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6be22b3f | 1 | /************************************************************************** |
2 | * Copyright(c) 2009-2011, 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 | /* $Id$ */ | |
16 | /////////////////////////////////////////////////////////////////////////////////////////////// | |
17 | // // | |
18 | // The line is defined by equations (1) // | |
19 | // a0*z+a1*x-a0*a1=0 and // | |
20 | // b0*z+b1*y-b0*b1=0 // | |
21 | // where x,y,z are NOT the lab axes but z is the lab axis along which the track // | |
22 | // has the largest lever arm and x,y are the remaining 2 axis in // | |
23 | // the order of fgkAxisID[z][0], fgkAxisID[z][1] // | |
24 | // The parameters are fParams[kA0,kB0,kA1,kB1] and the axis chosen as the independent // | |
25 | // var. is fParAxis (i.e. if fParAxis==kZ, then a0=ax,b0=bx, a1=ay,b1=by) // | |
26 | // // | |
27 | // // | |
28 | // The helix is defined by the equations (2) // | |
29 | // X(t) = (dr+R)*cos(phi0) - (R+sum{dRi})*cos(t+phi0) + sum{dRi*cos(phi0+ti)} // | |
30 | // Y(t) = (dr+R)*sin(phi0) - (R+sum{dRi})*sin(t+phi0) + sum{dRi*sin(phi0+ti)} // | |
31 | // Z(t) = dz - (R+sum{dRi})*t*tg(dip) + sum{dRi*ti}*tg(dip) // | |
32 | // where dRi is the change of the radius due to the ELoss at parameter ti // | |
33 | // // | |
34 | // Author: ruben.shahoyan@cern.ch // | |
35 | // // | |
36 | /////////////////////////////////////////////////////////////////////////////////////////////// | |
37 | ||
38 | #include "AliITSTPArrayFit.h" | |
39 | #include "AliExternalTrackParam.h" | |
40 | #include "AliSymMatrix.h" | |
41 | #include "AliLog.h" | |
42 | #include "AliParamSolver.h" | |
43 | #include "AliGeomManager.h" | |
44 | #include "AliITSgeomTGeo.h" | |
45 | #include "AliTracker.h" | |
46 | #include <TRandom.h> | |
66214d86 | 47 | #include <TGeoMatrix.h> |
6be22b3f | 48 | |
49 | ClassImp(AliITSTPArrayFit) | |
50 | ||
51 | const Int_t AliITSTPArrayFit::fgkAxisID[3][3] = { | |
52 | {AliITSTPArrayFit::kY,AliITSTPArrayFit::kZ,AliITSTPArrayFit::kX}, | |
53 | {AliITSTPArrayFit::kZ,AliITSTPArrayFit::kX,AliITSTPArrayFit::kY}, | |
54 | {AliITSTPArrayFit::kX,AliITSTPArrayFit::kY,AliITSTPArrayFit::kZ} }; | |
55 | ||
56 | const Int_t AliITSTPArrayFit::fgkAxisCID[3][6] = { | |
57 | {AliITSTPArrayFit::kYY,AliITSTPArrayFit::kYZ,AliITSTPArrayFit::kXY, | |
58 | AliITSTPArrayFit::kZZ,AliITSTPArrayFit::kXZ,AliITSTPArrayFit::kXX}, | |
59 | // | |
60 | {AliITSTPArrayFit::kZZ,AliITSTPArrayFit::kXZ,AliITSTPArrayFit::kYZ, | |
61 | AliITSTPArrayFit::kXX,AliITSTPArrayFit::kYX,AliITSTPArrayFit::kYY}, | |
62 | // | |
63 | {AliITSTPArrayFit::kXX,AliITSTPArrayFit::kXY,AliITSTPArrayFit::kXZ, | |
64 | AliITSTPArrayFit::kYY,AliITSTPArrayFit::kYZ,AliITSTPArrayFit::kZZ} | |
65 | }; | |
66 | // | |
67 | ||
68 | const Double_t AliITSTPArrayFit::fgkAlmostZero = 1E-55; | |
69 | const Double_t AliITSTPArrayFit::fgkCQConv = 0.299792458e-3;// R = PT/Bz/fgkCQConv with GeV,kGauss,cm | |
70 | const Double_t AliITSTPArrayFit::fgkZSpanITS[AliITSTPArrayFit::kMaxLrITS] = { | |
71 | 36. ,14.1,14.1, 38., 22.2,29.7, 51. ,43.1,48.9}; | |
72 | ||
73 | const Double_t AliITSTPArrayFit::fgkRLayITS[AliITSTPArrayFit::kMaxLrITS] = { | |
74 | 2.94, 3.9,7.6, 11.04, 15.0,23.9, 29.44 ,38.0,43.0}; | |
75 | ||
76 | const Int_t AliITSTPArrayFit::fgkPassivLrITS[3] = | |
77 | {AliITSTPArrayFit::kLrBeamPime,AliITSTPArrayFit::kLrShield1,AliITSTPArrayFit::kLrShield2}; | |
78 | ||
79 | const Int_t AliITSTPArrayFit::fgkActiveLrITS[6] = | |
80 | {AliITSTPArrayFit::kLrSPD1,AliITSTPArrayFit::kLrSPD2, | |
81 | AliITSTPArrayFit::kLrSDD1,AliITSTPArrayFit::kLrSDD2, | |
82 | AliITSTPArrayFit::kLrSSD1,AliITSTPArrayFit::kLrSSD2}; | |
83 | ||
84 | Double_t AliITSTPArrayFit::fgRhoLITS[AliITSTPArrayFit::kMaxLrITS] = { | |
85 | 1.48e-01, 2.48e-01,2.57e-01, 1.34e-01, 3.34e-01,3.50e-01, 2.22e-01, 2.38e-01,2.25e-01}; | |
86 | ||
87 | //____________________________________________________ | |
88 | AliITSTPArrayFit::AliITSTPArrayFit() : | |
89 | fPoints(0),fParSol(0),fBz(0),fCharge(0),fPntFirst(-1), | |
90 | fPntLast(-1),fNPBooked(0),fParAxis(-1),fCovI(0),fChi2NDF(0), | |
91 | fMaxIter(20),fIter(0),fEps(1e-6),fMass(0),fkAxID(0),fkAxCID(0),fCurT(0), | |
92 | fFirstPosT(0),fNElsPnt(0),fElsId(0),fElsDR(0) | |
93 | { | |
94 | // default constructor | |
95 | for (int i=kMaxParam;i--;) fParams[i] = 0; | |
96 | for (int i=kMaxParamSq;i--;) fParamsCov[i] = 0; | |
97 | SetMass(); | |
98 | } | |
99 | ||
100 | //____________________________________________________ | |
101 | AliITSTPArrayFit::AliITSTPArrayFit(Int_t np) : | |
102 | fPoints(0),fParSol(0),fBz(0),fCharge(0),fPntFirst(-1), | |
103 | fPntLast(-1),fNPBooked(np),fParAxis(-1),fCovI(0),fChi2NDF(0), | |
104 | fMaxIter(20),fIter(0),fEps(1e-6),fMass(0),fkAxID(0),fkAxCID(0),fCurT(0), | |
105 | fFirstPosT(0),fNElsPnt(0),fElsId(0),fElsDR(0) | |
106 | { | |
107 | // constructor with booking of np points | |
108 | for (int i=kMaxParam;i--;) fParams[i] = 0; | |
109 | for (int i=kMaxParamSq;i--;) fParamsCov[i] = 0; | |
110 | InitAux(); | |
111 | SetEps(); | |
112 | SetMass(); | |
113 | SetMaxIterations(); | |
114 | } | |
115 | ||
116 | //____________________________________________________ | |
117 | AliITSTPArrayFit::AliITSTPArrayFit(const AliITSTPArrayFit &src) : | |
118 | TObject(src),fPoints(src.fPoints),fParSol(0),fBz(src.fBz), | |
119 | fCharge(src.fCharge),fPntFirst(src.fPntFirst),fPntLast(src.fPntLast),fNPBooked(src.fNPBooked), | |
120 | fParAxis(src.fParAxis),fCovI(0),fChi2NDF(0),fMaxIter(20),fIter(0),fEps(0),fMass(src.fMass), | |
121 | fkAxID(0),fkAxCID(0),fCurT(0),fFirstPosT(0),fNElsPnt(0),fElsId(0),fElsDR(0) | |
122 | { | |
123 | // copy constructor | |
124 | InitAux(); | |
125 | memcpy(fCovI,src.fCovI,fNPBooked*6*sizeof(Double_t)); | |
126 | for (int i=kMaxParam;i--;) fParams[i] = src.fParams[i]; | |
127 | for (int i=kMaxParamSq;i--;) fParamsCov[i] = src.fParamsCov[i]; | |
128 | memcpy(fCurT,src.fCurT,fNPBooked*sizeof(Double_t)); | |
129 | SetEps(src.fEps); | |
130 | SetMaxIterations(src.fMaxIter); | |
131 | // | |
132 | } | |
133 | ||
134 | //____________________________________________________ | |
135 | AliITSTPArrayFit &AliITSTPArrayFit::operator =(const AliITSTPArrayFit& src) | |
136 | { | |
137 | // assignment operator | |
138 | if (this==&src) return *this; | |
139 | ((TObject*)this)->operator=(src); | |
140 | fPoints = src.fPoints; | |
141 | if (!fParSol) fParSol = new AliParamSolver(*src.fParSol); | |
142 | else *fParSol = *src.fParSol; | |
143 | fBz = src.fBz; | |
144 | fCharge = src.fCharge; | |
145 | fNPBooked = src.fNPBooked; | |
146 | fPntFirst = src.fPntFirst; | |
147 | fPntLast = src.fPntLast; | |
148 | InitAux(); | |
149 | memcpy(fCovI,src.fCovI,fNPBooked*6*sizeof(Double_t)); | |
150 | for (int i=kMaxParam;i--;) fParams[i] = src.fParams[i]; | |
151 | for (int i=kMaxParamSq;i--;) fParamsCov[i] = src.fParamsCov[i]; | |
152 | SetParAxis(src.fParAxis); | |
153 | fNElsPnt = src.fNElsPnt; | |
154 | fFirstPosT = src.fFirstPosT; | |
155 | memcpy(fCurT ,src.fCurT ,fNPBooked*sizeof(Double_t)); | |
156 | memcpy(fElsId ,src.fElsId ,fNPBooked*sizeof(Int_t)); | |
157 | memcpy(fElsDR ,src.fElsDR ,fNPBooked*sizeof(Double_t)); | |
158 | memcpy(fCurT ,src.fCurT ,fNPBooked*sizeof(Double_t)); | |
159 | SetEps(src.fEps); | |
160 | SetMaxIterations(src.fMaxIter); | |
161 | // | |
162 | return *this; | |
163 | // | |
164 | } | |
165 | ||
166 | //____________________________________________________ | |
167 | AliITSTPArrayFit::~AliITSTPArrayFit() | |
168 | { | |
169 | // destructor | |
170 | delete fParSol; | |
171 | delete[] fCovI; | |
172 | delete[] fCurT; | |
173 | delete[] fElsId; | |
174 | delete[] fElsDR; | |
175 | } | |
176 | ||
177 | //____________________________________________________ | |
178 | void AliITSTPArrayFit::Reset() | |
179 | { | |
180 | // reset to process new track | |
181 | if (fParSol) fParSol->Clear(); | |
182 | fPoints=0; | |
183 | fNElsPnt = 0; | |
184 | fFirstPosT = 0; | |
185 | // fBz = 0; | |
186 | fCharge = 0; | |
187 | fIter = 0; | |
188 | fPntFirst=fPntLast=-1; | |
189 | SetParAxis(-1); | |
190 | ResetBit(kFitDoneBit|kCovInvBit); | |
191 | } | |
192 | ||
193 | //____________________________________________________ | |
194 | void AliITSTPArrayFit::AttachPoints(const AliTrackPointArray* points, Int_t pfirst,Int_t plast) | |
195 | { | |
196 | // create from piece of AliTrackPointArray | |
197 | Reset(); | |
198 | fPoints = points; | |
199 | int np = points->GetNPoints(); | |
200 | if (fNPBooked<np) { | |
201 | fNPBooked = np; | |
202 | InitAux(); | |
203 | } | |
204 | fPntFirst = pfirst<0 ? 0 : pfirst; | |
205 | fPntLast = plast<fPntFirst ? np-1 : plast; | |
206 | // | |
207 | for (int i=kMaxParam;i--;) fParams[i] = 0; | |
208 | for (int i=kMaxParamSq;i--;) fParamsCov[i] = 0; | |
209 | // | |
210 | InvertPointsCovMat(); | |
211 | // | |
212 | } | |
213 | ||
214 | //____________________________________________________ | |
215 | Bool_t AliITSTPArrayFit::SetFirstLast(Int_t pfirst,Int_t plast) | |
216 | { | |
217 | // set first and last point to fit | |
218 | const AliTrackPointArray* pnts = fPoints; | |
219 | if (!pnts) {AliError("TrackPointArray is not attached yet"); return kFALSE;} | |
220 | AttachPoints(pnts,pfirst,plast); | |
221 | return kTRUE; | |
222 | // | |
223 | } | |
224 | ||
225 | //____________________________________________________ | |
226 | Bool_t AliITSTPArrayFit::InvertPointsCovMat() | |
227 | { | |
228 | // invert the cov.matrices of the points | |
229 | for (int i=fPntFirst;i<=fPntLast;i++) { | |
230 | // | |
66214d86 | 231 | float *cov = (float*)fPoints->GetCov() + i*6; // pointer on cov.matrix |
6be22b3f | 232 | // |
233 | Double_t t0 = cov[kYY]*cov[kZZ] - cov[kYZ]*cov[kYZ]; | |
234 | Double_t t1 = cov[kXY]*cov[kZZ] - cov[kXZ]*cov[kYZ]; | |
235 | Double_t t2 = cov[kXY]*cov[kYZ] - cov[kXZ]*cov[kYY]; | |
236 | Double_t det = cov[kXX]*t0 - cov[kXY]*t1 + cov[kXZ]*t2; | |
66214d86 | 237 | if (IsZero(det,1e-18)) { // one of errors is 0, fix this |
238 | double norm[3]; | |
239 | TGeoHMatrix hcov; | |
240 | TGeoRotation hrot,hrotI; | |
241 | GetNormal(norm,cov); | |
242 | double phi = TMath::ATan2(norm[1],norm[0]); | |
243 | hrot.SetAngles(-phi*TMath::RadToDeg(),0.,0.); | |
244 | hrotI.SetAngles(phi*TMath::RadToDeg(),0.,0.); | |
245 | // | |
246 | Double_t hcovel[9]; | |
247 | hcovel[0] = cov[kXX]; | |
248 | hcovel[1] = cov[kXY]; | |
249 | hcovel[2] = cov[kXZ]; | |
250 | hcovel[3] = cov[kXY]; | |
251 | hcovel[4] = cov[kYY]; | |
252 | hcovel[5] = cov[kYZ]; | |
253 | hcovel[6] = cov[kXZ]; | |
254 | hcovel[7] = cov[kYZ]; | |
255 | hcovel[8] = cov[kZZ]; | |
256 | hcov.SetRotation(hcovel); | |
257 | // | |
258 | Double_t *hcovscl = hcov.GetRotationMatrix(); | |
259 | // printf(">> %+e %+e %+e\n %+e %+e %+e\n %+e %+e %+e\n\n",hcovscl[0],hcovscl[1],hcovscl[2],hcovscl[3],hcovscl[4],hcovscl[5],hcovscl[6],hcovscl[7],hcovscl[8]); | |
260 | // printf("Rot by %+.e (%+.e %+.e %+.e)\n",phi, norm[0],norm[1],norm[2]); | |
261 | hcov.Multiply(&hrotI); | |
262 | hcov.MultiplyLeft(&hrot); | |
263 | // printf("|| %+e %+e %+e\n %+e %+e %+e\n %+e %+e %+e\n\n",hcovscl[0],hcovscl[1],hcovscl[2],hcovscl[3],hcovscl[4],hcovscl[5],hcovscl[6],hcovscl[7],hcovscl[8]); | |
264 | if (hcovscl[0]<1e-8) hcovscl[0] = 1e-8; | |
265 | if (hcovscl[4]<1e-8) hcovscl[4] = 1e-8; | |
266 | if (hcovscl[8]<1e-8) hcovscl[8] = 1e-8; | |
267 | // printf("** %+e %+e %+e\n %+e %+e %+e\n %+e %+e %+e\n\n",hcovscl[0],hcovscl[1],hcovscl[2],hcovscl[3],hcovscl[4],hcovscl[5],hcovscl[6],hcovscl[7],hcovscl[8]); | |
268 | hcov.Multiply(&hrot); | |
269 | hcov.MultiplyLeft(&hrotI); | |
270 | // printf("^^ %+e %+e %+e\n %+e %+e %+e\n %+e %+e %+e\n\n",hcovscl[0],hcovscl[1],hcovscl[2],hcovscl[3],hcovscl[4],hcovscl[5],hcovscl[6],hcovscl[7],hcovscl[8]); | |
271 | cov[kXX] = hcovscl[0]; | |
272 | cov[kXY] = hcovscl[1]; | |
273 | cov[kXZ] = hcovscl[2]; | |
274 | cov[kYY] = hcovscl[4]; | |
275 | cov[kYZ] = hcovscl[5]; | |
276 | cov[kZZ] = hcovscl[8]; | |
277 | } | |
278 | t0 = cov[kYY]*cov[kZZ] - cov[kYZ]*cov[kYZ]; | |
279 | t1 = cov[kXY]*cov[kZZ] - cov[kXZ]*cov[kYZ]; | |
280 | t2 = cov[kXY]*cov[kYZ] - cov[kXZ]*cov[kYY]; | |
281 | det = cov[kXX]*t0 - cov[kXY]*t1 + cov[kXZ]*t2; | |
282 | // | |
abd7ef79 | 283 | AliDebug(2,Form("%+.4e %+.4e %+.4e -> %+.4e",t0,t1,t2,det)); |
66214d86 | 284 | if (IsZero(det,fgkAlmostZero)) { |
6be22b3f | 285 | AliInfo(Form("Cov.Matrix for point %d is singular",i)); |
286 | return kFALSE; | |
287 | } | |
288 | // | |
289 | Double_t *covI = GetCovI(i); | |
290 | covI[kXX] = t0/det; | |
291 | covI[kXY] = -t1/det; | |
292 | covI[kXZ] = t2/det; | |
293 | covI[kYY] = (cov[kXX]*cov[kZZ] - cov[kXZ]*cov[kXZ])/det; | |
294 | covI[kYZ] = (cov[kXY]*cov[kXZ] - cov[kXX]*cov[kYZ])/det; | |
295 | covI[kZZ] = (cov[kXX]*cov[kYY] - cov[kXY]*cov[kXY])/det; | |
296 | // | |
297 | } | |
298 | SetCovInv(); | |
299 | return kTRUE; | |
300 | } | |
301 | ||
302 | //____________________________________________________ | |
303 | void AliITSTPArrayFit::InitAux() | |
304 | { | |
305 | // init auxiliary space | |
306 | if (fCovI) delete[] fCovI; | |
307 | if (fCurT) delete[] fCurT; | |
308 | // | |
309 | fCovI = new Double_t[6*fNPBooked]; | |
310 | fCurT = new Double_t[fNPBooked+kMaxLrITS]; | |
311 | fElsId = new Int_t[fNPBooked+kMaxLrITS]; | |
312 | fElsDR = new Double_t[fNPBooked+kMaxLrITS]; | |
313 | memset(fElsDR,0,(fNPBooked+kMaxLrITS)*sizeof(Double_t)); | |
314 | memset(fCovI,0,fNPBooked*6*sizeof(Double_t)); | |
315 | // | |
316 | } | |
317 | ||
318 | //____________________________________________________ | |
319 | Bool_t AliITSTPArrayFit::FitLineCrude() | |
320 | { | |
321 | // perform linear fit w/o accounting the errors | |
322 | // fit is done in the parameterization | |
323 | // x = res[0] + res[1]*z | |
324 | // y = res[2] + res[3]*z | |
325 | // where x,y,z are NOT the lab axes but z is the lab axis along which the track | |
326 | // has the largest lever arm and x,y are the remaining 2 axis in | |
327 | // the order of fgkAxisID[z][0], fgkAxisID[z][1] | |
328 | // | |
329 | int np = fPntLast - fPntFirst + 1; | |
330 | if (np<2) { | |
331 | AliError("At least 2 points are needed for straight line fit"); | |
332 | return kFALSE; | |
333 | } | |
334 | // | |
335 | if (fParAxis<0) SetParAxis(ChoseParAxis()); | |
336 | Double_t sZ=0,sZZ=0,sY=0,sYZ=0,sX=0,sXZ=0,det=0; | |
337 | // | |
338 | const float *coord[3] = {fPoints->GetX(),fPoints->GetY(),fPoints->GetZ()}; | |
339 | const Float_t *varZ = coord[ fParAxis ]; | |
340 | const Float_t *varX = coord[ fkAxID[kX] ]; | |
341 | const Float_t *varY = coord[ fkAxID[kY] ]; | |
342 | // | |
343 | for (int i=fPntFirst;i<=fPntLast;i++) { | |
344 | sZ += varZ[i]; | |
345 | sZZ += varZ[i]*varZ[i]; | |
346 | // | |
347 | sX += varX[i]; | |
348 | sXZ += varX[i]*varZ[i]; | |
349 | // | |
350 | sY += varY[i]; | |
351 | sYZ += varY[i]*varZ[i]; | |
352 | } | |
353 | det = sZZ*np-sZ*sZ; | |
354 | if (TMath::Abs(det)<fgkAlmostZero) return kFALSE; | |
355 | fParams[0] = (sX*sZZ-sZ*sXZ)/det; | |
356 | fParams[1] = (sXZ*np-sZ*sX)/det; | |
357 | // | |
358 | fParams[2] = (sY*sZZ-sZ*sYZ)/det; | |
359 | fParams[3] = (sYZ*np-sZ*sY)/det; | |
360 | // | |
361 | return kTRUE; | |
362 | // | |
363 | } | |
364 | ||
365 | //____________________________________________________ | |
366 | void AliITSTPArrayFit::SetParAxis(Int_t ax) | |
367 | { | |
368 | // select the axis which will be used as a parameter for the line: longest baseline | |
369 | if (ax>kZ) { | |
370 | AliInfo(Form("Wrong axis choice: %d",ax)); | |
371 | fParAxis = -1; | |
372 | } | |
373 | fParAxis = ax; | |
374 | if (ax>=0) { | |
375 | fkAxID = fgkAxisID[ax]; | |
376 | fkAxCID = fgkAxisCID[ax]; | |
377 | } | |
378 | else { | |
379 | fkAxID = fkAxCID = 0; | |
380 | } | |
381 | // | |
382 | } | |
383 | ||
384 | //____________________________________________________ | |
385 | Int_t AliITSTPArrayFit::ChoseParAxis() const | |
386 | { | |
387 | // select the variable with largest base as a parameter | |
388 | Double_t cmn[3]={1.e9,1.e9,1.e9},cmx[3]={-1.e9,-1.e9,-1.e9}; | |
389 | // | |
390 | const float *coord[3] = {fPoints->GetX(),fPoints->GetY(),fPoints->GetZ()}; | |
391 | for (int i=fPntFirst;i<=fPntLast;i++) { | |
392 | for (int j=3;j--;) { | |
393 | Double_t val = coord[j][i]; | |
394 | if (cmn[j]>val) cmn[j] = val; | |
395 | if (cmx[j]<val) cmx[j] = val; | |
396 | } | |
397 | } | |
398 | // | |
399 | int axis = kZ; | |
400 | if (cmx[axis]-cmn[axis] < cmx[kX]-cmn[kX]) axis = kX; | |
401 | if (cmx[axis]-cmn[axis] < cmx[kY]-cmn[kY]) axis = kY; | |
402 | return axis; | |
403 | // | |
404 | } | |
405 | ||
406 | //____________________________________________________ | |
407 | Double_t AliITSTPArrayFit::GetPosition(Double_t *xyzPCA, const Double_t *xyz, const Double_t *covI) const | |
408 | { | |
409 | // calculate the position of the track at PCA to xyz | |
410 | Double_t t = GetParPCA(xyz,covI); | |
411 | GetPosition(xyzPCA,t); | |
412 | return t; | |
413 | } | |
414 | ||
415 | //____________________________________________________ | |
416 | Double_t AliITSTPArrayFit::GetPosition(Double_t *xyzPCA, const AliTrackPoint *pntCovInv) const | |
417 | { | |
418 | // calculate the position of the track at PCA to pntCovInv | |
419 | // NOTE: the covariance matrix of the point must be inverted | |
420 | Double_t covI[6],xyz[3] = {pntCovInv->GetX(),pntCovInv->GetY(),pntCovInv->GetZ()}; | |
421 | for (int i=6;i--;) covI[i] = pntCovInv->GetCov()[i]; | |
422 | Double_t t = GetParPCA(xyz,covI); | |
423 | GetPosition(xyzPCA,t); | |
424 | return t; | |
425 | } | |
426 | ||
427 | //____________________________________________________ | |
428 | void AliITSTPArrayFit::GetResiduals(Double_t *resPCA, const AliTrackPoint *pntCovInv) const | |
429 | { | |
430 | // calculate the residuals of the track at PCA to pntCovInv | |
431 | // NOTE: the covariance matrix of the point must be inverted | |
432 | GetPosition(resPCA,pntCovInv); | |
433 | resPCA[0] -= pntCovInv->GetX(); | |
434 | resPCA[1] -= pntCovInv->GetY(); | |
435 | resPCA[2] -= pntCovInv->GetZ(); | |
436 | } | |
437 | ||
438 | //____________________________________________________ | |
439 | void AliITSTPArrayFit::GetResiduals(Double_t *resPCA, const Double_t *xyz, const Double_t *covI) const | |
440 | { | |
441 | // calculate the residuals of the track at PCA to xyz | |
442 | GetPosition(resPCA,xyz,covI); | |
443 | resPCA[kX] -= xyz[kX]; | |
444 | resPCA[kY] -= xyz[kY]; | |
445 | resPCA[kZ] -= xyz[kZ]; | |
446 | } | |
447 | ||
448 | //____________________________________________________ | |
449 | Double_t AliITSTPArrayFit::GetParPCALine(const Double_t *xyz, const Double_t *covI) const | |
450 | { | |
451 | // get parameter for the point with least weighted distance to the point | |
452 | // | |
453 | Double_t rhs,denom; | |
454 | Double_t dx = fParams[kA0]-xyz[ fkAxID[kX] ]; | |
455 | Double_t dy = fParams[kA1]-xyz[ fkAxID[kY] ]; | |
456 | Double_t dz = -xyz[ fkAxID[kZ] ]; | |
457 | // | |
458 | if (covI) { | |
459 | Double_t tx = fParams[kB0]*covI[ fkAxCID[kXX] ] + fParams[kB1]*covI[ fkAxCID[kXY] ] + covI[ fkAxCID[kXZ] ]; | |
460 | Double_t ty = fParams[kB0]*covI[ fkAxCID[kXY] ] + fParams[kB1]*covI[ fkAxCID[kYY] ] + covI[ fkAxCID[kYZ] ]; | |
461 | Double_t tz = fParams[kB0]*covI[ fkAxCID[kXZ] ] + fParams[kB1]*covI[ fkAxCID[kYZ] ] + covI[ fkAxCID[kZZ] ]; | |
462 | rhs = tx*dx + ty*dy + tz*dz; | |
463 | denom = -(fParams[kB0]*(covI[ fkAxCID[kXZ] ] + tx) + fParams[kB1]*(covI[ fkAxCID[kYZ] ] + ty) + covI[ fkAxCID[kZZ] ]); | |
464 | } | |
465 | else { | |
466 | rhs = fParams[kB0]*dx + fParams[kB1]*dy + dz; | |
467 | denom = -(fParams[kB0]*fParams[kB0] + fParams[kB1]*fParams[kB1] + 1); | |
468 | } | |
469 | // | |
470 | return rhs/denom; | |
471 | // | |
472 | } | |
473 | ||
474 | //____________________________________________________ | |
475 | void AliITSTPArrayFit::GetDResDPosLine(Double_t *dXYZdP, /*const Double_t *xyz,*/ const Double_t *covI) const | |
476 | { | |
477 | // calculate detivative of the PCA residuals vs point position and fill in user provide | |
478 | // array in the format {dXdXp,dY/dXp,dZdXp, ... dXdZp,dYdZp,dZdZp} | |
479 | // | |
480 | Double_t dTdP[3]; | |
481 | GetDtDPosLine(dTdP, /*xyz,*/ covI); // derivative of the t-param over point position | |
482 | // | |
483 | for (int i=3;i--;) { | |
484 | int var = fkAxID[i]; | |
485 | Double_t *curd = dXYZdP + var*3; // d/dCoord_i | |
486 | curd[ fkAxID[kX] ] = fParams[kB0]*dTdP[var]; | |
487 | curd[ fkAxID[kY] ] = fParams[kB1]*dTdP[var]; | |
488 | curd[ fkAxID[kZ] ] = dTdP[var]; | |
489 | curd[ var ]-= 1.; | |
490 | } | |
491 | // | |
492 | } | |
493 | ||
494 | //____________________________________________________ | |
495 | void AliITSTPArrayFit::GetDResDParamsLine(Double_t *dXYZdP, const Double_t *xyz, const Double_t *covI) const | |
496 | { | |
497 | // calculate detivative of the PCA residuals vs line parameters and fill in user provide | |
498 | // array in the format {dXdP0,dYdP0,dZdP0, ... dXdPn,dYdPn,dZdPn} | |
499 | // | |
500 | Double_t dTdP[4]; | |
501 | Double_t t = GetDtDParamsLine(dTdP, xyz, covI); // derivative of the t-param over line params | |
502 | // | |
503 | Double_t *curd = dXYZdP + kA0*3; // d/dA0 | |
504 | curd[ fkAxID[kX] ] = fParams[kB0]*dTdP[kA0] + 1.; | |
505 | curd[ fkAxID[kY] ] = fParams[kB1]*dTdP[kA0]; | |
506 | curd[ fkAxID[kZ] ] = dTdP[kA0]; | |
507 | // | |
508 | curd = dXYZdP + kB0*3; // d/dB0 | |
509 | curd[ fkAxID[kX] ] = fParams[kB0]*dTdP[kB0] + t; | |
510 | curd[ fkAxID[kY] ] = fParams[kB1]*dTdP[kB0]; | |
511 | curd[ fkAxID[kZ] ] = dTdP[kB0]; | |
512 | // | |
513 | curd = dXYZdP + kA1*3; // d/dA1 | |
514 | curd[ fkAxID[kX] ] = fParams[kB0]*dTdP[kA1]; | |
515 | curd[ fkAxID[kY] ] = fParams[kB1]*dTdP[kA1] + 1.; | |
516 | curd[ fkAxID[kZ] ] = dTdP[kA1]; | |
517 | // | |
518 | curd = dXYZdP + kB1*3; // d/dB1 | |
519 | curd[ fkAxID[kX] ] = fParams[kB0]*dTdP[kB1]; | |
520 | curd[ fkAxID[kY] ] = fParams[kB1]*dTdP[kB1] + t; | |
521 | curd[ fkAxID[kZ] ] = dTdP[kB1]; | |
522 | // | |
523 | } | |
524 | ||
525 | //____________________________________________________ | |
526 | Double_t AliITSTPArrayFit::GetDtDParamsLine(Double_t *dtparam,const Double_t *xyz, const Double_t *covI) const | |
527 | { | |
528 | // get t-param detivative over the parameters for the point with least weighted distance to the point | |
529 | // | |
530 | Double_t rhs,denom; | |
531 | Double_t dx = fParams[kA0]-xyz[ fkAxID[kX] ]; | |
532 | Double_t dy = fParams[kA1]-xyz[ fkAxID[kY] ]; | |
533 | Double_t dz = -xyz[ fkAxID[kZ] ]; | |
534 | Double_t rhsDA0,rhsDA1,rhsDB0,rhsDB1,denDB0,denDB1; | |
535 | // | |
536 | if (covI) { | |
537 | Double_t tx = fParams[kB0]*covI[ fkAxCID[kXX] ] + fParams[kB1]*covI[ fkAxCID[kXY] ] + covI[ fkAxCID[kXZ] ]; | |
538 | Double_t ty = fParams[kB0]*covI[ fkAxCID[kXY] ] + fParams[kB1]*covI[ fkAxCID[kYY] ] + covI[ fkAxCID[kYZ] ]; | |
539 | Double_t tz = fParams[kB0]*covI[ fkAxCID[kXZ] ] + fParams[kB1]*covI[ fkAxCID[kYZ] ] + covI[ fkAxCID[kZZ] ]; | |
540 | rhs = tx*dx + ty*dy + tz*dz; | |
541 | denom = -(fParams[kB0]*(covI[ fkAxCID[kXZ] ] + tx) + fParams[kB1]*(covI[ fkAxCID[kYZ] ] + ty) + covI[ fkAxCID[kZZ] ]); | |
542 | // | |
543 | rhsDA0 = tx; | |
544 | rhsDA1 = ty; | |
545 | rhsDB0 = covI[ fkAxCID[kXX] ]*dx + covI[ fkAxCID[kXY] ]*dy + covI[ fkAxCID[kXZ] ]*dz; | |
546 | rhsDB1 = covI[ fkAxCID[kXY] ]*dx + covI[ fkAxCID[kYY] ]*dy + covI[ fkAxCID[kYZ] ]*dz; | |
547 | // | |
548 | denDB0 = -(tx + tx); | |
549 | denDB1 = -(ty + ty); | |
550 | } | |
551 | else { | |
552 | rhs = fParams[kB0]*dx + fParams[kB1]*dy + dz; | |
553 | denom = -(fParams[kB0]*fParams[kB0] + fParams[kB1]*fParams[kB1] + 1); | |
554 | // | |
555 | rhsDA0 = fParams[kB0]; | |
556 | rhsDB0 = dx; | |
557 | rhsDA1 = fParams[kB1]; | |
558 | rhsDB1 = dy; | |
559 | // | |
560 | denDB0 = -(fParams[kB0]+fParams[kB0]); | |
561 | denDB1 = -(fParams[kB1]+fParams[kB1]); | |
562 | // | |
563 | } | |
564 | // | |
565 | Double_t denom2 = denom*denom; | |
566 | dtparam[kA0] = rhsDA0/denom; // denom does not depend on A0,A1 | |
567 | dtparam[kA1] = rhsDA1/denom; | |
568 | dtparam[kB0] = rhsDB0/denom - rhs/denom2 * denDB0; | |
569 | dtparam[kB1] = rhsDB1/denom - rhs/denom2 * denDB1; | |
570 | // | |
571 | return rhs/denom; | |
572 | } | |
573 | ||
574 | //____________________________________________________ | |
575 | void AliITSTPArrayFit::GetDtDPosLine(Double_t *dtpos,/*const Double_t *xyz,*/ const Double_t *covI) const | |
576 | { | |
577 | // get t-param detivative over the parameters for the point with least weighted distance to the point | |
578 | // | |
579 | // Double_t rhs; | |
580 | // Double_t dx = fParams[kA0]-xyz[ fkAxID[kX] ]; | |
581 | // Double_t dy = fParams[kA1]-xyz[ fkAxID[kY] ]; | |
582 | // Double_t dz = -xyz[ fkAxID[kZ] ]; | |
583 | Double_t denom; | |
584 | Double_t rhsDX,rhsDY,rhsDZ; | |
585 | // | |
586 | if (covI) { | |
587 | Double_t tx = fParams[kB0]*covI[ fkAxCID[kXX] ] + fParams[kB1]*covI[ fkAxCID[kXY] ] + covI[ fkAxCID[kXZ] ]; | |
588 | Double_t ty = fParams[kB0]*covI[ fkAxCID[kXY] ] + fParams[kB1]*covI[ fkAxCID[kYY] ] + covI[ fkAxCID[kYZ] ]; | |
589 | Double_t tz = fParams[kB0]*covI[ fkAxCID[kXZ] ] + fParams[kB1]*covI[ fkAxCID[kYZ] ] + covI[ fkAxCID[kZZ] ]; | |
590 | // rhs = tx*dx + ty*dy + tz*dz; | |
591 | denom = -(fParams[kB0]*(covI[ fkAxCID[kXZ] ] + tx) + fParams[kB1]*(covI[ fkAxCID[kYZ] ] + ty) + covI[ fkAxCID[kZZ] ]); | |
592 | // | |
593 | rhsDX = -tx; | |
594 | rhsDY = -ty; | |
595 | rhsDZ = -tz; | |
596 | } | |
597 | else { | |
598 | // rhs = fParams[kB0]*dx + fParams[kB1]*dy + dz; | |
599 | denom = -(fParams[kB0]*fParams[kB0] + fParams[kB1]*fParams[kB1] + 1); | |
600 | // | |
601 | rhsDX = -fParams[kB0]; | |
602 | rhsDY = -fParams[kB1]; | |
603 | rhsDZ = -1; | |
604 | // | |
605 | } | |
606 | // | |
607 | dtpos[ fkAxID[kX] ] = rhsDX/denom; | |
608 | dtpos[ fkAxID[kY] ] = rhsDY/denom; | |
609 | dtpos[ fkAxID[kZ] ] = rhsDZ/denom; | |
610 | // | |
611 | // return rhs/denom; | |
612 | } | |
613 | ||
614 | //____________________________________________________ | |
615 | void AliITSTPArrayFit::GetDResDParamsLine(Double_t *dXYZdP, Int_t ipnt) const | |
616 | { | |
617 | // calculate detivative of the PCA residuals vs line parameters and fill in user provide | |
618 | // array in the format {dXdP0,dYdP0,dZdP0, ... dXdPn,dYdPn,dZdPn} | |
619 | // | |
620 | if (ipnt<fPntFirst || ipnt>fPntLast) { | |
621 | AliError(Form("Attempt to access the point %d not in the fitted points [%d:%d]",ipnt,fPntFirst,fPntLast)); | |
622 | return; | |
623 | } | |
624 | GetDResDParamsLine(dXYZdP, GetPoint(ipnt) , IsCovIgnored() ? 0 : GetCovI(ipnt)); | |
625 | } | |
626 | ||
627 | //____________________________________________________ | |
628 | void AliITSTPArrayFit::GetDResDPosLine(Double_t *dXYZdP, Int_t ipnt) const | |
629 | { | |
630 | // calculate detivative of the PCA residuals vs point position and fill in user provide | |
631 | // array in the format {dXdXp,dY/dXp,dZdXp, ... dXdZp,dYdZp,dZdZp} | |
632 | // | |
633 | if (ipnt<fPntFirst || ipnt>fPntLast) { | |
634 | AliError(Form("Attempt to access the point %d not in the fitted points [%d:%d]",ipnt,fPntFirst,fPntLast)); | |
635 | return; | |
636 | } | |
637 | GetDResDPosLine(dXYZdP,IsCovIgnored() ? 0 : GetCovI(ipnt)); | |
638 | } | |
639 | ||
640 | //____________________________________________________ | |
641 | void AliITSTPArrayFit::GetDResDParams(Double_t *dXYZdP, Int_t ipnt) | |
642 | { | |
643 | // calculate detivative of the PCA residuals vs track parameters and fill in user provide | |
644 | // array in the format {dXdP0,dYdP0,dZdP0, ... dXdPn,dYdPn,dZdPn} | |
645 | // | |
646 | if (ipnt<fPntFirst || ipnt>fPntLast) { | |
647 | AliError(Form("Attempt to access the point %d not in the fitted points [%d:%d]",ipnt,fPntFirst,fPntLast)); | |
648 | return; | |
649 | } | |
650 | GetDResDParams(dXYZdP, GetPoint(ipnt) , IsCovIgnored() ? 0 : GetCovI(ipnt)); | |
651 | } | |
652 | ||
653 | //____________________________________________________ | |
654 | void AliITSTPArrayFit::GetDResDPos(Double_t *dXYZdP, Int_t ipnt) | |
655 | { | |
656 | // calculate detivative of the PCA residuals vs point position and fill in user provide | |
657 | // array in the format {dXdXp,dY/dXp,dZdXp, ... dXdZp,dYdZp,dZdZp} | |
658 | // | |
659 | if (ipnt<fPntFirst || ipnt>fPntLast) { | |
660 | AliError(Form("Attempt to access the point %d not in the fitted points [%d:%d]",ipnt,fPntFirst,fPntLast)); | |
661 | return; | |
662 | } | |
663 | GetDResDPos(dXYZdP, GetPoint(ipnt), IsCovIgnored() ? 0 : GetCovI(ipnt)); | |
664 | } | |
665 | ||
666 | //____________________________________________________ | |
667 | void AliITSTPArrayFit::GetDResDParams(Double_t *dXYZdP, const Double_t *xyz, const Double_t *covI) | |
668 | { | |
669 | // get residual detivatives over the track parameters for the point with least weighted distance to the point | |
670 | // | |
671 | if (!IsFieldON()) { // for the straight line calculate analytically | |
672 | GetDResDParamsLine(dXYZdP, xyz, covI); | |
673 | return; | |
674 | } | |
675 | // | |
676 | // calculate derivative numerically | |
677 | const Double_t delta = 0.01; | |
678 | Double_t xyzVar[4][3]; | |
679 | // | |
680 | for (int ipar = 5;ipar--;) { | |
681 | double sav = fParams[ipar]; | |
682 | fParams[ipar] -= delta; | |
683 | GetPosition(xyzVar[0],xyz,covI); | |
684 | fParams[ipar] += delta/2; | |
685 | GetPosition(xyzVar[1],xyz,covI); | |
686 | fParams[ipar] += delta; | |
687 | GetPosition(xyzVar[2],xyz,covI); | |
688 | fParams[ipar] += delta/2; | |
689 | GetPosition(xyzVar[3],xyz,covI); | |
690 | fParams[ipar] = sav; // restore | |
691 | // | |
692 | double *curd = dXYZdP + 3*ipar; | |
693 | for (int i=3;i--;) curd[i] = (8.*(xyzVar[2][i]-xyzVar[1][i]) - (xyzVar[3][i]-xyzVar[0][i]))/6./delta; | |
694 | } | |
695 | // | |
696 | } | |
697 | ||
698 | ||
699 | //____________________________________________________ | |
700 | void AliITSTPArrayFit::GetDResDPos(Double_t *dXYZdP, const Double_t *xyz, const Double_t *covI) | |
701 | { | |
702 | // get residuals detivative over the point position for the point with least weighted distance to the point | |
703 | // | |
704 | ||
705 | if (!IsFieldON()) { // for the straight line calculate analytically | |
706 | GetDResDPosLine(dXYZdP, /*xyz,*/ covI); | |
707 | return; | |
708 | } | |
709 | // | |
710 | // calculate derivative numerically | |
711 | const Double_t delta = 0.005; | |
712 | Double_t xyzVar[4][3]; | |
713 | Double_t xyzv[3] = {xyz[0],xyz[1],xyz[2]}; | |
714 | // | |
715 | for (int ipar = 3;ipar--;) { | |
716 | double sav = xyzv[ipar]; | |
717 | xyzv[ipar] -= delta; | |
718 | GetPosition(xyzVar[0],xyzv,covI); | |
719 | xyzv[ipar] += delta/2; | |
720 | GetPosition(xyzVar[1],xyzv,covI); | |
721 | xyzv[ipar] += delta; | |
722 | GetPosition(xyzVar[2],xyzv,covI); | |
723 | xyzv[ipar] += delta/2; | |
724 | GetPosition(xyzVar[3],xyzv,covI); | |
725 | xyzv[ipar] = sav; // restore | |
726 | // | |
727 | double *curd = dXYZdP + 3*ipar; | |
728 | for (int i=3;i--;) curd[i] = (8.*(xyzVar[2][i]-xyzVar[1][i]) - (xyzVar[3][i]-xyzVar[0][i]))/6./delta; | |
729 | curd[ipar] -= 1.; | |
730 | } | |
731 | // | |
732 | } | |
733 | ||
734 | //________________________________________________________________________________________________________ | |
735 | Double_t AliITSTPArrayFit::GetParPCAHelix(const Double_t* xyz, const Double_t* covI) const | |
736 | { | |
737 | // find track parameter t (eq.2) corresponding to point of closest approach to xyz | |
738 | // | |
739 | Double_t phi = GetParPCACircle(xyz[kX],xyz[kY]); | |
740 | Double_t cs = TMath::Cos(fParams[kPhi0]); | |
741 | Double_t sn = TMath::Sin(fParams[kPhi0]); | |
742 | Double_t xc = (fParams[kD0]+fParams[kR0])*cs; | |
743 | Double_t yc = (fParams[kD0]+fParams[kR0])*sn; | |
744 | Double_t dchi2,ddchi2; | |
745 | // | |
746 | Double_t dzD = -fParams[kR0]*fParams[kDip]; | |
747 | Double_t dphi = 0; | |
748 | // | |
749 | int it=0; | |
750 | do { | |
751 | cs = TMath::Cos(phi + fParams[kPhi0]); | |
752 | sn = TMath::Sin(phi + fParams[kPhi0]); | |
753 | // | |
754 | Double_t dxD = fParams[kR0]*sn; | |
755 | Double_t dyD = -fParams[kR0]*cs; | |
756 | Double_t dxDD = -dyD; | |
757 | Double_t dyDD = dxD; | |
758 | // | |
759 | Double_t dx = xc - fParams[kR0]*cs - xyz[kX]; | |
760 | Double_t dy = yc - fParams[kR0]*sn - xyz[kY]; | |
761 | Double_t dz = fParams[kDZ] + dzD*phi- xyz[kZ]; | |
762 | // | |
763 | if (covI) { | |
764 | Double_t tx = dx*covI[kXX] + dy*covI[kXY] + dz*covI[kXZ]; | |
765 | Double_t ty = dx*covI[kXY] + dy*covI[kYY] + dz*covI[kYZ]; | |
766 | Double_t tz = dx*covI[kXZ] + dy*covI[kYZ] + dz*covI[kZZ]; | |
767 | // | |
768 | Double_t ttx = dxD*covI[kXX] + dyD*covI[kXY] + dzD*covI[kXZ]; | |
769 | Double_t tty = dxD*covI[kXY] + dyD*covI[kYY] + dzD*covI[kYZ]; | |
770 | Double_t ttz = dxD*covI[kXZ] + dyD*covI[kYZ] + dzD*covI[kZZ]; | |
771 | // | |
772 | // chi2 = dx*tx + dy*ty + dz*tz; | |
773 | dchi2 = dxD*tx + dyD*ty + dzD*tz; | |
774 | ddchi2 = dxDD*tx + dyDD*ty + dxD *ttx + dyD *tty + dzD *ttz; | |
775 | // | |
776 | } | |
777 | else { | |
778 | // chi2 = dx*dx + dy*dy + dz*dz; | |
779 | dchi2 = dxD*dx + dyD*dy + dzD*dz; | |
780 | ddchi2 = dxDD*dx + dyDD*dy + + dxD*dxD + dyD*dyD + dzD*dzD; | |
781 | } | |
782 | // | |
783 | if (TMath::Abs(ddchi2)<fgkAlmostZero || TMath::Abs(dphi=dchi2/ddchi2)<fEps) break; | |
784 | phi -= dphi; | |
785 | } while(++it<fMaxIter); | |
786 | // | |
787 | return phi; | |
788 | } | |
789 | ||
790 | //________________________________________________________________________________________________________ | |
791 | Double_t AliITSTPArrayFit::GetParPCACircle(Double_t x,Double_t y) const | |
792 | { | |
793 | // find track parameter t (eq.2) corresponding to point on the circle with closest approach to x,y | |
794 | // | |
795 | Double_t r = fParams[kD0]+fParams[kR0]; | |
796 | Double_t t = TMath::ATan2( r*TMath::Sin(fParams[kPhi0])-y, r*TMath::Cos(fParams[kPhi0])-x ) - fParams[kPhi0]; | |
797 | if (fParams[kR0] < 0) t += TMath::Pi(); | |
798 | if (t > TMath::Pi()) t -= TMath::Pi()*2; | |
799 | if (t <-TMath::Pi()) t += TMath::Pi()*2; | |
800 | return t; | |
801 | } | |
802 | ||
803 | //________________________________________________________________________________________________________ | |
804 | Double_t AliITSTPArrayFit::GetHelixParAtR(Double_t r) const | |
805 | { | |
806 | // find helix parameter t (eq.2) corresponding to point on the circle of radius t | |
807 | // | |
808 | double gam = 1. - (r-fParams[kD0])*(r+fParams[kD0])/fParams[kR0]/(fParams[kD0]+fParams[kR0])/2.; | |
809 | return (TMath::Abs(gam)>1) ? -1e9 : TMath::ACos(gam); | |
810 | } | |
811 | ||
812 | //________________________________________________________________________________________________________ | |
813 | Double_t AliITSTPArrayFit::CalcChi2NDF() const | |
814 | { | |
815 | // calculate fit chi2/ndf | |
816 | Double_t chi2 = 0; | |
817 | Double_t dr[3]; // residuals | |
818 | //if (!IsFitDone()) return -1; | |
819 | for (int ipnt=fPntFirst;ipnt<=fPntLast;ipnt++) { | |
820 | GetResiduals(dr,ipnt); | |
821 | Double_t* covI = GetCovI(ipnt); | |
822 | chi2 += dr[kX]*(dr[kX]*covI[ kXX ]+dr[kY]*covI[ kXY ]+dr[kZ]*covI[ kXZ ]) | |
823 | + dr[kY]*(dr[kX]*covI[ kXY ]+dr[kY]*covI[ kYY ]+dr[kZ]*covI[ kYZ ]) | |
824 | + dr[kZ]*(dr[kX]*covI[ kXZ ]+dr[kY]*covI[ kYZ ]+dr[kZ]*covI[ kZZ ]); | |
825 | } | |
826 | int ndf = (fPntLast-fPntFirst+1)*3 - GetNParams(); | |
827 | chi2 /= ndf; | |
828 | return chi2; | |
829 | } | |
830 | ||
831 | //________________________________________________________________________________________________________ | |
832 | void AliITSTPArrayFit::GetResiduals(Double_t *res,Int_t ipnt) const | |
833 | { | |
834 | // calculate residuals at point | |
835 | if (ipnt<fPntFirst || ipnt>fPntLast) { | |
836 | AliError(Form("Attempt to access the point %d not in the fitted points [%d:%d]",ipnt,fPntFirst,fPntLast)); | |
837 | return; | |
838 | } | |
839 | GetPosition(res,fCurT[ipnt]); | |
840 | res[kX] -= fPoints->GetX()[ipnt]; | |
841 | res[kY] -= fPoints->GetY()[ipnt]; | |
842 | res[kZ] -= fPoints->GetZ()[ipnt]; | |
843 | } | |
844 | ||
845 | //________________________________________________________________________________________________________ | |
846 | void AliITSTPArrayFit::GetPosition(Double_t *xyz, Double_t t) const | |
847 | { | |
848 | // calculate track position for parameter value t | |
849 | if (IsFieldON()) { | |
850 | // | |
851 | Double_t rrho = fParams[kD0]+fParams[kR0]; | |
852 | Double_t xc = rrho*TMath::Cos(fParams[kPhi0]); | |
853 | Double_t yc = rrho*TMath::Sin(fParams[kPhi0]); | |
854 | Double_t r = fParams[kR0]; | |
855 | Double_t ze = 0; | |
856 | // | |
857 | if (IsELossON()) { | |
858 | if (t>0) { | |
859 | for (int i=fFirstPosT;i<fNElsPnt;i++) { // along the track direction | |
860 | int indE = fElsId[i]; | |
861 | if ( t<fCurT[indE] ) break; // does not reach this layer on its way to t | |
862 | xc += fElsDR[indE] * TMath::Cos(fParams[kPhi0] + fCurT[indE]); | |
863 | yc += fElsDR[indE] * TMath::Sin(fParams[kPhi0] + fCurT[indE]); | |
864 | ze += fElsDR[indE] * fCurT[indE]; | |
865 | r += fElsDR[indE]; | |
866 | //printf("ELoss@ %+.2e r:%+.3e got %+.3e\n",fCurT[indE],r,fElsDR[indE]); | |
867 | } | |
868 | } else { | |
869 | for (int i=fFirstPosT;i--;) { // against the track direction | |
870 | int indE = fElsId[i]; | |
871 | if ( t>=fCurT[indE] ) break; // does not reach this layer on its way to t | |
872 | xc += fElsDR[indE] * TMath::Cos(fParams[kPhi0] + fCurT[indE]); | |
873 | yc += fElsDR[indE] * TMath::Sin(fParams[kPhi0] + fCurT[indE]); | |
874 | ze += fElsDR[indE] * fCurT[indE]; | |
875 | r += fElsDR[indE]; | |
876 | //printf("ELoss@ %+.2e r:%+.3e got %+.3e\n",fCurT[indE],r,fElsDR[indE]); | |
877 | } | |
878 | } | |
879 | } | |
880 | // | |
881 | xyz[kZ] = fParams[kDZ] - fParams[kDip]*(t*r - ze); | |
882 | // | |
883 | t += fParams[kPhi0]; | |
884 | xyz[kX] = xc - r*TMath::Cos(t); | |
885 | xyz[kY] = yc - r*TMath::Sin(t); | |
886 | // printf("t: %+.3e xyz:%+.2e %+.2e %+.2e | R %+.6e -> %+.6e | sign %d\n",t-fParams[kPhi0],xyz[0],xyz[1],xyz[2],fParams[kR0],r,GetSignQB()); | |
887 | } | |
888 | else { | |
889 | xyz[ fkAxID[kX] ] = fParams[kA0] + fParams[kB0]*t; | |
890 | xyz[ fkAxID[kY] ] = fParams[kA1] + fParams[kB1]*t; | |
891 | xyz[ fParAxis ] = t; | |
892 | } | |
893 | } | |
894 | ||
895 | //________________________________________________________________________________________________________ | |
896 | void AliITSTPArrayFit::GetDirCos(Double_t *dircos, Double_t t) const | |
897 | { | |
898 | // calculate track direction cosines for parameter value t | |
899 | if (IsFieldON()) { | |
900 | dircos[kZ] = -fParams[kDip]; | |
901 | t += fParams[kPhi0]; | |
902 | dircos[kX] = TMath::Sin(t); | |
903 | dircos[kY] =-TMath::Cos(t); | |
904 | double gam = TMath::Sign(1/TMath::Sqrt(dircos[kZ]*dircos[kZ]+dircos[kY]*dircos[kY]+dircos[kX]*dircos[kX]),fParams[kR0]); | |
905 | for (int i=3;i--;) dircos[i] *= gam; | |
66214d86 | 906 | if (GetSignQB()>0) for (int i=3;i--;) dircos[i] = -dircos[i]; // positive tracks move along decreasing t |
6be22b3f | 907 | } |
908 | else { | |
909 | double gam = 1/TMath::Sqrt( fParams[kB0]*fParams[kB0] + fParams[kB1]*fParams[kB1] + 1.); | |
910 | dircos[ fkAxID[kX] ] = fParams[kB0]*gam; | |
911 | dircos[ fkAxID[kY] ] = fParams[kB1]*gam; | |
912 | dircos[ fParAxis ] = gam; | |
66214d86 | 913 | // decide direction |
914 | if (IsTypeCollision()) { | |
915 | static double xyzF[3],xyzL[3]; | |
916 | GetPosition(xyzF,fPntFirst); | |
917 | GetPosition(xyzL,fPntLast); | |
918 | double dif = fCurT[fPntLast] - fCurT[fPntFirst]; | |
919 | double dr = (xyzL[kX]-xyzF[kX])*(xyzL[kX]+xyzF[kX]) + (xyzL[kY]-xyzF[kY])*(xyzL[kY]+xyzF[kY]); | |
920 | if (dr*dif<0) for (int i=3;i--;) dircos[i] = -dircos[i]; // with increasing t the tracks comes closer to origin | |
921 | } | |
922 | else if (dircos[kY]>0) for (int i=3;i--;) dircos[i] = -dircos[i]; // cosmic tracks have negative angle to Y axis | |
6be22b3f | 923 | } |
66214d86 | 924 | // |
6be22b3f | 925 | } |
926 | ||
927 | //________________________________________________________________________________________________________ | |
928 | Double_t AliITSTPArrayFit::GetMachinePrec() | |
929 | { | |
930 | // estimate machine precision | |
931 | Double_t eps=1.0,a; | |
932 | do { a = 1. + (eps=eps/2.0); } while(a>1.); | |
933 | return TMath::Abs(2.*eps); | |
934 | } | |
935 | ||
936 | //________________________________________________________________________________________________________ | |
937 | Bool_t AliITSTPArrayFit::FitHelixCrude(Int_t extQ) | |
938 | { | |
939 | // crude estimate of helix parameters, w/o errors and Eloss. | |
940 | // 1st fit the circle (R,xc,yc) by minimizing | |
941 | // chi2 = sum{ (bx*xi + by*yi + xi^2+yi^2 + rho)^2 } vs bx,by,rho | |
942 | // with bx = -2*xc, by = -2*yc , rho = xc^2+yc^2 - R2 | |
943 | // | |
944 | // if charge is not imposed (extQ==0) then it will be determined from the collision type | |
945 | // | |
946 | Bool_t eloss = IsELossON(); | |
947 | // | |
948 | int np = fPntLast - fPntFirst + 1; | |
949 | if (np<2) { AliError("At least 3 points are needed for helix fit"); return kFALSE; } | |
950 | // | |
951 | const float *x=fPoints->GetX(),*y=fPoints->GetY(),*z=fPoints->GetZ(),*cov=fPoints->GetCov(); | |
952 | // | |
953 | // linear circle fit --------------------------------------------------- >>> | |
954 | Double_t sxx=0,sxy=0,syy=0,sx=0,sy=0,rhs0=0,rhs1=0,rhs2=0,minR=1E9; | |
955 | int minRId = 0; | |
956 | for (int i=fPntFirst;i<=fPntLast;i++) { | |
957 | Double_t xx = x[i]*x[i]; | |
958 | Double_t yy = y[i]*y[i]; | |
959 | Double_t xy = x[i]*y[i]; | |
960 | Double_t xxyy = xx + yy; | |
961 | // | |
962 | sxx += xx; | |
963 | sxy += xy; | |
964 | syy += yy; | |
965 | sx += x[i]; | |
966 | sy += y[i]; | |
967 | // | |
968 | rhs0 -= xxyy*x[i]; | |
969 | rhs1 -= xxyy*y[i]; | |
970 | rhs2 -= xxyy; | |
971 | // | |
972 | // remember Id of the point closest to origin, to determine the charge | |
973 | if (xxyy<minR) { minR = xxyy; minRId = i; } | |
974 | // | |
975 | if (eloss) { // find layer id | |
976 | int lrid,volid = fPoints->GetVolumeID()[i]; | |
977 | if (volid>0) lrid = fgkActiveLrITS[AliGeomManager::VolUIDToLayer(fPoints->GetVolumeID()[i])-1]; | |
978 | else { // missing layer info, find from radius | |
979 | double r = TMath::Sqrt(xxyy); | |
980 | for (lrid=kMaxLrITS;lrid--;) if ( IsZero(r-fgkRLayITS[ lrid ],1.) ) break; | |
981 | } | |
982 | fElsDR[i] = (lrid>=0 && lrid<kMaxLrITS) ? fgRhoLITS[ lrid ] : 0; // eloss for normal track | |
983 | } | |
984 | // | |
985 | } | |
986 | // | |
987 | Double_t mn00 = syy*np-sy*sy; | |
988 | Double_t mn01 = sxy*np-sy*sx; | |
989 | Double_t mn02 = sxy*sy-syy*sx; | |
990 | Double_t det = sxx*mn00 - sxy*mn01 + sx*mn02; | |
991 | if (TMath::Abs(det)<fgkAlmostZero) return kFALSE; | |
992 | // | |
993 | Double_t mn11 = sxx*np-sx*sx; | |
994 | Double_t mn12 = sxx*sy-sxy*sx; | |
995 | Double_t mn22 = sxx*syy-sxy*sxy; | |
996 | // | |
997 | Double_t mi00 = mn00/det; | |
998 | Double_t mi01 = -mn01/det; | |
999 | Double_t mi02 = mn02/det; | |
1000 | Double_t mi11 = mn11/det; | |
1001 | Double_t mi12 = -mn12/det; | |
1002 | Double_t mi22 = mn22/det; | |
1003 | // | |
1004 | Double_t xc = -(rhs0*mi00 + rhs1*mi01 + rhs2*mi02)/2; | |
1005 | Double_t yc = -(rhs0*mi01 + rhs1*mi11 + rhs2*mi12)/2; | |
1006 | Double_t rho2 = (rhs0*mi02 + rhs1*mi12 + rhs2*mi22); | |
1007 | // | |
1008 | Double_t dcen = xc*xc + yc*yc; | |
1009 | Double_t rad = dcen - rho2; | |
1010 | rad = (rad>fgkAlmostZero) ? (TMath::Sqrt(rad)):fgkAlmostZero; | |
1011 | // | |
1012 | // printf("Rad: %+e xc: %+e yc: %+e\n",rad,xc,yc); | |
1013 | // linear circle fit --------------------------------------------------- <<< | |
1014 | // | |
1015 | // decide sign(Q*B) and fill cicrle parameters ------------------------- >>> | |
1016 | int sqb; | |
1017 | if (extQ) { | |
1018 | SetCharge(extQ); | |
1019 | sqb = fBz<0 ? -GetCharge():GetCharge(); | |
1020 | } | |
1021 | else { | |
1022 | // determine the charge from the collision type and field sign | |
1023 | // the negative Q*B will have positive Vc x V0 product Z component | |
1024 | // with Vc={-xc,-yc} : vector from circle center to the origin | |
1025 | // and V0 - track direction vector (take {0,-1,1} for cosmics) | |
1026 | // If Bz is not provided, assume positive Bz | |
1027 | sqb = ( IsTypeCosmics() ? xc:(yc*x[minRId]-xc*y[minRId]) ) > 0 ? -1:1; | |
1028 | SetCharge( fBz<0 ? -sqb : sqb); | |
1029 | } | |
1030 | // | |
1031 | dcen = TMath::Sqrt(dcen); | |
1032 | fParams[kD0] = dcen-rad; | |
1033 | Double_t phi = TMath::ATan2(yc,xc); | |
1034 | if (sqb<0) phi += TMath::Pi(); | |
1035 | if (phi > TMath::Pi()) phi -= 2.*TMath::Pi(); | |
1036 | else if (phi <-TMath::Pi()) phi += 2.*TMath::Pi(); | |
1037 | fParams[kPhi0] = phi; | |
1038 | fParams[kR0] = sqb<0 ? -rad:rad; | |
1039 | // | |
1040 | // decide sign(Q*B) and fill cicrle parameters ------------------------- <<< | |
1041 | // | |
1042 | // find z-offset and dip + the parameter t of closest approach to hits - >>> | |
1043 | // | |
1044 | UInt_t hitLrPos=0; // pattern of hit layers at pos | |
1045 | UInt_t hitLrNeg=0; // and negative t's | |
1046 | ||
1047 | Double_t ss=0,st=0,sz=0,stt=0,szt=0; | |
1048 | for (int i=fPntFirst;i<=fPntLast;i++) { | |
1049 | // | |
1050 | Double_t ze2 = cov[i*6 + kZZ]; | |
1051 | Double_t t = TMath::ATan2(yc-y[i],xc-x[i]) - fParams[kPhi0]; // angle at measured z | |
1052 | if (fParams[kR0]<0) t += TMath::Pi(); | |
1053 | if (t > TMath::Pi()) t -= TMath::Pi()*2; | |
1054 | else if (t <-TMath::Pi()) t += TMath::Pi()*2; | |
1055 | if (ze2<fgkAlmostZero) ze2 = 1E-8; | |
1056 | ze2 = 1./ze2; | |
1057 | ss += ze2; | |
1058 | st += t*ze2; | |
1059 | stt+= t*t*ze2; | |
1060 | sz += z[i]*ze2; | |
1061 | szt+= z[i]*t*ze2; | |
1062 | // | |
1063 | fCurT[i] = t; // parameter of the closest approach to the point | |
1064 | // printf("%d %+e %+e %+e %+e\n",i,x[i],y[i],z[i],t); | |
1065 | if (eloss) { | |
1066 | double r = TMath::Sqrt(x[i]*x[i]+y[i]*y[i]); | |
1067 | int lr; | |
1068 | for (lr=kMaxLrITS;lr--;) if ( IsZero(r-fgkRLayITS[ lr ],1.) ) break; | |
1069 | if (lr<kMaxLrITS) { | |
1070 | if (t>0) hitLrPos |= (1<<lr); // set bit of the layer | |
1071 | else hitLrNeg |= (1<<lr); // set bit of the layer | |
1072 | } | |
1073 | } | |
1074 | } | |
1075 | det = ss*stt - st*st; | |
1076 | if (TMath::Abs(det)<fgkAlmostZero) { // no Z dependence | |
1077 | fParams[kDZ] = sz/ss; | |
1078 | fParams[kDip] = 0; | |
1079 | } | |
1080 | else { | |
1081 | fParams[kDZ] = (sz*stt-st*szt)/det; | |
1082 | fParams[kDip] = -(ss*szt-st*sz)/det/fParams[kR0]; | |
1083 | } | |
1084 | // | |
1085 | // find z-offset and dip + the parameter t of closest approach to hits - <<< | |
1086 | // | |
1087 | // fill info needed to account for ELoss ------------------------------- >>> | |
1088 | if (eloss) { | |
1089 | fNElsPnt = fPntLast - fPntFirst + 1; | |
1090 | // | |
1091 | // to account for the energy loss in the passive volumes, calculate the relevant t-parameters | |
1092 | double* tcur = fCurT + fPntFirst; | |
1093 | double* ecur = fElsDR+ fPntFirst; | |
1094 | // | |
1095 | for (int ilp=3;ilp--;) { | |
1096 | int id = fgkPassivLrITS[ilp]; | |
1097 | double tp = GetHelixParAtR( fgkRLayITS[ id ] ); | |
1098 | if (tp<0) continue; // does not hit this radius | |
1099 | // | |
1100 | tcur[fNElsPnt] = GetSignQB()>0 ? -tp : tp; | |
1101 | ecur[fNElsPnt] = fgRhoLITS[ id ]; | |
1102 | fNElsPnt++; | |
1103 | // printf("Passive on lr %d %+e\n",ilp,tcur[fNElsPnt-1]); | |
1104 | // | |
1105 | if (IsTypeCosmics() && !IsZero(tp)) { // 2 crossings for cosmics | |
1106 | tcur[fNElsPnt] = -tcur[fNElsPnt-1]; | |
1107 | ecur[fNElsPnt] = ecur[fNElsPnt-1]; | |
1108 | fNElsPnt++; | |
1109 | //printf("Passive* on lr %d %+e\n",ilp,-tcur[fNElsPnt-1]); | |
1110 | } | |
1111 | // | |
1112 | } | |
1113 | // check if some active layers did not miss the hit, treat them as passive | |
1114 | for (int ilp=6;ilp--;) { | |
1115 | int id = fgkActiveLrITS[ilp]; | |
1116 | double tp = GetHelixParAtR( fgkRLayITS[ id ] ); | |
1117 | if (tp<0) continue; // does not hit this radius | |
1118 | // | |
1119 | if ( (GetSignQB()>0||IsTypeCosmics()) && !(hitLrNeg & (1<<id)) ) { | |
1120 | tcur[fNElsPnt] = -tp; | |
1121 | ecur[fNElsPnt] = fgRhoLITS[ id ]; | |
1122 | fNElsPnt++; | |
1123 | //printf("Missed on lr %d %+e\n",ilp,-tp); | |
1124 | } | |
1125 | // | |
1126 | if ( (GetSignQB()<0||IsTypeCosmics()) && !(hitLrPos & (1<<id)) ) { | |
1127 | tcur[fNElsPnt] = tp; | |
1128 | ecur[fNElsPnt] = fgRhoLITS[ id ]; | |
1129 | fNElsPnt++; | |
1130 | //printf("Missed* on lr %d %e\n",ilp,tp); | |
1131 | } | |
1132 | } | |
1133 | // | |
1134 | TMath::Sort(fNElsPnt,fCurT+fPntFirst,fElsId,kFALSE); // index e-loss points in increasing order | |
1135 | // find the position of smallest positive t-param | |
1136 | for (fFirstPosT=0;fFirstPosT<fNElsPnt;fFirstPosT++) if (fCurT[ fElsId[ fFirstPosT ] ]>0) break; | |
1137 | // | |
1138 | Double_t cdip = 1./TMath::Sqrt(1.+fParams[kDip]*fParams[kDip]); | |
1139 | Double_t ptot = TMath::Abs(fParams[kR0]*fgkCQConv*fBz/cdip); // momentum and energy | |
1140 | Double_t etot = TMath::Sqrt(ptot*ptot + fMass*fMass); // in the point of closest approach to beam | |
1141 | Double_t normS[3]; | |
1142 | // | |
1143 | // Positive t-params: along the track direction for negative track, against for positive | |
1144 | Double_t pcur = ptot, ecurr = etot; | |
1145 | for (int ip=fFirstPosT;ip<fNElsPnt;ip++) { | |
1146 | int tID = fElsId[ip]; | |
1147 | Double_t t = fCurT[ tID ]; | |
1148 | // | |
1149 | if (tID>fPntLast) { // this is not a hit layer but passive layer | |
1150 | double php = TMath::ATan2(yc-fParams[kR0]*TMath::Cos(fParams[kPhi0]+t), | |
1151 | xc-fParams[kR0]*TMath::Cos(fParams[kPhi0]+t)); | |
1152 | normS[0] = -TMath::Cos(php); // normal to the cylinder at intersection point | |
1153 | normS[1] = -TMath::Sin(php); | |
1154 | normS[2] = 0; | |
1155 | } | |
1156 | else GetNormal(normS,fPoints->GetCov()+tID*6); // vector normal to hit module | |
1157 | fElsDR[tID] = GetDRofELoss(t,cdip,fElsDR[tID],normS,ptot,etot); | |
1158 | } | |
1159 | // | |
1160 | // negaive t-params: against the track direction for negative track, along for positive | |
1161 | pcur = ptot; | |
1162 | ecurr = etot; | |
1163 | for (int ip=fFirstPosT;ip--;) { | |
1164 | int tID = fElsId[ip]; | |
1165 | Double_t t = fCurT[ tID ]; | |
1166 | // | |
1167 | if (tID>fPntLast) { // this is not a hit layer but passive layer | |
1168 | double php = TMath::ATan2(yc-fParams[kR0]*TMath::Cos(fParams[kPhi0]+t), | |
1169 | xc-fParams[kR0]*TMath::Cos(fParams[kPhi0]+t)); | |
1170 | normS[0] = -TMath::Cos(php); // normal to the cylinder at intersection point | |
1171 | normS[1] = -TMath::Sin(php); | |
1172 | normS[2] = 0; | |
1173 | } | |
1174 | else GetNormal(normS,fPoints->GetCov()+tID*6); // vector normal to hit module | |
1175 | // | |
1176 | fElsDR[tID] = GetDRofELoss(t,cdip,fElsDR[tID],normS,ptot,etot); | |
1177 | } | |
1178 | } | |
1179 | // fill info needed to account for ELoss ------------------------------- <<< | |
1180 | // | |
1181 | return kTRUE; | |
1182 | } | |
1183 | ||
1184 | //____________________________________________________ | |
1185 | Double_t AliITSTPArrayFit::FitHelix(Int_t extQ, Double_t extPT,Double_t extPTerr) | |
1186 | { | |
1187 | // fit by helix accounting for the errors of all coordinates (and energy loss if requested) | |
1188 | // | |
1189 | // If extQ is non-0, its sign is imposed as a charge of the track | |
1190 | // If extPT>0 and extPTerr>=0, constrain to measured tr.momentum PT | |
1191 | // with corresponding error (err=0 -> rel.err=1e-6) | |
1192 | // | |
1193 | double chiprev=1e99; | |
1194 | //const Double_t kMaxTEffect = 1E-6; | |
1195 | Double_t dXYZdGlo[3*5],dXYZdLoc[3],xyzRes[3]; | |
1196 | // | |
1197 | SetFitDone(kFALSE); | |
1198 | fChi2NDF = -1; | |
1199 | // | |
1200 | if (!FitHelixCrude(extQ)) return -1; // get initial estimate, ignoring the errors | |
1201 | // | |
1202 | if (!IsCovInv()) InvertPointsCovMat(); // prepare inverted errors | |
1203 | if (!fParSol) fParSol = new AliParamSolver(5); | |
1204 | fParSol->SetNGlobal(5); | |
1205 | // | |
1206 | // printf("-1 | %+.2e %+.2e %+.2e %+.2e %+.2e | chi2: %+.4e\n",fParams[0],fParams[1],fParams[2],fParams[3],fParams[4],CalcChi2NDF()); | |
1207 | int iter = 0; | |
1208 | fChi2NDF = 1e99; | |
1209 | Bool_t converged = kFALSE; | |
1210 | while(iter<fMaxIter) { | |
1211 | chiprev = fChi2NDF; | |
1212 | fParSol->Clear(); | |
1213 | for (int ip=fPntFirst;ip<=fPntLast;ip++) { | |
1214 | // | |
1215 | GetResiduals(xyzRes, ip); // current residuals at point ip | |
1216 | Double_t rrho = fParams[kR0]+fParams[kD0]; | |
1217 | Double_t cs0 = TMath::Cos(fParams[kPhi0]); | |
1218 | Double_t sn0 = TMath::Sin(fParams[kPhi0]); | |
1219 | Double_t cst = TMath::Cos(fCurT[ip]+fParams[kPhi0]); | |
1220 | Double_t snt = TMath::Sin(fCurT[ip]+fParams[kPhi0]); | |
1221 | // | |
1222 | int offs = kD0; // dXYZ/dD0 | |
1223 | dXYZdGlo[offs + kX] = cs0; | |
1224 | dXYZdGlo[offs + kY] = sn0; | |
1225 | dXYZdGlo[offs + kZ] = 0; | |
1226 | // | |
1227 | offs = kPhi0*3; // dXYZ/dPhi0 | |
1228 | dXYZdGlo[offs + kX] = -rrho*sn0; | |
1229 | dXYZdGlo[offs + kY] = rrho*cs0; | |
1230 | dXYZdGlo[offs + kZ] = 0; | |
1231 | // | |
1232 | offs = kR0*3; // dXYZ/dR0 | |
1233 | dXYZdGlo[offs + kX] = cs0 - cst; | |
1234 | dXYZdGlo[offs + kY] = sn0 - snt; | |
1235 | dXYZdGlo[offs + kZ] = -fParams[kDip]*fCurT[ip]; | |
1236 | // | |
1237 | offs = kDZ*3; // dXYZ/dDZ | |
1238 | dXYZdGlo[offs + kX] = 0; | |
1239 | dXYZdGlo[offs + kY] = 0; | |
1240 | dXYZdGlo[offs + kZ] = 1.; | |
1241 | // | |
1242 | offs = kDip*3; // dXYZ/dDip | |
1243 | dXYZdGlo[offs + kX] = 0; | |
1244 | dXYZdGlo[offs + kY] = 0; | |
1245 | dXYZdGlo[offs + kZ] = -fParams[kR0]*fCurT[ip]; | |
1246 | // | |
1247 | dXYZdLoc[kX] = fParams[kR0]*snt; | |
1248 | dXYZdLoc[kY] = -fParams[kR0]*cst; | |
1249 | dXYZdLoc[kZ] = -fParams[kR0]*fParams[kDip]; | |
1250 | // | |
1251 | fParSol->AddEquation(dXYZdGlo,dXYZdLoc,xyzRes,GetCovI(ip)); | |
1252 | } | |
1253 | // | |
1254 | if (extPT>0) { // add constraint on pt | |
1255 | if (extPTerr<fgkAlmostZero) extPTerr = 1e-6*extPT; | |
1256 | Double_t cf = fBz*GetCharge()*fgkCQConv; | |
1257 | Double_t err2i = extPTerr/cf; | |
1258 | err2i = 1./err2i/err2i; | |
1259 | // printf("Constrain R to %+e\n",extPT/cf); | |
1260 | fParSol->AddConstraint(kR0,-extPT/cf+fParams[kR0],err2i); | |
1261 | } | |
1262 | if (!fParSol->Solve()) { AliError("Failed to fit helix"); return -1; } | |
1263 | Double_t *deltaG = fParSol->GetGlobals(); | |
1264 | Double_t *deltaT = fParSol->GetLocals(); | |
1265 | for (int ipar=5;ipar--;) fParams[ipar] -= deltaG[ipar]; | |
1266 | for (int ip=fPntFirst;ip<=fPntLast;ip++) fCurT[ip] -= deltaT[ip-fPntFirst]; | |
1267 | iter++; | |
1268 | // | |
1269 | fChi2NDF = CalcChi2NDF(); | |
1270 | // printf("%d | %+.2e %+.2e %+.2e %+.2e %+.2e | chi2: %+.4e %+.4e\n",iter,deltaG[0],deltaG[1],deltaG[2],deltaG[3],deltaG[4],fChi2NDF,fChi2NDF-chiprev); | |
1271 | // printf("->> %+.2e %+.2e %+.2e %+.2e %+.2e | Chi2: %+.6e %+.6e\n",fParams[0],fParams[1],fParams[2],fParams[3],fParams[4],fChi2NDF,fChi2NDF-chiprev); | |
1272 | double difchi2 = chiprev - fChi2NDF; | |
1273 | if ( difchi2<fEps && TMath::Abs(difchi2)<1e-4) {converged = kTRUE; break;} | |
1274 | // if (errT*TMath::Abs(fParams[kR0])<kMaxTEffect && errP<fEps) {converged = kTRUE; break;} | |
1275 | } | |
1276 | // | |
1277 | if (!converged) { | |
1278 | AliDebug(2,Form("Max number of %d iteration reached, Current chi2:%.3e, chi2 change %+.3e",iter, | |
1279 | fChi2NDF,chiprev-fChi2NDF)); | |
1280 | for (int ip=fPntFirst;ip<=fPntLast;ip++) | |
1281 | AliDebug(2,Form("P%2d| %+.3e %+.3e %+.3e\n",ip,fPoints->GetX()[ip],fPoints->GetY()[ip],fPoints->GetZ()[ip])); | |
1282 | ||
1283 | } | |
1284 | fIter = iter; | |
1285 | SetCharge( fParams[kR0]>0 ? (fBz<0?-1:1):(fBz>0?-1:1) ); | |
1286 | SetFitDone(); | |
1287 | // printf("F1>> %+.7e %+.7e %+.7e %+.7e %.7e\n",fParams[0],fParams[1],fParams[2],fParams[3],fParams[4]); | |
1288 | // | |
1289 | return fChi2NDF; | |
1290 | } | |
1291 | ||
1292 | //____________________________________________________ | |
1293 | Double_t AliITSTPArrayFit::FitLine() | |
1294 | { | |
1295 | // fit by helix accounting for the errors of all coordinates (and energy loss if requested) | |
1296 | // | |
1297 | double chiprev=1e99; | |
1298 | // const Double_t kMaxTEffect = 1.e-6; | |
1299 | Double_t dXYZdGlo[3*4],dXYZdLoc[3],xyzRes[3]; | |
1300 | SetFitDone(kFALSE); | |
1301 | fChi2NDF = -1; | |
1302 | // | |
1303 | if (fParAxis<0) SetParAxis(ChoseParAxis()); | |
1304 | // | |
1305 | const float *xyzp[3]={fPoints->GetX(),fPoints->GetY(),fPoints->GetZ()}; | |
1306 | if (!IsCovInv()) InvertPointsCovMat(); | |
1307 | if (!FitLineCrude()) return -1; // get initial estimate, ignoring the errors | |
1308 | // | |
1309 | if (!fParSol) fParSol = new AliParamSolver(5); | |
1310 | fParSol->SetNGlobal(4); | |
1311 | // initial set of parameters | |
1312 | for (int ip=fPntFirst;ip<=fPntLast;ip++) fCurT[ip] = xyzp[fParAxis][ip]; // use measured param-coordinate | |
1313 | // | |
1314 | int iter = 0; | |
1315 | Bool_t converged = kFALSE; | |
1316 | fChi2NDF = 1e99; | |
1317 | while(iter<fMaxIter) { | |
1318 | chiprev = fChi2NDF; | |
1319 | fParSol->Clear(); | |
1320 | for (int ip=fPntFirst;ip<=fPntLast;ip++) { | |
1321 | // | |
1322 | int offs; | |
1323 | GetResiduals(xyzRes, ip); // current residuals at point ip | |
1324 | // | |
1325 | offs = kA0*3; // dXYZ/dA0 | |
1326 | dXYZdGlo[offs + fkAxID[kX]] = 1; | |
1327 | dXYZdGlo[offs + fkAxID[kY]] = 0; | |
1328 | dXYZdGlo[offs + fParAxis ] = 0; | |
1329 | // | |
1330 | offs = kB0*3; // dXYZ/dB0 | |
1331 | dXYZdGlo[offs + fkAxID[kX]] = fCurT[ip]; | |
1332 | dXYZdGlo[offs + fkAxID[kY]] = 0; | |
1333 | dXYZdGlo[offs + fParAxis ] = 0; | |
1334 | // | |
1335 | offs = kA1*3; // dXYZ/dA1 | |
1336 | dXYZdGlo[offs + fkAxID[kX]] = 0; | |
1337 | dXYZdGlo[offs + fkAxID[kY]] = 1; | |
1338 | dXYZdGlo[offs + fParAxis ] = 0; | |
1339 | // | |
1340 | offs = kB1*3; // dXYZ/dB1 | |
1341 | dXYZdGlo[offs + fkAxID[kX]] = 0; | |
1342 | dXYZdGlo[offs + fkAxID[kY]] = fCurT[ip]; | |
1343 | dXYZdGlo[offs + fParAxis ] = 0; | |
1344 | // | |
1345 | dXYZdLoc[ fkAxID[kX] ] = fParams[kB0]; // dX/dt | |
1346 | dXYZdLoc[ fkAxID[kY] ] = fParams[kB1]; // dY/dt | |
1347 | dXYZdLoc[ fParAxis ] = 1; | |
1348 | // | |
1349 | fParSol->AddEquation(dXYZdGlo,dXYZdLoc,xyzRes,GetCovI(ip)); | |
1350 | } | |
1351 | // | |
1352 | if (!fParSol->Solve()) { AliError("Failed to fit line"); return -1; } | |
1353 | Double_t *deltaG = fParSol->GetGlobals(); | |
1354 | Double_t *deltaT = fParSol->GetLocals(); | |
1355 | for (int ipar=4;ipar--;) fParams[ipar] -= deltaG[ipar]; | |
1356 | for (int ip=fPntFirst;ip<=fPntLast;ip++) fCurT[ip] -= deltaT[ip-fPntFirst]; | |
1357 | iter++; | |
1358 | fChi2NDF = CalcChi2NDF(); | |
1359 | // printf("%d %+e %+e | %+.2e %+.2e %+.2e %+.2e | chi2: %+.4e %+.4e\n",iter,errP,errT, deltaG[0],deltaG[1],deltaG[2],deltaG[3],fChi2NDF,fChi2NDF-chiprev); | |
1360 | // printf("->> %+.2e %+.2e %+.2e %+.2e %+.2e | Chi2: %+.6e %+.6e\n",fParams[0],fParams[1],fParams[2],fParams[3],fParams[4],fChi2NDF,fChi2NDF-chiprev); | |
1361 | double difchi2 = chiprev - fChi2NDF; | |
1362 | if ( difchi2<fEps && TMath::Abs(difchi2)<1e-4) {converged = kTRUE; break;} | |
1363 | chiprev = fChi2NDF; | |
1364 | // if (errT<kMaxTEffect && errP<fEps) {converged = kTRUE; break;} | |
1365 | } | |
1366 | // | |
1367 | if (!converged) { | |
1368 | AliDebug(2,Form("Max number of %d iteration reached, Current chi2:%.3e, chi2 change %+.3e",iter, | |
1369 | fChi2NDF,chiprev-fChi2NDF)); | |
1370 | for (int ip=fPntFirst;ip<=fPntLast;ip++) | |
1371 | AliDebug(2,Form("P%2d| %+.3e %+.3e %+.3e\n",ip,fPoints->GetX()[ip],fPoints->GetY()[ip],fPoints->GetZ()[ip])); | |
1372 | } | |
1373 | fIter = iter; | |
1374 | SetFitDone(); | |
1375 | //printf("F1>> %+.2e %+.2e %+.2e %+.2e\n",fParams[0],fParams[1],fParams[2],fParams[3]); | |
1376 | return fChi2NDF; | |
1377 | // | |
1378 | } | |
1379 | ||
1380 | //____________________________________________________ | |
1381 | void AliITSTPArrayFit::GetNormal(Double_t *norm, const Float_t *covMat) | |
1382 | { | |
1383 | // obtain the lab normal vector to the sensor from the covariance matrix | |
1384 | // in such a way that when the local frame of the sensor coincides with | |
1385 | // the lab frame, the vector {0,1,0} is obtained | |
1386 | Double_t tgxy = TMath::Tan(0.5*TMath::ATan2(2.*covMat[kXY],covMat[kYY]-covMat[kXX])); | |
1387 | Double_t tgyz = TMath::Tan(0.5*TMath::ATan2(2.*covMat[kYZ],covMat[kZZ]-covMat[kYY])); | |
1388 | norm[kY] = 1./TMath::Sqrt(1 + tgxy*tgxy + tgyz*tgyz); | |
1389 | norm[kX] = norm[kY]*tgxy; | |
1390 | norm[kZ] = norm[kY]*tgyz; | |
1391 | // | |
1392 | } | |
1393 | ||
1394 | //____________________________________________________ | |
1395 | Double_t AliITSTPArrayFit::GetDRofELoss(Double_t t,Double_t cdip,Double_t rhoL,const Double_t *normS, | |
1396 | Double_t &p,Double_t &e) const | |
1397 | { | |
1398 | // Calculate energy loss of the particle at given t-param on the layer with rhoL (thickness*density) with | |
1399 | // normal vector normS in the lab. The particle before eloss has energy "e" and momentum "p" | |
1400 | // cdip = cosine of the dip angle = 1/sqrt(1+tgL^2) | |
1401 | // Return the change DR of the radius due to the ELoss | |
1402 | // | |
1403 | // NOTE: with B>0 the negative particles propagate along increasing t-param and positive | |
1404 | // particles - against. | |
1405 | // t-param = 0 corresponds to the point of closest approach of the track to the beam. | |
1406 | // Since the fitted helix parameters of the track are defined in this PCA point, when the correction | |
1407 | // is applied upstream of the PCS, the energy must be increased (DR>0) rather than decreased (DR<0) | |
1408 | // | |
1409 | Double_t dirTr[3]; | |
1410 | dirTr[0] = -TMath::Sin(fParams[kPhi0]+t); | |
1411 | dirTr[1] = TMath::Cos(fParams[kPhi0]+t); | |
1412 | dirTr[2] = fParams[kDip]; | |
1413 | // cosine of the impact angle | |
1414 | Double_t cosImp = cdip*TMath::Abs(dirTr[0]*normS[0]+dirTr[1]*normS[1]+dirTr[2]*normS[2]); | |
1415 | // | |
1416 | if (cosImp<0.3) cosImp = 0.3; //? | |
1417 | Double_t dE = AliExternalTrackParam::BetheBlochSolid(p/fMass)*rhoL/cosImp; | |
1418 | Double_t dP = e/p*dE; | |
1419 | // | |
1420 | if (t*GetSignQB() < 0) { | |
1421 | dP = -dP; | |
1422 | dE = -dE; | |
1423 | } | |
1424 | // | |
1425 | if (p+dP<0) { | |
1426 | AliInfo(Form("Estimated PLoss %.3f is larger than particle momentum %.3f. Skipping",dP,p)); | |
1427 | return 0; | |
1428 | } | |
1429 | // | |
1430 | p += dP; | |
1431 | e += dE; | |
1432 | // | |
1433 | return fCharge*dP*cdip/fBz/fgkCQConv; | |
1434 | } | |
1435 | ||
1436 | //_____________________________________________________________ | |
1437 | Double_t AliITSTPArrayFit::GetLineOffset(Int_t axis) const | |
1438 | { | |
1439 | // return intercept of the parameterization coord = intercept + slope*t for given axis | |
1440 | if (fParAxis<0) return -1E6; // no line fit | |
1441 | if (axis==fParAxis) return 0; | |
1442 | if (fParAxis==kX) return fParams[axis==kY ? kA0 : kA1 ]; | |
1443 | if (fParAxis==kY) return fParams[axis==kZ ? kA0 : kA1 ]; | |
1444 | return fParams[axis==kX ? kA0 : kA1 ]; | |
1445 | } | |
1446 | ||
1447 | //_____________________________________________________________ | |
1448 | Double_t AliITSTPArrayFit::GetLineSlope(Int_t axis) const | |
1449 | { | |
1450 | // return intercept of the parameterization coord = intercept + slope*t for given axis | |
1451 | if (fParAxis<0) return -1E6; // no line fit | |
1452 | if (axis==fParAxis) return 1.; | |
1453 | if (fParAxis==kX) return fParams[axis==kY ? kB0 : kB1 ]; | |
1454 | if (fParAxis==kY) return fParams[axis==kZ ? kB0 : kB1 ]; | |
1455 | return fParams[axis==kX ? kB0 : kB1 ]; | |
1456 | } | |
1457 | ||
1458 | //_____________________________________________________________ | |
1459 | void AliITSTPArrayFit::Print(Option_t *) const | |
1460 | { | |
1461 | const char kCxyz[] = "XYZ"; | |
1462 | if (!fPoints) return; | |
1463 | // | |
1464 | printf("Track of %3d points in Bz=%+.1f |Fit ",fPntLast-fPntFirst+1,fBz); | |
1465 | if ( IsFitDone() ) { | |
1466 | if (IsFieldON()) | |
1467 | printf("Helix: Chi2: %5.1f | %+.2e %+.2e %+.2e %+.2e %+.2e\n", | |
1468 | fChi2NDF,fParams[kD0],fParams[kPhi0],fParams[kR0],fParams[kDZ],fParams[kDip]); | |
1469 | else | |
1470 | printf("Line%c: Chi2: %5.1f | %+.2e %+.2e %+.2e %+.2e\n", | |
1471 | kCxyz[fParAxis],fChi2NDF,fParams[kA0],fParams[kB0],fParams[kA1],fParams[kB1]); | |
1472 | } | |
1473 | else printf("N/A\n"); | |
1474 | } | |
1475 | ||
1476 | ||
1477 | ||
1478 | ||
1479 | //____________________________________________________ | |
1480 | void AliITSTPArrayFit::BuildMaterialLUT(Int_t ntri) | |
1481 | { | |
1482 | // Fill a look-up table with mean material a la AliITSTrackerMI | |
1483 | // | |
1484 | if (!AliGeomManager::GetGeometry()) AliFatal("Geometry is not loaded"); | |
1485 | // | |
1486 | // detector layer to check: dX,dZ,Ymin,Ymax | |
1487 | const double kLayr[9][4] = {{0. ,60. , 2.80,3.00}, // beam pipe | |
1488 | {1.28,7.07,-0.20,0.22}, // SPD1 | |
1489 | {1.28,7.07,-0.20,0.22}, // SPD2 | |
1490 | {0. ,76.0, 10.4,11.8}, // Shield1 | |
1491 | {7.02,7.53,-1.00,4.50}, // SDD1 | |
1492 | {7.02,7.53,-1.00,4.50}, // SDD2 | |
1493 | {0. ,102., 29.0,30.0}, // Shield2 | |
1494 | {7.50,4.20,-0.15,4.50}, // SSD1 | |
1495 | {7.50,4.20,-0.15,4.50}}; // SSD2 | |
1496 | // | |
1497 | // | |
1498 | // build <dens*L> for detectors (track hitting the sensor in normal direction) | |
1499 | double pg1[3],pg2[3],res[7]; | |
1500 | // | |
1501 | int sID = 0; | |
1502 | int actLrID = 0; | |
1503 | for (int lr=0;lr<9;lr++) { | |
1504 | // | |
1505 | Bool_t active = kFALSE; | |
1506 | const double* tpars = kLayr[lr]; | |
1507 | // | |
1508 | if (IsZero(tpars[0])) { // passive layer | |
1509 | active = kFALSE; | |
1510 | AliInfo(Form("Probing passive layer (total layer #%d)",lr)); | |
1511 | } | |
1512 | else { | |
1513 | active = kTRUE; | |
1514 | sID += AliGeomManager::LayerSize(++actLrID); | |
1515 | AliInfo(Form("Probing sensors of active layer #%d (total layers #%d)",actLrID,lr)); | |
1516 | } | |
1517 | double shift = TMath::Abs(tpars[2]-tpars[3])*1E-4; | |
1518 | double rhol = 0; | |
1519 | for (int i=ntri;i--;) { | |
1520 | // | |
1521 | if (active) { | |
1522 | int ssID = sID -1 - AliGeomManager::LayerSize(actLrID)*gRandom->Rndm(); | |
1523 | pg1[0] = pg2[0] = (gRandom->Rndm()-0.5)*tpars[0] + shift; // local X | |
1524 | pg2[0] -= 2*shift; | |
1525 | pg1[1] = tpars[2]; | |
1526 | pg2[1] = tpars[3]; | |
1527 | pg1[2] = pg2[2] = (gRandom->Rndm()-0.5)*tpars[1] + shift; // local Z | |
1528 | pg2[2] -= 2*shift; | |
1529 | AliITSgeomTGeo::LocalToGlobal(ssID,pg1,pg1); | |
1530 | AliITSgeomTGeo::LocalToGlobal(ssID,pg2,pg2); | |
1531 | } | |
1532 | else { | |
1533 | double ang = gRandom->Rndm()*TMath::Pi()*2; | |
1534 | pg1[0] = tpars[2]*TMath::Cos(ang)+shift; | |
1535 | pg2[0] = tpars[3]*TMath::Cos(ang)-shift; | |
1536 | pg1[1] = tpars[2]*TMath::Sin(ang); | |
1537 | pg2[1] = tpars[3]*TMath::Sin(ang); | |
1538 | pg1[2] = pg2[2] = (gRandom->Rndm()-0.5)*tpars[1]+shift; // local Z | |
1539 | pg2[2] -= 2*shift; | |
1540 | } | |
1541 | ||
1542 | // | |
1543 | AliTracker::MeanMaterialBudget(pg1,pg2,res); | |
1544 | rhol += res[0]*res[4]; // rho*L | |
1545 | } | |
1546 | fgRhoLITS[lr] = rhol/ntri; | |
1547 | AliInfo(Form("Obtained <rho*L> = %e\n",fgRhoLITS[lr])); | |
1548 | } | |
1549 | // | |
1550 | return; | |
1551 | } | |
1552 | ||
6be22b3f | 1553 | //____________________________________________________ |
1554 | Double_t AliITSTPArrayFit::GetPCA2PlaneInfo(Double_t *xyz, Double_t *dir, Int_t axis, Double_t axval) const | |
1555 | { | |
1556 | // calculate the PCA to plane normal ti axis and crossing it at axval | |
1557 | // fill the position and direction cosines at this point | |
1558 | // | |
1559 | double xyzp[3] = {0,0,0}; // create fake point | |
1560 | xyzp[axis] = axval; | |
1561 | double covI[6] = {1e-4,0,0,1e-4,0,1e-4}; // fake cov.matrix loose in all directions | |
1562 | covI[4*axis - axis*(axis+1)/2] = 1e8; // except axis | |
1563 | // | |
1564 | double t = GetPosition(xyz, xyzp, covI); // got pca | |
1565 | // | |
1566 | if (dir) GetDirCos(dir,t); | |
1567 | return t; | |
1568 | } | |
1569 | ||
66214d86 | 1570 | //____________________________________________________ |
1571 | void AliITSTPArrayFit::GetT0Info(Double_t* xyz, Double_t *dir) const | |
1572 | { | |
1573 | // get direction cosines for t = 0; | |
1574 | GetPosition(xyz, 0); | |
1575 | if (dir) GetDirCos(dir,0); | |
1576 | } | |
1577 | ||
1578 | //____________________________________________________ | |
1579 | Bool_t AliITSTPArrayFit::CalcErrorMatrix() | |
1580 | { | |
1581 | // compute covariance matrix in lenear approximation of residuals on parameters | |
1582 | static AliSymMatrix cv(5); | |
1583 | static Double_t dres[5][3]; | |
1584 | cv.Reset(); | |
1585 | int npar = IsFieldON() ? 5:4; | |
1586 | // | |
1587 | for (int ip=fPntFirst;ip<=fPntLast;ip++) { | |
1588 | GetDResDParams(&dres[0][0],ip); | |
1589 | Double_t* covI = GetCovI(ip); | |
1590 | for (int i=npar;i--;) | |
1591 | for (int j=i+1;j--;) | |
1592 | cv(i,j) += dres[i][kX]*(dres[j][kX]*covI[ kXX ] + dres[j][kY]*covI[ kXY ] + dres[j][kZ]*covI[ kXZ ]) | |
1593 | + dres[i][kY]*(dres[j][kX]*covI[ kXY ] + dres[j][kY]*covI[ kYY ] + dres[j][kZ]*covI[ kYZ ]) | |
1594 | + dres[i][kZ]*(dres[j][kX]*covI[ kXZ ] + dres[j][kY]*covI[ kYZ ] + dres[j][kZ]*covI[ kZZ ]); | |
1595 | } | |
1596 | cv.SetSizeUsed(npar); | |
1597 | if (cv.InvertChol()) { | |
1598 | cv.Print("l"); | |
1599 | int cnt = 0; | |
1600 | for (int i=npar;i--;) for (int j=i+1;j--;)fParamsCov[cnt++] = cv(i,j); | |
1601 | return kTRUE; | |
1602 | } | |
1603 | // | |
1604 | return kFALSE; | |
1605 | } |