1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
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 **************************************************************************/
18 //-----------------------------------------------------------------
19 // Implementation of the derived class for track residuals
20 // based on linear chi2 minimization
21 // The minimization relies on the fact that the alignment parameters
22 // (angles and translations) are small.
23 // TLinearFitter used for minimization
24 // Possibility to fix Paramaters
25 // FixParameter()ReleaseParameter();
26 // Possibility to define fraction of outliers to be skipped
28 // marian.ivanov@cern.ch
30 //-----------------------------------------------------------------
34 #include <TGeoMatrix.h>
37 #include "AliAlignObj.h"
38 #include "AliTrackPointArray.h"
39 #include "AliTrackResidualsLinear.h"
40 #include "AliAlignObj.h"
41 #include "TLinearFitter.h"
42 #include "TDecompSVD.h"
44 ClassImp(AliTrackResidualsLinear)
46 //______________________________________________________________________________
47 AliTrackResidualsLinear::AliTrackResidualsLinear():
53 // Default constructor
54 for (Int_t ipar=0; ipar<6; ipar++){
55 fBFixed[ipar] = kFALSE;
59 for (Int_t icov=0; icov<36; icov++){ fCovar[icov]=0;}
62 //______________________________________________________________________________
63 AliTrackResidualsLinear::AliTrackResidualsLinear(Int_t ntracks):
64 AliTrackResiduals(ntracks),
65 fFitter(new TLinearFitter(6,"hyp6")),
70 for (Int_t ipar=0; ipar<6; ipar++){
71 fBFixed[ipar] = kFALSE;
75 for (Int_t icov=0; icov<36; icov++){ fCovar[icov]=0;}
78 //______________________________________________________________________________
79 AliTrackResidualsLinear::AliTrackResidualsLinear(const AliTrackResidualsLinear &res):
80 AliTrackResiduals(res),
81 fFitter(new TLinearFitter(*(res.fFitter))),
82 fFraction(res.fFraction),
83 fChi2Orig(res.fChi2Orig)
87 for (Int_t ipar=0; ipar<6; ipar++){
88 fBFixed[ipar] = res.fBFixed[ipar];
89 fFixed[ipar] = res.fFixed[ipar];
90 fParams[ipar] = res.fParams[ipar];
92 for (Int_t icov=0; icov<36; icov++){ fCovar[icov]= res.fCovar[icov];}
93 fChi2Orig = res.fChi2Orig;
96 //______________________________________________________________________________
97 AliTrackResidualsLinear &AliTrackResidualsLinear::operator= (const AliTrackResidualsLinear& res)
99 // Assignment operator
100 ((AliTrackResiduals *)this)->operator=(res);
103 //______________________________________________________________________________
104 AliTrackResidualsLinear::~AliTrackResidualsLinear()
113 //______________________________________________________________________________
114 Bool_t AliTrackResidualsLinear::Minimize()
116 // Implementation of fast linear Chi2 minimizer
117 // based on TLinear fitter
119 if (!fFitter) fFitter = new TLinearFitter(6,"hyp6");
120 fFitter->StoreData(kTRUE);
121 fFitter->ClearPoints();
124 for (Int_t itrack = 0; itrack < fLast; itrack++) {
125 if (!fVolArray[itrack] || !fTrackArray[itrack]) continue;
126 for (Int_t ipoint = 0; ipoint < fVolArray[itrack]->GetNPoints(); ipoint++) {
127 fVolArray[itrack]->GetPoint(p1,ipoint);
128 fTrackArray[itrack]->GetPoint(p2,ipoint);
132 Bool_t isOK = Update();
133 if (!isOK) return isOK;
136 fAlignObj->GetMatrix(matrix);
142 //______________________________________________________________________________
143 void AliTrackResidualsLinear::AddPoints(AliTrackPoint &p, AliTrackPoint &pprime)
146 // add points to linear fitter - option with correlation betwee measurement in different dimensions
148 // pprime - track extrapolation point
150 Float_t xyz[3],xyzp[3];
151 Float_t cov[6],covp[6];
152 p.GetXYZ(xyz,cov); pprime.GetXYZ(xyzp,covp);
155 TMatrixD mcov(3,3); // local point covariance
156 mcov(0,0) = cov[0]; mcov(0,1) = cov[1]; mcov(0,2) = cov[2];
157 mcov(1,0) = cov[1]; mcov(1,1) = cov[3]; mcov(1,2) = cov[4];
158 mcov(2,0) = cov[2]; mcov(2,1) = cov[4]; mcov(2,2) = cov[5];
159 TMatrixD mcovp(3,3); // extrapolation point covariance
160 mcovp(0,0) = covp[0]; mcovp(0,1) = covp[1]; mcovp(0,2) = covp[2];
161 mcovp(1,0) = covp[1]; mcovp(1,1) = covp[3]; mcovp(1,2) = covp[4];
162 mcovp(2,0) = covp[2]; mcovp(2,1) = covp[4]; mcovp(2,2) = covp[5];
165 if (!mcov.IsValid()) return;
166 TMatrixD mcovBack = mcov; // for debug purposes
170 TDecompSVD svd(mcov); // mcov = svd.fU * covDiagonal * svd.fV.Invert
171 if (!svd.Decompose()) return; // decomposition failed
172 TMatrixD matrixV = svd.GetV(); // transformation matrix to diagonalize covariance matrix
173 Double_t covDiagonal[3] = {svd.GetSig()[0],svd.GetSig()[1],svd.GetSig()[2]}; // diagonalized covariance matrix
176 TMatrixD deltaR(3,1);
177 deltaR(0,0) = (xyzp[0]-xyz[0]);
178 deltaR(1,0) = (xyzp[1]-xyz[1]);
179 deltaR(2,0) = (xyzp[2]-xyz[2]);
181 // parametrization matrix
183 TMatrixD mparam(3,6);
184 mparam(0,0) = 1; mparam(1,0) = 0; mparam(2,0) = 0; // xshift
185 mparam(0,1) = 0; mparam(1,1) = 1; mparam(2,1) = 0; // yshift
186 mparam(0,2) = 0; mparam(1,2) = 0; mparam(2,2) = 1; // zshift
187 mparam(0,3) = 0; mparam(1,3) =-xyz[2]; mparam(2,3) = xyz[1]; // x rotation
188 mparam(0,4) = xyz[2]; mparam(1,4) = 0; mparam(2,4) =-xyz[0]; // y rotation
189 mparam(0,5) =-xyz[1]; mparam(1,5) = xyz[0]; mparam(2,5) = 0; // z rotation
192 TMatrixD deltaT(matrixV, TMatrixD::kTransposeMult, deltaR); // tranformed delta
193 TMatrixD mparamT(matrixV,TMatrixD::kTransposeMult, mparam); // tranformed linear transformation
194 if (AliLog::GetDebugLevel("","AliTrackResidualsLinear")>2){
198 // covDiag = U^-1 * mcov * V -- diagonalization of covariance matrix
200 TMatrixD matrixU = svd.GetU(); // transformation matrix to diagonalize covariance matrix
201 TMatrixD matrixUI= svd.GetU();
204 TMatrixD test0 = matrixUI*matrixV; // test matrix - should be unit matrix
205 TMatrixD test1 = matrixUI*mcovBack*matrixV; // test matrix - diagonal - should be diagonal with covDiagonal on diag
206 TMatrixD test2 = matrixU.T()*matrixV; // test ortogonality - shoul be unit
207 printf("Test matrix 2 - should be unit\n");
209 printf("Test matrix 0 - should be unit\n");
211 printf("Test matrix 1 - should be diagonal\n");
213 printf("Diagonal matrix\n");
214 svd.GetSig().Print();
215 printf("Original param matrix\n");
217 printf("Rotated param matrix\n");
221 printf("Trans Matrix:\n");
223 printf("Delta Orig\n");
225 printf("Delta Rotated");
232 for (Int_t idim = 1; idim<3; idim++){
233 Double_t yf; // input points to fit in TLinear fitter
234 Double_t xf[6]; // input points to fit
236 for (Int_t ipar =0; ipar<6; ipar++) xf[ipar] = mparamT(idim,ipar);
237 if (covDiagonal[idim]>0.){
238 fFitter->AddPoint(xf,yf, TMath::Sqrt(covDiagonal[idim]));
240 Double_t chi2 = (yf*yf)/covDiagonal[idim];
241 fChi2Orig += (yf*yf)/covDiagonal[idim];
242 if (chi2>100 && AliLog::GetDebugLevel("","AliTrackResidualsLinear")>1){
243 printf("Too big chi2- %f\n",chi2);
244 printf("Delta Orig\n");
246 printf("Delta Rotated");
249 printf("Too big chi2 - End\n");
257 if (AliLog::GetDebugLevel("","AliTrackResidualsLinear")>1){
258 TMatrixD matChi0=(mcov.Invert()*deltaR);
259 TMatrixD matChi2=deltaR.T()*matChi0;
260 printf("Chi2:\t%f\t%f", matChi2(0,0), sumChi2);
266 //______________________________________________________________________________
267 Bool_t AliTrackResidualsLinear::Update()
269 // Find the alignment parameters
270 // using TLinear fitter + fill data containers
275 // TLinear fitter put as first parameter offset - fixing parameter shifted by one
277 fFitter->FixParameter(0);
278 for (Int_t ipar =0; ipar<6; ipar++){
279 if (fBFixed[ipar]) fFitter->FixParameter(ipar+1,fFixed[ipar]);
282 fFitter->EvalRobust(fFraction);
287 fFitter->ReleaseParameter(0);
288 for (Int_t ipar=0; ipar<6; ipar++) {
289 if (fBFixed[ipar]) fFitter->ReleaseParameter(ipar+1);
294 fChi2 = fFitter->GetChisquare();
297 fFitter->GetParameters(vector);
298 fParams[0] = vector[1];
299 fParams[1] = vector[2];
300 fParams[2] = vector[3];
301 fParams[3] = vector[4];
302 fParams[4] = vector[5];
303 fParams[5] = vector[6];
305 fFitter->GetCovarianceMatrix(covar);
306 for (Int_t i0=0; i0 <6; i0++)
307 for (Int_t j0=0; j0 <6; j0++){
308 fCovar[i0*6+j0] = covar(i0+1,j0+1);
311 fAlignObj->SetPars(fParams[0], fParams[1], fParams[2],
312 TMath::RadToDeg()*fParams[3],
313 TMath::RadToDeg()*fParams[4],
314 TMath::RadToDeg()*fParams[5]);