006b5f7f |
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 | // Implementation of the ITS track class |
18 | // |
19 | // Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch |
20 | //------------------------------------------------------------------------- |
21 | |
22 | #include <TMatrixD.h> |
23 | |
24 | #include <TMath.h> |
25 | #include <iostream.h> |
26 | |
27 | #include "AliCluster.h" |
28 | #include "../TPC/AliTPCtrack.h" |
29 | #include "AliITStrackV2.h" |
30 | |
31 | ClassImp(AliITStrackV2) |
32 | |
33 | const Int_t kWARN=1; |
34 | |
35 | //____________________________________________________________________________ |
36 | AliITStrackV2::AliITStrackV2(const AliTPCtrack& t) throw (const Char_t *) { |
37 | //------------------------------------------------------------------ |
38 | //Convertion TPC track -> ITS track |
39 | //------------------------------------------------------------------ |
40 | SetLabel(t.GetLabel()); |
41 | SetChi2(0.); |
42 | SetNumberOfClusters(0); |
43 | fdEdx = 0.; |
44 | fAlpha = t.GetAlpha(); |
45 | if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi(); |
46 | else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi(); |
47 | |
48 | //Convertion of the track parameters |
49 | Double_t x,p[5]; t.GetExternalParameters(x,p); |
50 | fX=x; x=kConversionConstant; |
51 | fP0=p[0]; |
52 | fP1=p[1]; |
53 | fP2=p[2]; |
54 | fP3=p[3]; |
55 | fP4=p[4]/x; |
56 | |
57 | //Convertion of the covariance matrix |
58 | Double_t c[15]; t.GetExternalCovariance(c); |
59 | |
60 | fC00=c[0 ]; |
61 | fC10=c[1 ]; fC11=c[2 ]; |
62 | fC20=c[3 ]; fC21=c[4 ]; fC22=c[5 ]; |
63 | fC30=c[6 ]; fC31=c[7 ]; fC32=c[8 ]; fC33=c[9 ]; |
64 | fC40=c[10]/x; fC41=c[11]/x; fC42=c[12]/x; fC43=c[13]/x; fC44=c[14]/x/x; |
65 | |
66 | if (!Invariant()) throw "AliITStrackV2: conversion failed !\n"; |
67 | } |
68 | |
69 | //____________________________________________________________________________ |
70 | AliITStrackV2::AliITStrackV2(const AliITStrackV2& t) : AliKalmanTrack(t) { |
71 | //------------------------------------------------------------------ |
72 | //Copy constructor |
73 | //------------------------------------------------------------------ |
74 | fX=t.fX; |
75 | fAlpha=t.fAlpha; |
76 | fdEdx=t.fdEdx; |
77 | |
78 | fP0=t.fP0; fP1=t.fP1; fP2=t.fP2; fP3=t.fP3; fP4=t.fP4; |
79 | |
80 | fC00=t.fC00; |
81 | fC10=t.fC10; fC11=t.fC11; |
82 | fC20=t.fC20; fC21=t.fC21; fC22=t.fC22; |
83 | fC30=t.fC30; fC31=t.fC31; fC32=t.fC32; fC33=t.fC33; |
84 | fC40=t.fC40; fC41=t.fC41; fC42=t.fC42; fC43=t.fC43; fC44=t.fC44; |
85 | |
86 | Int_t n=GetNumberOfClusters(); |
87 | for (Int_t i=0; i<n; i++) fIndex[i]=t.fIndex[i]; |
88 | } |
89 | |
90 | //_____________________________________________________________________________ |
91 | Int_t AliITStrackV2::Compare(const TObject *o) const { |
92 | //----------------------------------------------------------------- |
93 | // This function compares tracks according to the their curvature |
94 | //----------------------------------------------------------------- |
95 | AliTPCtrack *t=(AliTPCtrack*)o; |
96 | Double_t co=TMath::Abs(t->Get1Pt()); |
97 | Double_t c =TMath::Abs(Get1Pt()); |
98 | if (c>co) return 1; |
99 | else if (c<co) return -1; |
100 | return 0; |
101 | } |
102 | |
103 | //_____________________________________________________________________________ |
104 | void AliITStrackV2::GetExternalCovariance(Double_t cc[15]) const { |
105 | //------------------------------------------------------------------------- |
106 | // This function returns an external representation of the covriance matrix. |
107 | // (See comments in AliTPCtrack.h about external track representation) |
108 | //------------------------------------------------------------------------- |
109 | Double_t a=kConvConst; |
110 | |
111 | cc[0 ]=fC00; |
112 | cc[1 ]=fC10; cc[2 ]=fC11; |
113 | cc[3 ]=fC20; cc[4 ]=fC21; cc[5 ]=fC22; |
114 | cc[6 ]=fC30; cc[7 ]=fC31; cc[8 ]=fC32; cc[9 ]=fC33; |
115 | cc[10]=fC40*a; cc[11]=fC41*a; cc[12]=fC42*a; cc[13]=fC43*a; cc[14]=fC44*a*a; |
116 | } |
117 | |
118 | //____________________________________________________________________________ |
119 | Int_t AliITStrackV2::PropagateToVertex(Double_t x0,Double_t rho,Double_t pm) { |
120 | //------------------------------------------------------------------ |
121 | //This function propagates a track to the minimal distance from the origin |
122 | //------------------------------------------------------------------ |
123 | Double_t xv=fP2*(fX*fP2 - fP0*TMath::Sqrt(1.- fP2*fP2)); //linear approxim. |
124 | Propagate(fAlpha,xv,0.,0.,pm); |
125 | return 0; |
126 | } |
127 | |
128 | //____________________________________________________________________________ |
129 | Int_t AliITStrackV2:: |
130 | GetGlobalXYZat(Double_t xk, Double_t &x, Double_t &y, Double_t &z) const { |
131 | //------------------------------------------------------------------ |
132 | //This function returns a track position in the global system |
133 | //------------------------------------------------------------------ |
134 | Double_t dx=xk-fX; |
135 | Double_t f1=fP2, f2=f1 + fP4*dx; |
136 | if (TMath::Abs(f2) >= 0.99999) { |
137 | Int_t n=GetNumberOfClusters(); |
138 | if (n>kWARN) cerr<<n<<" AliITStrackV2 warning: Propagation failed !\n"; |
139 | return 0; |
140 | } |
141 | |
142 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); |
143 | |
144 | Double_t yk = fP0 + dx*(f1+f2)/(r1+r2); |
145 | Double_t zk = fP1 + dx*(f1+f2)/(f1*r2 + f2*r1)*fP3; |
146 | |
147 | Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha); |
148 | x = xk*cs - yk*sn; |
149 | y = xk*sn + yk*cs; |
150 | z = zk; |
151 | |
152 | return 1; |
153 | } |
154 | |
155 | //_____________________________________________________________________________ |
156 | Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c) const |
157 | { |
158 | //----------------------------------------------------------------- |
159 | // This function calculates a predicted chi2 increment. |
160 | //----------------------------------------------------------------- |
161 | Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2(); |
162 | r00+=fC00; r01+=fC10; r11+=fC11; |
163 | |
164 | Double_t det=r00*r11 - r01*r01; |
165 | if (TMath::Abs(det) < 1.e-10) { |
166 | Int_t n=GetNumberOfClusters(); |
167 | if (n>4) cerr<<n<<" AliKalmanTrack warning: Singular matrix !\n"; |
168 | return 1e10; |
169 | } |
170 | Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01; |
171 | |
172 | Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1; |
173 | |
174 | return (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det; |
175 | } |
176 | |
177 | //_____________________________________________________________________________ |
178 | Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c,Double_t *m, |
179 | Double_t x0, Double_t pm=0.139) const { |
180 | //----------------------------------------------------------------- |
181 | // This function calculates a chi2 increment with a vertex contraint |
182 | //----------------------------------------------------------------- |
183 | TVectorD x(5); x(0)=fP0; x(1)=fP1; x(2)=fP2; x(3)=fP3; x(4)=fP4; |
184 | TMatrixD C(5,5); |
185 | C(0,0)=fC00; |
186 | C(1,0)=fC10; C(1,1)=fC11; |
187 | C(2,0)=fC20; C(2,1)=fC21; C(2,2)=fC22; |
188 | C(3,0)=fC30; C(3,1)=fC31; C(3,2)=fC32; C(3,3)=fC33; |
189 | C(4,0)=fC40; C(4,1)=fC41; C(4,2)=fC42; C(4,3)=fC43; C(4,4)=fC44; |
190 | |
191 | C(0,1)=C(1,0); |
192 | C(0,2)=C(2,0); C(1,2)=C(2,1); |
193 | C(0,3)=C(3,0); C(1,3)=C(3,1); C(2,3)=C(3,2); |
194 | C(0,4)=C(4,0); C(1,4)=C(4,1); C(2,4)=C(4,2); C(3,4)=C(4,3); |
195 | |
196 | TMatrixD H(4,5); H.UnitMatrix(); |
197 | Double_t dy=(c->GetY() - m[0]), dz=(c->GetZ() - m[1]); |
198 | |
199 | Double_t dr=TMath::Sqrt(fX*fX + dy*dy); |
200 | Double_t r =TMath::Sqrt(4/dr/dr - fP4*fP4); |
201 | Double_t sn=0.5*(fP4*fX + dy*r); |
202 | Double_t tg=0.5*fP4*dz/TMath::ASin(0.5*fP4*dr); |
203 | TVectorD mm(4); |
204 | mm(0)=m[0]=c->GetY(); mm(1)=m[1]=c->GetZ(); mm(2)=m[2]=sn; mm(3)=m[3]=tg; |
205 | |
206 | Double_t v22=0.,v33=0.; |
207 | //x0=0.; |
208 | if (x0!=0.) { |
209 | Double_t pp2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt()); |
210 | Double_t beta2=pp2/(pp2 + pm*pm); |
211 | x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp())); |
212 | Double_t theta2=14.1*14.1/(beta2*pp2*1e6)*x0; |
213 | v22 = theta2*(1.- GetSnp()*GetSnp())*(1. + GetTgl()*GetTgl()); |
214 | v33 = theta2*(1.+ GetTgl()*GetTgl())*(1. + GetTgl()*GetTgl()); |
215 | } |
216 | Double_t sy2=c->GetSigmaY2(), sz2=c->GetSigmaZ2(); |
217 | v22+=kSigmaYV*kSigmaYV/dr/dr; |
218 | v22+=sy2/dr/dr; |
219 | Double_t v20=sy2/dr; |
220 | |
221 | v33+=kSigmaZV*kSigmaZV/dr/dr; |
222 | v33+=sz2/dr/dr; |
223 | Double_t v31=sz2/dr; |
224 | |
225 | TMatrixD V(4,4); |
226 | V(0,0)=m[4 ]=sy2; V(0,1)=m[5 ]=0.; V(0,2)=m[6 ]=v20; V(0,3)=m[7 ]=0.; |
227 | V(1,0)=m[8 ]=0.; V(1,1)=m[9 ]=sz2; V(1,2)=m[10]=0.; V(1,3)=m[11]=v31; |
228 | V(2,0)=m[12]=v20; V(2,1)=m[13]=0.; V(2,2)=m[14]=v22; V(2,3)=m[15]=0.; |
229 | V(3,0)=m[16]=0.; V(3,1)=m[17]=v31; V(3,2)=m[18]=0.; V(3,3)=m[19]=v33; |
230 | |
231 | TVectorD res=x; res*=H; res-=mm; //res*=-1; |
232 | TMatrixD tmp(H,TMatrixD::kMult,C); |
233 | TMatrixD R(tmp,TMatrixD::kMult,TMatrixD(TMatrixD::kTransposed,H)); R+=V; |
234 | |
235 | Double_t det=R.Determinant(); |
236 | if (TMath::Abs(det) < 1.e-25) { |
237 | Int_t n=GetNumberOfClusters(); |
238 | if (n>kWARN) cerr<<n<<" AliITStrackV2 warning: Singular matrix !\n"; |
239 | return 1e10; |
240 | } |
241 | |
242 | R.Invert(); |
243 | |
244 | TVectorD rs=res; |
245 | res*=R; |
246 | return rs*res; |
247 | } |
248 | |
249 | //____________________________________________________________________________ |
250 | Int_t |
251 | AliITStrackV2::PropagateTo(Double_t xk,Double_t x0,Double_t rho,Double_t pm) { |
252 | //------------------------------------------------------------------ |
253 | //This function propagates a track |
254 | //------------------------------------------------------------------ |
255 | Double_t x1=fX, x2=xk, dx=x2-x1; |
256 | Double_t f1=fP2, f2=f1 + fP4*dx; |
257 | if (TMath::Abs(f2) >= 0.99999) { |
258 | Int_t n=GetNumberOfClusters(); |
259 | if (n>kWARN) cerr<<n<<" AliITStrackV2 warning: Propagation failed !\n"; |
260 | return 0; |
261 | } |
262 | |
263 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); |
264 | |
265 | fP0 += dx*(f1+f2)/(r1+r2); |
266 | fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3; |
267 | fP2 += dx*fP4; |
268 | |
269 | //f = F - 1 |
270 | |
271 | Double_t f02= dx/(r1*r1*r1); |
272 | Double_t f04=0.5*dx*dx/(r1*r1*r1); |
273 | Double_t f12= dx*fP3*f1/(r1*r1*r1); |
274 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); |
275 | Double_t f13= dx/r1; |
276 | Double_t f24= dx; |
277 | |
278 | //b = C*ft |
279 | Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30; |
280 | Double_t b02=f24*fC40; |
281 | Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31; |
282 | Double_t b12=f24*fC41; |
283 | Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32; |
284 | Double_t b22=f24*fC42; |
285 | Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43; |
286 | Double_t b42=f24*fC44; |
287 | Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33; |
288 | Double_t b32=f24*fC43; |
289 | |
290 | //a = f*b = f*C*ft |
291 | Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42; |
292 | Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32; |
293 | Double_t a22=f24*b42; |
294 | |
295 | //F*C*Ft = C + (b + bt + a) |
296 | fC00 += b00 + b00 + a00; |
297 | fC10 += b10 + b01 + a01; |
298 | fC20 += b20 + b02 + a02; |
299 | fC30 += b30; |
300 | fC40 += b40; |
301 | fC11 += b11 + b11 + a11; |
302 | fC21 += b21 + b12 + a12; |
303 | fC31 += b31; |
304 | fC41 += b41; |
305 | fC22 += b22 + b22 + a22; |
306 | fC32 += b32; |
307 | fC42 += b42; |
308 | |
309 | fX=x2; |
310 | |
311 | Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt()); |
312 | Double_t beta2=p2/(p2 + pm*pm); |
313 | |
314 | //Multiple scattering****************** |
315 | //x0=0.; |
316 | if (x0!=0) { |
317 | x0*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); |
318 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0; |
319 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); |
320 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); |
321 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); |
322 | fC44 += theta2*fP3*fP4*fP3*fP4; |
323 | } |
324 | |
325 | //Energy losses************************ |
326 | if (rho!=0.) { |
327 | rho*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); |
328 | Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*rho; |
329 | if (x1 < x2) dE=-dE; |
330 | fP4*=(1.- sqrt(p2+pm*pm)/p2*dE); |
331 | } |
332 | |
333 | if (!Invariant()) {cout<<"Propagate !\n"; return 0;} |
334 | |
335 | return 1; |
336 | } |
337 | |
338 | //____________________________________________________________________________ |
339 | Int_t AliITStrackV2::Update(const AliCluster* c, Double_t chi2, UInt_t index) { |
340 | //------------------------------------------------------------------ |
341 | //This function updates track parameters |
342 | //------------------------------------------------------------------ |
343 | Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4; |
344 | Double_t c00=fC00; |
345 | Double_t c10=fC10, c11=fC11; |
346 | Double_t c20=fC20, c21=fC21, c22=fC22; |
347 | Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33; |
348 | Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44; |
349 | |
350 | |
351 | Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2(); |
352 | r00+=fC00; r01+=fC10; r11+=fC11; |
353 | Double_t det=r00*r11 - r01*r01; |
354 | Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det; |
355 | |
356 | Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11; |
357 | Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11; |
358 | Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11; |
359 | Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11; |
360 | Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11; |
361 | |
362 | Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1; |
363 | Double_t sf=fP2 + k20*dy + k21*dz; |
364 | /* |
365 | if (TMath::Abs(sf) >= 0.99999) { |
366 | Int_t n=GetNumberOfClusters(); |
367 | if (n>kWARN) cerr<<n<<" AliITStrackV2 warning: Filtering failed !\n"; |
368 | return 0; |
369 | } |
370 | */ |
371 | fP0 += k00*dy + k01*dz; |
372 | fP1 += k10*dy + k11*dz; |
373 | fP2 = sf; |
374 | fP3 += k30*dy + k31*dz; |
375 | fP4 += k40*dy + k41*dz; |
376 | |
377 | Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40; |
378 | Double_t c12=fC21, c13=fC31, c14=fC41; |
379 | |
380 | fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11; |
381 | fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13; |
382 | fC40-=k00*c04+k01*c14; |
383 | |
384 | fC11-=k10*c01+k11*fC11; |
385 | fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13; |
386 | fC41-=k10*c04+k11*c14; |
387 | |
388 | fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13; |
389 | fC42-=k20*c04+k21*c14; |
390 | |
391 | fC33-=k30*c03+k31*c13; |
392 | fC43-=k30*c04+k31*c14; |
393 | |
394 | fC44-=k40*c04+k41*c14; |
395 | |
396 | if (!Invariant()) { |
397 | fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4; |
398 | fC00=c00; |
399 | fC10=c10; fC11=c11; |
400 | fC20=c20; fC21=c21; fC22=c22; |
401 | fC30=c30; fC31=c31; fC32=c32; fC33=c33; |
402 | fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44; |
403 | return 0; |
404 | } |
405 | |
406 | Int_t n=GetNumberOfClusters(); |
407 | fIndex[n]=index; |
408 | SetNumberOfClusters(n+1); |
409 | SetChi2(GetChi2()+chi2); |
410 | |
411 | return 1; |
412 | } |
413 | |
414 | |
415 | //____________________________________________________________________________ |
416 | Int_t AliITStrackV2::Update(const Double_t* m, Double_t chi2, UInt_t index) { |
417 | //------------------------------------------------------------------ |
418 | //This function updates track parameters with a vertex constraint |
419 | //------------------------------------------------------------------ |
420 | Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4; |
421 | Double_t c00=fC00; |
422 | Double_t c10=fC10, c11=fC11; |
423 | Double_t c20=fC20, c21=fC21, c22=fC22; |
424 | Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33; |
425 | Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44; |
426 | |
427 | |
428 | TVectorD x(5); x(0)=fP0; x(1)=fP1; x(2)=fP2; x(3)=fP3; x(4)=fP4; |
429 | TMatrixD C(5,5); |
430 | C(0,0)=fC00; |
431 | C(1,0)=fC10; C(1,1)=fC11; |
432 | C(2,0)=fC20; C(2,1)=fC21; C(2,2)=fC22; |
433 | C(3,0)=fC30; C(3,1)=fC31; C(3,2)=fC32; C(3,3)=fC33; |
434 | C(4,0)=fC40; C(4,1)=fC41; C(4,2)=fC42; C(4,3)=fC43; C(4,4)=fC44; |
435 | |
436 | C(0,1)=C(1,0); |
437 | C(0,2)=C(2,0); C(1,2)=C(2,1); |
438 | C(0,3)=C(3,0); C(1,3)=C(3,1); C(2,3)=C(3,2); |
439 | C(0,4)=C(4,0); C(1,4)=C(4,1); C(2,4)=C(4,2); C(3,4)=C(4,3); |
440 | |
441 | TMatrixD H(4,5); H.UnitMatrix(); |
442 | TMatrixD Ht(TMatrixD::kTransposed,H); |
443 | TVectorD mm(4); mm(0)=m[0]; mm(1)=m[1]; mm(2)=m[2]; mm(3)=m[3]; |
444 | TMatrixD V(4,4); |
445 | V(0,0)=m[4 ]; V(0,1)=m[5 ]; V(0,2)=m[6 ]; V(0,3)=m[7 ]; |
446 | V(1,0)=m[8 ]; V(1,1)=m[9 ]; V(1,2)=m[10]; V(1,3)=m[11]; |
447 | V(2,0)=m[12]; V(2,1)=m[13]; V(2,2)=m[14]; V(2,3)=m[15]; |
448 | V(3,0)=m[16]; V(3,1)=m[17]; V(3,2)=m[18]; V(3,3)=m[19]; |
449 | |
450 | TMatrixD tmp(H,TMatrixD::kMult,C); |
451 | TMatrixD R(tmp,TMatrixD::kMult,Ht); R+=V; |
452 | |
453 | R.Invert(); |
454 | |
455 | TMatrixD K(C,TMatrixD::kMult,Ht); K*=R; |
456 | |
457 | TVectorD savex=x; |
458 | x*=H; x-=mm; x*=-1; x*=K; x+=savex; |
459 | |
460 | TMatrixD saveC=C; |
461 | C.Mult(K,tmp); C-=saveC; C*=-1; |
462 | |
463 | fP0=x(0); fP1=x(1); fP2=x(2); fP3=x(3); fP4=x(4); |
464 | fC00=C(0,0); |
465 | fC10=C(1,0); fC11=C(1,1); |
466 | fC20=C(2,0); fC21=C(2,1); fC22=C(2,2); |
467 | fC30=C(3,0); fC31=C(3,1); fC32=C(3,2); fC33=C(3,3); |
468 | fC40=C(4,0); fC41=C(4,1); fC42=C(4,2); fC43=C(4,3); fC44=C(4,4); |
469 | |
470 | |
471 | if (!Invariant()) { |
472 | fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4; |
473 | fC00=c00; |
474 | fC10=c10; fC11=c11; |
475 | fC20=c20; fC21=c21; fC22=c22; |
476 | fC30=c30; fC31=c31; fC32=c32; fC33=c33; |
477 | fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44; |
478 | return 0; |
479 | } |
480 | |
481 | Int_t n=GetNumberOfClusters(); |
482 | fIndex[n]=index; |
483 | SetNumberOfClusters(n+1); |
484 | SetChi2(GetChi2()+chi2); |
485 | |
486 | return 1; |
487 | } |
488 | |
489 | Int_t AliITStrackV2::Invariant() const { |
490 | //------------------------------------------------------------------ |
491 | // This function is for debugging purpose only |
492 | //------------------------------------------------------------------ |
493 | //if (TMath::Abs(fP1)>11.5) |
494 | //if (fP1*fP4<0) {cout<<"fP1*fP4="<<fP1*fP4<<' '<<fP1<<endl; return 0;} |
495 | if (TMath::Abs(fP2)>=1) {cout<<"fP2="<<fP2<<endl; return 0;} |
496 | |
497 | if (fC00<=0) {cout<<"fC00="<<fC00<<endl; return 0;} |
498 | if (fC11<=0) {cout<<"fC11="<<fC11<<endl; return 0;} |
499 | if (fC22<=0) {cout<<"fC22="<<fC22<<endl; return 0;} |
500 | if (fC33<=0) {cout<<"fC33="<<fC33<<endl; return 0;} |
501 | if (fC44<=0) {cout<<"fC44="<<fC44<<endl; return 0;} |
502 | |
503 | TMatrixD m(5,5); |
504 | m(0,0)=fC00; |
505 | m(1,0)=fC10; m(1,1)=fC11; |
506 | m(2,0)=fC20; m(2,1)=fC21; m(2,2)=fC22; |
507 | m(3,0)=fC30; m(3,1)=fC31; m(3,2)=fC32; m(3,3)=fC33; |
508 | m(4,0)=fC40; m(4,1)=fC41; m(4,2)=fC42; m(4,3)=fC43; m(4,4)=fC44; |
509 | |
510 | m(0,1)=m(1,0); |
511 | m(0,2)=m(2,0); m(1,2)=m(2,1); |
512 | m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2); |
513 | m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3); |
514 | /* |
515 | Double_t det=m.Determinant(); |
516 | |
517 | if (det <= 0) { |
518 | cout<<" bad determinant "<<det<<endl; |
519 | m.Print(); |
520 | return 0; |
521 | } |
522 | */ |
523 | return 1; |
524 | } |
525 | |
526 | //____________________________________________________________________________ |
527 | Int_t AliITStrackV2::Propagate(Double_t alp, Double_t xk, |
528 | Double_t x0,Double_t rho,Double_t pm) { |
529 | //------------------------------------------------------------------ |
530 | //This function propagates a track |
531 | //------------------------------------------------------------------ |
532 | Double_t p0=fP0,p1=fP1,p2=fP2,p3=fP3,p4=fP4; |
533 | Double_t c00=fC00; |
534 | Double_t c10=fC10, c11=fC11; |
535 | Double_t c20=fC20, c21=fC21, c22=fC22; |
536 | Double_t c30=fC30, c31=fC31, c32=fC32, c33=fC33; |
537 | Double_t c40=fC40, c41=fC41, c42=fC42, c43=fC43, c44=fC44; |
538 | |
539 | |
540 | Double_t dalp=alp-fAlpha; |
541 | |
542 | Double_t ca=TMath::Cos(dalp), sa=TMath::Sin(dalp); |
543 | Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2); |
544 | |
545 | Double_t pp2=fP2*ca - cf*sa; |
546 | if (TMath::Abs(pp2) >= 0.99999) { |
547 | Int_t n=GetNumberOfClusters(); |
548 | if (n>kWARN) cerr<<n<<" AliITStrackV2 warning: Rotation failed !\n"; |
549 | return 0; |
550 | } |
551 | |
552 | fAlpha = alp; |
553 | if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi(); |
554 | else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi(); |
555 | |
556 | Double_t x1=fX, y1=fP0; |
557 | |
558 | fX = x1*ca + y1*sa; |
559 | fP0=-x1*sa + y1*ca; |
560 | fP2 = pp2; |
561 | |
562 | cf=ca + sf*sa/cf; |
563 | |
564 | if (!Invariant()) {cout<<dalp<<" Rotate !\n"; return 0;} |
565 | |
566 | x1=fX; Double_t x2=xk, dx=x2-x1; |
567 | Double_t f1=fP2, f2=f1 + fP4*dx; |
568 | if (TMath::Abs(f2) >= 0.99999) { |
569 | Int_t n=GetNumberOfClusters(); |
570 | if (n>kWARN) cerr<<n<<" AliITStrackV2 warning: Propagation failed !\n"; |
571 | return 0; |
572 | } |
573 | |
574 | Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2); |
575 | |
576 | fP0 += dx*(f1+f2)/(r1+r2); |
577 | fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3; |
578 | fP2 += dx*fP4; |
579 | |
580 | //f = F - 1 |
581 | Double_t f02= dx/(r1*r1*r1); |
582 | Double_t f04=0.5*dx*dx/(r1*r1*r1); |
583 | Double_t f12= dx*fP3*f1/(r1*r1*r1); |
584 | Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); |
585 | Double_t f13= dx/r1; |
586 | Double_t f24= dx; |
587 | /* |
588 | //b = C*ft |
589 | Double_t b00=f02*fC20 + f03*fC30, b01=f12*fC20 + f13*fC30 + f14*fC40; |
590 | Double_t b02=f23*fC30; |
591 | Double_t b10=f02*fC21 + f03*fC31, b11=f12*fC21 + f13*fC31 + f14*fC41; |
592 | Double_t b12=f23*fC31; |
593 | Double_t b20=f02*fC22 + f03*fC32, b21=f12*fC22 + f13*fC32 + f14*fC42; |
594 | Double_t b22=f23*fC32; |
595 | Double_t b30=f02*fC32 + f03*fC33, b31=f12*fC32 + f13*fC33 + f14*fC43; |
596 | Double_t b32=f23*fC33; |
597 | Double_t b40=f02*fC42 + f03*fC43, b41=f12*fC42 + f13*fC43 + f14*fC44; |
598 | Double_t b42=f23*fC43; |
599 | |
600 | //a = f*b = f*C*ft |
601 | Double_t a00=f02*b20+f03*b30,a01=f02*b21+f03*b31,a02=f02*b22+f03*b32; |
602 | Double_t a11=f12*b21+f13*b31+f14*b41,a12=f12*b22+f13*b32+f14*b42; |
603 | Double_t a22=f23*b32; |
604 | |
605 | //F*C*Ft = C + (b + bt + a) |
606 | fC00 += b00 + b00 + a00; |
607 | fC10 += b10 + b01 + a01; |
608 | fC20 += b20 + b02 + a02; |
609 | fC30 += b30; |
610 | fC40 += b40; |
611 | fC11 += b11 + b11 + a11; |
612 | fC21 += b21 + b12 + a12; |
613 | fC31 += b31; |
614 | fC41 += b41; |
615 | fC22 += b22 + b22 + a22; |
616 | fC32 += b32; |
617 | fC42 += b42; |
618 | */ |
619 | |
620 | TMatrixD F(5,5); F.UnitMatrix(); |
621 | F(0,0)=-(f1+f2)/(r1+r2)*sa + ca; F(0,2)=f02*cf; F(0,4)=f04; |
622 | F(1,0)=-(f1+f2)/(f1*r2 + f2*r1)*fP3*sa; F(1,2)=f12*cf; F(1,4)=f14; F(1,3)=f13; |
623 | F(2,0)=-fP4*sa; F(2,2)=cf; F(2,4)=f24; |
624 | |
625 | TMatrixD C(5,5); |
626 | C(0,0)=fC00; |
627 | C(1,0)=fC10; C(1,1)=fC11; |
628 | C(2,0)=fC20; C(2,1)=fC21; C(2,2)=fC22; |
629 | C(3,0)=fC30; C(3,1)=fC31; C(3,2)=fC32; C(3,3)=fC33; |
630 | C(4,0)=fC40; C(4,1)=fC41; C(4,2)=fC42; C(4,3)=fC43; C(4,4)=fC44; |
631 | |
632 | C(0,1)=C(1,0); |
633 | C(0,2)=C(2,0); C(1,2)=C(2,1); |
634 | C(0,3)=C(3,0); C(1,3)=C(3,1); C(2,3)=C(3,2); |
635 | C(0,4)=C(4,0); C(1,4)=C(4,1); C(2,4)=C(4,2); C(3,4)=C(4,3); |
636 | |
637 | TMatrixD tmp(C,TMatrixD::kMult,TMatrixD(TMatrixD::kTransposed, F)); |
638 | C.Mult(F,tmp); |
639 | |
640 | fC00=C(0,0); |
641 | fC10=C(1,0); fC11=C(1,1); |
642 | fC20=C(2,0); fC21=C(2,1); fC22=C(2,2); |
643 | fC30=C(3,0); fC31=C(3,1); fC32=C(3,2); fC33=C(3,3); |
644 | fC40=C(4,0); fC41=C(4,1); fC42=C(4,2); fC43=C(4,3); fC44=C(4,4); |
645 | |
646 | pp2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt()); |
647 | Double_t beta2=pp2/(pp2 + pm*pm); |
648 | |
649 | //Multiple scattering****************** |
650 | //x0=0.; |
651 | if (x0!=0.) { |
652 | x0*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); |
653 | Double_t theta2=14.1*14.1/(beta2*pp2*1e6)*x0; |
654 | fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); |
655 | fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); |
656 | fC43 += theta2*fP3*fP4*(1. + fP3*fP3); |
657 | fC44 += theta2*fP3*fP4*fP3*fP4; |
658 | } |
659 | |
660 | //Energy losses************************ |
661 | if (rho!=0.) { |
662 | rho*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2)); |
663 | Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*rho; |
664 | if (x1 < x2) dE=-dE; |
665 | fP4*=(1.- sqrt(pp2+pm*pm)/pp2*dE); |
666 | } |
667 | |
668 | if (!Invariant()) { |
669 | fP0=p0; fP1=p1; fP2=p2; fP3=p3; fP4=p4; |
670 | fC00=c00; |
671 | fC10=c10; fC11=c11; |
672 | fC20=c20; fC21=c21; fC22=c22; |
673 | fC30=c30; fC31=c31; fC32=c32; fC33=c33; |
674 | fC40=c40; fC41=c41; fC42=c42; fC43=c43; fC44=c44; |
675 | return 0; |
676 | } |
677 | |
678 | fX=x2; |
679 | |
680 | return 1; |
681 | } |
682 | |
683 | Double_t AliITStrackV2::GetD() const { |
684 | //------------------------------------------------------------------ |
685 | //This function calculates the transverse impact parameter |
686 | //------------------------------------------------------------------ |
687 | Double_t sn=fP4*fX - fP2, cs=fP4*fP0 + TMath::Sqrt(1.- fP2*fP2); |
688 | Double_t a=2*(fX*fP2 - fP0*TMath::Sqrt(1.- fP2*fP2))-fP4*(fX*fX + fP0*fP0); |
689 | if (fP4<0) a=-a; |
690 | return a/(1 + TMath::Sqrt(sn*sn + cs*cs)); |
691 | } |
692 | |
693 | |
694 | Int_t AliITStrackV2::Improve(Double_t x0,Double_t yv,Double_t zv) { |
695 | //------------------------------------------------------------------ |
696 | //This function improves angular track parameters |
697 | //------------------------------------------------------------------ |
698 | Double_t dy=fP0-yv, dz=fP1-zv; |
699 | Double_t r2=fX*fX+dy*dy; |
700 | Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt()); |
701 | Double_t beta2=p2/(p2 + 0.14*0.14); |
702 | x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp())); |
703 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0; |
704 | |
705 | Double_t par=0.5*(fP4*fX + dy*TMath::Sqrt(4/r2-fP4*fP4)); |
706 | Double_t sigma2 = theta2*(1.- GetSnp()*GetSnp())*(1. + GetTgl()*GetTgl()); |
707 | sigma2 += fC00/r2*(1.- dy*dy/r2)*(1.- dy*dy/r2); |
708 | sigma2 += kSigmaYV*kSigmaYV/r2; |
709 | sigma2 += 0.25*fC44*fX*fX; |
710 | Double_t eps2=sigma2/(fC22+sigma2), eps=TMath::Sqrt(eps2); |
711 | if (10*r2*fC44<fC22) { |
712 | fP2 = eps2*fP2 + (1-eps2)*par; |
713 | fC22*=eps2; fC21*=eps; fC20*=eps; fC32*=eps; fC42*=eps; |
714 | } |
715 | |
716 | par=0.5*fP4*dz/TMath::ASin(0.5*fP4*TMath::Sqrt(r2)); |
717 | sigma2=theta2; |
718 | sigma2 += fC11/r2+fC00*dy*dy*dz*dz/(r2*r2*r2); |
719 | sigma2 += kSigmaZV*kSigmaZV/r2; |
720 | eps2=sigma2/(fC33+sigma2); eps=TMath::Sqrt(eps2); |
721 | Double_t tgl=fP3; |
722 | fP3 = eps2*fP3 + (1-eps2)*par; |
723 | fC33*=eps2; fC32*=eps; fC31*=eps; fC30*=eps; fC43*=eps; |
724 | |
725 | eps=TMath::Sqrt((1+fP3*fP3)/(1+tgl*tgl)); |
726 | fP4*=eps; |
727 | fC44*=eps*eps; fC43*=eps;fC42*=eps; fC41*=eps; fC40*=eps; |
728 | |
729 | if (!Invariant()) return 0; |
730 | return 1; |
731 | } |
732 | |
733 | /* |
734 | Int_t AliITStrackV2::Improve(Double_t x0,Double_t xv,Double_t yv) { |
735 | //------------------------------------------------------------------ |
736 | //This function improves angular track parameters |
737 | //------------------------------------------------------------------ |
738 | TMatrixD I(5,5); |
739 | TVectorD v(5); v(0)=fP0; v(1)=fP1; v(2)=fP2; v(3)=fP3; v(4)=fP4; |
740 | |
741 | Double_t r2=fX*fX+fP0*fP0; |
742 | Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt()); |
743 | Double_t beta2=p2/(p2 + 0.14*0.14); |
744 | x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp())); |
745 | Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0; |
746 | |
747 | v(2)=0.5*(fP4*fX + fP0*TMath::Sqrt(4/r2-fP4*fP4)); |
748 | Double_t sigma2 = theta2*(1.- GetSnp()*GetSnp())*(1. + GetTgl()*GetTgl()); |
749 | sigma2 += fC00/r2*(1.- fP0*fP0/r2)*(1.- fP0*fP0/r2); |
750 | sigma2 += kSigmaYV*kSigmaYV/r2; |
751 | I(2,2)=1/sigma2; |
752 | |
753 | v(3)=0.5*fP4*fP1/TMath::ASin(0.5*fP4*TMath::Sqrt(r2)); |
754 | sigma2=theta2; |
755 | sigma2 += fC11/r2+fC00*fP0*fP0*fP1*fP1/(r2*r2*r2); |
756 | sigma2 += kSigmaZV*kSigmaZV/r2; |
757 | I(3,3)=1/sigma2; |
758 | |
759 | Double_t tgl=fP3; |
760 | |
761 | TVectorD x(5); x(0)=fP0; x(1)=fP1; x(2)=fP2; x(3)=fP3; x(4)=fP4; |
762 | TMatrixD C(5,5); |
763 | C(0,0)=fC00; |
764 | C(1,0)=fC10; C(1,1)=fC11; |
765 | C(2,0)=fC20; C(2,1)=fC21; C(2,2)=fC22; |
766 | C(3,0)=fC30; C(3,1)=fC31; C(3,2)=fC32; C(3,3)=fC33; |
767 | C(4,0)=fC40; C(4,1)=fC41; C(4,2)=fC42; C(4,3)=fC43; C(4,4)=fC44; |
768 | |
769 | C(0,1)=C(1,0); |
770 | C(0,2)=C(2,0); C(1,2)=C(2,1); |
771 | C(0,3)=C(3,0); C(1,3)=C(3,1); C(2,3)=C(3,2); |
772 | C(0,4)=C(4,0); C(1,4)=C(4,1); C(2,4)=C(4,2); C(3,4)=C(4,3); |
773 | |
774 | TMatrixD tmp(I,TMatrixD::kMult,C),U(5,5); U.UnitMatrix(); |
775 | U+=tmp; |
776 | U.Invert(); |
777 | TMatrixD W1(U); |
778 | TMatrixD W2(tmp,TMatrixD::kMult,W1); |
779 | |
780 | v*=W2; x*=W1; x+=v; |
781 | |
782 | C*=W1; |
783 | |
784 | |
785 | fP0=x(0); fP1=x(1); fP2=x(2); fP3=x(3); fP4=x(4); |
786 | fC00=C(0,0); |
787 | fC10=C(1,0); fC11=C(1,1); |
788 | fC20=C(2,0); fC21=C(2,1); fC22=C(2,2); |
789 | fC30=C(3,0); fC31=C(3,1); fC32=C(3,2); fC33=C(3,3); |
790 | fC40=C(4,0); fC41=C(4,1); fC42=C(4,2); fC43=C(4,3); fC44=C(4,4); |
791 | |
792 | eps=TMath::Sqrt((1+fP3*fP3)/(1+tgl*tgl)); |
793 | fP4*=eps; |
794 | fC44*=eps*eps; fC43*=eps;fC42*=eps; fC41*=eps; fC40*=eps; |
795 | |
796 | if (!Invariant()) return 0; |
797 | return 1; |
798 | } |
799 | */ |
800 | |