3 #include "AliITSUSeed.h"
5 #include "AliESDtrack.h"
10 //_________________________________________________________________________
11 AliITSUSeed::AliITSUSeed()
23 //_________________________________________________________________________
24 AliITSUSeed::~AliITSUSeed()
29 //_________________________________________________________________________
30 AliITSUSeed::AliITSUSeed(const AliITSUSeed& src)
31 :AliExternalTrackParam(src)
32 ,fHitsPattern(src.fHitsPattern)
34 ,fChi2Glo(src.fChi2Glo)
36 ,fChi2Penalty(src.fChi2Penalty)
40 for (int i=kNFElem;i--;) fFMatrix[i] = src.fFMatrix[i];
41 for (int i=kNKElem;i--;) fKMatrix[i] = src.fKMatrix[i];
42 for (int i=kNRElem;i--;) fRMatrix[i] = src.fRMatrix[i];
43 fResid[0]=src.fResid[0];
44 fResid[1]=src.fResid[1];
45 fCovIYZ[0]=src.fCovIYZ[0];
46 fCovIYZ[1]=src.fCovIYZ[1];
47 fCovIYZ[2]=src.fCovIYZ[2];
51 //_________________________________________________________________________
52 AliITSUSeed &AliITSUSeed::operator=(const AliITSUSeed& src)
55 if (this == &src) return *this;
57 new(this) AliITSUSeed(src);
61 //_________________________________________________________________________
62 void AliITSUSeed::Print(Option_t* opt) const
65 int lr,cl = GetLrCluster(lr);
66 printf("%cLr%d Cl:%4d Chi2Glo:%7.2f(%7.2f) Chi2Cl:%7.2f Penalty: %7.2f",IsKilled() ? '-':' ',
67 lr,cl,GetChi2Glo(),GetChi2GloNrm(),GetChi2Cl(), GetChi2Penalty());
70 const AliITSUSeed *sdc = this;
72 if (lrc<lr) printf(".");
74 sdc = sdc->GetParent(lrc);
76 printf("%c",sdc->GetClusterID()<0 ? '.': (sdc->IsFake() ? '-':'+'));
81 TString opts = opt; opts.ToLower();
82 if (opts.Contains("etp")) AliExternalTrackParam::Print();
83 if (opts.Contains("parent") && GetParent()) GetParent()->Print(opt);
86 //______________________________________________________________________________
87 void AliITSUSeed::InitFromESDTrack(const AliESDtrack* esdTr)
89 // init seed from ESD track
91 AliExternalTrackParam::operator=(*esdTr);
95 fChi2Glo = fChi2Cl = fChi2Penalty = 0;
100 //______________________________________________________________________________
101 Float_t AliITSUSeed::GetChi2GloNrm() const
103 int ndf = 2*GetNLayersHit() - 5;
104 return (ndf>0 ? fChi2Glo/ndf : fChi2Glo) + fChi2Penalty;
108 //______________________________________________________________________________
109 Int_t AliITSUSeed::Compare(const TObject* obj) const
111 // compare clusters accodring to specific mode
112 const AliITSUSeed* sd = (const AliITSUSeed*)obj;
113 const Float_t kTol = 1e-5;
114 if (!IsKilled() && sd->IsKilled()) return -1;
115 if ( IsKilled() &&!sd->IsKilled()) return 1;
117 float chi2This = GetChi2GloNrm();
118 float chi2Other = sd->GetChi2GloNrm();
120 if (chi2This+kTol<chi2Other) return -1;
121 else if (chi2This-kTol>chi2Other) return 1;
125 //______________________________________________________________________________
126 Bool_t AliITSUSeed::IsEqual(const TObject* obj) const
128 // compare clusters accodring to specific mode
129 const AliITSUSeed* sd = (const AliITSUSeed*)obj;
130 const Float_t kTol = 1e-5;
131 if (IsKilled() != sd->IsKilled()) return kFALSE;
132 return Abs(GetChi2GloNrm() - sd->GetChi2GloNrm())<kTol;
135 //______________________________________________________________________________
136 Bool_t AliITSUSeed::PropagateToX(Double_t xk, Double_t b)
138 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
140 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
142 Double_t crv=GetC(b);
143 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
144 Double_t x2r = crv*dx;
145 Double_t f1=fP[2], f2=f1 + x2r;
146 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
147 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
148 if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
150 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
153 &fC10=fC[1], &fC11=fC[2],
154 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
155 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
156 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
158 Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
159 if (TMath::Abs(r1)<kAlmost0) return kFALSE;
160 if (TMath::Abs(r2)<kAlmost0) return kFALSE;
163 double dy2dx = (f1+f2)/(r1+r2);
165 if (TMath::Abs(x2r)<0.05) {
166 fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov !
170 // for small dx/R the linear apporximation of the arc by the segment is OK,
171 // but at large dx/R the error is very large and leads to incorrect Z propagation
172 // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
173 // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
174 // Similarly, the rotation angle in linear in dx only for dx<<R
175 double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
176 double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
178 fP2 = TMath::Sin(rot + TMath::ASin(fP2));
186 double v0 = 1. + dy2dx*tg2;
187 double v1 = (r1i+r2i)*(dy2dx*(tg1+tg2)+2);
188 double v2 = (r1i+r2i)*v0;
190 double f24 = dx*crv/fP4;
192 double f04 = dx*v2*f24;
193 double f12 = dx*fP3* (f2*v1+dy2dx-tg2);
194 double f13 = dx*r2*v0;
195 double f14 = dx*f24*fP3*(f2*v2+dy2dx-tg2);
198 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
199 Double_t b02=f24*fC40;
200 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
201 Double_t b12=f24*fC41;
202 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
203 Double_t b22=f24*fC42;
204 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
205 Double_t b42=f24*fC44;
206 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
207 Double_t b32=f24*fC43;
210 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
211 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
212 Double_t a22=f24*b42;
214 //F*C*Ft = C + (b + bt + a)
215 fC00 += b00 + b00 + a00;
216 fC10 += b10 + b01 + a01;
217 fC20 += b20 + b02 + a02;
220 fC11 += b11 + b11 + a11;
221 fC21 += b21 + b12 + a12;
224 fC22 += b22 + b22 + a22;
228 // update stored transformation matrix F = Fnew*Fold
229 fFMatrix[kF04] += f04 + f24*fFMatrix[kF02];
230 fFMatrix[kF14] += f14 + f24*fFMatrix[kF12];
231 fFMatrix[kF02] += f02;
232 fFMatrix[kF12] += f12;
233 fFMatrix[kF13] += f13;
234 fFMatrix[kF24] += f24;
241 //______________________________________________________________________________
242 Bool_t AliITSUSeed::RotateToAlpha(Double_t alpha)
244 // Transform this track to the local coord. system rotated
245 // by angle "alpha" (rad) with respect to the global coord. system.
247 if (TMath::Abs(fP[2]) >= kAlmost1) {
248 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
252 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
253 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
257 Double_t &fC00=fC[0];
258 Double_t &fC10=fC[1];
259 Double_t &fC20=fC[3];
260 Double_t &fC21=fC[4];
261 Double_t &fC22=fC[5];
262 Double_t &fC30=fC[6];
263 Double_t &fC32=fC[8];
264 Double_t &fC40=fC[10];
265 Double_t &fC42=fC[12];
268 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
269 Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
270 // RS: check if rotation does no invalidate track model (cos(local_phi)>=0, i.e. particle
271 // direction in local frame is along the X axis
272 if ((cf*ca+sf*sa)<0) {
273 AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa));
277 Double_t tmp=sf*ca - cf*sa;
279 if (TMath::Abs(tmp) >= kAlmost1) {
280 if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
281 AliWarning(Form("Rotation failed ! %.10e",tmp));
289 if (TMath::Abs(cf)<kAlmost0) {
290 AliError(Form("Too small cosine value %f",cf));
294 Double_t rr=(ca+sf/cf*sa);
314 //______________________________________________________________________________
315 Bool_t AliITSUSeed::GetTrackingXAtXAlpha(double xOther, double alpOther, double bz, double &xdst)
317 // calculate X and Y in the tracking frame of the track, corresponding to other X,Alpha tracking
318 double ca=TMath::Cos(alpOther-fAlpha), sa=TMath::Sin(alpOther-fAlpha);
319 double &y=fP[0], &sf=fP[2], cf=Sqrt((1.-sf)*(1.+sf));
320 double eta = xOther - fX*ca - y*sa;
321 double xi = sf*ca - cf*sa;
322 if (Abs(xi)>= kAlmost1) return kFALSE;
323 double nu = xi + GetC(bz)*eta;
324 if (Abs(nu)>= kAlmost1) return kFALSE;
325 xdst = xOther*ca - sa*( y*ca-fX*sa + eta*(xi+nu)/(Sqrt((1.-xi)*(1.+xi)) + Sqrt((1.-nu)*(1.+nu))) );
329 //____________________________________________________________________
330 Double_t AliITSUSeed::GetPredictedChi2(Double_t p[2],Double_t cov[3])
332 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
333 // Store info needed for update and smoothing
334 Double_t sdd = fC[0] + cov[0];
335 Double_t sdz = fC[1] + cov[1];
336 Double_t szz = fC[2] + cov[2];
337 Double_t det = sdd*szz - sdz*sdz;
338 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
340 fCovIYZ[0] = szz*det;
341 fCovIYZ[1] = -sdz*det;
342 fCovIYZ[2] = sdd*det;
343 double &dy = fResid[0] = p[0] - fP[0];
344 double &dz = fResid[1] = p[1] - fP[1];
346 return dy*(dy*fCovIYZ[0]+dz*fCovIYZ[1]) + dz*(dy*fCovIYZ[1]+dz*(fCovIYZ[2]));
350 //____________________________________________________________________
351 Bool_t AliITSUSeed::Update()
353 // Update the track parameters with the measurement stored during GetPredictedChi2
355 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4],
357 &fC10=fC[kS10], &fC11=fC[kS11],
358 &fC20=fC[kS20], &fC21=fC[kS21], &fC22=fC[kS22],
359 &fC30=fC[kS30], &fC31=fC[kS31], &fC32=fC[kS32], &fC33=fC[kS33],
360 &fC40=fC[kS40], &fC41=fC[kS41], &fC42=fC[kS42], &fC43=fC[kS43], &fC44=fC[kS44];
362 double &r00=fCovIYZ[0],&r01=fCovIYZ[1],&r11=fCovIYZ[2];
363 double &dy=fResid[0], &dz=fResid[1];
365 // store info needed for smoothing in the fKMatrix
366 double &k00 = fKMatrix[kK00] = fC00*r00+fC10*r01;
367 double &k01 = fKMatrix[kK01] = fC00*r01+fC10*r11;
368 double &k10 = fKMatrix[kK10] = fC10*r00+fC11*r01;
369 double &k11 = fKMatrix[kK11] = fC10*r01+fC11*r11;
370 double &k20 = fKMatrix[kK20] = fC20*r00+fC21*r01;
371 double &k21 = fKMatrix[kK21] = fC20*r01+fC21*r11;
372 double &k30 = fKMatrix[kK30] = fC30*r00+fC31*r01;
373 double &k31 = fKMatrix[kK31] = fC30*r01+fC31*r11;
374 double &k40 = fKMatrix[kK40] = fC40*r00+fC41*r01;
375 double &k41 = fKMatrix[kK41] = fC40*r01+fC41*r11;
377 Double_t sf=fP2 + k20*dy + k21*dz;
378 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
380 fP0 += k00*dy + k01*dz;
381 fP1 += k10*dy + k11*dz;
383 fP3 += k30*dy + k31*dz;
384 fP4 += k40*dy + k41*dz;
386 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
387 Double_t c12=fC21, c13=fC31, c14=fC41;
389 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
390 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
391 fC40-=k00*c04+k01*c14;
393 fC11-=k10*c01+k11*fC11;
394 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
395 fC41-=k10*c04+k11*c14;
397 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
398 fC42-=k20*c04+k21*c14;
400 fC33-=k30*c03+k31*c13;
401 fC43-=k30*c04+k31*c14;
403 fC44-=k40*c04+k41*c14;
411 //____________________________________________________________________
412 Bool_t AliITSUSeed::Smooth(Double_t vecL[5],Double_t matL[15])
414 // Prepare MBF smoothing auxiliary params for smoothing at prev. point:
417 // \tilde{l_j} = -H_j^T N_{j}^{-1} z_j + B_{j}^T \hat{l_j}
418 // \tilde{L_j} = H_j^T N_{j}^{-1} H_j + B_j^T \hat{L_j} B_j
419 // \hat{l_j} = F_j^T \tilde{l_{j+1}}
420 // \hat{L_j} = F_j^T \tilde{L_{j+1}} F_j
422 // P_{j/N} = P_{j/j} - P_{j/j} \hat{L_j} P_{j/j}
423 // \hat{x_{j/N}} = \hat{x_{j/j}} - P_{j/j} \hat{l_j}
428 // H = {{1,0,0,0,0},{0,1,0,0,0}}
432 if (GetClusterID()<0) return kTRUE;
436 &k00=fKMatrix[kK00],&k01=fKMatrix[kK01],
437 &k10=fKMatrix[kK10],&k11=fKMatrix[kK11],
438 &k20=fKMatrix[kK20],&k21=fKMatrix[kK21],
439 &k30=fKMatrix[kK30],&k31=fKMatrix[kK31],
440 &k40=fKMatrix[kK40],&k41=fKMatrix[kK41];
443 &l10=matL[kS10], &l11=matL[kS11],
444 &l20=matL[kS20], &l21=matL[kS21], &l22=matL[kS22],
445 &l30=matL[kS30], &l31=matL[kS31], &l32=matL[kS32], &l33=matL[kS33],
446 &l40=matL[kS40], &l41=matL[kS41], &l42=matL[kS42], &l43=matL[kS43], &l44=matL[kS44];
448 // calculate correction
449 double corrVec[5]={0},corrMat[15]={0};
450 corrVec[0] = fC[kS00]*vecL[0] + fC[kS10]*vecL[1] + fC[kS20]*vecL[2] + fC[kS30]*vecL[3] + fC[kS40]*vecL[4];
451 corrVec[1] = fC[kS10]*vecL[0] + fC[kS11]*vecL[1] + fC[kS21]*vecL[2] + fC[kS31]*vecL[3] + fC[kS41]*vecL[4];
452 corrVec[2] = fC[kS20]*vecL[0] + fC[kS21]*vecL[1] + fC[kS22]*vecL[2] + fC[kS32]*vecL[3] + fC[kS42]*vecL[4];
453 corrVec[3] = fC[kS30]*vecL[0] + fC[kS31]*vecL[1] + fC[kS32]*vecL[2] + fC[kS33]*vecL[3] + fC[kS43]*vecL[4];
454 corrVec[4] = fC[kS40]*vecL[0] + fC[kS41]*vecL[1] + fC[kS42]*vecL[2] + fC[kS43]*vecL[3] + fC[kS44]*vecL[4];
456 double *crm = ProdABA(fC,matL);
457 for (int i=0;i<15;i++) corrMat[i] = crm[i];
459 double vcL0 = vecL[0], vcL1 = vecL[1];
460 vecL[0] -= k00*vcL0+k10*vcL1+k20*vecL[2]+k30*vecL[3]+k40*vecL[4] + fCovIYZ[0]*fResid[0] + fCovIYZ[1]*fResid[1];
461 vecL[1] -= k01*vcL0+k11*vcL1+k21*vecL[2]+k31*vecL[3]+k41*vecL[4] + fCovIYZ[1]*fResid[0] + fCovIYZ[2]*fResid[1];
464 double vcL0 = vecL[0], vcL1 = vecL[1];
465 vecL[0] -= k00*vcL0+k10*vcL1+fKMatrix[kK20]*vecL[2]+k30*vecL[3]+k40*vecL[4] + fCovIYZ[0]*fResid[0] + fCovIYZ[1]*fResid[1];
466 vecL[1] -= k01*vcL0+fKMatrix[kK11]*vcL1+k21*vecL[2]+k31*vecL[3]+k41*vecL[4] + fCovIYZ[1]*fResid[0] + fCovIYZ[2]*fResid[1];
467 vecL[3] += fFMatrix[kF13]*vecL[1];
468 vecL[4] = fFMatrix[kF04]*vecL[0] + fFMatrix[kF14]*vecL[1] + fFMatrix[kF24]*vecL[2] + fFMatrix[kF44]*vecL[4];
469 vecL[2] += fFMatrix[kF02]*vecL[0] + fFMatrix[kF12]*vecL[1];
472 // and \hat{l_j} in one go
474 // L = H^T * sg * H + (I-KH)^T * L * (I - KH)
475 double v00 = k00*l00+k10*l10+k20*l20+k30*l30+k40*l40;
476 double v10 = k00*l10+k10*l11+k20*l21+k30*l31+k40*l41;
477 double v20 = k00*l20+k10*l21+k20*l22+k30*l32+k40*l42;
478 double v30 = k00*l30+k10*l31+k20*l32+k30*l33+k40*l43;
479 double v40 = k00*l40+k10*l41+k20*l42+k30*l43+k40*l44;
481 double v01 = k01*l00+k11*l10+k21*l20+k31*l30+k41*l40;
482 double v11 = k01*l10+k11*l11+k21*l21+k31*l31+k41*l41;
483 double v21 = k01*l20+k11*l21+k21*l22+k31*l32+k41*l42;
484 double v31 = k01*l30+k11*l31+k21*l32+k31*l33+k41*l43;
485 double v41 = k01*l40+k11*l41+k21*l42+k31*l43+k41*l44;
487 // (H^T * K^T * L * K * H) - (L * K * H) - (H^T * K^T * L) + (H^T*N^-1*H)
488 l00 += k00*v00 + k10*v10 + k20*v20 + k30*v30 + k40*v40 - v00 - v00 + fCovIYZ[0];
489 l10 += k01*v00 + k11*v10 + k21*v20 + k31*v30 + k41*v40 - v01 - v10 + fCovIYZ[1];
490 l11 += k01*v01 + k11*v11 + k21*v21 + k31*v31 + k41*v41 - v11 - v11 + fCovIYZ[2];
500 printf("%+e\n%+e %+e\n%+e %+e %+e\n%+e %+e %+e %+e\n%+e %+e %+e %+e %+e\n",
501 corrMat[kS00],corrMat[kS10],corrMat[kS11],corrMat[kS20],corrMat[kS21],corrMat[kS22],
502 corrMat[kS30],corrMat[kS31],corrMat[kS32],corrMat[kS33],
503 corrMat[kS40],corrMat[kS41],corrMat[kS42],corrMat[kS43],corrMat[kS44]);
505 printf("SMcorr: %+e %+e %+e %+e %+e\n",corrVec[0],corrVec[1],corrVec[2],corrVec[3],corrVec[4]);
507 printf("State : "); this->AliExternalTrackParam::Print("");
509 printf("\nBefore transport back (RotElems: %+e %+e)\n",fRMatrix[kR00],fRMatrix[kR22]);
510 printf("Res: %+e %+e | Err: %+e %+e %+e\n",fResid[0],fResid[1],fCovIYZ[0],fCovIYZ[1],fCovIYZ[2]);
511 printf("Lr%d VecL: ",GetLayerID()); for (int i=0;i<5;i++) printf("%+e ",vecL[i]); printf("\n");
513 printf("%+e\n%+e %+e\n%+e %+e %+e\n%+e %+e %+e %+e\n%+e %+e %+e %+e %+e\n",
514 matL[kS00],matL[kS10],matL[kS11],matL[kS20],matL[kS21],matL[kS22],
515 matL[kS30],matL[kS31],matL[kS32],matL[kS33],matL[kS40],matL[kS41],matL[kS42],matL[kS43],matL[kS44]);
517 printf("F: "); for (int i=0;i<kNFElem;i++) printf("%+e ",fFMatrix[i]); printf("\n");
518 printf("K: "); for (int i=0;i<kNKElem;i++) printf("%+e ",fKMatrix[i]); printf("\n");
520 // apply rotation matrix (diagonal)
521 vecL[0] *= fRMatrix[kR00];
522 vecL[2] *= fRMatrix[kR22];
524 l00 *= fRMatrix[kR00]*fRMatrix[kR00];
525 l10 *= fRMatrix[kR00];
526 l20 *= fRMatrix[kR22]*fRMatrix[kR00];
527 l21 *= fRMatrix[kR22];
528 l22 *= fRMatrix[kR22]*fRMatrix[kR22];
529 l30 *= fRMatrix[kR00];
530 l32 *= fRMatrix[kR22];
531 l40 *= fRMatrix[kR00];
532 l42 *= fRMatrix[kR22];
534 // Apply translation matrix F^T. Note, that fFMatrix keeps non-trivial elems of F-1 = f, except the e-loss coeff f44
535 // We need F^T*L* F = L + (L*f) + (L*f)^T + f^T * (L*f)
538 &f02=fFMatrix[kF02],&f04=fFMatrix[kF04],
539 &f12=fFMatrix[kF12],&f13=fFMatrix[kF13],&f14=fFMatrix[kF14],
543 vecL[4] = f04*vecL[0]+f14*vecL[1]+f24*vecL[2]+f44*vecL[4];
544 vecL[3] += f13*vecL[1];
545 vecL[2] += f02*vecL[0]+f12*vecL[1];
550 Double_t b02=l00*f02+l10*f12, b03=l10*f13, b04=l00*f04+l10*f14+l20*f24+l40*f44;
551 Double_t b12=l10*f02+l11*f12, b13=l11*f13, b14=l10*f04+l11*f14+l21*f24+l41*f44;
552 Double_t b22=l20*f02+l21*f12, b23=l21*f13, b24=l20*f04+l21*f14+l22*f24+l42*f44;
553 Double_t b32=l30*f02+l31*f12, b33=l31*f13, b34=l30*f04+l31*f14+l32*f24+l43*f44;
554 Double_t b42=l40*f02+l41*f12, b43=l41*f13, b44=l40*f04+l41*f14+l42*f24+l44*f44;
556 //a = f^T * b = f^T * L * f, profit from symmetry
557 Double_t a22=f02*b02+f12*b12, a33=f13*b13, a44=f04*b04+f14*b14+f24*b24+f44*b44,
558 a32=f13*b12, //= a23=f02*b03+f12*b13,
559 a42=f02*b04+f12*b14, //f04*b02+f14*b12+f24*b22+f44*b42 = a24
560 a43=f13*b14; //f04*b03+f14*b13+f24*b23+f44*b43 = a34
562 // F^T*L* F = L + (b + b^T + a)
563 l44 += b44 + b44 + a44;
564 l43 += b43 + b34 + a43;
565 l42 += b42 + b24 + a42;
568 l33 += b33 + b33 + a33;
569 l32 += b32 + b23 + a32;
572 l22 += b22 + b23 + a22;
576 printf("After transport back\n");
577 printf("Lr%d VecL: ",GetLayerID()); for (int i=0;i<5;i++) printf("%+e ",vecL[i]); printf("\n");
579 printf("%+e\n%+e %+e\n%+e %+e %+e\n%+e %+e %+e %+e\n%+e %+e %+e %+e %+e\n",
580 matL[kS00],matL[kS10],matL[kS11],matL[kS20],matL[kS21],matL[kS22],
581 matL[kS30],matL[kS31],matL[kS32],matL[kS33],matL[kS40],matL[kS41],matL[kS42],matL[kS43],matL[kS44]);
586 //____________________________________________________________________
587 Double_t* AliITSUSeed::ProdABA(const double a[15],const double b[15]) const
589 // product of symmetric matrices A*B*A
591 const Short_t knd[5][5] = {
592 {kS00,kS10,kS20,kS30,kS40},
593 {kS10,kS11,kS21,kS31,kS41},
594 {kS20,kS21,kS22,kS32,kS42},
595 {kS30,kS31,kS32,kS33,kS43},
596 {kS40,kS41,kS42,kS43,kS44}
599 static double aba[15];
602 for (int i=5;i--;) for (int j=5;j--;) {
604 for (int k=5;k--;) ba[i][j] += b[knd[i][k]]*a[knd[k][j]];
607 // 2) A * ba, lower triangle only
608 for (int i=5;i--;) for (int j=i+1;j--;) {
610 for (int k=5;k--;) aba[knd[i][j]] += a[knd[i][k]]*ba[k][j];
617 //____________________________________________________________________
618 Bool_t AliITSUSeed::Smooth(Double_t vecL[5],Double_t matL[15])
620 // Prepare MBF smoothing auxiliary params for smoothing at prev. point:
623 // \tilde{l_j} = -H_j^T N_{j}^{-1} z_j + B_{j}^T \hat{l_j}
624 // \tilde{L_j} = H_j^T N_{j}^{-1} H_j + B_j^T \hat{L_j} B_j
625 // \hat{l_j} = F_j^T \tilde{l_{j+1}}
626 // \hat{L_j} = F_j^T \tilde{L_{j+1}} F_j
628 // P_{j/N} = P_{j/j} - P_{j/j} \hat{L_j} P_{j/j}
629 // \hat{x_{j/N}} = \hat{x_{j/j}} - P_{j/j} \hat{l_j}
634 // H = {{1,0,0,0,0},{0,1,0,0,0}}
636 // calc. \tilde{l_j} and \hat{l_j} in one go
638 if (GetClusterID()<0) return kTRUE;
641 &k00=fKMatrix[kK00],&k01=fKMatrix[kK01],
642 &k10=fKMatrix[kK10],&k11=fKMatrix[kK11],
643 &k20=fKMatrix[kK20],&k21=fKMatrix[kK21],
644 &k30=fKMatrix[kK30],&k31=fKMatrix[kK31],
645 &k40=fKMatrix[kK40],&k41=fKMatrix[kK41];
648 &matL10=matL[kS01], &matL11=matL[kS11],
649 &matL20=matL[kS20], &matL21=matL[kS21], &matL22=matL[kS22],
650 &matL30=matL[kS30], &matL31=matL[kS31], &matL32=matL[kS32], &matL33=matL[kS33],
651 &matL40=matL[kS40], &matL41=matL[kS41], &matL42=matL[kS42], &matL43=matL[kS43], &matL44=matL[kS44];
653 double vcL0 = vecL[0], vcL1 = vecL[1];
654 vecL[0] -= k00*vcL0+k10*vcL1+fKMatrix[kK20]*vecL[2]+k30*vecL[3]+k40*vecL[4] + fCovIYZ[0]*fResid[0] + fCovIYZ[1]*fResid[1];
655 vecL[1] -= k01*vcL0+fKMatrix[kK11]*vcL1+k21*vecL[2]+k31*vecL[3]+k41*vecL[4] + fCovIYZ[1]*fResid[0] + fCovIYZ[2]*fResid[1];
656 vecL[3] += fFMatrix[kF13]*vecL[1];
657 vecL[4] = fFMatrix[kF04]*vecL[0] + fFMatrix[kF14]*vecL[1] + fFMatrix[kF24]*vecL[2] + fFMatrix[kF44]*vecL[4];
658 vecL[2] += fFMatrix[kF02]*vecL[0] + fFMatrix[kF12]*vecL[1];
661 // L = H^T * sg * H + (I-KH)^T * L * (I - KH)
662 double v00 = k00*matL00+k10*matL10+k20*matL20+k30*matL30+k40*matL40;
663 double v10 = k00*matL10+k10*matL11+k20*matL21+k30*matL31+k40*matL41;
664 double v20 = k00*matL20+k10*matL12+k20*matL22+k30*matL32+k40*matL42;
665 double v30 = k00*matL30+k10*matL13+k20*matL23+k30*matL33+k40*matL43;
666 double v40 = k00*matL40+k10*matL14+k20*matL24+k30*matL34+k40*matL44;
668 double v01 = k01*matL00+k11*matL10+k21*matL20+k31*matL30+k41*matL40;
669 double v11 = k01*matL01+k11*matL11+k21*matL21+k31*matL31+k41*matL41;
670 double v21 = k01*matL02+k11*matL12+k21*matL22+k31*matL32+k41*matL42;
671 double v31 = k01*matL03+k11*matL13+k21*matL23+k31*matL33+k41*matL43;
672 double v41 = k01*matL04+k11*matL14+k21*matL24+k31*matL34+k41*matL44;
674 double t00 = k00*matL00+k10*matL01+k20*matL02+k30*matL03+k40*matL04;
675 double t10 = k00*matL10+k10*matL11+k20*matL12+k30*matL13+k40*matL14;
676 double t20 = k00*matL20+k10*matL21+k20*matL22+k30*matL23+k40*matL24;
677 double t30 = k00*matL30+k10*matL31+k20*matL32+k30*matL33+k40*matL34;
678 double t40 = k00*matL40+k10*matL41+k20*matL42+k30*matL43+k40*matL44;
680 double t01 = k01*matL00+k11*matL01+k21*matL02+k31*matL03+k41*matL04;
681 double t11 = k01*matL10+k11*matL11+k21*matL12+k31*matL13+k41*matL14;
682 double t21 = k01*matL20+k11*matL21+k21*matL22+k31*matL23+k41*matL24;
683 double t31 = k01*matL30+k11*matL31+k21*matL32+k31*matL33+k41*matL34;
684 double t41 = k01*matL40+k11*matL41+k21*matL42+k31*matL43+k41*matL44;
686 // (H^T * K^T * L * K * H) - (L * K * H) - (H^T * K^T * L) + (H^T*N^-1*H)
687 matL00 += k00*v00+k10*v10+k20*v20*k30*v30+k40*v40 - t00 - v00 + fCovIYZ[0];
688 matL01 += k01*v00+k11*v10+k21*v20*k31*v30+k41*v40 - t01 - v10 + fCovIYZ[1];
689 matL10 += k00*v01+k10*v11+k20*v21*k30*v31+k40*v41 - t10 - v01 + fCovIYZ[1];
690 matL11 += k01*v01+k11*v11+k21*v21*k31*v31+k41*v41 - t11 - v11 + fCovIYZ[2];
706 printf("Lr%d VecL: ",GetLayerID()); for (int i=0;i<5;i++) printf("%+e ",vecL[i]); printf("\n");
707 printf("F: "); for (int i=0;i<kNFElem;i++) printf("%+e ",fFMatrix[i]); printf("\n");
708 printf("K: "); for (int i=0;i<kNKElem;i++) printf("%+e ",fKMatrix[i]); printf("\n");
710 for (int j=0;j<5;j++) {
711 for (int i=0;i<5;i++) printf("%+e ",matL[j][i]); printf("\n");