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9c4c8863 | 1 | /************************************************************************** |
2 | * Copyright(c) 1998-1999, 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 | ||
16 | /////////////////////////////////////////////////////////////////////////////// | |
17 | // | |
18 | // Kalman-Filter-like fit | |
19 | // to a straight-line crossing a set of arbitrarily oriented planes. | |
20 | // The resulting line is given by the equation: | |
21 | // (x-x0)/vx = (y-y0)/1 = (z-z0)/vz | |
22 | // Parameters of the fit are: | |
23 | // x0,y0,z0 (a point on the line) and | |
24 | // vx,1,vz (a vector collinear with the line) | |
25 | // | |
26 | // LIMITATION: The line must not be perpendicular to the Y axis. | |
27 | // | |
28 | // Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch | |
29 | // | |
30 | ////////////////////////////////////////////////////////////////////////////// | |
31 | ||
32 | #include <TMatrixD.h> | |
33 | #include <TMatrixDSym.h> | |
34 | ||
35 | //#include "AliLog.h" | |
36 | #include "AliTrackFitterKalman.h" | |
37 | ||
38 | ClassImp(AliTrackFitterKalman) | |
39 | ||
40 | const Double_t AliTrackFitterKalman::fgkMaxChi2=33.; | |
41 | ||
42 | AliTrackFitterKalman:: | |
43 | AliTrackFitterKalman(AliTrackPointArray *array, Bool_t owner): | |
44 | AliTrackFitter(array,owner), | |
45 | fMaxChi2(fgkMaxChi2) | |
46 | { | |
47 | // | |
48 | // Constructor | |
49 | // | |
50 | } | |
51 | ||
52 | void AliTrackFitterKalman:: | |
53 | MakeSeed(const AliTrackPoint *p0, const AliTrackPoint *p1) { | |
54 | // | |
55 | // Make a seed out of the two track points | |
56 | // | |
57 | Double_t x0=p0->GetX(), y0=p0->GetY(), z0=p0->GetZ(); | |
58 | Double_t dx=p1->GetX()-x0, dy=p1->GetY()-y0, dz=p1->GetZ()-z0; | |
59 | Double_t vx=dx/dy; | |
60 | Double_t vz=dz/dy; | |
61 | Double_t par[5]={x0,y0,z0,vx,vz}; | |
62 | ||
63 | const Float_t *cv0=p0->GetCov(); | |
64 | const Float_t *cv1=p1->GetCov(); | |
65 | Double_t rdx2=(cv0[0]+cv1[0])/dx/dx; | |
66 | Double_t rdy2=(cv0[3]+cv1[3])/dy/dy; | |
67 | Double_t rdz2=(cv0[5]+cv1[5])/dz/dz; | |
68 | Double_t svx2=vx*vx*(rdx2+rdy2); | |
69 | Double_t svz2=vz*vz*(rdz2+rdy2); | |
70 | Double_t cov[15]={ | |
71 | cv0[0], | |
72 | cv0[1],cv0[3], | |
73 | cv0[2],cv0[4],cv0[5], | |
74 | 0.,0.,0.,svx2, | |
75 | 0.,0.,0.,0.,svz2 | |
76 | }; | |
77 | ||
78 | SetSeed(par,cov); | |
79 | } | |
80 | ||
81 | Bool_t AliTrackFitterKalman::AddPoint(const AliTrackPoint *p) | |
82 | { | |
83 | // | |
84 | // Add a point to the fit | |
85 | // | |
86 | ||
87 | if (!Propagate(p)) return kFALSE; | |
88 | Double_t chi2=GetPredictedChi2(p); | |
89 | if (chi2>fMaxChi2) return kFALSE; | |
90 | if (!Update(p,chi2)) return kFALSE; | |
91 | ||
92 | return kTRUE; | |
93 | } | |
94 | ||
95 | ||
96 | Double_t AliTrackFitterKalman::GetPredictedChi2(const AliTrackPoint *p) const { | |
97 | // | |
98 | // Calculate the predicted chi2 increment. | |
99 | // | |
100 | ||
101 | Float_t txyz[3]={GetParam()[0],GetParam()[1],GetParam()[2]}; | |
102 | TMatrixDSym &cv=*fCov; | |
103 | Float_t tcov[6]={ | |
104 | cv(0,0),cv(1,0),cv(2,0), | |
105 | cv(1,1),cv(2,1), | |
106 | cv(2,2) | |
107 | }; | |
108 | AliTrackPoint tp(txyz,tcov,p->GetVolumeID()); | |
109 | ||
110 | Double_t chi2=p->GetResidual(tp,kTRUE); | |
111 | ||
112 | return chi2; | |
113 | } | |
114 | ||
115 | ||
116 | Bool_t AliTrackFitterKalman::Propagate(const AliTrackPoint *p) { | |
117 | // | |
118 | // Propagate the track towards the measured point "p" | |
119 | // | |
120 | ||
121 | TMatrixDSym &cv=*fCov; | |
122 | Double_t s=p->GetY() - fParams[1]; | |
123 | Double_t sig2=s*s/12.; | |
124 | ||
125 | Double_t vx=fParams[3], vz=fParams[4]; | |
126 | fParams[0] += s*vx; | |
127 | fParams[1] += s; | |
128 | fParams[2] += s*vz; | |
129 | ||
130 | Double_t | |
131 | c00 = cv(0,0) + 2*s*cv(3,0) + s*s*cv(3,3) + vx*vx*sig2, | |
132 | ||
133 | c10 = cv(1,0) + s*cv(1,3) + vx*sig2, c11=cv(1,1) + sig2, | |
134 | ||
135 | c20 = cv(2,0) + s*(cv(4,0) + cv(2,3)) + s*s*cv(4,3) + vx*vz*sig2, | |
136 | c21 = cv(2,1) + s*cv(4,1) + vz*sig2, | |
137 | c22 = cv(2,2) + 2*s*cv(4,2) + s*s*cv(4,4) + vz*vz*sig2, | |
138 | ||
139 | c30 = cv(3,0) + s*cv(3,3), c31 = cv(3,1), | |
140 | c32 = cv(3,2) + s*cv(3,4), c33 = cv(3,3), | |
141 | ||
142 | c40 = cv(4,0) + s*cv(4,3), c41 = cv(4,1), | |
143 | c42 = cv(4,2) + s*cv(4,4), c43 = cv(4,3), c44 = cv(4,4); | |
144 | ||
145 | ||
146 | cv(0,0)=c00; cv(0,1)=c10; cv(0,2)=c20; cv(0,3)=c30; cv(0,4)=c40; | |
147 | cv(1,0)=c10; cv(1,1)=c11; cv(1,2)=c21; cv(1,3)=c31; cv(1,4)=c41; | |
148 | cv(2,0)=c20; cv(2,1)=c21; cv(2,2)=c22; cv(2,3)=c32; cv(2,4)=c42; | |
149 | cv(3,0)=c30; cv(3,1)=c31; cv(3,2)=c32; cv(3,3)=c33; cv(3,4)=c43; | |
150 | cv(4,0)=c40; cv(4,1)=c41; cv(4,2)=c42; cv(4,3)=c43; cv(4,4)=c44; | |
151 | ||
152 | return kTRUE; | |
153 | } | |
154 | ||
155 | Bool_t AliTrackFitterKalman::Update(const AliTrackPoint *p, Double_t chi2) { | |
156 | // | |
157 | // Update the track params using the measured point "p" | |
158 | // | |
159 | ||
160 | TMatrixDSym &c=*fCov; | |
161 | const Float_t *cov=p->GetCov(); | |
162 | ||
163 | TMatrixDSym v(3); | |
164 | v(0,0)=cov[0]+c(0,0); v(0,1)=cov[1]+c(0,1); v(0,2)=cov[2]+c(0,2); | |
165 | v(1,0)=cov[1]+c(1,0); v(1,1)=cov[3]+c(1,1); v(1,2)=cov[4]+c(1,2); | |
166 | v(2,0)=cov[2]+c(2,0); v(2,1)=cov[4]+c(2,1); v(2,2)=cov[5]+c(2,2); | |
167 | v.Invert(); | |
168 | ||
169 | TMatrixD ch(5,3); | |
170 | ch(0,0)=c(0,0); ch(0,1)=c(0,1); ch(0,2)=c(0,2); | |
171 | ch(1,0)=c(1,0); ch(1,1)=c(1,1); ch(1,2)=c(1,2); | |
172 | ch(2,0)=c(2,0); ch(2,1)=c(2,1); ch(2,2)=c(2,2); | |
173 | ch(3,0)=c(3,0); ch(3,1)=c(3,1); ch(3,2)=c(3,2); | |
174 | ch(4,0)=c(4,0); ch(4,1)=c(4,1); ch(4,2)=c(4,2); | |
175 | ||
176 | TMatrixD k(ch,TMatrixD::kMult,v); | |
177 | ||
178 | TMatrixD d(3,1); | |
179 | d(0,0) = p->GetX() - fParams[0]; | |
180 | d(1,0) = p->GetY() - fParams[1]; | |
181 | d(2,0) = p->GetZ() - fParams[2]; | |
182 | ||
183 | TMatrixD x(k,TMatrixD::kMult,d); | |
184 | ||
185 | fParams[0]+=x(0,0); | |
186 | fParams[1]+=x(1,0); | |
187 | fParams[2]+=x(2,0); | |
188 | fParams[3]+=x(3,0); | |
189 | fParams[4]+=x(4,0); | |
190 | ||
191 | TMatrixD hc(3,5); | |
192 | hc(0,0)=c(0,0);hc(0,1)=c(0,1);hc(0,2)=c(0,2);hc(0,3)=c(0,3);hc(0,4)=c(0,4); | |
193 | hc(1,0)=c(1,0);hc(1,1)=c(1,1);hc(1,2)=c(1,2);hc(1,3)=c(1,3);hc(1,4)=c(1,4); | |
194 | hc(2,0)=c(2,0);hc(2,1)=c(2,1);hc(2,2)=c(2,2);hc(2,3)=c(2,3);hc(2,4)=c(2,4); | |
195 | ||
196 | TMatrixD s(k,TMatrixD::kMult,hc); | |
197 | ||
198 | c(0,0)-=s(0,0);c(0,1)-=s(0,1);c(0,2)-=s(0,2);c(0,3)-=s(0,3);c(0,4)-=s(0,4); | |
199 | c(1,0)-=s(1,0);c(1,1)-=s(1,1);c(1,2)-=s(1,2);c(1,3)-=s(1,3);c(1,4)-=s(1,4); | |
200 | c(2,0)-=s(2,0);c(2,1)-=s(2,1);c(2,2)-=s(2,2);c(2,3)-=s(2,3);c(2,4)-=s(2,4); | |
201 | c(3,0)-=s(3,0);c(3,1)-=s(3,1);c(3,2)-=s(3,2);c(3,3)-=s(3,3);c(3,4)-=s(3,4); | |
202 | c(4,0)-=s(4,0);c(4,1)-=s(4,1);c(4,2)-=s(4,2);c(4,3)-=s(4,3);c(4,4)-=s(4,4); | |
203 | ||
204 | fChi2 += chi2; | |
205 | fNdf += 2; | |
206 | ||
207 | return kTRUE; | |
208 | } | |
209 | ||
210 | //_____________________________________________________________________________ | |
211 | Bool_t AliTrackFitterKalman::GetPCA(const AliTrackPoint &p, AliTrackPoint &i) const | |
212 | { | |
213 | // | |
214 | // Get the intersection point "i" between the track and the plane | |
215 | // the point "p" belongs to. | |
216 | // | |
217 | ||
218 | TMatrixD t(3,1); | |
219 | Double_t s=p.GetY() - fParams[1]; | |
220 | Double_t vx=fParams[3], vz=fParams[4]; | |
221 | t(0,0) = fParams[0] + s*vx; | |
222 | t(1,0) = fParams[1] + s; | |
223 | t(2,0) = fParams[2] + s*vz; | |
224 | ||
225 | TMatrixDSym tC(3); | |
226 | { | |
227 | Double_t sig2=s*s/12.; | |
228 | TMatrixDSym &cv=*fCov; | |
229 | tC(0,0) = cv(0,0) + 2*s*cv(3,0) + s*s*cv(3,3) + vx*vx*sig2; | |
230 | tC(1,0) = cv(1,0) + s*cv(1,3) + vx*sig2; | |
231 | tC(1,1) = cv(1,1) + sig2; | |
232 | tC(2,0) = cv(2,0) + s*(cv(4,0) + cv(2,3)) + s*s*cv(4,3) + vx*vz*sig2; | |
233 | tC(2,1) = cv(2,1) + s*cv(4,1) + vz*sig2; | |
234 | tC(2,2) = cv(2,2) + 2*s*cv(4,2) + s*s*cv(4,4) + vz*vz*sig2; | |
235 | ||
236 | tC(0,1) = tC(1,0); tC(0,2) = tC(2,0); | |
237 | tC(1,2) = tC(2,1); | |
238 | } | |
239 | ||
240 | TMatrixD m(3,1); | |
241 | m(0,0)=p.GetX(); | |
242 | m(1,0)=p.GetY(); | |
243 | m(2,0)=p.GetZ(); | |
244 | ||
245 | TMatrixDSym mC(3); | |
246 | { | |
247 | const Float_t *cv=p.GetCov(); | |
248 | mC(0,0)=cv[0]; mC(0,1)=cv[1]; mC(0,2)=cv[2]; | |
249 | mC(1,0)=cv[1]; mC(1,1)=cv[3]; mC(1,2)=cv[4]; | |
250 | mC(2,0)=cv[2]; mC(2,1)=cv[4]; mC(2,2)=cv[5]; | |
251 | } | |
252 | ||
253 | TMatrixDSym tmW(tC); | |
254 | tmW+=mC; | |
255 | tmW.Invert(); | |
256 | ||
257 | TMatrixD mW(mC,TMatrixD::kMult,tmW); | |
258 | TMatrixD tW(tC,TMatrixD::kMult,tmW); | |
259 | ||
260 | TMatrixD mi(mW,TMatrixD::kMult,m); | |
261 | TMatrixD ti(tW,TMatrixD::kMult,t); | |
262 | ti+=mi; | |
263 | ||
264 | TMatrixD iC(tC,TMatrixD::kMult,tmW); | |
265 | iC*=mC; | |
266 | ||
267 | Float_t cov[6]={ | |
268 | iC(0,0), iC(0,1), iC(0,2), | |
269 | iC(1,1), iC(1,2), | |
270 | iC(2,2) | |
271 | }; | |
272 | i.SetXYZ(ti(0,0),ti(1,0),ti(2,0),cov); | |
273 | UShort_t id=p.GetVolumeID(); | |
274 | i.SetVolumeID(id); | |
275 | ||
276 | return kTRUE; | |
277 | } | |
278 | ||
279 | ||
280 | //_____________________________________________________________________________ | |
281 | void | |
282 | AliTrackFitterKalman::SetSeed(const Double_t par[5], const Double_t cov[15]) { | |
283 | // | |
284 | // Set the initial approximation for the track parameters | |
285 | // | |
286 | for (Int_t i=0; i<5; i++) fParams[i]=par[i]; | |
287 | fParams[5]=0.; | |
288 | ||
289 | delete fCov; | |
290 | fCov=new TMatrixDSym(5); | |
291 | TMatrixDSym &cv=*fCov; | |
292 | ||
293 | cv(0,0)=cov[0 ]; | |
294 | cv(1,0)=cov[1 ]; cv(1,1)=cov[2 ]; | |
295 | cv(2,0)=cov[3 ]; cv(2,1)=cov[4 ]; cv(2,2)=cov[5 ]; | |
296 | cv(3,0)=cov[6 ]; cv(3,1)=cov[7 ]; cv(3,2)=cov[8 ]; cv(3,3)=cov[9 ]; | |
297 | cv(4,0)=cov[10]; cv(4,1)=cov[11]; cv(4,2)=cov[12]; cv(4,3)=cov[13]; cv(4,4)=cov[14]; | |
298 | ||
299 | cv(0,1)=cv(1,0); | |
300 | cv(0,2)=cv(2,0); cv(1,2)=cv(2,1); | |
301 | cv(0,3)=cv(3,0); cv(1,3)=cv(3,1); cv(2,3)=cv(3,2); | |
302 | cv(0,4)=cv(4,0); cv(1,4)=cv(4,1); cv(2,4)=cv(4,2); cv(3,4)=cv(4,3); | |
303 | ||
304 | } |