First commit of ITS tracking version 2 (Yu.Belikov)
[u/mrichter/AliRoot.git] / ITS / AliITStrackV2.cxx
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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
31ClassImp(AliITStrackV2)
32
33const Int_t kWARN=1;
34
35//____________________________________________________________________________
36AliITStrackV2::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//____________________________________________________________________________
70AliITStrackV2::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//_____________________________________________________________________________
91Int_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//_____________________________________________________________________________
104void 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//____________________________________________________________________________
119Int_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//____________________________________________________________________________
129Int_t AliITStrackV2::
130GetGlobalXYZat(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//_____________________________________________________________________________
156Double_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//_____________________________________________________________________________
178Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c,Double_t *m,
179Double_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//____________________________________________________________________________
250Int_t
251AliITStrackV2::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//____________________________________________________________________________
339Int_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//____________________________________________________________________________
416Int_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
489Int_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//____________________________________________________________________________
527Int_t AliITStrackV2::Propagate(Double_t alp, Double_t xk,
528Double_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
683Double_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
694Int_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/*
734Int_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