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f826d409 1//---------------------------------------------------------------------------------
2// Implementation of the AliKFParticleBase class
3// .
4// @author S.Gorbunov, I.Kisel
5// @version 1.0
6// @since 13.05.07
7//
8// Class to reconstruct and store the decayed particle parameters.
9// The method is described in CBM-SOFT note 2007-003,
10// ``Reconstruction of decayed particles based on the Kalman filter'',
11// http://www.gsi.de/documents/DOC-2007-May-14-1.pdf
12//
13// This class describes general mathematics which is used by AliKFParticle class
14//
15// -= Copyright &copy ALICE HLT Group =-
16//_________________________________________________________________________________
17
18
19#include "AliKFParticleBase.h"
20#include "TMath.h"
21
effa6338 22ClassImp(AliKFParticleBase)
f826d409 23
24
25AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0)
26{
27 //* Constructor
28
29 Initialize();
30}
e7b09c95 31
32void AliKFParticleBase::Initialize( const Double_t Param[], const Double_t Cov[], Int_t Charge, Double_t Mass )
33{
34 // Constructor from "cartesian" track, particle mass hypothesis should be provided
35 //
36 // Param[6] = { X, Y, Z, Px, Py, Pz } - position and momentum
37 // Cov [21] = lower-triangular part of the covariance matrix:
38 //
39 // ( 0 . . . . . )
40 // ( 1 2 . . . . )
41 // Cov. matrix = ( 3 4 5 . . . ) - numbering of covariance elements in Cov[]
42 // ( 6 7 8 9 . . )
43 // ( 10 11 12 13 14 . )
44 // ( 15 16 17 18 19 20 )
45
46
47 for( Int_t i=0; i<6 ; i++ ) fP[i] = Param[i];
48 for( Int_t i=0; i<21; i++ ) fC[i] = Cov[i];
49
50 Double_t energy = TMath::Sqrt( Mass*Mass + fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]);
51 fP[6] = energy;
52 fP[7] = 0;
53 fQ = Charge;
54 fNDF = 0;
55 fChi2 = 0;
56 fAtProductionVertex = 0;
57 fIsLinearized = 0;
58 fSFromDecay = 0;
59
60 Double_t energyInv = 1./energy;
61 Double_t
62 h0 = fP[3]*energyInv,
63 h1 = fP[4]*energyInv,
64 h2 = fP[5]*energyInv;
65
66 fC[21] = h0*fC[ 6] + h1*fC[10] + h2*fC[15];
67 fC[22] = h0*fC[ 7] + h1*fC[11] + h2*fC[16];
68 fC[23] = h0*fC[ 8] + h1*fC[12] + h2*fC[17];
69 fC[24] = h0*fC[ 9] + h1*fC[13] + h2*fC[18];
70 fC[25] = h0*fC[13] + h1*fC[14] + h2*fC[19];
71 fC[26] = h0*fC[18] + h1*fC[19] + h2*fC[20];
706952f5 72 fC[27] = ( h0*h0*fC[ 9] + h1*h1*fC[14] + h2*h2*fC[20]
73 + 2*(h0*h1*fC[13] + h0*h2*fC[18] + h1*h2*fC[19] ) );
e7b09c95 74 for( Int_t i=28; i<36; i++ ) fC[i] = 0;
75 fC[35] = 1.;
76}
77
f826d409 78void AliKFParticleBase::Initialize()
79{
80 //* Initialise covariance matrix and set current parameters to 0.0
81
82 for( Int_t i=0; i<8; i++) fP[i] = 0;
83 for(Int_t i=0;i<36;++i) fC[i]=0.;
84 fC[0] = fC[2] = fC[5] = 100.;
85 fC[35] = 1.;
86 fNDF = -3;
87 fChi2 = 0.;
88 fQ = 0;
89 fSFromDecay = 0;
90 fAtProductionVertex = 0;
91 fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.;
92 fIsLinearized = 0;
93}
94
95void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z )
96{
97 //* Set decay vertex parameters for linearisation
98
99 fVtxGuess[0] = x;
100 fVtxGuess[1] = y;
101 fVtxGuess[2] = z;
102 fIsLinearized = 1;
103}
104
105
5fc72f28 106Int_t AliKFParticleBase::GetMomentum( Double_t &p, Double_t &error ) const
f826d409 107{
108 //* Calculate particle momentum
109
110 Double_t x = fP[3];
111 Double_t y = fP[4];
112 Double_t z = fP[5];
113 Double_t x2 = x*x;
114 Double_t y2 = y*y;
115 Double_t z2 = z*z;
116 Double_t p2 = x2+y2+z2;
5fc72f28 117 p = TMath::Sqrt(p2);
118 error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) );
119 if( error>0 && p>1.e-4 ){
120 error = TMath::Sqrt(error)/p;
f826d409 121 return 0;
122 }
123 return 1;
124}
125
5fc72f28 126Int_t AliKFParticleBase::GetPt( Double_t &pt, Double_t &error ) const
706952f5 127{
128 //* Calculate particle transverse momentum
129
130 Double_t px = fP[3];
131 Double_t py = fP[4];
132 Double_t px2 = px*px;
133 Double_t py2 = py*py;
134 Double_t pt2 = px2+py2;
5fc72f28 135 pt = TMath::Sqrt(pt2);
136 error = (px2*fC[9] + py2*fC[14] + 2*px*py*fC[13] );
137 if( error>0 && pt>1.e-4 ){
138 error = TMath::Sqrt(error)/pt;
706952f5 139 return 0;
140 }
5fc72f28 141 error = 1.e10;
706952f5 142 return 1;
143}
144
5fc72f28 145Int_t AliKFParticleBase::GetEta( Double_t &eta, Double_t &error ) const
706952f5 146{
147 //* Calculate particle pseudorapidity
148
149 Double_t px = fP[3];
150 Double_t py = fP[4];
151 Double_t pz = fP[5];
152 Double_t pt2 = px*px + py*py;
153 Double_t p2 = pt2 + pz*pz;
154 Double_t p = TMath::Sqrt(p2);
155 Double_t a = p + pz;
156 Double_t b = p - pz;
5fc72f28 157 eta = 1.e10;
706952f5 158 if( b > 1.e-8 ){
159 Double_t c = a/b;
5fc72f28 160 if( c>1.e-8 ) eta = 0.5*TMath::Log(a/b);
706952f5 161 }
162 Double_t h3 = -px*pz;
163 Double_t h4 = -py*pz;
164 Double_t p2pt2 = p2*pt2;
165
5fc72f28 166 error = (h3*h3*fC[9] + h4*h4*fC[14] + pt2*fC[20] +
706952f5 167 2*( h3*(h4*fC[13] + fC[18]) + h4*fC[19] )
168 );
169
5fc72f28 170 if( error>0 && p2pt2>1.e-4 ){
171 error = TMath::Sqrt(error/p2pt2);
706952f5 172 return 0;
173 }
5fc72f28 174 error = 1.e10;
706952f5 175 return 1;
176}
177
5fc72f28 178Int_t AliKFParticleBase::GetPhi( Double_t &phi, Double_t &error ) const
706952f5 179{
180 //* Calculate particle polar angle
181
182 Double_t px = fP[3];
183 Double_t py = fP[4];
184 Double_t px2 = px*px;
185 Double_t py2 = py*py;
186 Double_t pt2 = px2 + py2;
5fc72f28 187 phi = TMath::ATan2(py,px);
188 error = (py2*fC[9] + px2*fC[14] - 2*px*py*fC[13] );
189 if( error>0 && pt2>1.e-4 ){
190 error = TMath::Sqrt(error)/pt2;
706952f5 191 return 0;
192 }
5fc72f28 193 error = 1.e10;
706952f5 194 return 1;
195}
196
5fc72f28 197Int_t AliKFParticleBase::GetR( Double_t &r, Double_t &error ) const
706952f5 198{
199 //* Calculate distance to the origin
200
201 Double_t x = fP[0];
202 Double_t y = fP[1];
203 Double_t x2 = x*x;
204 Double_t y2 = y*y;
5fc72f28 205 r = TMath::Sqrt(x2 + y2);
206 error = (x2*fC[0] + y2*fC[2] - 2*x*y*fC[1] );
207 if( error>0 && r>1.e-4 ){
208 error = TMath::Sqrt(error)/r;
706952f5 209 return 0;
210 }
5fc72f28 211 error = 1.e10;
706952f5 212 return 1;
213}
214
5fc72f28 215Int_t AliKFParticleBase::GetMass( Double_t &m, Double_t &error ) const
f826d409 216{
217 //* Calculate particle mass
218
219 // s = sigma^2 of m2/2
220
221 Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20]
222 + fP[6]*fP[6]*fC[27]
223 +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19])
224 - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) )
225 );
706952f5 226 Double_t m2 = TMath::Abs(fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5]);
5fc72f28 227 m = TMath::Sqrt(m2);
228 if( m>1.e-10 ){
616ffc76 229 if( s>=0 ){
5fc72f28 230 error = TMath::Sqrt(s)/m;
616ffc76 231 return 0;
232 }
f826d409 233 }
5fc72f28 234 error = 1.e20;
f826d409 235 return 1;
236}
237
238
5fc72f28 239Int_t AliKFParticleBase::GetDecayLength( Double_t &l, Double_t &error ) const
f826d409 240{
241 //* Calculate particle decay length [cm]
242
243 Double_t x = fP[3];
244 Double_t y = fP[4];
245 Double_t z = fP[5];
246 Double_t t = fP[7];
247 Double_t x2 = x*x;
248 Double_t y2 = y*y;
249 Double_t z2 = z*z;
250 Double_t p2 = x2+y2+z2;
5fc72f28 251 l = t*TMath::Sqrt(p2);
f826d409 252 if( p2>1.e-4){
5fc72f28 253 error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20]
f826d409 254 + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) )
255 + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]);
5fc72f28 256 error = TMath::Sqrt(TMath::Abs(error));
f826d409 257 return 0;
258 }
5fc72f28 259 error = 1.e20;
f826d409 260 return 1;
261}
262
5fc72f28 263Int_t AliKFParticleBase::GetLifeTime( Double_t &tauC, Double_t &error ) const
f826d409 264{
265 //* Calculate particle decay time [s]
266
267 Double_t m, dm;
268 GetMass( m, dm );
269 Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]);
5fc72f28 270 tauC = fP[7]*m;
271 error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm;
272 if( error > 0 ){
273 error = TMath::Sqrt( error );
f826d409 274 return 0;
275 }
5fc72f28 276 error = 1.e20;
f826d409 277 return 1;
278}
279
280
281void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter )
282{
283 //* Add daughter via operator+=
284
285 AddDaughter( Daughter );
286}
287
706952f5 288Double_t AliKFParticleBase::GetSCorrection( const Double_t Part[], const Double_t XYZ[] )
289{
290 //* Get big enough correction for S error to let the particle Part be fitted to XYZ point
291
292 Double_t d[3] = { XYZ[0]-Part[0], XYZ[1]-Part[1], XYZ[2]-Part[2] };
293 Double_t p2 = Part[3]*Part[3]+Part[4]*Part[4]+Part[5]*Part[5];
294 Double_t sigmaS = (p2>1.e-4) ? ( .1+3.*TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2]) )/TMath::Sqrt(p2) : 1.;
295 return sigmaS;
296}
616ffc76 297
298void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const
299{
e7b09c95 300 //* Get additional covariances V used during measurement
301
616ffc76 302 Double_t b[3];
303 GetFieldValue( XYZ, b );
304 const Double_t kCLight = 0.000299792458;
305 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
306
307 Transport( GetDStoPoint(XYZ), m, V );
308
706952f5 309 Double_t sigmaS = GetSCorrection( m, XYZ );
616ffc76 310
311 Double_t h[6];
312
313 h[0] = m[3]*sigmaS;
314 h[1] = m[4]*sigmaS;
315 h[2] = m[5]*sigmaS;
316 h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ();
317 h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ();
318 h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ();
319
616ffc76 320 V[ 0]+= h[0]*h[0];
321 V[ 1]+= h[1]*h[0];
322 V[ 2]+= h[1]*h[1];
323 V[ 3]+= h[2]*h[0];
324 V[ 4]+= h[2]*h[1];
325 V[ 5]+= h[2]*h[2];
326
327 V[ 6]+= h[3]*h[0];
328 V[ 7]+= h[3]*h[1];
329 V[ 8]+= h[3]*h[2];
330 V[ 9]+= h[3]*h[3];
331
332 V[10]+= h[4]*h[0];
333 V[11]+= h[4]*h[1];
334 V[12]+= h[4]*h[2];
335 V[13]+= h[4]*h[3];
336 V[14]+= h[4]*h[4];
337
338 V[15]+= h[5]*h[0];
339 V[16]+= h[5]*h[1];
340 V[17]+= h[5]*h[2];
341 V[18]+= h[5]*h[3];
342 V[19]+= h[5]*h[4];
343 V[20]+= h[5]*h[5];
344}
345
616ffc76 346
f826d409 347void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter )
348{
349 //* Add daughter
350
616ffc76 351 if( fNDF<-1 ){ // first daughter -> just copy
352 fNDF = -1;
353 fQ = Daughter.GetQ();
354 for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i];
355 for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i];
356 fSFromDecay = 0;
357 return;
358 }
359
f826d409 360 TransportToDecayVertex();
361
362 Double_t b[3];
363 Int_t maxIter = 1;
364
365 if( !fIsLinearized ){
366 if( fNDF==-1 ){
367 Double_t ds, ds1;
616ffc76 368 GetDStoParticle(Daughter, ds, ds1);
f826d409 369 TransportToDS( ds );
616ffc76 370 Double_t m[8];
371 Double_t mCd[36];
372 Daughter.Transport( ds1, m, mCd );
373 fVtxGuess[0] = .5*( fP[0] + m[0] );
374 fVtxGuess[1] = .5*( fP[1] + m[1] );
375 fVtxGuess[2] = .5*( fP[2] + m[2] );
376 } else {
377 fVtxGuess[0] = fP[0];
378 fVtxGuess[1] = fP[1];
379 fVtxGuess[2] = fP[2];
f826d409 380 }
f826d409 381 maxIter = 3;
382 }
383
384 for( Int_t iter=0; iter<maxIter; iter++ ){
385
386 {
387 GetFieldValue( fVtxGuess, b );
388 const Double_t kCLight = 0.000299792458;
389 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
390 }
f826d409 391
616ffc76 392 Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36];
de0d0ceb 393 if( fNDF==-1 ){
616ffc76 394 GetMeasurement( fVtxGuess, tmpP, tmpC );
395 ffP = tmpP;
396 ffC = tmpC;
f826d409 397 }
398
e7b09c95 399 Double_t m[8], mV[36];
de0d0ceb 400
e7b09c95 401 if( Daughter.fC[35]>0 ){
402 Daughter.GetMeasurement( fVtxGuess, m, mV );
403 } else {
404 for( Int_t i=0; i<8; i++ ) m[i] = Daughter.fP[i];
405 for( Int_t i=0; i<36; i++ ) mV[i] = Daughter.fC[i];
406 }
de0d0ceb 407
f826d409 408 //*
409
410 Double_t mS[6];
411 {
616ffc76 412 Double_t mSi[6] = { ffC[0]+mV[0],
413 ffC[1]+mV[1], ffC[2]+mV[2],
414 ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] };
de0d0ceb 415
f826d409 416 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
417 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
418 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
419 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
420 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
421 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
422
706952f5 423 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
424
f826d409 425 s = ( s > 1.E-20 ) ?1./s :0;
426 mS[0]*=s;
427 mS[1]*=s;
428 mS[2]*=s;
429 mS[3]*=s;
430 mS[4]*=s;
431 mS[5]*=s;
432 }
433
434 //* Residual (measured - estimated)
435
616ffc76 436 Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] };
de0d0ceb 437
f826d409 438
439 //* CHt = CH' - D'
440
441 Double_t mCHt0[7], mCHt1[7], mCHt2[7];
442
616ffc76 443 mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ;
444 mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ;
445 mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ;
446 mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8];
447 mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12];
448 mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17];
449 mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23];
f826d409 450
451 //* Kalman gain K = mCH'*S
452
453 Double_t k0[7], k1[7], k2[7];
454
455 for(Int_t i=0;i<7;++i){
456 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
457 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
458 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
459 }
460
4bbc290d 461 //* New estimation of the vertex position
f826d409 462
463 if( iter<maxIter-1 ){
464 for(Int_t i=0; i<3; ++i)
616ffc76 465 fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2];
f826d409 466 continue;
467 }
468
469 // last itearation -> update the particle
470
471 //* Add the daughter momentum to the particle momentum
472
616ffc76 473 ffP[ 3] += m[ 3];
474 ffP[ 4] += m[ 4];
475 ffP[ 5] += m[ 5];
476 ffP[ 6] += m[ 6];
f826d409 477
616ffc76 478 ffC[ 9] += mV[ 9];
479 ffC[13] += mV[13];
480 ffC[14] += mV[14];
481 ffC[18] += mV[18];
482 ffC[19] += mV[19];
483 ffC[20] += mV[20];
484 ffC[24] += mV[24];
485 ffC[25] += mV[25];
486 ffC[26] += mV[26];
487 ffC[27] += mV[27];
f826d409 488
de0d0ceb 489
490 //* New estimation of the vertex position r += K*zeta
f826d409 491
492 for(Int_t i=0;i<7;++i)
616ffc76 493 fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
f826d409 494
495 //* New covariance matrix C -= K*(mCH')'
de0d0ceb 496
f826d409 497 for(Int_t i=0, k=0;i<7;++i){
de0d0ceb 498 for(Int_t j=0;j<=i;++j,++k){
616ffc76 499 fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] );
de0d0ceb 500 }
f826d409 501 }
de0d0ceb 502
f826d409 503 //* Calculate Chi^2
504
505 fNDF += 2;
506 fQ += Daughter.GetQ();
507 fSFromDecay = 0;
508 fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
509 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
706952f5 510 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
de0d0ceb 511
f826d409 512 }
513}
514
706952f5 515
f826d409 516void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx )
517{
706952f5 518 //* Set production vertex for the particle, when the particle was not used in the vertex fit
f826d409 519
520 const Double_t *m = Vtx.fP, *mV = Vtx.fC;
521
e7b09c95 522 Bool_t noS = ( fC[35]<=0 ); // no decay length allowed
523
524 if( noS ){
525 TransportToDecayVertex();
526 fP[7] = 0;
527 fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0;
528 } else {
529 TransportToDS( GetDStoPoint( m ) );
530 fP[7] = -fSFromDecay;
531 Convert(1);
532 }
533
f826d409 534 Double_t mAi[6];
706952f5 535 mAi[0] = fC[2]*fC[5] - fC[4]*fC[4];
536 mAi[1] = fC[3]*fC[4] - fC[1]*fC[5];
537 mAi[3] = fC[1]*fC[4] - fC[2]*fC[3];
538 Double_t det = (fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]);
aac1d51b 539 if( det>1.e-20 ) det = 1./det;
706952f5 540 else det = 0;
541
f826d409 542 mAi[0] *= det;
543 mAi[1] *= det;
544 mAi[3] *= det;
aac1d51b 545 mAi[2] = ( fC[0]*fC[5] - fC[3]*fC[3] )*det;
546 mAi[4] = ( fC[1]*fC[3] - fC[0]*fC[4] )*det;
547 mAi[5] = ( fC[0]*fC[2] - fC[1]*fC[1] )*det;
f826d409 548
549 Double_t mB[5][3];
550
551 mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3];
552 mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4];
553 mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5];
554
555 mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3];
556 mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4];
557 mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5];
558
559 mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3];
560 mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4];
561 mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5];
562
563 mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3];
564 mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4];
565 mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5];
566
567 mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3];
568 mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4];
569 mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5];
570
571 Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
572
573 {
574 Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2],
575 fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] };
706952f5 576
f826d409 577 Double_t mAVi[6];
706952f5 578 mAVi[0] = mAV[2]*mAV[5] - mAV[4]*mAV[4];
579 mAVi[1] = mAV[3]*mAV[4] - mAV[1]*mAV[5];
580 mAVi[2] = mAV[0]*mAV[5] - mAV[3]*mAV[3];
581 mAVi[3] = mAV[1]*mAV[4] - mAV[2]*mAV[3];
582 mAVi[4] = mAV[1]*mAV[3] - mAV[0]*mAV[4];
583 mAVi[5] = mAV[0]*mAV[2] - mAV[1]*mAV[1];
f826d409 584
e7b09c95 585 det = ( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] );
f826d409 586
aac1d51b 587 if( TMath::Abs(det) > 1.E-20 ){
706952f5 588
589 Double_t dChi2 = ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0]
590 +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1]
591 +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )/det ;
592
593 // Take Abs(dChi2) here. Negative value of 'det' or 'dChi2' shows that the particle
594 // was not used in the production vertex fit
595
596 fChi2+= TMath::Abs( dChi2 );
597 }
f826d409 598 fNDF += 2;
f826d409 599 }
600
601 fP[0] = m[0];
602 fP[1] = m[1];
603 fP[2] = m[2];
604 fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
605 fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
606 fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
607 fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2];
608 fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2];
609
610 Double_t d0, d1, d2;
611
612 fC[0] = mV[0];
613 fC[1] = mV[1];
614 fC[2] = mV[2];
615 fC[3] = mV[3];
616 fC[4] = mV[4];
617 fC[5] = mV[5];
618
619 d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6];
620 d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7];
621 d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8];
622
623 fC[ 6]+= d0;
624 fC[ 7]+= d1;
625 fC[ 8]+= d2;
626 fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
627
628 d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10];
629 d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11];
630 d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12];
631
632 fC[10]+= d0;
633 fC[11]+= d1;
634 fC[12]+= d2;
635 fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
636 fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
637
638 d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15];
639 d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16];
640 d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17];
641
642 fC[15]+= d0;
643 fC[16]+= d1;
644 fC[17]+= d2;
645 fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
646 fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
647 fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
648
649 d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21];
650 d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22];
651 d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23];
652
653 fC[21]+= d0;
654 fC[22]+= d1;
655 fC[23]+= d2;
656 fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
657 fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
658 fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
659 fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
660
661 d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28];
662 d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29];
663 d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30];
664
665 fC[28]+= d0;
666 fC[29]+= d1;
667 fC[30]+= d2;
668 fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
669 fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
670 fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
671 fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
672 fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2];
673
e7b09c95 674 if( noS ){
675 fP[7] = 0;
676 fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0;
677 } else {
678 TransportToDS( fP[7] );
679 Convert(0);
680 }
681
f826d409 682 fSFromDecay = 0;
f826d409 683}
684
685
686
e7b09c95 687void AliKFParticleBase::SetMassConstraint( Double_t Mass, Double_t SigmaMass )
f826d409 688{
706952f5 689 //* Set hard( SigmaMass=0 ) or soft (SigmaMass>0) mass constraint
690
691 Double_t m2 = Mass*Mass; // measurement, weighted by Mass
692 Double_t s2 = m2*SigmaMass*SigmaMass; // sigma^2
693
694 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
695 Double_t e0 = TMath::Sqrt(m2+p2);
f826d409 696
697 Double_t mH[8];
698 mH[0] = mH[1] = mH[2] = 0.;
699 mH[3] = -2*fP[3];
700 mH[4] = -2*fP[4];
701 mH[5] = -2*fP[5];
706952f5 702 mH[6] = 2*fP[6];//e0;
f826d409 703 mH[7] = 0;
f826d409 704
706952f5 705 Double_t zeta = e0*e0 - e0*fP[6];
706 zeta = m2 - (fP[6]*fP[6]-p2);
f826d409 707
706952f5 708 Double_t mCHt[8], s2_est=0;
709 for( Int_t i=0; i<8; ++i ){
f826d409 710 mCHt[i] = 0.0;
711 for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j];
706952f5 712 s2_est += mH[i]*mCHt[i];
f826d409 713 }
714
706952f5 715 if( s2_est<1.e-20 ) return; // calculated mass error is already 0,
716 // the particle can not be constrained on mass
717
718 Double_t w2 = 1./( s2 + s2_est );
719 fChi2 += zeta*zeta*w2;
f826d409 720 fNDF += 1;
721 for( Int_t i=0, ii=0; i<8; ++i ){
706952f5 722 Double_t ki = mCHt[i]*w2;
f826d409 723 fP[i]+= ki*zeta;
724 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j];
725 }
726}
727
728
e7b09c95 729void AliKFParticleBase::SetNoDecayLength()
730{
731 //* Set no decay length for resonances
732
733 TransportToDecayVertex();
734
735 Double_t h[8];
736 h[0] = h[1] = h[2] = h[3] = h[4] = h[5] = h[6] = 0;
737 h[7] = 1;
738
739 Double_t zeta = 0 - fP[7];
740 for(Int_t i=0;i<8;++i) zeta -= h[i]*(fP[i]-fP[i]);
741
742 Double_t s = fC[35];
743 if( s>1.e-20 ){
744 s = 1./s;
745 fChi2 += zeta*zeta*s;
746 fNDF += 1;
747 for( Int_t i=0, ii=0; i<7; ++i ){
748 Double_t ki = fC[28+i]*s;
749 fP[i]+= ki*zeta;
750 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*fC[28+j];
751 }
752 }
753 fP[7] = 0;
754 fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0;
755}
756
757
f826d409 758void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters,
706952f5 759 const AliKFParticleBase *Parent, Double_t Mass, Bool_t IsConstrained )
f826d409 760{
761 //* Full reconstruction in one go
762
763 Int_t maxIter = 1;
764 bool wasLinearized = fIsLinearized;
706952f5 765 if( !fIsLinearized || IsConstrained ){
616ffc76 766 //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!!
767 fVtxGuess[0] = GetX();
768 fVtxGuess[1] = GetY();
769 fVtxGuess[2] = GetZ();
f826d409 770 fIsLinearized = 1;
771 maxIter = 3;
772 }
773
706952f5 774 Double_t constraintC[6];
775
776 if( IsConstrained ){
777 for(Int_t i=0;i<6;++i) constraintC[i]=fC[i];
778 } else {
779 for(Int_t i=0;i<6;++i) constraintC[i]=0.;
780 constraintC[0] = constraintC[2] = constraintC[5] = 100.;
781 }
782
783
f826d409 784 for( Int_t iter=0; iter<maxIter; iter++ ){
f826d409 785 fAtProductionVertex = 0;
786 fSFromDecay = 0;
787 fP[0] = fVtxGuess[0];
788 fP[1] = fVtxGuess[1];
789 fP[2] = fVtxGuess[2];
790 fP[3] = 0;
791 fP[4] = 0;
792 fP[5] = 0;
793 fP[6] = 0;
794 fP[7] = 0;
706952f5 795
796 for(Int_t i=0;i<6; ++i) fC[i]=constraintC[i];
797 for(Int_t i=6;i<36;++i) fC[i]=0.;
f826d409 798 fC[35] = 1.;
799
706952f5 800 fNDF = IsConstrained ?0 :-3;
f826d409 801 fChi2 = 0.;
802 fQ = 0;
803
4bbc290d 804 for( Int_t itr =0; itr<NDaughters; itr++ ){
805 AddDaughter( *vDaughters[itr] );
806 }
f826d409 807 if( iter<maxIter-1){
808 for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i];
809 }
810 }
811 fIsLinearized = wasLinearized;
812
813 if( Mass>=0 ) SetMassConstraint( Mass );
814 if( Parent ) SetProductionVertex( *Parent );
815}
816
817
818void AliKFParticleBase::Convert( bool ToProduction )
819{
820 //* Tricky function - convert the particle error along its trajectory to
821 //* the value which corresponds to its production/decay vertex
822 //* It is done by combination of the error of decay length with the position errors
823
824 Double_t fld[3];
825 {
826 GetFieldValue( fP, fld );
827 const Double_t kCLight = fQ*0.000299792458;
828 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
829 }
830
831 Double_t h[6];
832
833 h[0] = fP[3];
834 h[1] = fP[4];
835 h[2] = fP[5];
836 if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; }
837 h[3] = h[1]*fld[2]-h[2]*fld[1];
838 h[4] = h[2]*fld[0]-h[0]*fld[2];
839 h[5] = h[0]*fld[1]-h[1]*fld[0];
840
841 Double_t c;
842
843 c = fC[28]+h[0]*fC[35];
844 fC[ 0]+= h[0]*(c+fC[28]);
845 fC[28] = c;
846
847 fC[ 1]+= h[1]*fC[28] + h[0]*fC[29];
848 c = fC[29]+h[1]*fC[35];
849 fC[ 2]+= h[1]*(c+fC[29]);
850 fC[29] = c;
851
852 fC[ 3]+= h[2]*fC[28] + h[0]*fC[30];
853 fC[ 4]+= h[2]*fC[29] + h[1]*fC[30];
854 c = fC[30]+h[2]*fC[35];
855 fC[ 5]+= h[2]*(c+fC[30]);
856 fC[30] = c;
857
858 fC[ 6]+= h[3]*fC[28] + h[0]*fC[31];
859 fC[ 7]+= h[3]*fC[29] + h[1]*fC[31];
860 fC[ 8]+= h[3]*fC[30] + h[2]*fC[31];
861 c = fC[31]+h[3]*fC[35];
862 fC[ 9]+= h[3]*(c+fC[31]);
863 fC[31] = c;
864
865 fC[10]+= h[4]*fC[28] + h[0]*fC[32];
866 fC[11]+= h[4]*fC[29] + h[1]*fC[32];
867 fC[12]+= h[4]*fC[30] + h[2]*fC[32];
868 fC[13]+= h[4]*fC[31] + h[3]*fC[32];
869 c = fC[32]+h[4]*fC[35];
870 fC[14]+= h[4]*(c+fC[32]);
871 fC[32] = c;
872
873 fC[15]+= h[5]*fC[28] + h[0]*fC[33];
874 fC[16]+= h[5]*fC[29] + h[1]*fC[33];
875 fC[17]+= h[5]*fC[30] + h[2]*fC[33];
876 fC[18]+= h[5]*fC[31] + h[3]*fC[33];
877 fC[19]+= h[5]*fC[32] + h[4]*fC[33];
878 c = fC[33]+h[5]*fC[35];
879 fC[20]+= h[5]*(c+fC[33]);
880 fC[33] = c;
881
882 fC[21]+= h[0]*fC[34];
883 fC[22]+= h[1]*fC[34];
884 fC[23]+= h[2]*fC[34];
885 fC[24]+= h[3]*fC[34];
886 fC[25]+= h[4]*fC[34];
887 fC[26]+= h[5]*fC[34];
888}
889
890
891void AliKFParticleBase::TransportToDecayVertex()
892{
893 //* Transport the particle to its decay vertex
894
895 if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay );
896 if( fAtProductionVertex ) Convert(0);
897 fAtProductionVertex = 0;
898}
899
900void AliKFParticleBase::TransportToProductionVertex()
901{
902 //* Transport the particle to its production vertex
616ffc76 903
f826d409 904 if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] );
905 if( !fAtProductionVertex ) Convert( 1 );
906 fAtProductionVertex = 1;
907}
908
909
910void AliKFParticleBase::TransportToDS( Double_t dS )
911{
912 //* Transport the particle on dS parameter (SignedPath/Momentum)
616ffc76 913
f826d409 914 Transport( dS, fP, fC );
915 fSFromDecay+= dS;
916}
917
918
919Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const
920{
921 //* Get dS to a certain space point without field
922
923 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
924 if( p2<1.e-4 ) p2 = 1;
925 return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2;
926}
927
928
929Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] )
930 const
931{
616ffc76 932
f826d409 933 //* Get dS to a certain space point for Bz field
f826d409 934 const Double_t kCLight = 0.000299792458;
935 Double_t bq = B*fQ*kCLight;
936 Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4];
937 if( pt2<1.e-4 ) return 0;
938 Double_t dx = xyz[0] - fP[0];
939 Double_t dy = xyz[1] - fP[1];
940 Double_t a = dx*fP[3]+dy*fP[4];
706952f5 941 Double_t dS;
942
943 if( TMath::Abs(bq)<1.e-8 ) dS = a/pt2;
944 else dS = TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq;
945
946 if(0){
947
948 Double_t px = fP[3];
949 Double_t py = fP[4];
950 Double_t pz = fP[5];
951 Double_t ss[2], g[2][5];
952
953 ss[0] = dS;
954 ss[1] = -dS;
955 for( Int_t i=0; i<2; i++){
956 Double_t bs = bq*ss[i];
957 Double_t c = TMath::Cos(bs), s = TMath::Sin(bs);
958 Double_t cB,sB;
959 if( TMath::Abs(bq)>1.e-8){
960 cB= (1-c)/bq;
961 sB= s/bq;
962 }else{
bfd20868 963 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
964 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i];
706952f5 965 cB = .5*sB*bs;
966 }
967 g[i][0] = fP[0] + sB*px + cB*py;
968 g[i][1] = fP[1] - cB*px + sB*py;
969 g[i][2] = fP[2] + ss[i]*pz;
970 g[i][3] = + c*px + s*py;
971 g[i][4] = - s*px + c*py;
972 }
973
974 Int_t i=0;
975
976 Double_t dMin = 1.e10;
977 for( Int_t j=0; j<2; j++){
978 Double_t xx = g[j][0]-xyz[0];
979 Double_t yy = g[j][1]-xyz[1];
980 Double_t zz = g[j][2]-xyz[2];
981 Double_t d = xx*xx + yy*yy + zz*zz;
982 if( d<dMin ){
983 dMin = d;
984 i = j;
985 }
986 }
987
988 dS = ss[i];
989
990 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
5fc72f28 991 Double_t ddx = x-xyz[0];
992 Double_t ddy = y-xyz[1];
993 Double_t ddz = z-xyz[2];
994 Double_t c = ddx*ppx + ddy*ppy + ddz*pz ;
706952f5 995 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
996 if( TMath::Abs(pp2)>1.e-8 ){
997 dS+=c/pp2;
998 }
999 }
1000 return dS;
f826d409 1001}
1002
1003
1004void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p,
616ffc76 1005 Double_t &DS, Double_t &DS1 )
f826d409 1006 const
1007{
1008 //* Get dS to another particle for Bz field
f826d409 1009 Double_t px = fP[3];
1010 Double_t py = fP[4];
1011 Double_t pz = fP[5];
1012
1013 Double_t px1 = p.fP[3];
1014 Double_t py1 = p.fP[4];
1015 Double_t pz1 = p.fP[5];
1016
1017 const Double_t kCLight = 0.000299792458;
1018
1019 Double_t bq = B*fQ*kCLight;
1020 Double_t bq1 = B*p.fQ*kCLight;
f826d409 1021 Double_t s=0, ds=0, s1=0, ds1=0;
1022
1023 if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){
4bbc290d 1024
f826d409 1025 Double_t dx = (p.fP[0] - fP[0]);
1026 Double_t dy = (p.fP[1] - fP[1]);
1027 Double_t d2 = (dx*dx+dy*dy);
1028
1029 Double_t p2 = (px *px + py *py);
1030 Double_t p21 = (px1*px1 + py1*py1);
1031
1032 Double_t a = (px*py1 - py*px1);
1033 Double_t b = (px*px1 + py*py1);
1034
1035 Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ;
1036 Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ;
1037 Double_t l2 = ldx*ldx + ldy*ldy;
1038
1039 Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b;
1040 Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b;
1041
1042 Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ;
1043 Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ;
1044
1045 Double_t sa = 4*l2*p2 - ca*ca;
1046 Double_t sa1 = 4*l2*p21 - ca1*ca1;
e7b09c95 1047
f826d409 1048 if(sa<0) sa=0;
1049 if(sa1<0)sa1=0;
1050
1051 if( TMath::Abs(bq)>1.e-8){
1052 s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq;
1053 ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq;
1054 } else {
1055 s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2;
1056 ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2;
1057 if( ds<0 ) ds = 0;
1058 ds = TMath::Sqrt(ds);
1059 }
1060
1061 if( TMath::Abs(bq1)>1.e-8){
1062 s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1;
1063 ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1;
1064 } else {
1065 s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21;
1066 ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21;
1067 if( ds1<0 ) ds1 = 0;
1068 ds1 = TMath::Sqrt(ds1);
1069 }
1070 }
1071
f826d409 1072 Double_t ss[2], ss1[2], g[2][5],g1[2][5];
1073
1074 ss[0] = s + ds;
1075 ss[1] = s - ds;
1076 ss1[0] = s1 + ds1;
1077 ss1[1] = s1 - ds1;
1078 for( Int_t i=0; i<2; i++){
1079 Double_t bs = bq*ss[i];
5fc72f28 1080 Double_t c = TMath::Cos(bs), sss = TMath::Sin(bs);
f826d409 1081 Double_t cB,sB;
1082 if( TMath::Abs(bq)>1.e-8){
1083 cB= (1-c)/bq;
5fc72f28 1084 sB= sss/bq;
f826d409 1085 }else{
bfd20868 1086 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
1087 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i];
f826d409 1088 cB = .5*sB*bs;
1089 }
1090 g[i][0] = fP[0] + sB*px + cB*py;
1091 g[i][1] = fP[1] - cB*px + sB*py;
1092 g[i][2] = fP[2] + ss[i]*pz;
5fc72f28 1093 g[i][3] = + c*px + sss*py;
1094 g[i][4] = - sss*px + c*py;
f826d409 1095
1096 bs = bq1*ss1[i];
5fc72f28 1097 c = TMath::Cos(bs); sss = TMath::Sin(bs);
f826d409 1098 if( TMath::Abs(bq1)>1.e-8){
1099 cB= (1-c)/bq1;
5fc72f28 1100 sB= sss/bq1;
f826d409 1101 }else{
bfd20868 1102 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
1103 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss1[i];
f826d409 1104 cB = .5*sB*bs;
1105 }
1106
e7b09c95 1107 g1[i][0] = p.fP[0] + sB*px1 + cB*py1;
1108 g1[i][1] = p.fP[1] - cB*px1 + sB*py1;
1109 g1[i][2] = p.fP[2] + ss[i]*pz1;
5fc72f28 1110 g1[i][3] = + c*px1 + sss*py1;
1111 g1[i][4] = - sss*px1 + c*py1;
f826d409 1112 }
1113
1114 Int_t i=0, i1=0;
1115
1116 Double_t dMin = 1.e10;
1117 for( Int_t j=0; j<2; j++){
1118 for( Int_t j1=0; j1<2; j1++){
1119 Double_t xx = g[j][0]-g1[j1][0];
1120 Double_t yy = g[j][1]-g1[j1][1];
1121 Double_t zz = g[j][2]-g1[j1][2];
1122 Double_t d = xx*xx + yy*yy + zz*zz;
1123 if( d<dMin ){
1124 dMin = d;
1125 i = j;
1126 i1 = j1;
1127 }
1128 }
1129 }
1130
1131 DS = ss[i];
1132 DS1 = ss1[i1];
91468b27 1133 if(0){
1134 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
1135 Double_t x1=g1[i1][0], y1= g1[i1][1], z1= g1[i1][2], ppx1= g1[i1][3], ppy1= g1[i1][4];
1136 Double_t dx = x1-x;
1137 Double_t dy = y1-y;
1138 Double_t dz = z1-z;
1139 Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1;
1140 Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1;
1141 Double_t c = dx*ppx + dy*ppy + dz*pz ;
1142 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
1143 Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1;
706952f5 1144 Double_t det = pp2*pp21 - a*a;
91468b27 1145 if( TMath::Abs(det)>1.e-8 ){
1146 DS+=(a*b-pp21*c)/det;
1147 DS1+=(a*c-pp2*b)/det;
1148 }
f826d409 1149 }
1150}
1151
1152
1153
1154void AliKFParticleBase::TransportCBM( Double_t dS,
1155 Double_t P[], Double_t C[] ) const
1156{
1157 //* Transport the particle on dS, output to P[],C[], for CBM field
1158
1159 if( fQ==0 ){
1160 TransportLine( dS, P, C );
1161 return;
1162 }
1163
1164 const Double_t kCLight = 0.000299792458;
1165
1166 Double_t c = fQ*kCLight;
1167
1168 // construct coefficients
1169
1170 Double_t
1171 px = fP[3],
1172 py = fP[4],
1173 pz = fP[5];
1174
1175 Double_t sx=0, sy=0, sz=0, syy=0, syz=0, syyy=0, ssx=0, ssy=0, ssz=0, ssyy=0, ssyz=0, ssyyy=0;
1176
1177 { // get field integrals
1178
1179 Double_t fld[3][3];
1180 Double_t p0[3], p1[3], p2[3];
1181
1182 // line track approximation
1183
1184 p0[0] = fP[0];
1185 p0[1] = fP[1];
1186 p0[2] = fP[2];
1187
1188 p2[0] = fP[0] + px*dS;
1189 p2[1] = fP[1] + py*dS;
1190 p2[2] = fP[2] + pz*dS;
1191
1192 p1[0] = 0.5*(p0[0]+p2[0]);
1193 p1[1] = 0.5*(p0[1]+p2[1]);
1194 p1[2] = 0.5*(p0[2]+p2[2]);
1195
1196 // first order track approximation
1197 {
1198 GetFieldValue( p0, fld[0] );
1199 GetFieldValue( p1, fld[1] );
1200 GetFieldValue( p2, fld[2] );
1201
1202 Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.;
1203 Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.;
1204
1205 p1[0] -= ssy1*pz;
1206 p1[2] += ssy1*px;
1207 p2[0] -= ssy2*pz;
1208 p2[2] += ssy2*px;
1209 }
1210
1211 GetFieldValue( p0, fld[0] );
1212 GetFieldValue( p1, fld[1] );
1213 GetFieldValue( p2, fld[2] );
1214
1215 sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.;
1216 sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.;
1217 sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.;
1218
1219 ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.;
1220 ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.;
1221 ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.;
1222
1223 Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360.
1224 Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520.
1225 for(Int_t n=0; n<3; n++)
1226 for(Int_t m=0; m<3; m++)
1227 {
1228 syz += c2[n][m]*fld[n][1]*fld[m][2];
1229 ssyz += cc2[n][m]*fld[n][1]*fld[m][2];
1230 }
1231
1232 syz *= c*c*dS*dS/360.;
1233 ssyz *= c*c*dS*dS*dS/2520.;
1234
1235 syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS;
1236 syyy = syy*syy*syy / 1296;
1237 syy = syy*syy/72;
1238
1239 ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+
1240 fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+
1241 fld[2][1]*( 3*fld[2][1] )
1242 )*dS*dS*dS*c*c/2520.;
1243 ssyyy =
1244 (
1245 fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+
1246 fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+
1247 fld[2][1]*( 19*fld[2][1] ) )+
1248 fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+
1249 fld[2][1]*( 62*fld[2][1] ) )+
1250 fld[2][1]*fld[2][1] *( 3*fld[2][1] )
1251 )*dS*dS*dS*dS*c*c*c/90720.;
1252
1253 }
1254
1255 Double_t mJ[8][8];
1256 for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0;
1257
1258 mJ[0][0]=1; mJ[0][1]=0; mJ[0][2]=0; mJ[0][3]=dS-ssyy; mJ[0][4]=ssx; mJ[0][5]=ssyyy-ssy;
1259 mJ[1][0]=0; mJ[1][1]=1; mJ[1][2]=0; mJ[1][3]=-ssz; mJ[1][4]=dS; mJ[1][5]=ssx+ssyz;
1260 mJ[2][0]=0; mJ[2][1]=0; mJ[2][2]=1; mJ[2][3]=ssy-ssyyy; mJ[2][4]=-ssx; mJ[2][5]=dS-ssyy;
1261
1262 mJ[3][0]=0; mJ[3][1]=0; mJ[3][2]=0; mJ[3][3]=1-syy; mJ[3][4]=sx; mJ[3][5]=syyy-sy;
1263 mJ[4][0]=0; mJ[4][1]=0; mJ[4][2]=0; mJ[4][3]=-sz; mJ[4][4]=1; mJ[4][5]=sx+syz;
1264 mJ[5][0]=0; mJ[5][1]=0; mJ[5][2]=0; mJ[5][3]=sy-syyy; mJ[5][4]=-sx; mJ[5][5]=1-syy;
1265 mJ[6][6] = mJ[7][7] = 1;
1266
1267 P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz;
1268 P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz;
1269 P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz;
1270 P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz;
1271 P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz;
1272 P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz;
1273 P[6] = fP[6];
1274 P[7] = fP[7];
1275
1276 MultQSQt( mJ[0], fC, C);
1277
1278}
1279
1280
5fc72f28 1281void AliKFParticleBase::TransportBz( Double_t b, Double_t ss,
1282 Double_t p[], Double_t cc[] ) const
f826d409 1283{
1284 //* Transport the particle on dS, output to P[],C[], for Bz field
616ffc76 1285
f826d409 1286 const Double_t kCLight = 0.000299792458;
5fc72f28 1287 b = b*fQ*kCLight;
1288 Double_t bs= b*ss;
f826d409 1289 Double_t s = TMath::Sin(bs), c = TMath::Cos(bs);
1290 Double_t sB, cB;
616ffc76 1291 if( TMath::Abs(bs)>1.e-10){
5fc72f28 1292 sB= s/b;
1293 cB= (1-c)/b;
f826d409 1294 }else{
bfd20868 1295 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
1296 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss;
f826d409 1297 cB = .5*sB*bs;
1298 }
1299
1300 Double_t px = fP[3];
1301 Double_t py = fP[4];
1302 Double_t pz = fP[5];
1303
5fc72f28 1304 p[0] = fP[0] + sB*px + cB*py;
1305 p[1] = fP[1] - cB*px + sB*py;
1306 p[2] = fP[2] + ss*pz;
1307 p[3] = c*px + s*py;
1308 p[4] = -s*px + c*py;
1309 p[5] = fP[5];
1310 p[6] = fP[6];
1311 p[7] = fP[7];
f826d409 1312
1313 Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 },
616ffc76 1314 {0,1,0, -cB, sB, 0, 0, 0 },
5fc72f28 1315 {0,0,1, 0, 0, ss, 0, 0 },
616ffc76 1316 {0,0,0, c, s, 0, 0, 0 },
1317 {0,0,0, -s, c, 0, 0, 0 },
1318 {0,0,0, 0, 0, 1, 0, 0 },
1319 {0,0,0, 0, 0, 0, 1, 0 },
1320 {0,0,0, 0, 0, 0, 0, 1 } };
f826d409 1321 Double_t mA[8][8];
1322 for( Int_t k=0,i=0; i<8; i++)
1323 for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k];
1324
1325 Double_t mJC[8][8];
1326 for( Int_t i=0; i<8; i++ )
1327 for( Int_t j=0; j<8; j++ ){
1328 mJC[i][j]=0;
1329 for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j];
1330 }
1331
1332 for( Int_t k=0,i=0; i<8; i++)
1333 for( Int_t j=0; j<=i; j++, k++ ){
5fc72f28 1334 cc[k] = 0;
1335 for( Int_t l=0; l<8; l++ ) cc[k]+=mJC[i][l]*mJ[j][l];
f826d409 1336 }
1337
1338 return;
1339 /*
1340 Double_t cBC13 = cB*fC[13];
1341 Double_t C17 = fC[17];
1342 Double_t C18 = fC[18];
1343 fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14];
1344
1345 Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13];
1346 Double_t mJC14= fC[11] - cBC13 + sB*fC[14];
1347
1348 fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB;
1349 fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB;
1350
706952f5 1351 Double_t mJC23= fC[ 8] + S*fC[18];
1352 Double_t mJC24= fC[12] + S*fC[19];
1353 fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB;
1354 fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB;
f826d409 1355
1356 fC[15]+= C18*sB + fC[19]*cB;
1357 fC[16]+= -C18*cB + fC[19]*sB;
706952f5 1358 fC[17]+= fC[20]*S;
f826d409 1359 fC[18] = C18*c + fC[19]*s;
1360 fC[19] = -C18*s + fC[19]*c;
1361
706952f5 1362 fC[ 5]+= (C17 + C17 + fC[17])*S;
f826d409 1363
1364 Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14];
1365 Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14];
1366 Double_t C6= fC[6], C7= fC[7], C8= fC[8];
1367
1368 fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB;
1369 fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB;
706952f5 1370 fC[ 8]= c*C8 + s*fC[12] +fC[18]*S;
f826d409 1371 fC[ 9]= mJC33*c +mJC34*s;
1372
1373 fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB;
1374 fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB;
706952f5 1375 fC[12]= -s*C8 + c*fC[12] +fC[19]*S;
f826d409 1376 fC[13]= mJC43*c +mJC44*s;
1377 fC[14]=-mJC43*s +mJC44*c;
1378 */
1379}
1380
1381
1382Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const
1383{
1384 //* Calculate distance from vertex [cm]
1385
1386 return GetDistanceFromVertex( Vtx.fP );
1387}
1388
1389Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const
1390{
1391 //* Calculate distance from vertex [cm]
1392
1393 Double_t mP[8], mC[36];
1394 Transport( GetDStoPoint(vtx), mP, mC );
1395 Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]};
1396 return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] );
1397}
1398
616ffc76 1399Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p )
f826d409 1400 const
1401{
616ffc76 1402 //* Calculate distance to other particle [cm]
f826d409 1403
1404 Double_t dS, dS1;
616ffc76 1405 GetDStoParticle( p, dS, dS1 );
f826d409 1406 Double_t mP[8], mC[36], mP1[8], mC1[36];
616ffc76 1407 Transport( dS, mP, mC );
1408 p.Transport( dS1, mP1, mC1 );
f826d409 1409 Double_t dx = mP[0]-mP1[0];
1410 Double_t dy = mP[1]-mP1[1];
1411 Double_t dz = mP[2]-mP1[2];
1412 return TMath::Sqrt(dx*dx+dy*dy+dz*dz);
1413}
1414
1415Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const
1416{
1417 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1418
1419 return GetDeviationFromVertex( Vtx.fP, Vtx.fC );
1420}
1421
1422
1423Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const
1424{
1425 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1426 //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix
1427
1428 Double_t mP[8];
1429 Double_t mC[36];
1430
1431 Transport( GetDStoPoint(v), mP, mC );
1432
1433 Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]};
1434
1435 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1436 (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) );
1437
1438
1439 Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS };
1440
1441 Double_t mSi[6] =
1442 { mC[0] +h[0]*h[0],
1443 mC[1] +h[1]*h[0], mC[2] +h[1]*h[1],
1444 mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] };
1445
1446 if( Cv ){
1447 mSi[0]+=Cv[0];
1448 mSi[1]+=Cv[1];
1449 mSi[2]+=Cv[2];
1450 mSi[3]+=Cv[3];
1451 mSi[4]+=Cv[4];
1452 mSi[5]+=Cv[5];
1453 }
1454
1455 Double_t mS[6];
1456
1457 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1458 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1459 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1460 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1461 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1462 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1463
1464 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1465 s = ( s > 1.E-20 ) ?1./s :0;
1466
1467 return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0]
1468 +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1]
1469 +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2);
1470}
1471
1472
616ffc76 1473Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p )
f826d409 1474 const
1475{
616ffc76 1476 //* Calculate sqrt(Chi2/ndf) deviation from other particle
f826d409 1477
1478 Double_t dS, dS1;
616ffc76 1479 GetDStoParticle( p, dS, dS1 );
f826d409 1480 Double_t mP1[8], mC1[36];
616ffc76 1481 p.Transport( dS1, mP1, mC1 );
f826d409 1482
1483 Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]};
1484
1485 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
616ffc76 1486 (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) );
f826d409 1487
1488 Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS };
1489
1490 mC1[0] +=h[0]*h[0];
1491 mC1[1] +=h[1]*h[0];
1492 mC1[2] +=h[1]*h[1];
1493 mC1[3] +=h[2]*h[0];
1494 mC1[4] +=h[2]*h[1];
1495 mC1[5] +=h[2]*h[2];
1496
1497 return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.);
1498}
1499
1500
1501
de0d0ceb 1502void AliKFParticleBase::SubtractFromVertex( AliKFParticleBase &Vtx ) const
f826d409 1503{
1504 //* Subtract the particle from the vertex
de0d0ceb 1505
f826d409 1506 Double_t fld[3];
1507 {
de0d0ceb 1508 GetFieldValue( Vtx.fP, fld );
f826d409 1509 const Double_t kCLight = 0.000299792458;
1510 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
1511 }
1512
1513 Double_t m[8];
1514 Double_t mCm[36];
f826d409 1515
de0d0ceb 1516 if( Vtx.fIsLinearized ){
1517 GetMeasurement( Vtx.fVtxGuess, m, mCm );
1518 } else {
1519 GetMeasurement( Vtx.fP, m, mCm );
f826d409 1520 }
de0d0ceb 1521
f826d409 1522 Double_t mV[6];
1523
de0d0ceb 1524 mV[ 0] = mCm[ 0];
1525 mV[ 1] = mCm[ 1];
1526 mV[ 2] = mCm[ 2];
1527 mV[ 3] = mCm[ 3];
1528 mV[ 4] = mCm[ 4];
1529 mV[ 5] = mCm[ 5];
f826d409 1530
1531 //*
1532
1533 Double_t mS[6];
1534 {
de0d0ceb 1535 Double_t mSi[6] = { mV[0]-Vtx.fC[0],
1536 mV[1]-Vtx.fC[1], mV[2]-Vtx.fC[2],
1537 mV[3]-Vtx.fC[3], mV[4]-Vtx.fC[4], mV[5]-Vtx.fC[5] };
f826d409 1538
1539 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1540 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1541 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1542 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1543 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1544 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1545
1546 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1547 s = ( s > 1.E-20 ) ?1./s :0;
1548 mS[0]*=s;
1549 mS[1]*=s;
1550 mS[2]*=s;
1551 mS[3]*=s;
1552 mS[4]*=s;
1553 mS[5]*=s;
1554 }
1555
1556 //* Residual (measured - estimated)
1557
de0d0ceb 1558 Double_t zeta[3] = { m[0]-Vtx.fP[0], m[1]-Vtx.fP[1], m[2]-Vtx.fP[2] };
f826d409 1559
1560 //* mCHt = mCH' - D'
1561
1562 Double_t mCHt0[3], mCHt1[3], mCHt2[3];
1563
de0d0ceb 1564 mCHt0[0]=Vtx.fC[ 0] ; mCHt1[0]=Vtx.fC[ 1] ; mCHt2[0]=Vtx.fC[ 3] ;
1565 mCHt0[1]=Vtx.fC[ 1] ; mCHt1[1]=Vtx.fC[ 2] ; mCHt2[1]=Vtx.fC[ 4] ;
1566 mCHt0[2]=Vtx.fC[ 3] ; mCHt1[2]=Vtx.fC[ 4] ; mCHt2[2]=Vtx.fC[ 5] ;
f826d409 1567
1568 //* Kalman gain K = mCH'*S
1569
1570 Double_t k0[3], k1[3], k2[3];
1571
1572 for(Int_t i=0;i<3;++i){
1573 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
1574 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
1575 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
1576 }
1577
1578 //* New estimation of the vertex position r += K*zeta
1579
de0d0ceb 1580 Double_t dChi2 = -(mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
1581 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
1582 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
1583
1584 if( Vtx.fChi2 - dChi2 < 0 ) return;
1585
f826d409 1586 for(Int_t i=0;i<3;++i)
de0d0ceb 1587 Vtx.fP[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
f826d409 1588
1589 //* New covariance matrix C -= K*(mCH')'
1590
1591 for(Int_t i=0, k=0;i<3;++i){
1592 for(Int_t j=0;j<=i;++j,++k)
de0d0ceb 1593 Vtx.fC[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
f826d409 1594 }
1595
1596 //* Calculate Chi^2
de0d0ceb 1597
1598 Vtx.fNDF -= 2;
1599 Vtx.fChi2 -= dChi2;
f826d409 1600}
1601
1602
1603
1604void AliKFParticleBase::TransportLine( Double_t dS,
1605 Double_t P[], Double_t C[] ) const
1606{
1607 //* Transport the particle as a straight line
1608
1609 P[0] = fP[0] + dS*fP[3];
1610 P[1] = fP[1] + dS*fP[4];
1611 P[2] = fP[2] + dS*fP[5];
1612 P[3] = fP[3];
1613 P[4] = fP[4];
1614 P[5] = fP[5];
1615 P[6] = fP[6];
1616 P[7] = fP[7];
1617
1618 Double_t c6 = fC[ 6] + dS*fC[ 9];
1619 Double_t c11 = fC[11] + dS*fC[14];
1620 Double_t c17 = fC[17] + dS*fC[20];
1621 Double_t sc13 = dS*fC[13];
1622 Double_t sc18 = dS*fC[18];
1623 Double_t sc19 = dS*fC[19];
1624
1625 C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 );
1626 C[ 2] = fC[ 2] + dS*( fC[11] + c11 );
1627 C[ 5] = fC[ 5] + dS*( fC[17] + c17 );
1628
1629 C[ 7] = fC[ 7] + sc13;
1630 C[ 8] = fC[ 8] + sc18;
1631 C[ 9] = fC[ 9];
1632
1633 C[12] = fC[12] + sc19;
1634
1635 C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] );
1636 C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] );
1637 C[ 4] = fC[ 4] + dS*( fC[16] + C[12] );
1638 C[ 6] = c6;
1639
1640 C[10] = fC[10] + sc13;
1641 C[11] = c11;
1642
1643 C[13] = fC[13];
1644 C[14] = fC[14];
1645 C[15] = fC[15] + sc18;
1646 C[16] = fC[16] + sc19;
1647 C[17] = c17;
1648
1649 C[18] = fC[18];
1650 C[19] = fC[19];
1651 C[20] = fC[20];
1652 C[21] = fC[21] + dS*fC[24];
1653 C[22] = fC[22] + dS*fC[25];
1654 C[23] = fC[23] + dS*fC[26];
1655
1656 C[24] = fC[24];
1657 C[25] = fC[25];
1658 C[26] = fC[26];
1659 C[27] = fC[27];
1660 C[28] = fC[28] + dS*fC[31];
1661 C[29] = fC[29] + dS*fC[32];
1662 C[30] = fC[30] + dS*fC[33];
1663
1664 C[31] = fC[31];
1665 C[32] = fC[32];
1666 C[33] = fC[33];
1667 C[34] = fC[34];
1668 C[35] = fC[35];
1669}
1670
1671
1672void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] )
1673{
1674 //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric
1675
1676 const Int_t kN= 8;
1677 Double_t mA[kN*kN];
1678
1679 for( Int_t i=0, ij=0; i<kN; i++ ){
1680 for( Int_t j=0; j<kN; j++, ++ij ){
1681 mA[ij] = 0 ;
1682 for( Int_t k=0; k<kN; ++k ) mA[ij]+= S[( k<=i ) ? i*(i+1)/2+k :k*(k+1)/2+i] * Q[ j*kN+k];
1683 }
1684 }
1685
1686 for( Int_t i=0; i<kN; i++ ){
1687 for( Int_t j=0; j<=i; j++ ){
1688 Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i;
1689 SOut[ij] = 0 ;
1690 for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ];
1691 }
1692 }
1693}
1694
1695
1696// 72-charachters line to define the printer border
1697//3456789012345678901234567890123456789012345678901234567890123456789012