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Corrected initialization
[u/mrichter/AliRoot.git] / STEER / AliTrackFitterRieman.cxx
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98937d93 1#include "TMatrixDSym.h"
2#include "TMatrixD.h"
3#include "AliTrackFitterRieman.h"
24d4520d 4#include "AliLog.h"
98937d93 5
6ClassImp(AliTrackFitterRieman)
7
8AliTrackFitterRieman::AliTrackFitterRieman():
9 AliTrackFitter()
10{
11 //
12 // default constructor
13 //
14 fAlpha = 0.;
15 for (Int_t i=0;i<9;i++) fSumXY[i] = 0;
46ae650f 16 fSumYY = 0;
98937d93 17 for (Int_t i=0;i<9;i++) fSumXZ[i] = 0;
46ae650f 18 fSumZZ = 0;
19 fNUsed = 0;
98937d93 20 fConv = kFALSE;
21}
22
23
24AliTrackFitterRieman::AliTrackFitterRieman(AliTrackPointArray *array, Bool_t owner):
25 AliTrackFitter(array,owner)
26{
27 //
28 // Constructor
29 //
30 fAlpha = 0.;
31 for (Int_t i=0;i<9;i++) fSumXY[i] = 0;
46ae650f 32 fSumYY = 0;
98937d93 33 for (Int_t i=0;i<9;i++) fSumXZ[i] = 0;
46ae650f 34 fSumZZ = 0;
35 fNUsed = 0;
98937d93 36 fConv = kFALSE;
37}
38
39AliTrackFitterRieman::AliTrackFitterRieman(const AliTrackFitterRieman &rieman):
40 AliTrackFitter(rieman)
41{
42 //
43 // copy constructor
44 //
45 fAlpha = rieman.fAlpha;
46 for (Int_t i=0;i<9;i++) fSumXY[i] = rieman.fSumXY[i];
46ae650f 47 fSumYY = rieman.fSumYY;
98937d93 48 for (Int_t i=0;i<9;i++) fSumXZ[i] = rieman.fSumXZ[i];
46ae650f 49 fSumZZ = rieman.fSumZZ;
50 fNUsed = rieman.fNUsed;
98937d93 51 fConv = rieman.fConv;
52}
53
54//_____________________________________________________________________________
55AliTrackFitterRieman &AliTrackFitterRieman::operator =(const AliTrackFitterRieman& rieman)
56{
57 // assignment operator
58 //
59 if(this==&rieman) return *this;
60 ((AliTrackFitter *)this)->operator=(rieman);
61
62 fAlpha = rieman.fAlpha;
63 for (Int_t i=0;i<9;i++) fSumXY[i] = rieman.fSumXY[i];
46ae650f 64 fSumYY = rieman.fSumYY;
98937d93 65 for (Int_t i=0;i<9;i++) fSumXZ[i] = rieman.fSumXZ[i];
46ae650f 66 fSumZZ = rieman.fSumZZ;
67 fNUsed = rieman.fNUsed;
98937d93 68 fConv = rieman.fConv;
69
70 return *this;
71}
72
73AliTrackFitterRieman::~AliTrackFitterRieman()
74{
75 // destructor
76 //
77}
78
79void AliTrackFitterRieman::Reset()
80{
81 // Reset the track parameters and
82 // rieman sums
83 AliTrackFitter::Reset();
84 fAlpha = 0.;
85 for (Int_t i=0;i<9;i++) fSumXY[i] = 0;
46ae650f 86 fSumYY = 0;
98937d93 87 for (Int_t i=0;i<9;i++) fSumXZ[i] = 0;
46ae650f 88 fSumZZ = 0;
89 fNUsed = 0;
98937d93 90 fConv =kFALSE;
91}
92
cc345ce3 93Bool_t AliTrackFitterRieman::Fit(const TArrayI *volIds,const TArrayI *volIdsFit,
98937d93 94 AliAlignObj::ELayerID layerRangeMin,
95 AliAlignObj::ELayerID layerRangeMax)
96{
97 // Fit the track points. The method takes as an input
cc345ce3 98 // the set of id's (volids) of the volumes in which
99 // one wants to calculate the residuals.
100 // The following parameters are used to define the
98937d93 101 // range of volumes to be used in the fitting
102 // As a result two AliTrackPointArray's obects are filled.
103 // The first one contains the space points with
cc345ce3 104 // volume id's from volids list. The second array of points represents
105 // the track extrapolations corresponding to the space points
98937d93 106 // in the first array. The two arrays can be used to find
cc345ce3 107 // the residuals in the volids and consequently construct a
98937d93 108 // chi2 function to be minimized during the alignment
109 // procedures. For the moment the track extrapolation is taken
cc345ce3 110 // at the space-point reference plane. The reference plane is
111 // found using the covariance matrix of the point
112 // (assuming sigma(x)=0 at the reference coordinate system.
98937d93 113
46ae650f 114 Reset();
98937d93 115
116 Int_t npoints = fPoints->GetNPoints();
117 if (npoints < 3) return kFALSE;
118
cc345ce3 119 Bool_t isAlphaCalc = kFALSE;
46ae650f 120 AliTrackPoint p,plocal;
cc345ce3 121// fPoints->GetPoint(p,0);
122// fAlpha = TMath::ATan2(p.GetY(),p.GetX());
98937d93 123
124 Int_t npVolId = 0;
46ae650f 125 fNUsed = 0;
98937d93 126 Int_t *pindex = new Int_t[npoints];
cc345ce3 127 fX = new Float_t[npoints];
128 fY = new Float_t[npoints];
129 fZ = new Float_t[npoints];
130 fSy = new Float_t[npoints];
131 fSz = new Float_t[npoints];
98937d93 132 for (Int_t ipoint = 0; ipoint < npoints; ipoint++)
133 {
134 fPoints->GetPoint(p,ipoint);
135 UShort_t iVolId = p.GetVolumeID();
cc345ce3 136 if (FindVolId(volIds,iVolId)) {
98937d93 137 pindex[npVolId] = ipoint;
138 npVolId++;
139 }
cc345ce3 140 if (volIdsFit != 0x0) {
141 if (!FindVolId(volIdsFit,iVolId)) continue;
46ae650f 142 }
143 else {
144 if (iVolId < AliAlignObj::LayerToVolUID(layerRangeMin,0) ||
145 iVolId > AliAlignObj::LayerToVolUID(layerRangeMax,
c041444f 146 AliAlignObj::LayerSize(layerRangeMax))) continue;
46ae650f 147 }
cc345ce3 148 if (!isAlphaCalc) {
149 fAlpha = p.GetAngle();
150 isAlphaCalc = kTRUE;
151 }
46ae650f 152 plocal = p.Rotate(fAlpha);
153 AddPoint(plocal.GetX(),plocal.GetY(),plocal.GetZ(),
154 TMath::Sqrt(plocal.GetCov()[3]),TMath::Sqrt(plocal.GetCov()[5]));
155 fNUsed++;
98937d93 156 }
157
24d4520d 158 if (npVolId == 0 || fNUsed < 3) {
98937d93 159 delete [] pindex;
cc345ce3 160 delete [] fX;
161 delete [] fY;
162 delete [] fZ;
163 delete [] fSy;
164 delete [] fSz;
98937d93 165 return kFALSE;
166 }
167
168 Update();
169
cc345ce3 170 delete [] fX;
171 delete [] fY;
172 delete [] fZ;
173 delete [] fSy;
174 delete [] fSz;
175
98937d93 176 if (!fConv) {
177 delete [] pindex;
178 return kFALSE;
179 }
180
181 if ((fParams[0] == 0) ||
182 ((-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1) <= 0)) {
183 delete [] pindex;
184 return kFALSE;
185 }
186
cc345ce3 187
188 if (fNUsed < fMinNPoints) {
189 delete [] pindex;
190 return kFALSE;
191 }
192
46ae650f 193 fPVolId = new AliTrackPointArray(npVolId);
194 fPTrack = new AliTrackPointArray(npVolId);
98937d93 195 AliTrackPoint p2;
196 for (Int_t ipoint = 0; ipoint < npVolId; ipoint++)
197 {
198 Int_t index = pindex[ipoint];
199 fPoints->GetPoint(p,index);
200 if (GetPCA(p,p2)) {
cc345ce3 201 Float_t xyz[3],xyz2[3];
202 p.GetXYZ(xyz); p2.GetXYZ(xyz2);
203 // printf("residuals %f %d %d %f %f %f %f %f %f\n",fChi2,fNUsed,fConv,xyz[0],xyz[1],xyz[2],xyz2[0]-xyz[0],xyz2[1]-xyz[1],xyz2[2]-xyz[2]);
46ae650f 204 fPVolId->AddPoint(ipoint,&p);
205 fPTrack->AddPoint(ipoint,&p2);
98937d93 206 }
207 }
208
209 delete [] pindex;
210
46ae650f 211 // debug info
212// Float_t chi2 = 0, chi22 = 0;
213// for (Int_t ipoint = 0; ipoint < npoints; ipoint++)
214// {
215// fPoints->GetPoint(p,ipoint);
216// UShort_t iVolId = p.GetVolumeID();
217// if (volIdFit != 0) {
218// if (iVolId != volIdFit) continue;
219// }
220// else {
221// if (iVolId < AliAlignObj::LayerToVolUID(layerRangeMin,0) ||
c041444f 222// iVolId > AliAlignObj::LayerToVolUID(layerRangeMax,AliAlignObj::LayerSize(layerRangeMax))) continue;
46ae650f 223// }
224// plocal = p.Rotate(fAlpha);
225// Float_t delta = (fParams[0]*(plocal.GetX()*plocal.GetX()+plocal.GetY()*plocal.GetY())+
226// 2.*plocal.GetX()*fParams[1]+
227// fParams[2]-
228// 2.*plocal.GetY())/
229// (2.*TMath::Sqrt(plocal.GetCov()[3]));
230// // Float_t delta2 = (fParams[3]+
231// // plocal.GetX()*fParams[4]+
232// // plocal.GetX()*plocal.GetX()*fParams[5]-
233// // plocal.GetZ())/
234// // (TMath::Sqrt(plocal.GetCov()[5]));
235// Double_t r = TMath::Sqrt(plocal.GetX()*plocal.GetX()+plocal.GetY()*plocal.GetY());
236// Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
237// Float_t delta2 = (fParams[3]+
238// r*fParams[4]+r*r*r*fParams[4]*Rm1*Rm1/24-
239// plocal.GetZ())/
240// (TMath::Sqrt(plocal.GetCov()[5]));
241// chi2 += delta*delta;
242// chi22 += delta2*delta2;
243// // printf("pulls %d %d %f %f\n",ipoint,iVolId,delta,delta2);
244
245// }
246// printf("My chi2 = %f + %f = %f\n",chi2,chi22,chi2+chi22);
247
98937d93 248 return kTRUE;
249}
250
251void AliTrackFitterRieman::AddPoint(Float_t x, Float_t y, Float_t z, Float_t sy, Float_t sz)
252{
253 //
254 // Rieman update
255 //
256 //------------------------------------------------------
257 // XY direction
258 //
259 // (x-x0)^2+(y-y0)^2-R^2=0 ===>
260 //
261 // (x^2+y^2 -2*x*x0 - 2*y*y0+ x0^2 -y0^2 -R^2 =0; ==>
262 //
46ae650f 263 // substitution t = 1/(x^2+y^2), u = 2*x*t, v = 2*y*t, D0 = R^2 - x0^2- y0^2
98937d93 264 //
265 // 1 - u*x0 - v*y0 - t *D0 =0 ; - linear equation
266 //
267 // next substition a = 1/y0 b = -x0/y0 c = -D0/y0
268 //
269 // final linear equation : a + u*b +t*c - v =0;
270 //
271 // Minimization :
272 //
273 // sum( (a + ui*b +ti*c - vi)^2)/(sigmai)^2 = min;
274 //
275 // where sigmai is the error of maesurement (a + ui*b +ti*c - vi)
276 //
277 // neglecting error of xi, and supposing xi>>yi sigmai ~ sigmaVi ~ 2*sigmay*t
278 //
cc345ce3 279 fX[fNUsed] = x; fY[fNUsed]=y; fZ[fNUsed]=z; fSy[fNUsed]=sy; fSz[fNUsed]=sz;
98937d93 280 //
281 // XY part
282 //
283 Double_t t = x*x+y*y;
284 if (t<2) return;
285 t = 1./t;
286 Double_t u = 2.*x*t;
287 Double_t v = 2.*y*t;
288 Double_t error = 2.*sy*t;
289 error *=error;
290 Double_t weight = 1./error;
291 fSumXY[0] +=weight;
292 fSumXY[1] +=u*weight; fSumXY[2]+=v*weight; fSumXY[3]+=t*weight;
293 fSumXY[4] +=u*u*weight; fSumXY[5]+=t*t*weight;
294 fSumXY[6] +=u*v*weight; fSumXY[7]+=u*t*weight; fSumXY[8]+=v*t*weight;
46ae650f 295 fSumYY += v*v*weight;
98937d93 296 //
297 // XZ part
298 //
cc345ce3 299 if (1) {
46ae650f 300 weight = 1./(sz*sz);
cc345ce3 301// fSumXZ[0] +=weight;
302// fSumXZ[1] +=weight*x; fSumXZ[2] +=weight*x*x; fSumXZ[3] +=weight*x*x*x; fSumXZ[4] += weight*x*x*x*x;
303// fSumXZ[5] +=weight*z; fSumXZ[6] +=weight*x*z; fSumXZ[7] +=weight*x*x*z;
46ae650f 304 fSumZZ += z*z*weight;
305 }
306 else {
307 weight = 1./(sz*sz);
308 fSumXZ[0] +=weight;
309 Double_t r = TMath::Sqrt(x*x+y*y);
310 fSumXZ[1] +=weight*r; fSumXZ[2] +=weight*r*r; fSumXZ[3] +=weight*z; fSumXZ[4] += weight*r*z;
311 // Now the auxulary sums
312 fSumXZ[5] +=weight*r*r*r/24; fSumXZ[6] +=weight*r*r*r*r/12; fSumXZ[7] +=weight*r*r*r*z/24;
313 fSumXZ[8] +=weight*r*r*r*r*r*r/(24*24);
314 fSumZZ += z*z*weight;
315 }
98937d93 316}
317
318void AliTrackFitterRieman::Update(){
319 //
320 // Rieman update
321 //
322 //
323 for (Int_t i=0;i<6;i++)fParams[i]=0;
46ae650f 324 fChi2 = 0;
325 fNdf = 0;
98937d93 326 Int_t conv=0;
327 //
328 // XY part
329 //
330 TMatrixDSym smatrix(3);
331 TMatrixD sums(1,3);
332 //
333 // smatrix(0,0) = s0; smatrix(1,1)=su2; smatrix(2,2)=st2;
334 // smatrix(0,1) = su; smatrix(0,2)=st; smatrix(1,2)=sut;
335 // sums(0,0) = sv; sums(0,1)=suv; sums(0,2)=svt;
336
337 smatrix(0,0) = fSumXY[0]; smatrix(1,1)=fSumXY[4]; smatrix(2,2)=fSumXY[5];
338 smatrix(0,1) = fSumXY[1]; smatrix(0,2)=fSumXY[3]; smatrix(1,2)=fSumXY[7];
339 sums(0,0) = fSumXY[2]; sums(0,1) =fSumXY[6]; sums(0,2) =fSumXY[8];
340 smatrix.Invert();
341 if (smatrix.IsValid()){
342 for (Int_t i=0;i<3;i++)
343 for (Int_t j=0;j<=i;j++){
344 (*fCov)(i,j)=smatrix(i,j);
345 }
346 TMatrixD res = sums*smatrix;
347 fParams[0] = res(0,0);
348 fParams[1] = res(0,1);
349 fParams[2] = res(0,2);
46ae650f 350 TMatrixD tmp = res*sums.T();
351 fChi2 += fSumYY - tmp(0,0);
352 fNdf += fNUsed - 3;
98937d93 353 conv++;
354 }
355 //
356 // XZ part
357 //
cc345ce3 358 if (1) {
359 Double_t x0 = -fParams[1]/fParams[0];
360 Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
361
362 for (Int_t i=0;i<fNUsed;i++){
363 Double_t phi = TMath::ASin((fX[i]-x0)*Rm1);
364 Double_t phi0 = TMath::ASin((0.-x0)*Rm1);
365 Double_t weight = 1/fSz[i];
366 weight *=weight;
367 Double_t dphi = (phi-phi0)/Rm1;
368 fSumXZ[0] +=weight;
369 fSumXZ[1] +=weight*dphi;
370 fSumXZ[2] +=weight*dphi*dphi;
371 fSumXZ[3] +=weight*fZ[i];
372 fSumXZ[4] +=weight*dphi*fZ[i];
373 }
374
375 TMatrixDSym smatrixz(2);
376 smatrixz(0,0) = fSumXZ[0]; smatrixz(0,1) = fSumXZ[1]; smatrixz(1,1) = fSumXZ[2];
46ae650f 377 smatrixz.Invert();
cc345ce3 378 TMatrixD sumsxz(1,2);
46ae650f 379 if (smatrixz.IsValid()){
cc345ce3 380 sumsxz(0,0) = fSumXZ[3];
381 sumsxz(0,1) = fSumXZ[4];
46ae650f 382 TMatrixD res = sumsxz*smatrixz;
383 fParams[3] = res(0,0);
384 fParams[4] = res(0,1);
cc345ce3 385 fParams[5] = 0;
386 for (Int_t i=0;i<2;i++)
46ae650f 387 for (Int_t j=0;j<=i;j++){
cc345ce3 388 (*fCov)(i+3,j+3)=smatrixz(i,j);
46ae650f 389 }
390 TMatrixD tmp = res*sumsxz.T();
391 fChi2 += fSumZZ - tmp(0,0);
cc345ce3 392 fNdf += fNUsed - 2;
46ae650f 393 conv++;
394 }
395 }
396 else {
397 Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
398 fSumXZ[1] += fSumXZ[5]*Rm1*Rm1;
399 fSumXZ[2] += fSumXZ[6]*Rm1*Rm1 + fSumXZ[8]*Rm1*Rm1*Rm1*Rm1;
400 fSumXZ[4] += fSumXZ[7]*Rm1*Rm1;
401
402 TMatrixDSym smatrixz(2);
403 smatrixz(0,0) = fSumXZ[0]; smatrixz(0,1) = fSumXZ[1]; smatrixz(1,1) = fSumXZ[2];
404 smatrixz.Invert();
405 TMatrixD sumsxz(1,2);
406 if (smatrixz.IsValid()){
407 sumsxz(0,0) = fSumXZ[3];
408 sumsxz(0,1) = fSumXZ[4];
409 TMatrixD res = sumsxz*smatrixz;
410 fParams[3] = res(0,0);
411 fParams[4] = res(0,1);
412 fParams[5] = 0;
413 for (Int_t i=0;i<2;i++)
414 for (Int_t j=0;j<=i;j++){
415 (*fCov)(i+3,j+3)=smatrixz(i,j);
416 }
417 TMatrixD tmp = res*sumsxz.T();
418 fChi2 += fSumZZ - tmp(0,0);
419 fNdf += fNUsed - 2;
420 conv++;
98937d93 421 }
98937d93 422 }
423
424 // (x-x0)^2+(y-y0)^2-R^2=0 ===>
425 //
426 // (x^2+y^2 -2*x*x0 - 2*y*y0+ x0^2 -y0^2 -R^2 =0; ==>
427 // substitution t = 1/(x^2+y^2), u = 2*x*t, y = 2*y*t, D0 = R^2 - x0^2- y0^2
428 //
429 // 1 - u*x0 - v*y0 - t *D0 =0 ; - linear equation
430 //
431 // next substition a = 1/y0 b = -x0/y0 c = -D0/y0
432 // final linear equation : a + u*b +t*c - v =0;
433 //
434 // fParam[0] = 1/y0
435 // fParam[1] = -x0/y0
436 // fParam[2] = - (R^2 - x0^2 - y0^2)/y0
437 if (conv>1) fConv =kTRUE;
438 else
439 fConv=kFALSE;
440}
441
442Double_t AliTrackFitterRieman::GetYat(Double_t x){
443 if (!fConv) return 0.;
444 Double_t res2 = (x*fParams[0]+fParams[1]);
445 res2*=res2;
446 res2 = 1.-fParams[2]*fParams[0]+fParams[1]*fParams[1]-res2;
447 if (res2<0) return 0;
448 res2 = TMath::Sqrt(res2);
449 res2 = (1-res2)/fParams[0];
450 return res2;
451}
452
cc345ce3 453Double_t AliTrackFitterRieman::GetDYat(Double_t x) const {
98937d93 454 if (!fConv) return 0.;
455 Double_t x0 = -fParams[1]/fParams[0];
456 if (-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1<0) return 0;
457 Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
458 if ( 1./(Rm1*Rm1)-(x-x0)*(x-x0)<=0) return 0;
459 Double_t res = (x-x0)/TMath::Sqrt(1./(Rm1*Rm1)-(x-x0)*(x-x0));
460 if (fParams[0]<0) res*=-1.;
461 return res;
462}
463
464
465
cc345ce3 466Double_t AliTrackFitterRieman::GetZat(Double_t x) const {
98937d93 467 if (!fConv) return 0.;
468 Double_t x0 = -fParams[1]/fParams[0];
469 if (-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1<=0) return 0;
470 Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
471 Double_t phi = TMath::ASin((x-x0)*Rm1);
472 Double_t phi0 = TMath::ASin((0.-x0)*Rm1);
473 Double_t dphi = (phi-phi0);
474 Double_t res = fParams[3]+fParams[4]*dphi/Rm1;
475 return res;
476}
477
cc345ce3 478Double_t AliTrackFitterRieman::GetDZat(Double_t x) const {
98937d93 479 if (!fConv) return 0.;
480 Double_t x0 = -fParams[1]/fParams[0];
481 if (-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1<=0) return 0;
482 Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
483 Double_t res = fParams[4]/TMath::Cos(TMath::ASin((x-x0)*Rm1));
484 return res;
485}
486
487
488Double_t AliTrackFitterRieman::GetC(){
489 return fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
490}
491
492Bool_t AliTrackFitterRieman::GetXYZat(Double_t r, Float_t *xyz){
493 if (!fConv) return kFALSE;
494 Double_t res2 = (r*fParams[0]+fParams[1]);
495 res2*=res2;
496 res2 = 1.-fParams[2]*fParams[0]+fParams[1]*fParams[1]-res2;
497 if (res2<0) return kFALSE;
498 res2 = TMath::Sqrt(res2);
499 res2 = (1-res2)/fParams[0];
500
501 if (!fConv) return kFALSE;
502 Double_t x0 = -fParams[1]/fParams[0];
503 if (-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1<=0) return 0;
504 Double_t Rm1 = fParams[0]/TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1);
505 Double_t phi = TMath::ASin((r-x0)*Rm1);
506 Double_t phi0 = TMath::ASin((0.-x0)*Rm1);
507 Double_t dphi = (phi-phi0);
508 Double_t res = fParams[3]+fParams[4]*dphi/Rm1;
509
510 Double_t sin = TMath::Sin(fAlpha);
511 Double_t cos = TMath::Cos(fAlpha);
512 xyz[0] = r*cos - res2*sin;
513 xyz[1] = res2*cos + r*sin;
514 xyz[2] = res;
515
516 return kTRUE;
517}
518
519Bool_t AliTrackFitterRieman::GetPCA(const AliTrackPoint &p, AliTrackPoint &p2) const
520{
521 // Get the closest to a given spacepoint track trajectory point
522 // Look for details in the description of the Fit() method
523
524 if (!fConv) return kFALSE;
525
526 // First X and Y coordinates
527 Double_t sin = TMath::Sin(fAlpha);
528 Double_t cos = TMath::Cos(fAlpha);
529 // fParam[0] = 1/y0
530 // fParam[1] = -x0/y0
531 // fParam[2] = - (R^2 - x0^2 - y0^2)/y0
532 if (fParams[0] == 0) return kFALSE;
cc345ce3 533 // Track parameters in the global coordinate system
98937d93 534 Double_t x0 = -fParams[1]/fParams[0]*cos - 1./fParams[0]*sin;
535 Double_t y0 = 1./fParams[0]*cos - fParams[1]/fParams[0]*sin;
536 if ((-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1) <= 0) return kFALSE;
537 Double_t R = TMath::Sqrt(-fParams[2]*fParams[0]+fParams[1]*fParams[1]+1)/
538 fParams[0];
539
cc345ce3 540 // Define space-point refence plane
541 Double_t alphap = p.GetAngle();
542 Double_t sinp = TMath::Sin(alphap);
543 Double_t cosp = TMath::Cos(alphap);
544 Double_t x = p.GetX()*cosp + p.GetY()*sinp;
545 Double_t y = p.GetY()*cosp - p.GetX()*sinp;
546 Double_t x0p= x0*cosp + y0*sinp;
547 Double_t y0p= y0*cosp - x0*sinp;
24d4520d 548 if ((R*R - (x-x0p)*(x-x0p))<0) {
549 AliWarning(Form("Track extrapolation failed ! (Track radius = %f, track circle x = %f, space-point x = %f, reference plane angle = %f\n",R,x0p,x,alphap));
550 return kFALSE;
551 }
cc345ce3 552 Double_t temp = TMath::Sqrt(R*R - (x-x0p)*(x-x0p));
553 Double_t y1 = y0p + temp;
554 Double_t y2 = y0p - temp;
555 Double_t yprime = y1;
556 if(TMath::Abs(y2-y) < TMath::Abs(y1-y)) yprime = y2;
557
558 // Back to the global coordinate system
559 Double_t xsecond = x*cosp - yprime*sinp;
560 Double_t ysecond = yprime*cosp + x*sinp;
561
562 // Now Z coordinate and track angles
563 Double_t x2 = xsecond*cos + ysecond*sin;
564 Double_t zsecond = GetZat(x2);
565 Double_t dydx = GetDYat(x2);
566 Double_t dzdx = GetDZat(x2);
567
568 // Fill the cov matrix of the track extrapolation point
569 Double_t cov[6] = {0,0,0,0,0,0};
570 Double_t sigmax = 100*100.;
571 cov[0] = sigmax; cov[1] = sigmax*dydx; cov[2] = sigmax*dzdx;
572 cov[3] = sigmax*dydx*dydx; cov[4] = sigmax*dydx*dzdx;
573 cov[5] = sigmax*dzdx*dzdx;
574
575 Float_t newcov[6];
576 newcov[0] = cov[0]*cos*cos-
577 2*cov[1]*sin*cos+
578 cov[3]*sin*sin;
579 newcov[1] = cov[1]*(cos*cos-sin*sin)-
580 (cov[3]-cov[0])*sin*cos;
581 newcov[2] = cov[2]*cos-
582 cov[4]*sin;
583 newcov[3] = cov[0]*sin*sin+
584 2*cov[1]*sin*cos+
585 cov[3]*cos*cos;
586 newcov[4] = cov[4]*cos+
587 cov[2]*sin;
588 newcov[5] = cov[5];
589
590 p2.SetXYZ(xsecond,ysecond,zsecond,newcov);
98937d93 591
592 return kTRUE;
593}