Algorithm corrected
[u/mrichter/AliRoot.git] / ITS / AliITSTPArrayFit.cxx
CommitLineData
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
49ClassImp(AliITSTPArrayFit)
50
51const 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
56const 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
68const Double_t AliITSTPArrayFit::fgkAlmostZero = 1E-55;
69const Double_t AliITSTPArrayFit::fgkCQConv = 0.299792458e-3;// R = PT/Bz/fgkCQConv with GeV,kGauss,cm
70const Double_t AliITSTPArrayFit::fgkZSpanITS[AliITSTPArrayFit::kMaxLrITS] = {
71 36. ,14.1,14.1, 38., 22.2,29.7, 51. ,43.1,48.9};
72
73const 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
76const Int_t AliITSTPArrayFit::fgkPassivLrITS[3] =
77 {AliITSTPArrayFit::kLrBeamPime,AliITSTPArrayFit::kLrShield1,AliITSTPArrayFit::kLrShield2};
78
79const Int_t AliITSTPArrayFit::fgkActiveLrITS[6] =
80 {AliITSTPArrayFit::kLrSPD1,AliITSTPArrayFit::kLrSPD2,
81 AliITSTPArrayFit::kLrSDD1,AliITSTPArrayFit::kLrSDD2,
82 AliITSTPArrayFit::kLrSSD1,AliITSTPArrayFit::kLrSSD2};
83
84Double_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//____________________________________________________
88AliITSTPArrayFit::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//____________________________________________________
101AliITSTPArrayFit::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//____________________________________________________
117AliITSTPArrayFit::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//____________________________________________________
135AliITSTPArrayFit &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//____________________________________________________
167AliITSTPArrayFit::~AliITSTPArrayFit()
168{
169 // destructor
170 delete fParSol;
171 delete[] fCovI;
172 delete[] fCurT;
173 delete[] fElsId;
174 delete[] fElsDR;
175}
176
177//____________________________________________________
178void 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//____________________________________________________
194void 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//____________________________________________________
215Bool_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//____________________________________________________
226Bool_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//____________________________________________________
303void 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//____________________________________________________
319Bool_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//____________________________________________________
366void 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//____________________________________________________
385Int_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//____________________________________________________
407Double_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//____________________________________________________
416Double_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//____________________________________________________
428void 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//____________________________________________________
439void 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//____________________________________________________
449Double_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//____________________________________________________
475void 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//____________________________________________________
495void 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//____________________________________________________
526Double_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//____________________________________________________
575void 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//____________________________________________________
615void 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//____________________________________________________
628void 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//____________________________________________________
641void 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//____________________________________________________
654void 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//____________________________________________________
667void 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//____________________________________________________
700void 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//________________________________________________________________________________________________________
735Double_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//________________________________________________________________________________________________________
791Double_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//________________________________________________________________________________________________________
804Double_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//________________________________________________________________________________________________________
813Double_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//________________________________________________________________________________________________________
832void 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//________________________________________________________________________________________________________
846void 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//________________________________________________________________________________________________________
896void 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//________________________________________________________________________________________________________
928Double_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//________________________________________________________________________________________________________
937Bool_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//____________________________________________________
1185Double_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//____________________________________________________
1293Double_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//____________________________________________________
1381void 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//____________________________________________________
1395Double_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//_____________________________________________________________
1437Double_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//_____________________________________________________________
1448Double_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//_____________________________________________________________
1459void 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//____________________________________________________
1480void 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//____________________________________________________
1554Double_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//____________________________________________________
1571void 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//____________________________________________________
1579Bool_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}