/PTOT
152 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 153 } else {
4284483e 154 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 155 }
4284483e 156 // Recover track parameters (charge back for forward motion)
dade8580 157 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
c04e3238 158}
159
160 //__________________________________________________________________________
4284483e 161void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
162{
163 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
164 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
165 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
166 Double_t forwardBackward; // +1 if forward, -1 if backward
167 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
168 else forwardBackward = -1.0;
169 // sign of charge (sign of fInverseBendingMomentum if forward motion)
170 // must be changed if backward extrapolation
171 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
172 Double_t v3[7], v3New[7];
173 Double_t dZ, step;
174 Int_t stepNumber = 0;
175
176 // Extrapolation loop (until within tolerance)
177 Double_t residue = zEnd - trackParam->GetZ();
178 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
179 dZ = zEnd - trackParam->GetZ();
180 // step lenght assuming linear trajectory
181 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
182 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
183 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
184 do { // reduce step lenght while zEnd oversteped
185 if (stepNumber > fgkMaxStepNumber) {
186 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
187 break;
188 }
189 stepNumber ++;
190 step = TMath::Abs(step);
191 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
192 residue = zEnd - v3New[2];
193 step *= dZ/(v3New[2]-trackParam->GetZ());
194 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
195 RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
196 }
197
198 // terminate the extropolation with a straight line up to the exact "zEnd" value
199 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
200 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
201 trackParam->SetZ(zEnd);
202}
203
204 //__________________________________________________________________________
205void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 206{
dade8580 207 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 208 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
209 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 210 v3[0] = trackParam->GetNonBendingCoor(); // X
211 v3[1] = trackParam->GetBendingCoor(); // Y
212 v3[2] = trackParam->GetZ(); // Z
c04e3238 213 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
214 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 215 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
216 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
217 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
218 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 219}
220
221 //__________________________________________________________________________
dade8580 222void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 223{
dade8580 224 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 225 /// assumed to be calculated for forward motion in Z.
226 /// "InverseBendingMomentum" is signed with "charge".
dade8580 227 trackParam->SetNonBendingCoor(v3[0]); // X
228 trackParam->SetBendingCoor(v3[1]); // Y
229 trackParam->SetZ(v3[2]); // Z
230 Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]);
c04e3238 231 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 232 trackParam->SetBendingSlope(v3[4]/v3[5]);
233 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
208f139e 234}
235
236 //__________________________________________________________________________
237void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd)
238{
239 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
240 /// On return, results from the extrapolation are updated in trackParam.
241
242 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
243
244 // Save the actual track parameters
245 AliMUONTrackParam trackParamSave(*trackParam);
246 Double_t nonBendingCoor = trackParamSave.GetNonBendingCoor();
247 Double_t nonBendingSlope = trackParamSave.GetNonBendingSlope();
248 Double_t bendingCoor = trackParamSave.GetBendingCoor();
249 Double_t bendingSlope = trackParamSave.GetBendingSlope();
250 Double_t inverseBendingMomentum = trackParamSave.GetInverseBendingMomentum();
251 Double_t zBegin = trackParamSave.GetZ();
252
253 // Extrapolate track parameters to "zEnd"
254 ExtrapToZ(trackParam,zEnd);
255 Double_t extrapNonBendingCoor = trackParam->GetNonBendingCoor();
256 Double_t extrapNonBendingSlope = trackParam->GetNonBendingSlope();
257 Double_t extrapBendingCoor = trackParam->GetBendingCoor();
258 Double_t extrapBendingSlope = trackParam->GetBendingSlope();
259 Double_t extrapInverseBendingMomentum = trackParam->GetInverseBendingMomentum();
260
261 // Get the pointer to the parameter covariance matrix
262 if (!trackParam->CovariancesExist()) {
263 //cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: track parameter covariance matrix does not exist"<<endl;
264 //cout<<" -> nothing to extrapolate !!"<<endl;
265 return;
266 }
267 TMatrixD* paramCov = trackParam->GetCovariances();
268
269 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
270 TMatrixD jacob(5,5);
271 jacob = 0.;
272 Double_t dParam[5];
273 for (Int_t i=0; i<5; i++) {
274 // Skip jacobian calculation for parameters with no associated error
275 if ((*paramCov)(i,i) == 0.) continue;
276 // Small variation of parameter i only
277 for (Int_t j=0; j<5; j++) {
278 if (j==i) {
279 dParam[j] = TMath::Sqrt((*paramCov)(i,i));
280 if (j == 4) dParam[j] *= TMath::Sign(1.,-inverseBendingMomentum); // variation always in the same direction
281 } else dParam[j] = 0.;
282 }
283 // Set new parameters
284 trackParamSave.SetNonBendingCoor (nonBendingCoor + dParam[0]);
285 trackParamSave.SetNonBendingSlope (nonBendingSlope + dParam[1]);
286 trackParamSave.SetBendingCoor (bendingCoor + dParam[2]);
287 trackParamSave.SetBendingSlope (bendingSlope + dParam[3]);
288 trackParamSave.SetInverseBendingMomentum(inverseBendingMomentum + dParam[4]);
289 trackParamSave.SetZ (zBegin);
290 // Extrapolate new track parameters to "zEnd"
291 ExtrapToZ(&trackParamSave,zEnd);
292 // Calculate the jacobian
293 jacob(0,i) = (trackParamSave.GetNonBendingCoor() - extrapNonBendingCoor ) / dParam[i];
294 jacob(1,i) = (trackParamSave.GetNonBendingSlope() - extrapNonBendingSlope ) / dParam[i];
295 jacob(2,i) = (trackParamSave.GetBendingCoor() - extrapBendingCoor ) / dParam[i];
296 jacob(3,i) = (trackParamSave.GetBendingSlope() - extrapBendingSlope ) / dParam[i];
297 jacob(4,i) = (trackParamSave.GetInverseBendingMomentum() - extrapInverseBendingMomentum) / dParam[i];
298 }
299
300 // Extrapolate track parameter covariances to "zEnd"
301 TMatrixD tmp((*paramCov),TMatrixD::kMultTranspose,jacob);
302 (*paramCov) = TMatrixD(jacob,TMatrixD::kMult,tmp);
303
c04e3238 304}
305
306 //__________________________________________________________________________
307void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
308{
309 /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station"
310 /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut"
311 /// (index 0 and 1 for first and second chambers).
312 Double_t extZ[2], z1, z2;
313 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
314 // range of station to be checked ????
315 z1 = AliMUONConstants::DefaultChamberZ(2 * station);
316 z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1);
317 // First and second Z to extrapolate at
318 if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;}
319 else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;}
320 else {
208f139e 321 cout<<"E-AliMUONTrackExtrap::ExtrapToStation: Starting Z ("<<trackParamIn->GetZ()
c04e3238 322 <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
323 exit(-1);
324 }
325 extZ[i1] = z1;
326 extZ[i2] = z2;
327 // copy of track parameters
328 trackParamOut[i1] = *trackParamIn;
329 // first extrapolation
330 ExtrapToZ(&(trackParamOut[i1]),extZ[0]);
331 trackParamOut[i2] = trackParamOut[i1];
332 // second extrapolation
333 ExtrapToZ(&(trackParamOut[i2]),extZ[1]);
334 return;
208f139e 335}
336
337 //__________________________________________________________________________
338void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
339{
8cde4af5 340 /// Extrapolation to the vertex (at the z position "zVtx") without Branson and energy loss corrections.
208f139e 341 /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
342 /// Include multiple Coulomb scattering effects in trackParam covariances.
343
8cde4af5 344 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
345
208f139e 346 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
347 cout<<"W-AliMUONTrackExtrap::ExtrapToVertexUncorrected: Starting Z ("<<trackParam->GetZ()
348 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
349 exit(-1);
350 }
351
04b2ac53 352/*
8cde4af5 353 // Check whether the geometry is available and get absorber boundaries
354 if (!gGeoManager) {
fac70e25 355 cout<<"E-AliMUONTrackExtrap::ExtrapToVertexUncorrected: no TGeo"<<endl;
8cde4af5 356 return;
357 }
358 TGeoNode *absNode = gGeoManager->GetVolume("ALIC")->GetNode("ABSM_1");
359 if (!absNode) {
fac70e25 360 cout<<"E-AliMUONTrackExtrap::ExtrapToVertexUncorrected: failed to get absorber node"<<endl;
8cde4af5 361 return;
362 }
7dc68cf4 363 Double_t kZAbsBeg, kZAbsEnd;
364 absNode->GetVolume()->GetShape()->GetAxisRange(3,kZAbsBeg,kZAbsEnd);
8cde4af5 365 const Double_t *absPos = absNode->GetMatrix()->GetTranslation();
7dc68cf4 366 kZAbsBeg = absPos[2] - kZAbsBeg; // spectro. (z<0)
367 kZAbsEnd = absPos[2] - kZAbsEnd; // spectro. (z<0)
04b2ac53 368*/
7dc68cf4 369 static const Double_t kZAbsBeg = -90.;
370 static const Double_t kZAbsEnd = -505.;
04b2ac53 371
8cde4af5 372 // Check the vertex position relatively to the absorber
7dc68cf4 373 if (zVtx < kZAbsBeg && zVtx > kZAbsEnd) { // spectro. (z<0)
8cde4af5 374 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
7dc68cf4 375 <<") inside the front absorber ("<<kZAbsBeg<<","<<kZAbsEnd<<")"<<endl;
376 } else if (zVtx < kZAbsEnd ) { // spectro. (z<0)
8cde4af5 377 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
7dc68cf4 378 <<") downstream the front absorber (zAbsorberEnd = "<<kZAbsEnd<<")"<<endl;
208f139e 379 ExtrapToZCov(trackParam,zVtx);
380 return;
381 }
382
8cde4af5 383 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
7dc68cf4 384 if (trackParam->GetZ() > kZAbsBeg) { // spectro. (z<0)
8cde4af5 385 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
7dc68cf4 386 <<") upstream the front absorber (zAbsorberBegin = "<<kZAbsBeg<<")"<<endl;
8cde4af5 387 ExtrapToZCov(trackParam,zVtx);
388 return;
7dc68cf4 389 } else if (trackParam->GetZ() > kZAbsEnd) { // spectro. (z<0)
8cde4af5 390 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
7dc68cf4 391 <<") inside the front absorber ("<<kZAbsBeg<<","<<kZAbsEnd<<")"<<endl;
208f139e 392 } else {
7dc68cf4 393 ExtrapToZCov(trackParam,kZAbsEnd);
208f139e 394 }
395
8cde4af5 396 // Then add MCS effect in absorber to the parameters covariances
397 AliMUONTrackParam trackParamIn(*trackParam);
7dc68cf4 398 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, kZAbsBeg));
8cde4af5 399 Double_t trackXYZIn[3];
400 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
401 trackXYZIn[1] = trackParamIn.GetBendingCoor();
402 trackXYZIn[2] = trackParamIn.GetZ();
403 Double_t trackXYZOut[3];
404 trackXYZOut[0] = trackParam->GetNonBendingCoor();
405 trackXYZOut[1] = trackParam->GetBendingCoor();
406 trackXYZOut[2] = trackParam->GetZ();
407 Double_t pathLength = 0.;
408 Double_t f0 = 0.;
409 Double_t f1 = 0.;
410 Double_t f2 = 0.;
411 Double_t meanRho = 0.;
412 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
413 AddMCSEffectInAbsorber(trackParam,pathLength,f0,f1,f2);
208f139e 414
415 // finally go to the vertex
416 ExtrapToZCov(trackParam,zVtx);
417
418}
419
420 //__________________________________________________________________________
8cde4af5 421void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
422{
423 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
424 /// at the end of the front absorber using the absorber correction parameters
425
426 // absorber related covariance parameters
427 Double_t bendingSlope = param->GetBendingSlope();
428 Double_t nonBendingSlope = param->GetNonBendingSlope();
429 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
430 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
431 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
432 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
433 Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
434 Double_t varSlop = alpha2 * f0;
435
436 TMatrixD* paramCov = param->GetCovariances();
437 // Non bending plane
438 (*paramCov)(0,0) += varCoor; (*paramCov)(0,1) += covCorrSlope;
439 (*paramCov)(1,0) += covCorrSlope; (*paramCov)(1,1) += varSlop;
440 // Bending plane
441 (*paramCov)(2,2) += varCoor; (*paramCov)(2,3) += covCorrSlope;
442 (*paramCov)(3,2) += covCorrSlope; (*paramCov)(3,3) += varSlop;
443
444}
445
446 //__________________________________________________________________________
447void AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t &pathLength,
448 Double_t &f0, Double_t &f1, Double_t &f2, Double_t &meanRho)
449{
450 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
451 /// Calculated assuming a linear propagation between track positions trackXYZIn and trackXYZOut
452 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
453 // f0: 0th moment of z calculated with the inverse radiation-length distribution
454 // f1: 1st moment of z calculated with the inverse radiation-length distribution
455 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
456 // meanRho: average density of crossed material (g/cm3)
457
458 // Reset absorber's parameters
459 pathLength = 0.;
460 f0 = 0.;
461 f1 = 0.;
462 f2 = 0.;
463 meanRho = 0.;
464
465 // Check whether the geometry is available
466 if (!gGeoManager) {
467 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
468 return;
469 }
470
471 // Initialize starting point and direction
472 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
473 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
474 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
475 if (pathLength < TGeoShape::Tolerance()) return;
476 Double_t b[3];
477 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
478 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
479 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
480 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
481 if (!currentnode) {
482 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
483 return;
484 }
485
486 // loop over absorber slices and calculate absorber's parameters
487 Double_t rho = 0.; // material density (g/cm3)
488 Double_t x0 = 0.; // radiation-length (cm-1)
489 Double_t localPathLength = 0;
490 Double_t remainingPathLength = pathLength;
491 Double_t zB = trackXYZIn[2];
492 Double_t zE, dzB, dzE;
493 do {
494 // Get material properties
495 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
496 rho = material->GetDensity();
497 x0 = material->GetRadLen();
498 if (!material->IsMixture()) x0 /= rho; // different normalization in the modeler for mixture
499
500 // Get path length within this material
501 gGeoManager->FindNextBoundary(remainingPathLength);
502 localPathLength = gGeoManager->GetStep() + 1.e-6;
503 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
504 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
505 else {
506 currentnode = gGeoManager->Step();
507 if (!currentnode) {
508 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
509 f0 = f1 = f2 = meanRho = 0.;
510 return;
511 }
512 if (!gGeoManager->IsEntering()) {
513 // make another small step to try to enter in new absorber slice
514 gGeoManager->SetStep(0.001);
515 currentnode = gGeoManager->Step();
516 if (!gGeoManager->IsEntering() || !currentnode) {
517 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
518 f0 = f1 = f2 = meanRho = 0.;
519 return;
520 }
521 localPathLength += 0.001;
522 }
523 }
524
525 // calculate absorber's parameters
526 zE = b[2] * localPathLength + zB;
527 dzB = zB - trackXYZIn[2];
528 dzE = zE - trackXYZIn[2];
529 f0 += localPathLength / x0;
530 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
531 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
532 meanRho += localPathLength * rho;
533
534 // prepare next step
535 zB = zE;
536 remainingPathLength -= localPathLength;
537 } while (remainingPathLength > TGeoShape::Tolerance());
538
539 meanRho /= pathLength;
540}
541
542 //__________________________________________________________________________
543void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 544{
545 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
546 /// through a material of thickness "dZ" and of radiation length "x0"
547 /// assuming linear propagation and using the small angle approximation.
548
549 Double_t bendingSlope = param->GetBendingSlope();
550 Double_t nonBendingSlope = param->GetNonBendingSlope();
551 Double_t inverseTotalMomentum2 = param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum() *
552 (1.0 + bendingSlope * bendingSlope) /
553 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
554 // Path length in the material
555 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
556 Double_t pathLength2 = pathLength * pathLength;
557 // relativistic velocity
558 Double_t velo = 1.;
559 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
560 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
561 theta02 *= theta02 * inverseTotalMomentum2 * pathLength / x0;
562
563 // Add effects of multiple Coulomb scattering in track parameter covariances
564 TMatrixD* paramCov = param->GetCovariances();
565 Double_t varCoor = pathLength2 * theta02 / 3.;
566 Double_t varSlop = theta02;
567 Double_t covCorrSlope = pathLength * theta02 / 2.;
568 // Non bending plane
569 (*paramCov)(0,0) += varCoor; (*paramCov)(0,1) += covCorrSlope;
570 (*paramCov)(1,0) += covCorrSlope; (*paramCov)(1,1) += varSlop;
571 // Bending plane
572 (*paramCov)(2,2) += varCoor; (*paramCov)(2,3) += covCorrSlope;
573 (*paramCov)(3,2) += covCorrSlope; (*paramCov)(3,3) += varSlop;
574
c04e3238 575}
576
577 //__________________________________________________________________________
fac70e25 578void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx,
579 Bool_t CorrectForMCS, Bool_t CorrectForEnergyLoss)
c04e3238 580{
581 /// Extrapolation to the vertex.
fac70e25 582 /// Returns the track parameters resulting from the extrapolation of the current TrackParam.
8cde4af5 583 /// Changes parameters according to Branson correction through the absorber and energy loss
c04e3238 584
8cde4af5 585 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 586
8cde4af5 587 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
fac70e25 588 cout<<"F-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
8cde4af5 589 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
590 exit(-1);
c04e3238 591 }
8cde4af5 592
fac70e25 593 // Check if correction required
594 if (!CorrectForMCS && !CorrectForEnergyLoss) {
595 ExtrapToZ(trackParam,zVtx);
596 return;
597 }
598
04b2ac53 599/*
8cde4af5 600 // Check whether the geometry is available and get absorber boundaries
601 if (!gGeoManager) {
fac70e25 602 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: no TGeo"<<endl;
8cde4af5 603 return;
604 }
605 TGeoNode *absNode = gGeoManager->GetVolume("ALIC")->GetNode("ABSM_1");
606 if (!absNode) {
fac70e25 607 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: failed to get absorber node"<<endl;
8cde4af5 608 return;
609 }
7dc68cf4 610 Double_t kZAbsBeg, kZAbsEnd;
611 absNode->GetVolume()->GetShape()->GetAxisRange(3,kZAbsBeg,kZAbsEnd);
8cde4af5 612 const Double_t *absPos = absNode->GetMatrix()->GetTranslation();
7dc68cf4 613 kZAbsBeg = absPos[2] - kZAbsBeg; // spectro. (z<0)
614 kZAbsEnd = absPos[2] - kZAbsEnd; // spectro. (z<0)
04b2ac53 615*/
7dc68cf4 616 static const Double_t kZAbsBeg = -90.;
617 static const Double_t kZAbsEnd = -505.;
8cde4af5 618
619 // Check the vertex position relatively to the absorber
7dc68cf4 620 if (zVtx < kZAbsBeg && zVtx > kZAbsEnd) { // spectro. (z<0)
8cde4af5 621 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
7dc68cf4 622 <<") inside the front absorber ("<<kZAbsBeg<<","<<kZAbsEnd<<")"<<endl;
623 } else if (zVtx < kZAbsEnd ) { // spectro. (z<0)
8cde4af5 624 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
7dc68cf4 625 <<") downstream the front absorber (zAbsorberEnd = "<<kZAbsEnd<<")"<<endl;
8cde4af5 626 ExtrapToZ(trackParam,zVtx);
627 return;
628 }
629
630 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
7dc68cf4 631 if (trackParam->GetZ() > kZAbsBeg) { // spectro. (z<0)
8cde4af5 632 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
7dc68cf4 633 <<") upstream the front absorber (zAbsorberBegin = "<<kZAbsBeg<<")"<<endl;
8cde4af5 634 ExtrapToZ(trackParam,zVtx);
635 return;
7dc68cf4 636 } else if (trackParam->GetZ() > kZAbsEnd) { // spectro. (z<0)
8cde4af5 637 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
7dc68cf4 638 <<") inside the front absorber ("<<kZAbsBeg<<","<<kZAbsEnd<<")"<<endl;
c04e3238 639 } else {
7dc68cf4 640 ExtrapToZ(trackParam,kZAbsEnd);
c04e3238 641 }
c04e3238 642
8cde4af5 643 // Get absorber correction parameters assuming linear propagation from vertex to the track position
644 Double_t trackXYZOut[3];
645 trackXYZOut[0] = trackParam->GetNonBendingCoor();
646 trackXYZOut[1] = trackParam->GetBendingCoor();
647 trackXYZOut[2] = trackParam->GetZ();
648 Double_t trackXYZIn[3];
7dc68cf4 649 trackXYZIn[2] = TMath::Min(zVtx, kZAbsBeg); // spectro. (z<0)
8cde4af5 650 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
651 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
652 Double_t pathLength = 0.;
653 Double_t f0 = 0.;
654 Double_t f1 = 0.;
655 Double_t f2 = 0.;
656 Double_t meanRho = 0.;
657 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
c04e3238 658
8cde4af5 659 // Calculate energy loss
660 Double_t pTot = trackParam->P();
661 Double_t charge = TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
662 Double_t deltaP = TotalMomentumEnergyLoss(pTot,pathLength,meanRho);
663
664 // Correct for half of energy loss
fac70e25 665 Double_t nonBendingSlope, bendingSlope;
666 if (CorrectForEnergyLoss) {
667 pTot += 0.5 * deltaP;
668 nonBendingSlope = trackParam->GetNonBendingSlope();
669 bendingSlope = trackParam->GetBendingSlope();
670 trackParam->SetInverseBendingMomentum(charge / pTot *
671 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
672 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
673 }
8cde4af5 674
fac70e25 675 if (CorrectForMCS) {
676 // Position of the Branson plane (spectro. (z<0))
677 Double_t zB = (f1>0.) ? trackXYZIn[2] - f2/f1 : 0.;
678
679 // Get track position in the Branson plane corrected for magnetic field effect
680 ExtrapToZ(trackParam,zVtx);
681 Double_t xB = trackParam->GetNonBendingCoor() + (zB - zVtx) * trackParam->GetNonBendingSlope();
682 Double_t yB = trackParam->GetBendingCoor() + (zB - zVtx) * trackParam->GetBendingSlope();
683
684 // Get track slopes corrected for multiple scattering (spectro. (z<0))
685 nonBendingSlope = (zB<0.) ? (xB - xVtx) / (zB - zVtx) : trackParam->GetNonBendingSlope();
686 bendingSlope = (zB<0.) ? (yB - yVtx) / (zB - zVtx) : trackParam->GetBendingSlope();
687
688 // Set track parameters at vertex
689 trackParam->SetNonBendingCoor(xVtx);
690 trackParam->SetBendingCoor(yVtx);
691 trackParam->SetZ(zVtx);
692 trackParam->SetNonBendingSlope(nonBendingSlope);
693 trackParam->SetBendingSlope(bendingSlope);
694 } else {
695 ExtrapToZ(trackParam,zVtx);
696 nonBendingSlope = trackParam->GetNonBendingSlope();
697 bendingSlope = trackParam->GetBendingSlope();
698 }
8cde4af5 699
700 // Correct for second half of energy loss
fac70e25 701 if (CorrectForEnergyLoss) pTot += 0.5 * deltaP;
8cde4af5 702
703 // Set track parameters at vertex
8cde4af5 704 trackParam->SetInverseBendingMomentum(charge / pTot *
fac70e25 705 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
706 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
707
708}
709
710 //__________________________________________________________________________
711Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
712{
713 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
714
715 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 716
fac70e25 717 // Check whether the geometry is available
718 if (!gGeoManager) {
719 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
720 return 0.;
721 }
722
723 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
724 Double_t trackXYZOut[3];
725 trackXYZOut[0] = trackParam->GetNonBendingCoor();
726 trackXYZOut[1] = trackParam->GetBendingCoor();
727 trackXYZOut[2] = trackParam->GetZ();
728 Double_t trackXYZIn[3];
729 trackXYZIn[0] = xVtx;
730 trackXYZIn[1] = yVtx;
731 trackXYZIn[2] = zVtx;
732 Double_t pathLength = 0.;
733 Double_t f0 = 0.;
734 Double_t f1 = 0.;
735 Double_t f2 = 0.;
736 Double_t meanRho = 0.;
737 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pathLength,f0,f1,f2,meanRho);
738
739 // Calculate energy loss
740 Double_t pTot = trackParam->P();
741 return TotalMomentumEnergyLoss(pTot,pathLength,meanRho);
c04e3238 742}
743
744 //__________________________________________________________________________
8cde4af5 745Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t pTotal, Double_t pathLength, Double_t rho)
c04e3238 746{
8cde4af5 747 /// Returns the total momentum energy loss in the front absorber
fac70e25 748 Double_t muMass = 0.105658369;
8cde4af5 749 Double_t p2=pTotal*pTotal;
750 Double_t beta2=p2/(p2 + muMass*muMass);
751 Double_t dE=ApproximateBetheBloch(beta2)*pathLength*rho;
752
753 return dE;
c04e3238 754}
755
756 //__________________________________________________________________________
71a2d3aa 757Double_t AliMUONTrackExtrap::ApproximateBetheBloch(Double_t beta2)
758{
759/// This is an approximation of the Bethe-Bloch formula with
760/// the density effect taken into account at beta*gamma > 3.5
761/// (the approximation is reasonable only for solid materials)
762
8cde4af5 763 if (beta2/(1-beta2)>3.5*3.5)
764 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
765
766 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
c04e3238 767}
768
769 //__________________________________________________________________________
770void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
771{
71a2d3aa 772/// <pre>
c04e3238 773/// ******************************************************************
774/// * *
775/// * Performs the tracking of one step in a magnetic field *
776/// * The trajectory is assumed to be a helix in a constant field *
777/// * taken at the mid point of the step. *
778/// * Parameters: *
779/// * input *
780/// * STEP =arc length of the step asked *
781/// * VECT =input vector (position,direction cos and momentum) *
782/// * CHARGE= electric charge of the particle *
783/// * output *
784/// * VOUT = same as VECT after completion of the step *
785/// * *
786/// * ==>Called by : <USER>, GUSWIM *
787/// * Author m.hansroul ********* *
788/// * modified s.egli, s.v.levonian *
789/// * modified v.perevoztchikov
790/// * *
791/// ******************************************************************
71a2d3aa 792/// </pre>
c04e3238 793
794// modif: everything in double precision
795
796 Double_t xyz[3], h[4], hxp[3];
797 Double_t h2xy, hp, rho, tet;
798 Double_t sint, sintt, tsint, cos1t;
799 Double_t f1, f2, f3, f4, f5, f6;
800
801 const Int_t kix = 0;
802 const Int_t kiy = 1;
803 const Int_t kiz = 2;
804 const Int_t kipx = 3;
805 const Int_t kipy = 4;
806 const Int_t kipz = 5;
807 const Int_t kipp = 6;
808
809 const Double_t kec = 2.9979251e-4;
810 //
811 // ------------------------------------------------------------------
812 //
813 // units are kgauss,centimeters,gev/c
814 //
815 vout[kipp] = vect[kipp];
816 if (TMath::Abs(charge) < 0.00001) {
817 for (Int_t i = 0; i < 3; i++) {
818 vout[i] = vect[i] + step * vect[i+3];
819 vout[i+3] = vect[i+3];
820 }
821 return;
822 }
823 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
824 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
825 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
826
827 //cmodif: call gufld (xyz, h) changed into:
828 GetField (xyz, h);
829
830 h2xy = h[0]*h[0] + h[1]*h[1];
831 h[3] = h[2]*h[2]+ h2xy;
832 if (h[3] < 1.e-12) {
833 for (Int_t i = 0; i < 3; i++) {
834 vout[i] = vect[i] + step * vect[i+3];
835 vout[i+3] = vect[i+3];
836 }
837 return;
838 }
839 if (h2xy < 1.e-12*h[3]) {
840 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
841 return;
842 }
843 h[3] = TMath::Sqrt(h[3]);
844 h[0] /= h[3];
845 h[1] /= h[3];
846 h[2] /= h[3];
847 h[3] *= kec;
848
849 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
850 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
851 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
852
853 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
854
855 rho = -charge*h[3]/vect[kipp];
856 tet = rho * step;
857
858 if (TMath::Abs(tet) > 0.15) {
859 sint = TMath::Sin(tet);
860 sintt = (sint/tet);
861 tsint = (tet-sint)/tet;
862 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
863 } else {
864 tsint = tet*tet/36.;
865 sintt = (1. - tsint);
866 sint = tet*sintt;
867 cos1t = 0.5*tet;
868 }
869
870 f1 = step * sintt;
871 f2 = step * cos1t;
872 f3 = step * tsint * hp;
873 f4 = -tet*cos1t;
874 f5 = sint;
875 f6 = tet * cos1t * hp;
876
877 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
878 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
879 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
880
881 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
882 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
883 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
884
885 return;
886}
887
888 //__________________________________________________________________________
889void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
890{
71a2d3aa 891/// <pre>
c04e3238 892/// ******************************************************************
893/// * *
894/// * Tracking routine in a constant field oriented *
895/// * along axis 3 *
896/// * Tracking is performed with a conventional *
897/// * helix step method *
898/// * *
899/// * ==>Called by : <USER>, GUSWIM *
900/// * Authors R.Brun, M.Hansroul ********* *
901/// * Rewritten V.Perevoztchikov
902/// * *
903/// ******************************************************************
71a2d3aa 904/// </pre>
c04e3238 905
906 Double_t hxp[3];
907 Double_t h4, hp, rho, tet;
908 Double_t sint, sintt, tsint, cos1t;
909 Double_t f1, f2, f3, f4, f5, f6;
910
911 const Int_t kix = 0;
912 const Int_t kiy = 1;
913 const Int_t kiz = 2;
914 const Int_t kipx = 3;
915 const Int_t kipy = 4;
916 const Int_t kipz = 5;
917 const Int_t kipp = 6;
918
919 const Double_t kec = 2.9979251e-4;
920
921//
922// ------------------------------------------------------------------
923//
924// units are kgauss,centimeters,gev/c
925//
926 vout[kipp] = vect[kipp];
927 h4 = field * kec;
928
929 hxp[0] = - vect[kipy];
930 hxp[1] = + vect[kipx];
931
932 hp = vect[kipz];
933
934 rho = -h4/vect[kipp];
935 tet = rho * step;
936 if (TMath::Abs(tet) > 0.15) {
937 sint = TMath::Sin(tet);
938 sintt = (sint/tet);
939 tsint = (tet-sint)/tet;
940 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
941 } else {
942 tsint = tet*tet/36.;
943 sintt = (1. - tsint);
944 sint = tet*sintt;
945 cos1t = 0.5*tet;
946 }
947
948 f1 = step * sintt;
949 f2 = step * cos1t;
950 f3 = step * tsint * hp;
951 f4 = -tet*cos1t;
952 f5 = sint;
953 f6 = tet * cos1t * hp;
954
955 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
956 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
957 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
958
959 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
960 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
961 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
962
963 return;
964}
8cde4af5 965
c04e3238 966 //__________________________________________________________________________
967void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
968{
71a2d3aa 969/// <pre>
c04e3238 970/// ******************************************************************
971/// * *
972/// * Runge-Kutta method for tracking a particle through a magnetic *
973/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
974/// * Standards, procedure 25.5.20) *
975/// * *
976/// * Input parameters *
977/// * CHARGE Particle charge *
978/// * STEP Step size *
979/// * VECT Initial co-ords,direction cosines,momentum *
980/// * Output parameters *
981/// * VOUT Output co-ords,direction cosines,momentum *
982/// * User routine called *
983/// * CALL GUFLD(X,F) *
984/// * *
985/// * ==>Called by : <USER>, GUSWIM *
986/// * Authors R.Brun, M.Hansroul ********* *
987/// * V.Perevoztchikov (CUT STEP implementation) *
988/// * *
989/// * *
990/// ******************************************************************
71a2d3aa 991/// </pre>
c04e3238 992
993 Double_t h2, h4, f[4];
994 Double_t xyzt[3], a, b, c, ph,ph2;
995 Double_t secxs[4],secys[4],seczs[4],hxp[3];
996 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
997 Double_t est, at, bt, ct, cba;
998 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
999
1000 Double_t x;
1001 Double_t y;
1002 Double_t z;
1003
1004 Double_t xt;
1005 Double_t yt;
1006 Double_t zt;
1007
1008 Double_t maxit = 1992;
1009 Double_t maxcut = 11;
1010
1011 const Double_t kdlt = 1e-4;
1012 const Double_t kdlt32 = kdlt/32.;
1013 const Double_t kthird = 1./3.;
1014 const Double_t khalf = 0.5;
1015 const Double_t kec = 2.9979251e-4;
1016
1017 const Double_t kpisqua = 9.86960440109;
1018 const Int_t kix = 0;
1019 const Int_t kiy = 1;
1020 const Int_t kiz = 2;
1021 const Int_t kipx = 3;
1022 const Int_t kipy = 4;
1023 const Int_t kipz = 5;
1024
1025 // *.
1026 // *. ------------------------------------------------------------------
1027 // *.
1028 // * this constant is for units cm,gev/c and kgauss
1029 // *
1030 Int_t iter = 0;
1031 Int_t ncut = 0;
1032 for(Int_t j = 0; j < 7; j++)
1033 vout[j] = vect[j];
1034
1035 Double_t pinv = kec * charge / vect[6];
1036 Double_t tl = 0.;
1037 Double_t h = step;
1038 Double_t rest;
1039
1040
1041 do {
1042 rest = step - tl;
1043 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1044 //cmodif: call gufld(vout,f) changed into:
1045
1046 GetField(vout,f);
1047
1048 // *
1049 // * start of integration
1050 // *
1051 x = vout[0];
1052 y = vout[1];
1053 z = vout[2];
1054 a = vout[3];
1055 b = vout[4];
1056 c = vout[5];
1057
1058 h2 = khalf * h;
1059 h4 = khalf * h2;
1060 ph = pinv * h;
1061 ph2 = khalf * ph;
1062 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1063 secys[0] = (c * f[0] - a * f[2]) * ph2;
1064 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1065 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1066 if (ang2 > kpisqua) break;
1067
1068 dxt = h2 * a + h4 * secxs[0];
1069 dyt = h2 * b + h4 * secys[0];
1070 dzt = h2 * c + h4 * seczs[0];
1071 xt = x + dxt;
1072 yt = y + dyt;
1073 zt = z + dzt;
1074 // *
1075 // * second intermediate point
1076 // *
1077
1078 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1079 if (est > h) {
1080 if (ncut++ > maxcut) break;
1081 h *= khalf;
1082 continue;
1083 }
1084
1085 xyzt[0] = xt;
1086 xyzt[1] = yt;
1087 xyzt[2] = zt;
1088
1089 //cmodif: call gufld(xyzt,f) changed into:
1090 GetField(xyzt,f);
1091
1092 at = a + secxs[0];
1093 bt = b + secys[0];
1094 ct = c + seczs[0];
1095
1096 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1097 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1098 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1099 at = a + secxs[1];
1100 bt = b + secys[1];
1101 ct = c + seczs[1];
1102 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1103 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1104 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1105 dxt = h * (a + secxs[2]);
1106 dyt = h * (b + secys[2]);
1107 dzt = h * (c + seczs[2]);
1108 xt = x + dxt;
1109 yt = y + dyt;
1110 zt = z + dzt;
1111 at = a + 2.*secxs[2];
1112 bt = b + 2.*secys[2];
1113 ct = c + 2.*seczs[2];
1114
1115 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1116 if (est > 2.*TMath::Abs(h)) {
1117 if (ncut++ > maxcut) break;
1118 h *= khalf;
1119 continue;
1120 }
1121
1122 xyzt[0] = xt;
1123 xyzt[1] = yt;
1124 xyzt[2] = zt;
1125
1126 //cmodif: call gufld(xyzt,f) changed into:
1127 GetField(xyzt,f);
1128
1129 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1130 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1131 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1132
1133 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1134 secys[3] = (ct*f[0] - at*f[2])* ph2;
1135 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1136 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1137 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1138 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1139
1140 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1141 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1142 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1143
1144 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1145 if (ncut++ > maxcut) break;
1146 h *= khalf;
1147 continue;
1148 }
1149
1150 ncut = 0;
1151 // * if too many iterations, go to helix
1152 if (iter++ > maxit) break;
1153
1154 tl += h;
1155 if (est < kdlt32)
1156 h *= 2.;
1157 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1158 vout[0] = x;
1159 vout[1] = y;
1160 vout[2] = z;
1161 vout[3] = cba*a;
1162 vout[4] = cba*b;
1163 vout[5] = cba*c;
1164 rest = step - tl;
1165 if (step < 0.) rest = -rest;
1166 if (rest < 1.e-5*TMath::Abs(step)) return;
1167
1168 } while(1);
1169
1170 // angle too big, use helix
1171
1172 f1 = f[0];
1173 f2 = f[1];
1174 f3 = f[2];
1175 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1176 rho = -f4*pinv;
1177 tet = rho * step;
1178
1179 hnorm = 1./f4;
1180 f1 = f1*hnorm;
1181 f2 = f2*hnorm;
1182 f3 = f3*hnorm;
1183
1184 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1185 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1186 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1187
1188 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1189
1190 rho1 = 1./rho;
1191 sint = TMath::Sin(tet);
1192 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1193
1194 g1 = sint*rho1;
1195 g2 = cost*rho1;
1196 g3 = (tet-sint) * hp*rho1;
1197 g4 = -cost;
1198 g5 = sint;
1199 g6 = cost * hp;
1200
1201 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1202 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1203 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1204
1205 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1206 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1207 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1208
1209 return;
1210}
8cde4af5 1211
c04e3238 1212//___________________________________________________________
1213 void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
1214{
1215 /// interface for arguments in double precision (Why ? ChF)
1216 Float_t x[3], b[3];
1217
1218 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
1219
1220 if (fgkField) fgkField->Field(x,b);
1221 else {
1222 cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
1223 exit(-1);
1224 }
1225
1226 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
1227
1228 return;
1229}