]>
Commit | Line | Data |
---|---|---|
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 | ||
31 | #include <Riostream.h> | |
32 | ||
33 | #include "AliMUONTrackExtrap.h" | |
34 | #include "AliMUONTrackParam.h" | |
35 | #include "AliMUONConstants.h" | |
36 | #include "AliMagF.h" | |
37 | #include "AliLog.h" | |
38 | #include "AliTracker.h" | |
39 | ||
40 | ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context | |
41 | ||
42 | const AliMagF* AliMUONTrackExtrap::fgkField = 0x0; | |
43 | ||
44 | //__________________________________________________________________________ | |
45 | void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd) | |
46 | { | |
47 | /// Track parameter extrapolation to the plane at "Z". | |
48 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
49 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z | |
50 | Double_t forwardBackward; // +1 if forward, -1 if backward | |
51 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
52 | else forwardBackward = -1.0; | |
dade8580 | 53 | Double_t v3[7], v3New[7]; // 7 in parameter ???? |
54 | Int_t i3, stepNumber; | |
c04e3238 | 55 | Int_t maxStepNumber = 5000; // in parameter ???? |
56 | // For safety: return kTRUE or kFALSE ???? | |
57 | // Parameter vector for calling EXTRAP_ONESTEP | |
dade8580 | 58 | ConvertTrackParamForExtrap(trackParam, v3, forwardBackward); |
c04e3238 | 59 | // sign of charge (sign of fInverseBendingMomentum if forward motion) |
60 | // must be changed if backward extrapolation | |
61 | Double_t chargeExtrap = forwardBackward * | |
62 | TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); | |
63 | Double_t stepLength = 6.0; // in parameter ???? | |
64 | // Extrapolation loop | |
65 | stepNumber = 0; | |
dade8580 | 66 | while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && // spectro. z<0 |
c04e3238 | 67 | (stepNumber < maxStepNumber)) { |
68 | stepNumber++; | |
69 | // Option for switching between helix and Runge-Kutta ???? | |
dade8580 | 70 | //ExtrapOneStepRungekutta(chargeExtrap, stepLength, v3, v3New); |
71 | ExtrapOneStepHelix(chargeExtrap, stepLength, v3, v3New); | |
72 | if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0 | |
c04e3238 | 73 | // better use TArray ???? |
dade8580 | 74 | for (i3 = 0; i3 < 7; i3++) |
75 | {v3[i3] = v3New[i3];} | |
c04e3238 | 76 | } |
77 | // check maxStepNumber ???? | |
78 | // Interpolation back to exact Z (2nd order) | |
79 | // should be in function ???? using TArray ???? | |
dade8580 | 80 | Double_t dZ12 = v3New[2] - v3[2]; // 1->2 |
c04e3238 | 81 | if (TMath::Abs(dZ12) > 0) { |
dade8580 | 82 | Double_t dZ1i = zEnd - v3[2]; // 1-i |
83 | Double_t dZi2 = v3New[2] - zEnd; // i->2 | |
84 | Double_t xPrime = (v3New[0] - v3[0]) / dZ12; | |
85 | Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12; | |
86 | Double_t yPrime = (v3New[1] - v3[1]) / dZ12; | |
87 | Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12; | |
88 | v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X | |
89 | v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y | |
90 | v3[2] = zEnd; // Z | |
c04e3238 | 91 | Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i); |
92 | Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i); | |
93 | // (PX, PY, PZ)/PTOT assuming forward motion | |
dade8580 | 94 | v3[5] = |
c04e3238 | 95 | 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT |
dade8580 | 96 | v3[3] = xPrimeI * v3[5]; // PX/PTOT |
97 | v3[4] = yPrimeI * v3[5]; // PY/PTOT | |
c04e3238 | 98 | } else { |
99 | cout<<"W-AliMUONTrackExtrap::ExtrapToZ: Extrap. to Z not reached, Z = "<<zEnd<<endl; | |
100 | } | |
dade8580 | 101 | // Track parameters from 3 parameters, |
c04e3238 | 102 | // with charge back for forward motion |
dade8580 | 103 | RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam); |
c04e3238 | 104 | } |
105 | ||
106 | //__________________________________________________________________________ | |
dade8580 | 107 | void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t *v3, Double_t forwardBackward) |
c04e3238 | 108 | { |
dade8580 | 109 | /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam. |
c04e3238 | 110 | /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward" |
111 | /// to know whether the particle is going forward (+1) or backward (-1). | |
dade8580 | 112 | v3[0] = trackParam->GetNonBendingCoor(); // X |
113 | v3[1] = trackParam->GetBendingCoor(); // Y | |
114 | v3[2] = trackParam->GetZ(); // Z | |
c04e3238 | 115 | Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); |
116 | Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()); | |
dade8580 | 117 | v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT |
118 | v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0 | |
119 | v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT | |
120 | v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT | |
c04e3238 | 121 | } |
122 | ||
123 | //__________________________________________________________________________ | |
dade8580 | 124 | void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam) |
c04e3238 | 125 | { |
dade8580 | 126 | /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3", |
c04e3238 | 127 | /// assumed to be calculated for forward motion in Z. |
128 | /// "InverseBendingMomentum" is signed with "charge". | |
dade8580 | 129 | trackParam->SetNonBendingCoor(v3[0]); // X |
130 | trackParam->SetBendingCoor(v3[1]); // Y | |
131 | trackParam->SetZ(v3[2]); // Z | |
132 | Double_t pYZ = v3[6] * TMath::Sqrt(1.0 - v3[3] * v3[3]); | |
c04e3238 | 133 | trackParam->SetInverseBendingMomentum(charge/pYZ); |
dade8580 | 134 | trackParam->SetBendingSlope(v3[4]/v3[5]); |
135 | trackParam->SetNonBendingSlope(v3[3]/v3[5]); | |
c04e3238 | 136 | } |
137 | ||
138 | //__________________________________________________________________________ | |
139 | void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut) | |
140 | { | |
141 | /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station" | |
142 | /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut" | |
143 | /// (index 0 and 1 for first and second chambers). | |
144 | Double_t extZ[2], z1, z2; | |
145 | Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings | |
146 | // range of station to be checked ???? | |
147 | z1 = AliMUONConstants::DefaultChamberZ(2 * station); | |
148 | z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1); | |
149 | // First and second Z to extrapolate at | |
150 | if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;} | |
151 | else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;} | |
152 | else { | |
153 | cout<<"E-AliMUONTrackExtrap::ExtrapToStationAliError: Starting Z ("<<trackParamIn->GetZ() | |
154 | <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl; | |
155 | exit(-1); | |
156 | } | |
157 | extZ[i1] = z1; | |
158 | extZ[i2] = z2; | |
159 | // copy of track parameters | |
160 | trackParamOut[i1] = *trackParamIn; | |
161 | // first extrapolation | |
162 | ExtrapToZ(&(trackParamOut[i1]),extZ[0]); | |
163 | trackParamOut[i2] = trackParamOut[i1]; | |
164 | // second extrapolation | |
165 | ExtrapToZ(&(trackParamOut[i2]),extZ[1]); | |
166 | return; | |
167 | } | |
168 | ||
169 | //__________________________________________________________________________ | |
170 | void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx) | |
171 | { | |
172 | /// Extrapolation to the vertex. | |
173 | /// Returns the track parameters resulting from the extrapolation in the current TrackParam. | |
174 | /// Changes parameters according to Branson correction through the absorber | |
175 | ||
176 | Double_t zAbsorber = -503.0; // to be coherent with the Geant absorber geometry !!!! | |
177 | // spectro. (z<0) | |
178 | // Extrapolates track parameters upstream to the "Z" end of the front absorber | |
179 | ExtrapToZ(trackParam,zAbsorber); // !!! | |
180 | // Makes Branson correction (multiple scattering + energy loss) | |
181 | BransonCorrection(trackParam,xVtx,yVtx,zVtx); | |
182 | // Makes a simple magnetic field correction through the absorber | |
183 | FieldCorrection(trackParam,zAbsorber); | |
184 | } | |
185 | ||
186 | ||
187 | // Keep this version for future developments | |
188 | //__________________________________________________________________________ | |
189 | // void AliMUONTrackExtrap::BransonCorrection(AliMUONTrackParam* trackParam) | |
190 | // { | |
191 | // /// Branson correction of track parameters | |
192 | // // the entry parameters have to be calculated at the end of the absorber | |
193 | // Double_t zEndAbsorber, zBP, xBP, yBP; | |
194 | // Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta; | |
195 | // Int_t sign; | |
196 | // // Would it be possible to calculate all that from Geant configuration ???? | |
197 | // // and to get the Branson parameters from a function in ABSO module ???? | |
198 | // // with an eventual contribution from other detectors like START ???? | |
199 | // // Radiation lengths outer part theta > 3 degres | |
200 | // static Double_t x01[9] = { 18.8, // C (cm) | |
201 | // 10.397, // Concrete (cm) | |
202 | // 0.56, // Plomb (cm) | |
203 | // 47.26, // Polyethylene (cm) | |
204 | // 0.56, // Plomb (cm) | |
205 | // 47.26, // Polyethylene (cm) | |
206 | // 0.56, // Plomb (cm) | |
207 | // 47.26, // Polyethylene (cm) | |
208 | // 0.56 }; // Plomb (cm) | |
209 | // // inner part theta < 3 degres | |
210 | // static Double_t x02[3] = { 18.8, // C (cm) | |
211 | // 10.397, // Concrete (cm) | |
212 | // 0.35 }; // W (cm) | |
213 | // // z positions of the materials inside the absober outer part theta > 3 degres | |
214 | // static Double_t z1[10] = { 90, 315, 467, 472, 477, 482, 487, 492, 497, 502 }; | |
215 | // // inner part theta < 3 degres | |
216 | // static Double_t z2[4] = { 90, 315, 467, 503 }; | |
217 | // static Bool_t first = kTRUE; | |
218 | // static Double_t zBP1, zBP2, rLimit; | |
219 | // // Calculates z positions of the Branson's planes: zBP1 for outer part and zBP2 for inner part (only at the first call) | |
220 | // if (first) { | |
221 | // first = kFALSE; | |
222 | // Double_t aNBP = 0.0; | |
223 | // Double_t aDBP = 0.0; | |
224 | // Int_t iBound; | |
225 | // | |
226 | // for (iBound = 0; iBound < 9; iBound++) { | |
227 | // aNBP = aNBP + | |
228 | // (z1[iBound+1] * z1[iBound+1] * z1[iBound+1] - | |
229 | // z1[iBound] * z1[iBound] * z1[iBound] ) / x01[iBound]; | |
230 | // aDBP = aDBP + | |
231 | // (z1[iBound+1] * z1[iBound+1] - z1[iBound] * z1[iBound] ) / x01[iBound]; | |
232 | // } | |
233 | // zBP1 = (2.0 * aNBP) / (3.0 * aDBP); | |
234 | // aNBP = 0.0; | |
235 | // aDBP = 0.0; | |
236 | // for (iBound = 0; iBound < 3; iBound++) { | |
237 | // aNBP = aNBP + | |
238 | // (z2[iBound+1] * z2[iBound+1] * z2[iBound+1] - | |
239 | // z2[iBound] * z2[iBound ] * z2[iBound] ) / x02[iBound]; | |
240 | // aDBP = aDBP + | |
241 | // (z2[iBound+1] * z2[iBound+1] - z2[iBound] * z2[iBound]) / x02[iBound]; | |
242 | // } | |
243 | // zBP2 = (2.0 * aNBP) / (3.0 * aDBP); | |
244 | // rLimit = z2[3] * TMath::Tan(3.0 * (TMath::Pi()) / 180.); | |
245 | // } | |
246 | // | |
247 | // pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); | |
248 | // sign = 1; | |
249 | // if (trackParam->GetInverseBendingMomentum() < 0) sign = -1; | |
250 | // pZ = pYZ / (TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope())); | |
251 | // pX = pZ * trackParam->GetNonBendingSlope(); | |
252 | // pY = pZ * trackParam->GetBendingSlope(); | |
253 | // pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX); | |
254 | // xEndAbsorber = trackParam->GetNonBendingCoor(); | |
255 | // yEndAbsorber = trackParam->GetBendingCoor(); | |
256 | // radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber; | |
257 | // | |
258 | // if (radiusEndAbsorber2 > rLimit*rLimit) { | |
259 | // zEndAbsorber = z1[9]; | |
260 | // zBP = zBP1; | |
261 | // } else { | |
262 | // zEndAbsorber = z2[3]; | |
263 | // zBP = zBP2; | |
264 | // } | |
265 | // | |
266 | // xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP); | |
267 | // yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP); | |
268 | // | |
269 | // // new parameters after Branson and energy loss corrections | |
270 | // pZ = pTotal * zBP / TMath::Sqrt(xBP * xBP + yBP * yBP + zBP * zBP); | |
271 | // pX = pZ * xBP / zBP; | |
272 | // pY = pZ * yBP / zBP; | |
273 | // trackParam->SetBendingSlope(pY/pZ); | |
274 | // trackParam->SetNonBendingSlope(pX/pZ); | |
275 | // | |
276 | // pT = TMath::Sqrt(pX * pX + pY * pY); | |
277 | // theta = TMath::ATan2(pT, pZ); | |
278 | // pTotal = TotalMomentumEnergyLoss(rLimit, pTotal, theta, xEndAbsorber, yEndAbsorber); | |
279 | // | |
280 | // trackParam->SetInverseBendingMomentum((sign / pTotal) * | |
281 | // TMath::Sqrt(1.0 + | |
282 | // trackParam->GetBendingSlope() * trackParam->GetBendingSlope() + | |
283 | // trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()) / | |
284 | // TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope())); | |
285 | // | |
286 | // // vertex position at (0,0,0) | |
287 | // // should be taken from vertex measurement ??? | |
288 | // trackParam->SetBendingCoor(0.); | |
289 | // trackParam->SetNonBendingCoor(0.); | |
290 | // trackParam->SetZ(0.); | |
291 | // } | |
292 | ||
293 | void AliMUONTrackExtrap::BransonCorrection(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx) | |
294 | { | |
295 | /// Branson correction of track parameters | |
296 | // the entry parameters have to be calculated at the end of the absorber | |
297 | // simplified version: the z positions of Branson's planes are no longer calculated | |
298 | // but are given as inputs. One can use the macros MUONTestAbso.C and DrawTestAbso.C | |
299 | // to test this correction. | |
300 | // Would it be possible to calculate all that from Geant configuration ???? | |
301 | // and to get the Branson parameters from a function in ABSO module ???? | |
302 | // with an eventual contribution from other detectors like START ???? | |
303 | // change to take into account the vertex postition (real, reconstruct,....) | |
304 | ||
305 | Double_t zBP, xBP, yBP; | |
306 | Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta; | |
307 | Int_t sign; | |
308 | static Bool_t first = kTRUE; | |
309 | static Double_t zBP1, zBP2, rLimit, thetaLimit, zEndAbsorber; | |
310 | // zBP1 for outer part and zBP2 for inner part (only at the first call) | |
311 | if (first) { | |
312 | first = kFALSE; | |
313 | ||
314 | zEndAbsorber = -503; // spectro (z<0) | |
315 | thetaLimit = 3.0 * (TMath::Pi()) / 180.; | |
316 | rLimit = TMath::Abs(zEndAbsorber) * TMath::Tan(thetaLimit); | |
317 | zBP1 = -450; // values close to those calculated with EvalAbso.C | |
318 | zBP2 = -480; | |
319 | } | |
320 | ||
321 | pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); | |
322 | sign = 1; | |
323 | if (trackParam->GetInverseBendingMomentum() < 0) sign = -1; | |
324 | pZ = trackParam->Pz(); | |
325 | pX = trackParam->Px(); | |
326 | pY = trackParam->Py(); | |
327 | pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX); | |
328 | xEndAbsorber = trackParam->GetNonBendingCoor(); | |
329 | yEndAbsorber = trackParam->GetBendingCoor(); | |
330 | radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber; | |
331 | ||
332 | if (radiusEndAbsorber2 > rLimit*rLimit) { | |
333 | zBP = zBP1; | |
334 | } else { | |
335 | zBP = zBP2; | |
336 | } | |
337 | ||
338 | xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP); | |
339 | yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP); | |
340 | ||
341 | // new parameters after Branson and energy loss corrections | |
342 | // Float_t zSmear = zBP - gRandom->Gaus(0.,2.); // !!! possible smearing of Z vertex position | |
343 | ||
344 | Float_t zSmear = zBP ; | |
345 | ||
346 | pZ = pTotal * (zSmear-zVtx) / TMath::Sqrt((xBP-xVtx) * (xBP-xVtx) + (yBP-yVtx) * (yBP-yVtx) +( zSmear-zVtx) * (zSmear-zVtx) ); | |
347 | pX = pZ * (xBP - xVtx)/ (zSmear-zVtx); | |
348 | pY = pZ * (yBP - yVtx) / (zSmear-zVtx); | |
349 | trackParam->SetBendingSlope(pY/pZ); | |
350 | trackParam->SetNonBendingSlope(pX/pZ); | |
351 | ||
352 | ||
353 | pT = TMath::Sqrt(pX * pX + pY * pY); | |
354 | theta = TMath::ATan2(pT, TMath::Abs(pZ)); | |
355 | pTotal = TotalMomentumEnergyLoss(thetaLimit, pTotal, theta); | |
356 | ||
357 | trackParam->SetInverseBendingMomentum((sign / pTotal) * | |
358 | TMath::Sqrt(1.0 + | |
359 | trackParam->GetBendingSlope() * trackParam->GetBendingSlope() + | |
360 | trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()) / | |
361 | TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope())); | |
362 | ||
363 | // vertex position at (0,0,0) | |
364 | // should be taken from vertex measurement ??? | |
365 | ||
366 | trackParam->SetBendingCoor(xVtx); | |
367 | trackParam->SetNonBendingCoor(yVtx); | |
368 | trackParam->SetZ(zVtx); | |
369 | ||
370 | } | |
371 | ||
372 | //__________________________________________________________________________ | |
373 | Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta) | |
374 | { | |
375 | /// Returns the total momentum corrected from energy loss in the front absorber | |
376 | // One can use the macros MUONTestAbso.C and DrawTestAbso.C | |
377 | // to test this correction. | |
378 | // Momentum energy loss behaviour evaluated with the simulation of single muons (april 2002) | |
379 | Double_t deltaP, pTotalCorrected; | |
380 | ||
381 | // Parametrization to be redone according to change of absorber material ???? | |
382 | // See remark in function BransonCorrection !!!! | |
383 | // The name is not so good, and there are many arguments !!!! | |
384 | if (theta < thetaLimit ) { | |
385 | if (pTotal < 20) { | |
386 | deltaP = 2.5938 + 0.0570 * pTotal - 0.001151 * pTotal * pTotal; | |
387 | } else { | |
388 | deltaP = 3.0714 + 0.011767 *pTotal; | |
389 | } | |
390 | deltaP *= 0.75; // AZ | |
391 | } else { | |
392 | if (pTotal < 20) { | |
393 | deltaP = 2.1207 + 0.05478 * pTotal - 0.00145079 * pTotal * pTotal; | |
394 | } else { | |
395 | deltaP = 2.6069 + 0.0051705 * pTotal; | |
396 | } | |
397 | deltaP *= 0.9; // AZ | |
398 | } | |
399 | pTotalCorrected = pTotal + deltaP / TMath::Cos(theta); | |
400 | return pTotalCorrected; | |
401 | } | |
402 | ||
403 | //__________________________________________________________________________ | |
404 | void AliMUONTrackExtrap::FieldCorrection(AliMUONTrackParam *trackParam, Double_t zEnd) | |
405 | { | |
406 | /// Correction of the effect of the magnetic field in the absorber | |
407 | // Assume a constant field along Z axis. | |
408 | Float_t b[3],x[3]; | |
409 | Double_t bZ; | |
410 | Double_t pYZ,pX,pY,pZ,pT; | |
411 | Double_t pXNew,pYNew; | |
412 | Double_t c; | |
413 | ||
414 | pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); | |
415 | c = TMath::Sign(1.0,trackParam->GetInverseBendingMomentum()); // particle charge | |
416 | ||
417 | pZ = trackParam->Pz(); | |
418 | pX = trackParam->Px(); | |
419 | pY = trackParam->Py(); | |
420 | pT = TMath::Sqrt(pX*pX+pY*pY); | |
421 | ||
422 | if (TMath::Abs(pZ) <= 0) return; | |
423 | x[2] = zEnd/2; | |
424 | x[0] = x[2]*trackParam->GetNonBendingSlope(); | |
425 | x[1] = x[2]*trackParam->GetBendingSlope(); | |
426 | ||
427 | // Take magn. field value at position x. | |
428 | if (fgkField) fgkField->Field(x,b); | |
429 | else { | |
430 | cout<<"F-AliMUONTrackExtrap::FieldCorrection: fgkField = 0x0"<<endl; | |
431 | exit(-1); | |
432 | } | |
433 | bZ = b[2]; | |
434 | ||
435 | // Transverse momentum rotation | |
436 | // Parameterized with the study of DeltaPhi = phiReco - phiGen as a function of pZ. | |
437 | Double_t phiShift = c*0.436*0.0003*bZ*zEnd/pZ; | |
438 | // Rotate momentum around Z axis. | |
439 | pXNew = pX*TMath::Cos(phiShift) - pY*TMath::Sin(phiShift); | |
440 | pYNew = pX*TMath::Sin(phiShift) + pY*TMath::Cos(phiShift); | |
441 | ||
442 | trackParam->SetBendingSlope(pYNew/pZ); | |
443 | trackParam->SetNonBendingSlope(pXNew/pZ); | |
444 | ||
445 | trackParam->SetInverseBendingMomentum(c/TMath::Sqrt(pYNew*pYNew+pZ*pZ)); | |
446 | ||
447 | } | |
448 | ||
449 | //__________________________________________________________________________ | |
450 | void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout) | |
451 | { | |
452 | /// ****************************************************************** | |
453 | /// * * | |
454 | /// * Performs the tracking of one step in a magnetic field * | |
455 | /// * The trajectory is assumed to be a helix in a constant field * | |
456 | /// * taken at the mid point of the step. * | |
457 | /// * Parameters: * | |
458 | /// * input * | |
459 | /// * STEP =arc length of the step asked * | |
460 | /// * VECT =input vector (position,direction cos and momentum) * | |
461 | /// * CHARGE= electric charge of the particle * | |
462 | /// * output * | |
463 | /// * VOUT = same as VECT after completion of the step * | |
464 | /// * * | |
465 | /// * ==>Called by : <USER>, GUSWIM * | |
466 | /// * Author m.hansroul ********* * | |
467 | /// * modified s.egli, s.v.levonian * | |
468 | /// * modified v.perevoztchikov | |
469 | /// * * | |
470 | /// ****************************************************************** | |
471 | ||
472 | // modif: everything in double precision | |
473 | ||
474 | Double_t xyz[3], h[4], hxp[3]; | |
475 | Double_t h2xy, hp, rho, tet; | |
476 | Double_t sint, sintt, tsint, cos1t; | |
477 | Double_t f1, f2, f3, f4, f5, f6; | |
478 | ||
479 | const Int_t kix = 0; | |
480 | const Int_t kiy = 1; | |
481 | const Int_t kiz = 2; | |
482 | const Int_t kipx = 3; | |
483 | const Int_t kipy = 4; | |
484 | const Int_t kipz = 5; | |
485 | const Int_t kipp = 6; | |
486 | ||
487 | const Double_t kec = 2.9979251e-4; | |
488 | // | |
489 | // ------------------------------------------------------------------ | |
490 | // | |
491 | // units are kgauss,centimeters,gev/c | |
492 | // | |
493 | vout[kipp] = vect[kipp]; | |
494 | if (TMath::Abs(charge) < 0.00001) { | |
495 | for (Int_t i = 0; i < 3; i++) { | |
496 | vout[i] = vect[i] + step * vect[i+3]; | |
497 | vout[i+3] = vect[i+3]; | |
498 | } | |
499 | return; | |
500 | } | |
501 | xyz[0] = vect[kix] + 0.5 * step * vect[kipx]; | |
502 | xyz[1] = vect[kiy] + 0.5 * step * vect[kipy]; | |
503 | xyz[2] = vect[kiz] + 0.5 * step * vect[kipz]; | |
504 | ||
505 | //cmodif: call gufld (xyz, h) changed into: | |
506 | GetField (xyz, h); | |
507 | ||
508 | h2xy = h[0]*h[0] + h[1]*h[1]; | |
509 | h[3] = h[2]*h[2]+ h2xy; | |
510 | if (h[3] < 1.e-12) { | |
511 | for (Int_t i = 0; i < 3; i++) { | |
512 | vout[i] = vect[i] + step * vect[i+3]; | |
513 | vout[i+3] = vect[i+3]; | |
514 | } | |
515 | return; | |
516 | } | |
517 | if (h2xy < 1.e-12*h[3]) { | |
518 | ExtrapOneStepHelix3(charge*h[2], step, vect, vout); | |
519 | return; | |
520 | } | |
521 | h[3] = TMath::Sqrt(h[3]); | |
522 | h[0] /= h[3]; | |
523 | h[1] /= h[3]; | |
524 | h[2] /= h[3]; | |
525 | h[3] *= kec; | |
526 | ||
527 | hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy]; | |
528 | hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz]; | |
529 | hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx]; | |
530 | ||
531 | hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz]; | |
532 | ||
533 | rho = -charge*h[3]/vect[kipp]; | |
534 | tet = rho * step; | |
535 | ||
536 | if (TMath::Abs(tet) > 0.15) { | |
537 | sint = TMath::Sin(tet); | |
538 | sintt = (sint/tet); | |
539 | tsint = (tet-sint)/tet; | |
540 | cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet; | |
541 | } else { | |
542 | tsint = tet*tet/36.; | |
543 | sintt = (1. - tsint); | |
544 | sint = tet*sintt; | |
545 | cos1t = 0.5*tet; | |
546 | } | |
547 | ||
548 | f1 = step * sintt; | |
549 | f2 = step * cos1t; | |
550 | f3 = step * tsint * hp; | |
551 | f4 = -tet*cos1t; | |
552 | f5 = sint; | |
553 | f6 = tet * cos1t * hp; | |
554 | ||
555 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0]; | |
556 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1]; | |
557 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2]; | |
558 | ||
559 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0]; | |
560 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1]; | |
561 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2]; | |
562 | ||
563 | return; | |
564 | } | |
565 | ||
566 | //__________________________________________________________________________ | |
567 | void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout) | |
568 | { | |
569 | /// ****************************************************************** | |
570 | /// * * | |
571 | /// * Tracking routine in a constant field oriented * | |
572 | /// * along axis 3 * | |
573 | /// * Tracking is performed with a conventional * | |
574 | /// * helix step method * | |
575 | /// * * | |
576 | /// * ==>Called by : <USER>, GUSWIM * | |
577 | /// * Authors R.Brun, M.Hansroul ********* * | |
578 | /// * Rewritten V.Perevoztchikov | |
579 | /// * * | |
580 | /// ****************************************************************** | |
581 | ||
582 | Double_t hxp[3]; | |
583 | Double_t h4, hp, rho, tet; | |
584 | Double_t sint, sintt, tsint, cos1t; | |
585 | Double_t f1, f2, f3, f4, f5, f6; | |
586 | ||
587 | const Int_t kix = 0; | |
588 | const Int_t kiy = 1; | |
589 | const Int_t kiz = 2; | |
590 | const Int_t kipx = 3; | |
591 | const Int_t kipy = 4; | |
592 | const Int_t kipz = 5; | |
593 | const Int_t kipp = 6; | |
594 | ||
595 | const Double_t kec = 2.9979251e-4; | |
596 | ||
597 | // | |
598 | // ------------------------------------------------------------------ | |
599 | // | |
600 | // units are kgauss,centimeters,gev/c | |
601 | // | |
602 | vout[kipp] = vect[kipp]; | |
603 | h4 = field * kec; | |
604 | ||
605 | hxp[0] = - vect[kipy]; | |
606 | hxp[1] = + vect[kipx]; | |
607 | ||
608 | hp = vect[kipz]; | |
609 | ||
610 | rho = -h4/vect[kipp]; | |
611 | tet = rho * step; | |
612 | if (TMath::Abs(tet) > 0.15) { | |
613 | sint = TMath::Sin(tet); | |
614 | sintt = (sint/tet); | |
615 | tsint = (tet-sint)/tet; | |
616 | cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet; | |
617 | } else { | |
618 | tsint = tet*tet/36.; | |
619 | sintt = (1. - tsint); | |
620 | sint = tet*sintt; | |
621 | cos1t = 0.5*tet; | |
622 | } | |
623 | ||
624 | f1 = step * sintt; | |
625 | f2 = step * cos1t; | |
626 | f3 = step * tsint * hp; | |
627 | f4 = -tet*cos1t; | |
628 | f5 = sint; | |
629 | f6 = tet * cos1t * hp; | |
630 | ||
631 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0]; | |
632 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1]; | |
633 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f3; | |
634 | ||
635 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0]; | |
636 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1]; | |
637 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f6; | |
638 | ||
639 | return; | |
640 | } | |
641 | //__________________________________________________________________________ | |
642 | void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout) | |
643 | { | |
644 | /// ****************************************************************** | |
645 | /// * * | |
646 | /// * Runge-Kutta method for tracking a particle through a magnetic * | |
647 | /// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of * | |
648 | /// * Standards, procedure 25.5.20) * | |
649 | /// * * | |
650 | /// * Input parameters * | |
651 | /// * CHARGE Particle charge * | |
652 | /// * STEP Step size * | |
653 | /// * VECT Initial co-ords,direction cosines,momentum * | |
654 | /// * Output parameters * | |
655 | /// * VOUT Output co-ords,direction cosines,momentum * | |
656 | /// * User routine called * | |
657 | /// * CALL GUFLD(X,F) * | |
658 | /// * * | |
659 | /// * ==>Called by : <USER>, GUSWIM * | |
660 | /// * Authors R.Brun, M.Hansroul ********* * | |
661 | /// * V.Perevoztchikov (CUT STEP implementation) * | |
662 | /// * * | |
663 | /// * * | |
664 | /// ****************************************************************** | |
665 | ||
666 | Double_t h2, h4, f[4]; | |
667 | Double_t xyzt[3], a, b, c, ph,ph2; | |
668 | Double_t secxs[4],secys[4],seczs[4],hxp[3]; | |
669 | Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt; | |
670 | Double_t est, at, bt, ct, cba; | |
671 | Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost; | |
672 | ||
673 | Double_t x; | |
674 | Double_t y; | |
675 | Double_t z; | |
676 | ||
677 | Double_t xt; | |
678 | Double_t yt; | |
679 | Double_t zt; | |
680 | ||
681 | Double_t maxit = 1992; | |
682 | Double_t maxcut = 11; | |
683 | ||
684 | const Double_t kdlt = 1e-4; | |
685 | const Double_t kdlt32 = kdlt/32.; | |
686 | const Double_t kthird = 1./3.; | |
687 | const Double_t khalf = 0.5; | |
688 | const Double_t kec = 2.9979251e-4; | |
689 | ||
690 | const Double_t kpisqua = 9.86960440109; | |
691 | const Int_t kix = 0; | |
692 | const Int_t kiy = 1; | |
693 | const Int_t kiz = 2; | |
694 | const Int_t kipx = 3; | |
695 | const Int_t kipy = 4; | |
696 | const Int_t kipz = 5; | |
697 | ||
698 | // *. | |
699 | // *. ------------------------------------------------------------------ | |
700 | // *. | |
701 | // * this constant is for units cm,gev/c and kgauss | |
702 | // * | |
703 | Int_t iter = 0; | |
704 | Int_t ncut = 0; | |
705 | for(Int_t j = 0; j < 7; j++) | |
706 | vout[j] = vect[j]; | |
707 | ||
708 | Double_t pinv = kec * charge / vect[6]; | |
709 | Double_t tl = 0.; | |
710 | Double_t h = step; | |
711 | Double_t rest; | |
712 | ||
713 | ||
714 | do { | |
715 | rest = step - tl; | |
716 | if (TMath::Abs(h) > TMath::Abs(rest)) h = rest; | |
717 | //cmodif: call gufld(vout,f) changed into: | |
718 | ||
719 | GetField(vout,f); | |
720 | ||
721 | // * | |
722 | // * start of integration | |
723 | // * | |
724 | x = vout[0]; | |
725 | y = vout[1]; | |
726 | z = vout[2]; | |
727 | a = vout[3]; | |
728 | b = vout[4]; | |
729 | c = vout[5]; | |
730 | ||
731 | h2 = khalf * h; | |
732 | h4 = khalf * h2; | |
733 | ph = pinv * h; | |
734 | ph2 = khalf * ph; | |
735 | secxs[0] = (b * f[2] - c * f[1]) * ph2; | |
736 | secys[0] = (c * f[0] - a * f[2]) * ph2; | |
737 | seczs[0] = (a * f[1] - b * f[0]) * ph2; | |
738 | ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]); | |
739 | if (ang2 > kpisqua) break; | |
740 | ||
741 | dxt = h2 * a + h4 * secxs[0]; | |
742 | dyt = h2 * b + h4 * secys[0]; | |
743 | dzt = h2 * c + h4 * seczs[0]; | |
744 | xt = x + dxt; | |
745 | yt = y + dyt; | |
746 | zt = z + dzt; | |
747 | // * | |
748 | // * second intermediate point | |
749 | // * | |
750 | ||
751 | est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt); | |
752 | if (est > h) { | |
753 | if (ncut++ > maxcut) break; | |
754 | h *= khalf; | |
755 | continue; | |
756 | } | |
757 | ||
758 | xyzt[0] = xt; | |
759 | xyzt[1] = yt; | |
760 | xyzt[2] = zt; | |
761 | ||
762 | //cmodif: call gufld(xyzt,f) changed into: | |
763 | GetField(xyzt,f); | |
764 | ||
765 | at = a + secxs[0]; | |
766 | bt = b + secys[0]; | |
767 | ct = c + seczs[0]; | |
768 | ||
769 | secxs[1] = (bt * f[2] - ct * f[1]) * ph2; | |
770 | secys[1] = (ct * f[0] - at * f[2]) * ph2; | |
771 | seczs[1] = (at * f[1] - bt * f[0]) * ph2; | |
772 | at = a + secxs[1]; | |
773 | bt = b + secys[1]; | |
774 | ct = c + seczs[1]; | |
775 | secxs[2] = (bt * f[2] - ct * f[1]) * ph2; | |
776 | secys[2] = (ct * f[0] - at * f[2]) * ph2; | |
777 | seczs[2] = (at * f[1] - bt * f[0]) * ph2; | |
778 | dxt = h * (a + secxs[2]); | |
779 | dyt = h * (b + secys[2]); | |
780 | dzt = h * (c + seczs[2]); | |
781 | xt = x + dxt; | |
782 | yt = y + dyt; | |
783 | zt = z + dzt; | |
784 | at = a + 2.*secxs[2]; | |
785 | bt = b + 2.*secys[2]; | |
786 | ct = c + 2.*seczs[2]; | |
787 | ||
788 | est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt); | |
789 | if (est > 2.*TMath::Abs(h)) { | |
790 | if (ncut++ > maxcut) break; | |
791 | h *= khalf; | |
792 | continue; | |
793 | } | |
794 | ||
795 | xyzt[0] = xt; | |
796 | xyzt[1] = yt; | |
797 | xyzt[2] = zt; | |
798 | ||
799 | //cmodif: call gufld(xyzt,f) changed into: | |
800 | GetField(xyzt,f); | |
801 | ||
802 | z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h; | |
803 | y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h; | |
804 | x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h; | |
805 | ||
806 | secxs[3] = (bt*f[2] - ct*f[1])* ph2; | |
807 | secys[3] = (ct*f[0] - at*f[2])* ph2; | |
808 | seczs[3] = (at*f[1] - bt*f[0])* ph2; | |
809 | a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird; | |
810 | b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird; | |
811 | c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird; | |
812 | ||
813 | est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2])) | |
814 | + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2])) | |
815 | + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2])); | |
816 | ||
817 | if (est > kdlt && TMath::Abs(h) > 1.e-4) { | |
818 | if (ncut++ > maxcut) break; | |
819 | h *= khalf; | |
820 | continue; | |
821 | } | |
822 | ||
823 | ncut = 0; | |
824 | // * if too many iterations, go to helix | |
825 | if (iter++ > maxit) break; | |
826 | ||
827 | tl += h; | |
828 | if (est < kdlt32) | |
829 | h *= 2.; | |
830 | cba = 1./ TMath::Sqrt(a*a + b*b + c*c); | |
831 | vout[0] = x; | |
832 | vout[1] = y; | |
833 | vout[2] = z; | |
834 | vout[3] = cba*a; | |
835 | vout[4] = cba*b; | |
836 | vout[5] = cba*c; | |
837 | rest = step - tl; | |
838 | if (step < 0.) rest = -rest; | |
839 | if (rest < 1.e-5*TMath::Abs(step)) return; | |
840 | ||
841 | } while(1); | |
842 | ||
843 | // angle too big, use helix | |
844 | ||
845 | f1 = f[0]; | |
846 | f2 = f[1]; | |
847 | f3 = f[2]; | |
848 | f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3); | |
849 | rho = -f4*pinv; | |
850 | tet = rho * step; | |
851 | ||
852 | hnorm = 1./f4; | |
853 | f1 = f1*hnorm; | |
854 | f2 = f2*hnorm; | |
855 | f3 = f3*hnorm; | |
856 | ||
857 | hxp[0] = f2*vect[kipz] - f3*vect[kipy]; | |
858 | hxp[1] = f3*vect[kipx] - f1*vect[kipz]; | |
859 | hxp[2] = f1*vect[kipy] - f2*vect[kipx]; | |
860 | ||
861 | hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz]; | |
862 | ||
863 | rho1 = 1./rho; | |
864 | sint = TMath::Sin(tet); | |
865 | cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet); | |
866 | ||
867 | g1 = sint*rho1; | |
868 | g2 = cost*rho1; | |
869 | g3 = (tet-sint) * hp*rho1; | |
870 | g4 = -cost; | |
871 | g5 = sint; | |
872 | g6 = cost * hp; | |
873 | ||
874 | vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1; | |
875 | vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2; | |
876 | vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3; | |
877 | ||
878 | vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1; | |
879 | vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2; | |
880 | vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3; | |
881 | ||
882 | return; | |
883 | } | |
884 | //___________________________________________________________ | |
885 | void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field) | |
886 | { | |
887 | /// interface for arguments in double precision (Why ? ChF) | |
888 | Float_t x[3], b[3]; | |
889 | ||
890 | x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2]; | |
891 | ||
892 | if (fgkField) fgkField->Field(x,b); | |
893 | else { | |
894 | cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl; | |
895 | exit(-1); | |
896 | } | |
897 | ||
898 | Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2]; | |
899 | ||
900 | return; | |
901 | } | |
902 |