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73042f01 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
0938c7d3 16/*
17$Log$
19364939 18Revision 1.12 2002/10/14 14:57:43 hristov
19Merging the VirtualMC branch to the main development branch (HEAD)
20
b9d0a01d 21Revision 1.9.6.1 2002/10/11 08:34:48 hristov
22Updating VirtualMC to v3-09-02
23
24Revision 1.11 2002/07/19 07:34:42 kowal2
25Logs added
26
0938c7d3 27*/
28
29
73042f01 30//-----------------------------------------------------------------
31// Implementation of the TPC track class
32//
33// Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch
34//-----------------------------------------------------------------
35
19364939 36#include <Riostream.h>
b19a0509 37
73042f01 38#include "AliTPCtrack.h"
39#include "AliTPCcluster.h"
40#include "AliTPCClustersRow.h"
41#include "AliTPCClustersArray.h"
42
43ClassImp(AliTPCtrack)
b9de75e1 44
73042f01 45//_________________________________________________________________________
46AliTPCtrack::AliTPCtrack(UInt_t index, const Double_t xx[5],
b19a0509 47const Double_t cc[15], Double_t xref, Double_t alpha) : AliKalmanTrack() {
73042f01 48 //-----------------------------------------------------------------
49 // This is the main track constructor.
50 //-----------------------------------------------------------------
73042f01 51 fX=xref;
be9c5115 52 fAlpha=alpha;
53 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
54 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
55 fdEdx=0.;
73042f01 56
b19a0509 57 fP0=xx[0]; fP1=xx[1]; fP2=xx[2]; fP3=xx[3]; fP4=xx[4];
73042f01 58
b19a0509 59 fC00=cc[0];
60 fC10=cc[1]; fC11=cc[2];
61 fC20=cc[3]; fC21=cc[4]; fC22=cc[5];
62 fC30=cc[6]; fC31=cc[7]; fC32=cc[8]; fC33=cc[9];
63 fC40=cc[10]; fC41=cc[11]; fC42=cc[12]; fC43=cc[13]; fC44=cc[14];
73042f01 64
be9c5115 65 fIndex[0]=index;
66 SetNumberOfClusters(1);
b9de75e1 67
68}
69
70//_____________________________________________________________________________
71AliTPCtrack::AliTPCtrack(const AliKalmanTrack& t,Double_t alpha) {
72 //-----------------------------------------------------------------
73 // Conversion AliKalmanTrack -> AliTPCtrack.
74 //-----------------------------------------------------------------
75 SetLabel(t.GetLabel());
76 SetChi2(0.);
7f6ddf58 77 SetMass(t.GetMass());
b9de75e1 78 SetNumberOfClusters(0);
79 //SetConvConst(t.GetConvConst());
80
81 fdEdx = 0.;
82 fAlpha = alpha;
83 if (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
84 else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
85
86 //Conversion of the track parameters
87 Double_t x,p[5]; t.GetExternalParameters(x,p);
88 fX=x; x=GetConvConst();
89 fP0=p[0];
90 fP1=p[1];
91 fP3=p[3];
92 fP4=p[4]/x;
93 fP2=fP4*fX - p[2];
94
95 //Conversion of the covariance matrix
96 Double_t c[15]; t.GetExternalCovariance(c);
97 c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;
98
99 Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
100 Double_t c32=fX*c[13] - c[8];
101 Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];
102
103 fC00=c[0 ];
104 fC10=c[1 ]; fC11=c[2 ];
105 fC20=c20; fC21=c21; fC22=c22;
106 fC30=c[6 ]; fC31=c[7 ]; fC32=c32; fC33=c[9 ];
107 fC40=c[10]; fC41=c[11]; fC42=c42; fC43=c[13]; fC44=c[14];
108
73042f01 109}
110
111//_____________________________________________________________________________
b19a0509 112AliTPCtrack::AliTPCtrack(const AliTPCtrack& t) : AliKalmanTrack(t) {
73042f01 113 //-----------------------------------------------------------------
114 // This is a track copy constructor.
115 //-----------------------------------------------------------------
be9c5115 116 fX=t.fX;
117 fAlpha=t.fAlpha;
73042f01 118 fdEdx=t.fdEdx;
119
be9c5115 120 fP0=t.fP0; fP1=t.fP1; fP2=t.fP2; fP3=t.fP3; fP4=t.fP4;
121
122 fC00=t.fC00;
123 fC10=t.fC10; fC11=t.fC11;
124 fC20=t.fC20; fC21=t.fC21; fC22=t.fC22;
125 fC30=t.fC30; fC31=t.fC31; fC32=t.fC32; fC33=t.fC33;
126 fC40=t.fC40; fC41=t.fC41; fC42=t.fC42; fC43=t.fC43; fC44=t.fC44;
127
128 Int_t n=GetNumberOfClusters();
129 for (Int_t i=0; i<n; i++) fIndex[i]=t.fIndex[i];
130}
131
132//_____________________________________________________________________________
133Int_t AliTPCtrack::Compare(const TObject *o) const {
134 //-----------------------------------------------------------------
135 // This function compares tracks according to the their curvature
136 //-----------------------------------------------------------------
137 AliTPCtrack *t=(AliTPCtrack*)o;
024a7fe9 138 //Double_t co=TMath::Abs(t->Get1Pt());
139 //Double_t c =TMath::Abs(Get1Pt());
140 Double_t co=t->GetSigmaY2()*t->GetSigmaZ2();
141 Double_t c =GetSigmaY2()*GetSigmaZ2();
be9c5115 142 if (c>co) return 1;
143 else if (c<co) return -1;
144 return 0;
145}
146
147//_____________________________________________________________________________
148void AliTPCtrack::GetExternalCovariance(Double_t cc[15]) const {
149 //-------------------------------------------------------------------------
150 // This function returns an external representation of the covriance matrix.
151 // (See comments in AliTPCtrack.h about external track representation)
152 //-------------------------------------------------------------------------
9b280d80 153 Double_t a=GetConvConst();
be9c5115 154
b9de75e1 155 Double_t c22=fX*fX*fC44-2*fX*fC42+fC22;
156 Double_t c32=fX*fC43-fC32;
157 Double_t c20=fX*fC40-fC20, c21=fX*fC41-fC21, c42=fX*fC44-fC42;
be9c5115 158
159 cc[0 ]=fC00;
160 cc[1 ]=fC10; cc[2 ]=fC11;
161 cc[3 ]=c20; cc[4 ]=c21; cc[5 ]=c22;
b9de75e1 162 cc[6 ]=fC30; cc[7 ]=fC31; cc[8 ]=c32; cc[9 ]=fC33;
163 cc[10]=fC40*a; cc[11]=fC41*a; cc[12]=c42*a; cc[13]=fC43*a; cc[14]=fC44*a*a;
be9c5115 164
165}
166
167//_____________________________________________________________________________
168Double_t AliTPCtrack::GetPredictedChi2(const AliCluster *c) const
169{
170 //-----------------------------------------------------------------
171 // This function calculates a predicted chi2 increment.
172 //-----------------------------------------------------------------
173 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
174 r00+=fC00; r01+=fC10; r11+=fC11;
175
176 Double_t det=r00*r11 - r01*r01;
177 if (TMath::Abs(det) < 1.e-10) {
178 Int_t n=GetNumberOfClusters();
179 if (n>4) cerr<<n<<" AliKalmanTrack warning: Singular matrix !\n";
180 return 1e10;
181 }
182 Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
183
184 Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1;
185
186 return (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det;
73042f01 187}
188
189//_____________________________________________________________________________
7f6ddf58 190Int_t AliTPCtrack::PropagateTo(Double_t xk,Double_t x0,Double_t rho) {
73042f01 191 //-----------------------------------------------------------------
192 // This function propagates a track to a reference plane x=xk.
193 //-----------------------------------------------------------------
b9de75e1 194 if (TMath::Abs(fP4*xk - fP2) >= 0.99999) {
be9c5115 195 Int_t n=GetNumberOfClusters();
196 if (n>4) cerr<<n<<" AliTPCtrack warning: Propagation failed !\n";
73042f01 197 return 0;
198 }
199
b19a0509 200 Double_t x1=fX, x2=x1+(xk-x1), dx=x2-x1, y1=fP0, z1=fP1;
b9de75e1 201 Double_t c1=fP4*x1 - fP2, r1=sqrt(1.- c1*c1);
202 Double_t c2=fP4*x2 - fP2, r2=sqrt(1.- c2*c2);
73042f01 203
b19a0509 204 fP0 += dx*(c1+c2)/(r1+r2);
b9de75e1 205 fP1 += dx*(c1+c2)/(c1*r2 + c2*r1)*fP3;
73042f01 206
207 //f = F - 1
208 Double_t rr=r1+r2, cc=c1+c2, xx=x1+x2;
b19a0509 209 Double_t f02=-dx*(2*rr + cc*(c1/r1 + c2/r2))/(rr*rr);
b9de75e1 210 Double_t f04= dx*(rr*xx + cc*(c1*x1/r1+c2*x2/r2))/(rr*rr);
73042f01 211 Double_t cr=c1*r2+c2*r1;
b9de75e1 212 Double_t f12=-dx*fP3*(2*cr + cc*(c2*c1/r1-r1 + c1*c2/r2-r2))/(cr*cr);
213 Double_t f13= dx*cc/cr;
214 Double_t f14=dx*fP3*(cr*xx-cc*(r1*x2-c2*c1*x1/r1+r2*x1-c1*c2*x2/r2))/(cr*cr);
73042f01 215
216 //b = C*ft
b9de75e1 217 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
218 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
219 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
220 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
221 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
73042f01 222
223 //a = f*b = f*C*ft
b9de75e1 224 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a11=f12*b21+f14*b41+f13*b31;
73042f01 225
226 //F*C*Ft = C + (a + b + bt)
b19a0509 227 fC00 += a00 + 2*b00;
228 fC10 += a01 + b01 + b10;
229 fC20 += b20;
230 fC30 += b30;
231 fC40 += b40;
232 fC11 += a11 + 2*b11;
233 fC21 += b21;
234 fC31 += b31;
235 fC41 += b41;
73042f01 236
237 fX=x2;
238
239 //Multiple scattering******************
b19a0509 240 Double_t d=sqrt((x1-fX)*(x1-fX)+(y1-fP0)*(y1-fP0)+(z1-fP1)*(z1-fP1));
be9c5115 241 Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
7f6ddf58 242 Double_t beta2=p2/(p2 + GetMass()*GetMass());
024a7fe9 243 //Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
244 Double_t theta2=1.0259e-6*10*10/20/(beta2*p2)*d*rho;
73042f01 245
b9de75e1 246 Double_t ey=fP4*fX - fP2, ez=fP3;
247 Double_t xz=fP4*ez, zz1=ez*ez+1, xy=fP2+ey;
73042f01 248
b19a0509 249 fC22 += (2*ey*ez*ez*fP2+1-ey*ey+ez*ez+fP2*fP2*ez*ez)*theta2;
b9de75e1 250 fC32 += ez*zz1*xy*theta2;
251 fC33 += zz1*zz1*theta2;
252 fC42 += xz*ez*xy*theta2;
253 fC43 += xz*zz1*theta2;
254 fC44 += xz*xz*theta2;
73042f01 255
256 //Energy losses************************
257 Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d*rho;
258 if (x1 < x2) dE=-dE;
b9de75e1 259 cc=fP4;
7f6ddf58 260 fP4*=(1.- sqrt(p2+GetMass()*GetMass())/p2*dE);
b9de75e1 261 fP2+=fX*(fP4-cc);
73042f01 262
263 return 1;
264}
265
266//_____________________________________________________________________________
7f6ddf58 267Int_t AliTPCtrack::PropagateToVertex(Double_t x0,Double_t rho)
73042f01 268{
269 //-----------------------------------------------------------------
270 // This function propagates tracks to the "vertex".
271 //-----------------------------------------------------------------
b9de75e1 272 Double_t c=fP4*fX - fP2;
273 Double_t tgf=-fP2/(fP4*fP0 + sqrt(1-c*c));
73042f01 274 Double_t snf=tgf/sqrt(1.+ tgf*tgf);
b9de75e1 275 Double_t xv=(fP2+snf)/fP4;
7f6ddf58 276 return PropagateTo(xv,x0,rho);
73042f01 277}
278
279//_____________________________________________________________________________
be9c5115 280Int_t AliTPCtrack::Update(const AliCluster *c, Double_t chisq, UInt_t index) {
73042f01 281 //-----------------------------------------------------------------
282 // This function associates a cluster with this track.
283 //-----------------------------------------------------------------
284 Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
b19a0509 285 r00+=fC00; r01+=fC10; r11+=fC11;
73042f01 286 Double_t det=r00*r11 - r01*r01;
287 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
288
b19a0509 289 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
290 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
291 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
292 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
293 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
73042f01 294
b19a0509 295 Double_t dy=c->GetY() - fP0, dz=c->GetZ() - fP1;
b9de75e1 296 Double_t cur=fP4 + k40*dy + k41*dz, eta=fP2 + k20*dy + k21*dz;
73042f01 297 if (TMath::Abs(cur*fX-eta) >= 0.99999) {
be9c5115 298 Int_t n=GetNumberOfClusters();
299 if (n>4) cerr<<n<<" AliTPCtrack warning: Filtering failed !\n";
300 return 0;
73042f01 301 }
302
b19a0509 303 fP0 += k00*dy + k01*dz;
304 fP1 += k10*dy + k11*dz;
305 fP2 = eta;
b9de75e1 306 fP3 += k30*dy + k31*dz;
307 fP4 = cur;
73042f01 308
b19a0509 309 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
310 Double_t c12=fC21, c13=fC31, c14=fC41;
73042f01 311
b19a0509 312 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
313 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
314 fC40-=k00*c04+k01*c14;
73042f01 315
b19a0509 316 fC11-=k10*c01+k11*fC11;
317 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
318 fC41-=k10*c04+k11*c14;
73042f01 319
b19a0509 320 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
321 fC42-=k20*c04+k21*c14;
73042f01 322
b19a0509 323 fC33-=k30*c03+k31*c13;
b9de75e1 324 fC43-=k40*c03+k41*c13;
73042f01 325
b19a0509 326 fC44-=k40*c04+k41*c14;
73042f01 327
be9c5115 328 Int_t n=GetNumberOfClusters();
329 fIndex[n]=index;
330 SetNumberOfClusters(n+1);
331 SetChi2(GetChi2()+chisq);
332
333 return 1;
73042f01 334}
335
336//_____________________________________________________________________________
337Int_t AliTPCtrack::Rotate(Double_t alpha)
338{
339 //-----------------------------------------------------------------
340 // This function rotates this track.
341 //-----------------------------------------------------------------
342 fAlpha += alpha;
be9c5115 343 if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
344 if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();
73042f01 345
b19a0509 346 Double_t x1=fX, y1=fP0;
73042f01 347 Double_t ca=cos(alpha), sa=sin(alpha);
b9de75e1 348 Double_t r1=fP4*fX - fP2;
73042f01 349
350 fX = x1*ca + y1*sa;
b19a0509 351 fP0=-x1*sa + y1*ca;
b9de75e1 352 fP2=fP2*ca + (fP4*y1 + sqrt(1.- r1*r1))*sa;
73042f01 353
b9de75e1 354 Double_t r2=fP4*fX - fP2;
73042f01 355 if (TMath::Abs(r2) >= 0.99999) {
be9c5115 356 Int_t n=GetNumberOfClusters();
357 if (n>4) cerr<<n<<" AliTPCtrack warning: Rotation failed !\n";
73042f01 358 return 0;
359 }
360
b9de75e1 361 Double_t y0=fP0 + sqrt(1.- r2*r2)/fP4;
362 if ((fP0-y0)*fP4 >= 0.) {
be9c5115 363 Int_t n=GetNumberOfClusters();
364 if (n>4) cerr<<n<<" AliTPCtrack warning: Rotation failed !!!\n";
73042f01 365 return 0;
366 }
367
368 //f = F - 1
b9de75e1 369 Double_t f00=ca-1, f24=(y1 - r1*x1/sqrt(1.- r1*r1))*sa,
370 f20=fP4*sa, f22=(ca + sa*r1/sqrt(1.- r1*r1))-1;
73042f01 371
372 //b = C*ft
b9de75e1 373 Double_t b00=fC00*f00, b02=fC00*f20+fC40*f24+fC20*f22;
374 Double_t b10=fC10*f00, b12=fC10*f20+fC41*f24+fC21*f22;
375 Double_t b20=fC20*f00, b22=fC20*f20+fC42*f24+fC22*f22;
376 Double_t b30=fC30*f00, b32=fC30*f20+fC43*f24+fC32*f22;
377 Double_t b40=fC40*f00, b42=fC40*f20+fC44*f24+fC42*f22;
73042f01 378
379 //a = f*b = f*C*ft
b9de75e1 380 Double_t a00=f00*b00, a02=f00*b02, a22=f20*b02+f24*b42+f22*b22;
73042f01 381
382 // *** Double_t dy2=fCyy;
383
384 //F*C*Ft = C + (a + b + bt)
b19a0509 385 fC00 += a00 + 2*b00;
386 fC10 += b10;
387 fC20 += a02+b20+b02;
388 fC30 += b30;
389 fC40 += b40;
390 fC21 += b12;
391 fC32 += b32;
392 fC22 += a22 + 2*b22;
393 fC42 += b42;
73042f01 394
395 // *** fCyy+=dy2*sa*sa*r1*r1/(1.- r1*r1);
396 // *** fCzz+=d2y*sa*sa*fT*fT/(1.- r1*r1);
397
398 return 1;
399}
400
b9de75e1 401void AliTPCtrack::ResetCovariance() {
402 //------------------------------------------------------------------
403 //This function makes a track forget its history :)
404 //------------------------------------------------------------------
405
406 fC00*=10.;
407 fC10=0.; fC11*=10.;
408 fC20=0.; fC21=0.; fC22*=10.;
409 fC30=0.; fC31=0.; fC32=0.; fC33*=10.;
410 fC40=0.; fC41=0.; fC42=0.; fC43=0.; fC44*=10.;
411
73042f01 412}