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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
f826d409 22ClassImp(AliKFParticleBase)
23
24
25AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0)
26{
27 //* Constructor
28
29 Initialize();
30}
31
f826d409 32void AliKFParticleBase::Initialize()
33{
34 //* Initialise covariance matrix and set current parameters to 0.0
35
36 for( Int_t i=0; i<8; i++) fP[i] = 0;
37 for(Int_t i=0;i<36;++i) fC[i]=0.;
38 fC[0] = fC[2] = fC[5] = 100.;
39 fC[35] = 1.;
40 fNDF = -3;
41 fChi2 = 0.;
42 fQ = 0;
43 fSFromDecay = 0;
44 fAtProductionVertex = 0;
45 fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.;
46 fIsLinearized = 0;
47}
48
49void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z )
50{
51 //* Set decay vertex parameters for linearisation
52
53 fVtxGuess[0] = x;
54 fVtxGuess[1] = y;
55 fVtxGuess[2] = z;
56 fIsLinearized = 1;
57}
58
59
60Int_t AliKFParticleBase::GetMomentum( Double_t &P, Double_t &Error ) const
61{
62 //* Calculate particle momentum
63
64 Double_t x = fP[3];
65 Double_t y = fP[4];
66 Double_t z = fP[5];
67 Double_t x2 = x*x;
68 Double_t y2 = y*y;
69 Double_t z2 = z*z;
70 Double_t p2 = x2+y2+z2;
71 P = TMath::Sqrt(p2);
72 Error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) );
73 if( Error>0 && P>1.e-4 ){
74 Error = TMath::Sqrt(Error)/P;
75 return 0;
76 }
77 return 1;
78}
79
80Int_t AliKFParticleBase::GetMass( Double_t &M, Double_t &Error ) const
81{
82 //* Calculate particle mass
83
84 // s = sigma^2 of m2/2
85
86 Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20]
87 + fP[6]*fP[6]*fC[27]
88 +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19])
89 - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) )
90 );
91 Double_t m2 = fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5];
92 if( s>=0 && m2>1.e-20 ){
93 M = TMath::Sqrt(m2);
94 Error = TMath::Sqrt(s/m2);
95 return 0;
96 }
97 M = 0;
4bbc290d 98 Error = 1.e20;
f826d409 99 return 1;
100}
101
102
103Int_t AliKFParticleBase::GetDecayLength( Double_t &L, Double_t &Error ) const
104{
105 //* Calculate particle decay length [cm]
106
107 Double_t x = fP[3];
108 Double_t y = fP[4];
109 Double_t z = fP[5];
110 Double_t t = fP[7];
111 Double_t x2 = x*x;
112 Double_t y2 = y*y;
113 Double_t z2 = z*z;
114 Double_t p2 = x2+y2+z2;
115 L = t*TMath::Sqrt(p2);
116 if( p2>1.e-4){
117 Error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20]
118 + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) )
119 + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]);
120 Error = TMath::Sqrt(TMath::Abs(Error));
121 return 0;
122 }
4bbc290d 123 Error = 1.e20;
f826d409 124 return 1;
125}
126
127Int_t AliKFParticleBase::GetLifeTime( Double_t &TauC, Double_t &Error ) const
128{
129 //* Calculate particle decay time [s]
130
131 Double_t m, dm;
132 GetMass( m, dm );
133 Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]);
134 TauC = fP[7]*m;
135 Error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm;
136 if( Error > 0 ){
137 Error = TMath::Sqrt( Error );
138 return 0;
139 }
4bbc290d 140 Error = 1.e20;
f826d409 141 return 1;
142}
143
144
145void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter )
146{
147 //* Add daughter via operator+=
148
149 AddDaughter( Daughter );
150}
151
f826d409 152void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter )
153{
154 //* Add daughter
155
156 TransportToDecayVertex();
157
158 Double_t b[3];
159 Int_t maxIter = 1;
160
161 if( !fIsLinearized ){
162 if( fNDF==-1 ){
163 Double_t ds, ds1;
164 GetDStoParticle(Daughter, ds, ds1);
165 TransportToDS( ds );
166 }
167 fVtxGuess[0] = fP[0];
168 fVtxGuess[1] = fP[1];
169 fVtxGuess[2] = fP[2];
170 maxIter = 3;
171 }
172
173 for( Int_t iter=0; iter<maxIter; iter++ ){
174
175 {
176 GetFieldValue( fVtxGuess, b );
177 const Double_t kCLight = 0.000299792458;
178 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
179 }
4bbc290d 180 if( fNDF==-1 ) TransportToDS( GetDStoPoint(fVtxGuess) );
f826d409 181
4bbc290d 182 fSFromDecay = 0;
183
f826d409 184 Double_t m[8];
185 Double_t mCd[36];
186
4bbc290d 187 Double_t dds = Daughter.GetDStoPoint(fVtxGuess);
188
f826d409 189 Daughter.Transport( Daughter.GetDStoPoint(fVtxGuess), m, mCd );
190
191 Double_t d[3] = { fVtxGuess[0]-m[0], fVtxGuess[1]-m[1], fVtxGuess[2]-m[2] };
192 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
4bbc290d 193 (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) );
f826d409 194
195 Double_t h[6];
196
197 h[0] = m[3]*sigmaS;
198 h[1] = m[4]*sigmaS;
199 h[2] = m[5]*sigmaS;
200 h[3] = ( h[1]*b[2]-h[2]*b[1] )*Daughter.GetQ();
201 h[4] = ( h[2]*b[0]-h[0]*b[2] )*Daughter.GetQ();
202 h[5] = ( h[0]*b[1]-h[1]*b[0] )*Daughter.GetQ();
203
204 //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex
205 {
206 Double_t zeta[3] = { fVtxGuess[0]-m[0], fVtxGuess[1]-m[1], fVtxGuess[2]-m[2] };
207
208 Double_t mVv[6] =
209 { mCd[ 0] + h[0]*h[0],
210 mCd[ 1] + h[1]*h[0], mCd[ 2] + h[1]*h[1],
211 mCd[ 3] + h[2]*h[0], mCd[ 4] + h[2]*h[1], mCd[ 5] + h[2]*h[2] };
212
213 Double_t mVvp[9]=
214 { mCd[ 6] + h[0]*h[3], mCd[ 7] + h[1]*h[3], mCd[ 8] + h[2]*h[3],
215 mCd[10] + h[0]*h[4], mCd[11] + h[1]*h[4], mCd[12] + h[2]*h[4],
216 mCd[15] + h[0]*h[5], mCd[16] + h[1]*h[5], mCd[17] + h[2]*h[5] };
217
218 Double_t mS[6] =
219 { mVv[2]*mVv[5] - mVv[4]*mVv[4],
220 mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3],
221 mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4],
222 mVv[0]*mVv[2] - mVv[1]*mVv[1] };
223
224 Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] );
225 s = ( s > 1.E-20 ) ?1./s :0;
226
227 mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s;
228
229 Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]),
230 (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]),
231 (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) };
232
233 Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2];
234 Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2];
235 Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2];
236
237 h[0] = px*sigmaS;
238 h[1] = py*sigmaS;
239 h[2] = pz*sigmaS;
240 h[3] = ( h[1]*b[2]-h[2]*b[1] )*Daughter.GetQ();
241 h[4] = ( h[2]*b[0]-h[0]*b[2] )*Daughter.GetQ();
242 h[5] = ( h[0]*b[1]-h[1]*b[0] )*Daughter.GetQ();
243 }
4bbc290d 244
f826d409 245 Double_t mV[28];
246
247 mV[ 0] = mCd[ 0] + h[0]*h[0];
248 mV[ 1] = mCd[ 1] + h[1]*h[0];
249 mV[ 2] = mCd[ 2] + h[1]*h[1];
250 mV[ 3] = mCd[ 3] + h[2]*h[0];
251 mV[ 4] = mCd[ 4] + h[2]*h[1];
252 mV[ 5] = mCd[ 5] + h[2]*h[2];
253
254 mV[ 6] = mCd[ 6] + h[3]*h[0];
255 mV[ 7] = mCd[ 7] + h[3]*h[1];
256 mV[ 8] = mCd[ 8] + h[3]*h[2];
257 mV[ 9] = mCd[ 9] + h[3]*h[3];
258
259 mV[10] = mCd[10] + h[4]*h[0];
260 mV[11] = mCd[11] + h[4]*h[1];
261 mV[12] = mCd[12] + h[4]*h[2];
262 mV[13] = mCd[13] + h[4]*h[3];
263 mV[14] = mCd[14] + h[4]*h[4];
264
265 mV[15] = mCd[15] + h[5]*h[0];
266 mV[16] = mCd[16] + h[5]*h[1];
267 mV[17] = mCd[17] + h[5]*h[2];
268 mV[18] = mCd[18] + h[5]*h[3];
269 mV[19] = mCd[19] + h[5]*h[4];
270 mV[20] = mCd[20] + h[5]*h[5];
271
272 mV[21] = mCd[21];
273 mV[22] = mCd[22];
274 mV[23] = mCd[23];
275 mV[24] = mCd[24];
276 mV[25] = mCd[25];
277 mV[26] = mCd[26];
278 mV[27] = mCd[27];
279
4bbc290d 280 //*
f826d409 281
282 if( fNDF<-1 ){ // first daughter -> just copy
283 fNDF = -1;
284 fQ = Daughter.GetQ();
285 for( Int_t i=0; i<7; i++) fP[i] = m[i];
286 for( Int_t i=0; i<28; i++) fC[i] = mV[i];
287 fSFromDecay = 0;
288 return;
289 }
290
291 //*
292
293 Double_t mS[6];
294 {
295 Double_t mSi[6] = { fC[0]+mV[0],
296 fC[1]+mV[1], fC[2]+mV[2],
297 fC[3]+mV[3], fC[4]+mV[4], fC[5]+mV[5] };
298
299 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
300 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
301 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
302 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
303 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
304 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
305
306 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
307 s = ( s > 1.E-20 ) ?1./s :0;
308 mS[0]*=s;
309 mS[1]*=s;
310 mS[2]*=s;
311 mS[3]*=s;
312 mS[4]*=s;
313 mS[5]*=s;
314 }
315
316 //* Residual (measured - estimated)
317
318 Double_t zeta[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
319
320
321 //* CHt = CH' - D'
322
323 Double_t mCHt0[7], mCHt1[7], mCHt2[7];
324
325 mCHt0[0]=fC[ 0] ; mCHt1[0]=fC[ 1] ; mCHt2[0]=fC[ 3] ;
326 mCHt0[1]=fC[ 1] ; mCHt1[1]=fC[ 2] ; mCHt2[1]=fC[ 4] ;
327 mCHt0[2]=fC[ 3] ; mCHt1[2]=fC[ 4] ; mCHt2[2]=fC[ 5] ;
328 mCHt0[3]=fC[ 6]-mV[ 6]; mCHt1[3]=fC[ 7]-mV[ 7]; mCHt2[3]=fC[ 8]-mV[ 8];
329 mCHt0[4]=fC[10]-mV[10]; mCHt1[4]=fC[11]-mV[11]; mCHt2[4]=fC[12]-mV[12];
330 mCHt0[5]=fC[15]-mV[15]; mCHt1[5]=fC[16]-mV[16]; mCHt2[5]=fC[17]-mV[17];
331 mCHt0[6]=fC[21]-mV[21]; mCHt1[6]=fC[22]-mV[22]; mCHt2[6]=fC[23]-mV[23];
332
333 //* Kalman gain K = mCH'*S
334
335 Double_t k0[7], k1[7], k2[7];
336
337 for(Int_t i=0;i<7;++i){
338 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
339 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
340 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
341 }
342
4bbc290d 343 //* New estimation of the vertex position
f826d409 344
345 if( iter<maxIter-1 ){
346 for(Int_t i=0; i<3; ++i)
347 fVtxGuess[i]= fP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2];
348 continue;
349 }
350
351 // last itearation -> update the particle
352
353 //* Add the daughter momentum to the particle momentum
354
355 fP[ 3] += m[ 3];
356 fP[ 4] += m[ 4];
357 fP[ 5] += m[ 5];
358 fP[ 6] += m[ 6];
359
360 fC[ 9] += mV[ 9];
361 fC[13] += mV[13];
362 fC[14] += mV[14];
363 fC[18] += mV[18];
364 fC[19] += mV[19];
365 fC[20] += mV[20];
366 fC[24] += mV[24];
367 fC[25] += mV[25];
368 fC[26] += mV[26];
369 fC[27] += mV[27];
370
371 //* New estimation of the vertex position r += K*zeta
372
373 for(Int_t i=0;i<7;++i)
374 fP[i] += k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
375
376 //* New covariance matrix C -= K*(mCH')'
4bbc290d 377
f826d409 378 for(Int_t i=0, k=0;i<7;++i){
379 for(Int_t j=0;j<=i;++j,++k)
380 fC[k] -= k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
381 }
382
383 //* Calculate Chi^2
384
385 fNDF += 2;
386 fQ += Daughter.GetQ();
387 fSFromDecay = 0;
388 fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
389 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
390 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
391 }
392}
393
394
395void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx )
396{
397 //* Set production vertex for the particle
398
399 const Double_t *m = Vtx.fP, *mV = Vtx.fC;
400
401 TransportToDS( GetDStoPoint( m ) );
402 fP[7] = -fSFromDecay;
403 Convert(1);
404
405 Double_t mAi[6];
406 mAi[0] = fC[4]*fC[4] - fC[2]*fC[5];
407 mAi[1] = fC[1]*fC[5] - fC[3]*fC[4];
408 mAi[3] = fC[2]*fC[3] - fC[1]*fC[4];
409 Double_t det = 1./(fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]);
410 mAi[0] *= det;
411 mAi[1] *= det;
412 mAi[3] *= det;
413 mAi[2] = ( fC[3]*fC[3] - fC[0]*fC[5] )*det;
414 mAi[4] = ( fC[0]*fC[4] - fC[1]*fC[3] )*det;
415 mAi[5] = ( fC[1]*fC[1] - fC[0]*fC[2] )*det;
416
417 Double_t mB[5][3];
418
419 mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3];
420 mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4];
421 mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5];
422
423 mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3];
424 mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4];
425 mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5];
426
427 mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3];
428 mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4];
429 mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5];
430
431 mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3];
432 mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4];
433 mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5];
434
435 mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3];
436 mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4];
437 mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5];
438
439 Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
440
441 {
442 Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2],
443 fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] };
444 Double_t mAVi[6];
445 mAVi[0] = mAV[4]*mAV[4] - mAV[2]*mAV[5];
446 mAVi[1] = mAV[1]*mAV[5] - mAV[3]*mAV[4];
447 mAVi[2] = mAV[3]*mAV[3] - mAV[0]*mAV[5] ;
448 mAVi[3] = mAV[2]*mAV[3] - mAV[1]*mAV[4];
449 mAVi[4] = mAV[0]*mAV[4] - mAV[1]*mAV[3] ;
450 mAVi[5] = mAV[1]*mAV[1] - mAV[0]*mAV[2] ;
451
452 det = 1./( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] );
453
454 fNDF += 2;
455 fChi2 +=
456 ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0]
457 +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1]
458 +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )*det;
459 }
460
461 fP[0] = m[0];
462 fP[1] = m[1];
463 fP[2] = m[2];
464 fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
465 fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
466 fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
467 fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2];
468 fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2];
469
470 Double_t d0, d1, d2;
471
472 fC[0] = mV[0];
473 fC[1] = mV[1];
474 fC[2] = mV[2];
475 fC[3] = mV[3];
476 fC[4] = mV[4];
477 fC[5] = mV[5];
478
479 d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6];
480 d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7];
481 d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8];
482
483 fC[ 6]+= d0;
484 fC[ 7]+= d1;
485 fC[ 8]+= d2;
486 fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
487
488 d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10];
489 d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11];
490 d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12];
491
492 fC[10]+= d0;
493 fC[11]+= d1;
494 fC[12]+= d2;
495 fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
496 fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
497
498 d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15];
499 d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16];
500 d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17];
501
502 fC[15]+= d0;
503 fC[16]+= d1;
504 fC[17]+= d2;
505 fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
506 fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
507 fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
508
509 d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21];
510 d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22];
511 d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23];
512
513 fC[21]+= d0;
514 fC[22]+= d1;
515 fC[23]+= d2;
516 fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
517 fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
518 fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
519 fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
520
521 d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28];
522 d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29];
523 d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30];
524
525 fC[28]+= d0;
526 fC[29]+= d1;
527 fC[30]+= d2;
528 fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
529 fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
530 fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
531 fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
532 fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2];
533
534 TransportToDS( fP[7] );
535 fSFromDecay = 0;
536 Convert(0);
537}
538
539
540
541
542void AliKFParticleBase::SetMassConstraint( Double_t Mass )
543{
544 //* Set hard mass constraint
545
546 Double_t mH[8];
547 mH[0] = mH[1] = mH[2] = 0.;
548 mH[3] = -2*fP[3];
549 mH[4] = -2*fP[4];
550 mH[5] = -2*fP[5];
551 mH[6] = 2*fP[6];
552 mH[7] = 0;
553 Double_t m2 = ( fP[6]*fP[6]
554 - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5] );
555
556 Double_t zeta = Mass*Mass - m2;
557 for(Int_t i=0;i<8;++i) zeta -= mH[i]*(fP[i]-fP[i]);
558
559 Double_t s = 0.;
560 Double_t mCHt[8];
561 for (Int_t i=0;i<8;++i ){
562 mCHt[i] = 0.0;
563 for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j];
564 s += mH[i]*mCHt[i];
565 }
566
567 if( s<1.e-20 ) return;
568 s = 1./s;
569 fChi2 += zeta*zeta*s;
570 fNDF += 1;
571 for( Int_t i=0, ii=0; i<8; ++i ){
572 Double_t ki = mCHt[i]*s;
573 fP[i]+= ki*zeta;
574 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j];
575 }
576}
577
578
579void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters,
4bbc290d 580 const AliKFParticleBase *Parent, Double_t Mass )
f826d409 581{
582 //* Full reconstruction in one go
583
584 Int_t maxIter = 1;
585 bool wasLinearized = fIsLinearized;
586 if( !fIsLinearized ){
587 fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0;
588 fIsLinearized = 1;
589 maxIter = 3;
590 }
591
592 for( Int_t iter=0; iter<maxIter; iter++ ){
f826d409 593 fAtProductionVertex = 0;
594 fSFromDecay = 0;
595 fP[0] = fVtxGuess[0];
596 fP[1] = fVtxGuess[1];
597 fP[2] = fVtxGuess[2];
598 fP[3] = 0;
599 fP[4] = 0;
600 fP[5] = 0;
601 fP[6] = 0;
602 fP[7] = 0;
603
604 for(Int_t i=0;i<36;++i) fC[i]=0.;
605
606 fC[0] = fC[2] = fC[5] = 100.;
607 fC[35] = 1.;
608
609 fNDF = -3;
610 fChi2 = 0.;
611 fQ = 0;
612
4bbc290d 613 for( Int_t itr =0; itr<NDaughters; itr++ ){
614 AddDaughter( *vDaughters[itr] );
615 }
f826d409 616 if( iter<maxIter-1){
617 for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i];
618 }
619 }
620 fIsLinearized = wasLinearized;
621
622 if( Mass>=0 ) SetMassConstraint( Mass );
623 if( Parent ) SetProductionVertex( *Parent );
624}
625
626
627void AliKFParticleBase::Convert( bool ToProduction )
628{
629 //* Tricky function - convert the particle error along its trajectory to
630 //* the value which corresponds to its production/decay vertex
631 //* It is done by combination of the error of decay length with the position errors
632
633 Double_t fld[3];
634 {
635 GetFieldValue( fP, fld );
636 const Double_t kCLight = fQ*0.000299792458;
637 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
638 }
639
640 Double_t h[6];
641
642 h[0] = fP[3];
643 h[1] = fP[4];
644 h[2] = fP[5];
645 if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; }
646 h[3] = h[1]*fld[2]-h[2]*fld[1];
647 h[4] = h[2]*fld[0]-h[0]*fld[2];
648 h[5] = h[0]*fld[1]-h[1]*fld[0];
649
650 Double_t c;
651
652 c = fC[28]+h[0]*fC[35];
653 fC[ 0]+= h[0]*(c+fC[28]);
654 fC[28] = c;
655
656 fC[ 1]+= h[1]*fC[28] + h[0]*fC[29];
657 c = fC[29]+h[1]*fC[35];
658 fC[ 2]+= h[1]*(c+fC[29]);
659 fC[29] = c;
660
661 fC[ 3]+= h[2]*fC[28] + h[0]*fC[30];
662 fC[ 4]+= h[2]*fC[29] + h[1]*fC[30];
663 c = fC[30]+h[2]*fC[35];
664 fC[ 5]+= h[2]*(c+fC[30]);
665 fC[30] = c;
666
667 fC[ 6]+= h[3]*fC[28] + h[0]*fC[31];
668 fC[ 7]+= h[3]*fC[29] + h[1]*fC[31];
669 fC[ 8]+= h[3]*fC[30] + h[2]*fC[31];
670 c = fC[31]+h[3]*fC[35];
671 fC[ 9]+= h[3]*(c+fC[31]);
672 fC[31] = c;
673
674 fC[10]+= h[4]*fC[28] + h[0]*fC[32];
675 fC[11]+= h[4]*fC[29] + h[1]*fC[32];
676 fC[12]+= h[4]*fC[30] + h[2]*fC[32];
677 fC[13]+= h[4]*fC[31] + h[3]*fC[32];
678 c = fC[32]+h[4]*fC[35];
679 fC[14]+= h[4]*(c+fC[32]);
680 fC[32] = c;
681
682 fC[15]+= h[5]*fC[28] + h[0]*fC[33];
683 fC[16]+= h[5]*fC[29] + h[1]*fC[33];
684 fC[17]+= h[5]*fC[30] + h[2]*fC[33];
685 fC[18]+= h[5]*fC[31] + h[3]*fC[33];
686 fC[19]+= h[5]*fC[32] + h[4]*fC[33];
687 c = fC[33]+h[5]*fC[35];
688 fC[20]+= h[5]*(c+fC[33]);
689 fC[33] = c;
690
691 fC[21]+= h[0]*fC[34];
692 fC[22]+= h[1]*fC[34];
693 fC[23]+= h[2]*fC[34];
694 fC[24]+= h[3]*fC[34];
695 fC[25]+= h[4]*fC[34];
696 fC[26]+= h[5]*fC[34];
697}
698
699
700void AliKFParticleBase::TransportToDecayVertex()
701{
702 //* Transport the particle to its decay vertex
703
704 if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay );
705 if( fAtProductionVertex ) Convert(0);
706 fAtProductionVertex = 0;
707}
708
709void AliKFParticleBase::TransportToProductionVertex()
710{
711 //* Transport the particle to its production vertex
712
713 if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] );
714 if( !fAtProductionVertex ) Convert( 1 );
715 fAtProductionVertex = 1;
716}
717
718
719void AliKFParticleBase::TransportToDS( Double_t dS )
720{
721 //* Transport the particle on dS parameter (SignedPath/Momentum)
722
723 Transport( dS, fP, fC );
724 fSFromDecay+= dS;
725}
726
727
728Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const
729{
730 //* Get dS to a certain space point without field
731
732 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
733 if( p2<1.e-4 ) p2 = 1;
734 return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2;
735}
736
737
738Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] )
739 const
740{
741 //* Get dS to a certain space point for Bz field
f826d409 742 const Double_t kCLight = 0.000299792458;
743 Double_t bq = B*fQ*kCLight;
744 Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4];
745 if( pt2<1.e-4 ) return 0;
746 Double_t dx = xyz[0] - fP[0];
747 Double_t dy = xyz[1] - fP[1];
748 Double_t a = dx*fP[3]+dy*fP[4];
749 if( TMath::Abs(bq)<1.e-8 ) return a/pt2;
750 return TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq;
751}
752
753
754void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p,
755 Double_t &DS, Double_t &DS1 )
756 const
757{
758 //* Get dS to another particle for Bz field
f826d409 759 Double_t px = fP[3];
760 Double_t py = fP[4];
761 Double_t pz = fP[5];
762
763 Double_t px1 = p.fP[3];
764 Double_t py1 = p.fP[4];
765 Double_t pz1 = p.fP[5];
766
767 const Double_t kCLight = 0.000299792458;
768
769 Double_t bq = B*fQ*kCLight;
770 Double_t bq1 = B*p.fQ*kCLight;
f826d409 771 Double_t s=0, ds=0, s1=0, ds1=0;
772
773 if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){
4bbc290d 774
f826d409 775 Double_t dx = (p.fP[0] - fP[0]);
776 Double_t dy = (p.fP[1] - fP[1]);
777 Double_t d2 = (dx*dx+dy*dy);
778
779 Double_t p2 = (px *px + py *py);
780 Double_t p21 = (px1*px1 + py1*py1);
781
782 Double_t a = (px*py1 - py*px1);
783 Double_t b = (px*px1 + py*py1);
784
785 Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ;
786 Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ;
787 Double_t l2 = ldx*ldx + ldy*ldy;
788
789 Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b;
790 Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b;
791
792 Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ;
793 Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ;
794
795 Double_t sa = 4*l2*p2 - ca*ca;
796 Double_t sa1 = 4*l2*p21 - ca1*ca1;
797 if(sa<0) sa=0;
798 if(sa1<0)sa1=0;
799
800 if( TMath::Abs(bq)>1.e-8){
801 s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq;
802 ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq;
803 } else {
804 s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2;
805 ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2;
806 if( ds<0 ) ds = 0;
807 ds = TMath::Sqrt(ds);
808 }
809
810 if( TMath::Abs(bq1)>1.e-8){
811 s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1;
812 ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1;
813 } else {
814 s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21;
815 ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21;
816 if( ds1<0 ) ds1 = 0;
817 ds1 = TMath::Sqrt(ds1);
818 }
819 }
820
f826d409 821 Double_t ss[2], ss1[2], g[2][5],g1[2][5];
822
823 ss[0] = s + ds;
824 ss[1] = s - ds;
825 ss1[0] = s1 + ds1;
826 ss1[1] = s1 - ds1;
827 for( Int_t i=0; i<2; i++){
828 Double_t bs = bq*ss[i];
829 Double_t c = TMath::Cos(bs), s = TMath::Sin(bs);
830 Double_t cB,sB;
831 if( TMath::Abs(bq)>1.e-8){
832 cB= (1-c)/bq;
833 sB= s/bq;
834 }else{
835 sB = (1. - bs*bs/6.)*ss[i];
836 cB = .5*sB*bs;
837 }
838 g[i][0] = fP[0] + sB*px + cB*py;
839 g[i][1] = fP[1] - cB*px + sB*py;
840 g[i][2] = fP[2] + ss[i]*pz;
841 g[i][3] = + c*px + s*py;
842 g[i][4] = - s*px + c*py;
843
844 bs = bq1*ss1[i];
845 c = TMath::Cos(bs); s = TMath::Sin(bs);
846 if( TMath::Abs(bq1)>1.e-8){
847 cB= (1-c)/bq1;
848 sB= s/bq1;
849 }else{
850 sB = (1. - bs*bs/6.)*ss1[i];
851 cB = .5*sB*bs;
852 }
853
854 g[i][0] = p.fP[0] + sB*px1 + cB*py1;
855 g[i][1] = p.fP[1] - cB*px1 + sB*py1;
856 g[i][2] = p.fP[2] + ss[i]*pz1;
857 g[i][3] = + c*px1 + s*py1;
858 g[i][4] = - s*px1 + c*py1;
859 }
860
861 Int_t i=0, i1=0;
862
863 Double_t dMin = 1.e10;
864 for( Int_t j=0; j<2; j++){
865 for( Int_t j1=0; j1<2; j1++){
866 Double_t xx = g[j][0]-g1[j1][0];
867 Double_t yy = g[j][1]-g1[j1][1];
868 Double_t zz = g[j][2]-g1[j1][2];
869 Double_t d = xx*xx + yy*yy + zz*zz;
870 if( d<dMin ){
871 dMin = d;
872 i = j;
873 i1 = j1;
874 }
875 }
876 }
877
878 DS = ss[i];
879 DS1 = ss1[i1];
880
881 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
882 Double_t x1=g[i1][0], y1= g[i1][1], z1= g[i1][2], ppx1= g[i1][3], ppy1= g[i1][4];
883 Double_t dx = x1-x;
884 Double_t dy = y1-y;
885 Double_t dz = z1-z;
886 Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1;
887 Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1;
888 Double_t c = dx*ppx + dy*ppy + dz*pz ;
889 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
890 Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1;
891 Double_t det = pp2*pp21 - a*a;
892 if( TMath::Abs(det)>1.e-8 ){
893 DS+=(a*b-pp21*c)/det;
894 DS1+=(a*c-pp2*b)/det;
895 }
896}
897
898
899
900void AliKFParticleBase::TransportCBM( Double_t dS,
901 Double_t P[], Double_t C[] ) const
902{
903 //* Transport the particle on dS, output to P[],C[], for CBM field
904
905 if( fQ==0 ){
906 TransportLine( dS, P, C );
907 return;
908 }
909
910 const Double_t kCLight = 0.000299792458;
911
912 Double_t c = fQ*kCLight;
913
914 // construct coefficients
915
916 Double_t
917 px = fP[3],
918 py = fP[4],
919 pz = fP[5];
920
921 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;
922
923 { // get field integrals
924
925 Double_t fld[3][3];
926 Double_t p0[3], p1[3], p2[3];
927
928 // line track approximation
929
930 p0[0] = fP[0];
931 p0[1] = fP[1];
932 p0[2] = fP[2];
933
934 p2[0] = fP[0] + px*dS;
935 p2[1] = fP[1] + py*dS;
936 p2[2] = fP[2] + pz*dS;
937
938 p1[0] = 0.5*(p0[0]+p2[0]);
939 p1[1] = 0.5*(p0[1]+p2[1]);
940 p1[2] = 0.5*(p0[2]+p2[2]);
941
942 // first order track approximation
943 {
944 GetFieldValue( p0, fld[0] );
945 GetFieldValue( p1, fld[1] );
946 GetFieldValue( p2, fld[2] );
947
948 Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.;
949 Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.;
950
951 p1[0] -= ssy1*pz;
952 p1[2] += ssy1*px;
953 p2[0] -= ssy2*pz;
954 p2[2] += ssy2*px;
955 }
956
957 GetFieldValue( p0, fld[0] );
958 GetFieldValue( p1, fld[1] );
959 GetFieldValue( p2, fld[2] );
960
961 sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.;
962 sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.;
963 sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.;
964
965 ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.;
966 ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.;
967 ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.;
968
969 Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360.
970 Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520.
971 for(Int_t n=0; n<3; n++)
972 for(Int_t m=0; m<3; m++)
973 {
974 syz += c2[n][m]*fld[n][1]*fld[m][2];
975 ssyz += cc2[n][m]*fld[n][1]*fld[m][2];
976 }
977
978 syz *= c*c*dS*dS/360.;
979 ssyz *= c*c*dS*dS*dS/2520.;
980
981 syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS;
982 syyy = syy*syy*syy / 1296;
983 syy = syy*syy/72;
984
985 ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+
986 fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+
987 fld[2][1]*( 3*fld[2][1] )
988 )*dS*dS*dS*c*c/2520.;
989 ssyyy =
990 (
991 fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+
992 fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+
993 fld[2][1]*( 19*fld[2][1] ) )+
994 fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+
995 fld[2][1]*( 62*fld[2][1] ) )+
996 fld[2][1]*fld[2][1] *( 3*fld[2][1] )
997 )*dS*dS*dS*dS*c*c*c/90720.;
998
999 }
1000
1001 Double_t mJ[8][8];
1002 for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0;
1003
1004 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;
1005 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;
1006 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;
1007
1008 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;
1009 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;
1010 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;
1011 mJ[6][6] = mJ[7][7] = 1;
1012
1013 P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz;
1014 P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz;
1015 P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz;
1016 P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz;
1017 P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz;
1018 P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz;
1019 P[6] = fP[6];
1020 P[7] = fP[7];
1021
1022 MultQSQt( mJ[0], fC, C);
1023
1024}
1025
1026
1027void AliKFParticleBase::TransportBz( Double_t B, Double_t S,
1028 Double_t P[], Double_t C[] ) const
1029{
1030 //* Transport the particle on dS, output to P[],C[], for Bz field
1031
1032 const Double_t kCLight = 0.000299792458;
1033 B = B*fQ*kCLight;
1034 Double_t bs= B*S;
1035 Double_t s = TMath::Sin(bs), c = TMath::Cos(bs);
1036 Double_t sB, cB;
1037 if( TMath::Abs(bs)>1.e-8){
1038 sB= s/B;
1039 cB= (1-c)/B;
1040 }else{
1041 sB = (1. - bs*bs/6.)*S;
1042 cB = .5*sB*bs;
1043 }
1044
1045 Double_t px = fP[3];
1046 Double_t py = fP[4];
1047 Double_t pz = fP[5];
1048
1049 P[0] = fP[0] + sB*px + cB*py;
1050 P[1] = fP[1] - cB*px + sB*py;
1051 P[2] = fP[2] + S*pz;
1052 P[3] = c*px + s*py;
1053 P[4] = -s*px + c*py;
1054 P[5] = fP[5];
1055 P[6] = fP[6];
1056 P[7] = fP[7];
1057
1058 Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 },
1059 {0,1,0, -cB, sB, 0, 0, 0 },
1060 {0,0,1, 0, 0, S, 0, 0 },
1061 {0,0,0, c, s, 0, 0, 0 },
1062 {0,0,0, -s, c, 0, 0, 0 },
1063 {0,0,0, 0, 0, 1, 0, 0 },
1064 {0,0,0, 0, 0, 0, 1, 0 },
1065 {0,0,0, 0, 0, 0, 0, 1 } };
1066 Double_t mA[8][8];
1067 for( Int_t k=0,i=0; i<8; i++)
1068 for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k];
1069
1070 Double_t mJC[8][8];
1071 for( Int_t i=0; i<8; i++ )
1072 for( Int_t j=0; j<8; j++ ){
1073 mJC[i][j]=0;
1074 for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j];
1075 }
1076
1077 for( Int_t k=0,i=0; i<8; i++)
1078 for( Int_t j=0; j<=i; j++, k++ ){
1079 C[k] = 0;
1080 for( Int_t l=0; l<8; l++ ) C[k]+=mJC[i][l]*mJ[j][l];
1081 }
1082
1083 return;
1084 /*
1085 Double_t cBC13 = cB*fC[13];
1086 Double_t C17 = fC[17];
1087 Double_t C18 = fC[18];
1088 fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14];
1089
1090 Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13];
1091 Double_t mJC14= fC[11] - cBC13 + sB*fC[14];
1092
1093 fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB;
1094 fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB;
1095
1096 Double_t mJC23= fC[ 8] + S*fC[18];
1097 Double_t mJC24= fC[12] + S*fC[19];
1098 fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB;
1099 fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB;
1100
1101 fC[15]+= C18*sB + fC[19]*cB;
1102 fC[16]+= -C18*cB + fC[19]*sB;
1103 fC[17]+= fC[20]*S;
1104 fC[18] = C18*c + fC[19]*s;
1105 fC[19] = -C18*s + fC[19]*c;
1106
1107 fC[ 5]+= (C17 + C17 + fC[17])*S;
1108
1109 Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14];
1110 Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14];
1111 Double_t C6= fC[6], C7= fC[7], C8= fC[8];
1112
1113 fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB;
1114 fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB;
1115 fC[ 8]= c*C8 + s*fC[12] +fC[18]*S;
1116 fC[ 9]= mJC33*c +mJC34*s;
1117
1118 fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB;
1119 fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB;
1120 fC[12]= -s*C8 + c*fC[12] +fC[19]*S;
1121 fC[13]= mJC43*c +mJC44*s;
1122 fC[14]=-mJC43*s +mJC44*c;
1123 */
1124}
1125
1126
1127Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const
1128{
1129 //* Calculate distance from vertex [cm]
1130
1131 return GetDistanceFromVertex( Vtx.fP );
1132}
1133
1134Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const
1135{
1136 //* Calculate distance from vertex [cm]
1137
1138 Double_t mP[8], mC[36];
1139 Transport( GetDStoPoint(vtx), mP, mC );
1140 Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]};
1141 return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] );
1142}
1143
1144Double_t AliKFParticleBase::GetDistanceFromParticleBz( Double_t B,
1145 const AliKFParticleBase &p )
1146 const
1147{
1148 //* Calculate distance other particle [cm] for Bz field
1149
1150 Double_t dS, dS1;
1151 GetDStoParticleBz( B, p, dS, dS1 );
1152 Double_t mP[8], mC[36], mP1[8], mC1[36];
1153 TransportBz( B, dS, mP, mC );
1154 p.TransportBz( B, dS1, mP1, mC1 );
1155 Double_t dx = mP[0]-mP1[0];
1156 Double_t dy = mP[1]-mP1[1];
1157 Double_t dz = mP[2]-mP1[2];
1158 return TMath::Sqrt(dx*dx+dy*dy+dz*dz);
1159}
1160
1161Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const
1162{
1163 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1164
1165 return GetDeviationFromVertex( Vtx.fP, Vtx.fC );
1166}
1167
1168
1169Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const
1170{
1171 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1172 //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix
1173
1174 Double_t mP[8];
1175 Double_t mC[36];
1176
1177 Transport( GetDStoPoint(v), mP, mC );
1178
1179 Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]};
1180
1181 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1182 (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) );
1183
1184
1185 Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS };
1186
1187 Double_t mSi[6] =
1188 { mC[0] +h[0]*h[0],
1189 mC[1] +h[1]*h[0], mC[2] +h[1]*h[1],
1190 mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] };
1191
1192 if( Cv ){
1193 mSi[0]+=Cv[0];
1194 mSi[1]+=Cv[1];
1195 mSi[2]+=Cv[2];
1196 mSi[3]+=Cv[3];
1197 mSi[4]+=Cv[4];
1198 mSi[5]+=Cv[5];
1199 }
1200
1201 Double_t mS[6];
1202
1203 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1204 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1205 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1206 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1207 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1208 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1209
1210 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1211 s = ( s > 1.E-20 ) ?1./s :0;
1212
1213 return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0]
1214 +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1]
1215 +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2);
1216}
1217
1218
1219Double_t AliKFParticleBase::GetDeviationFromParticleBz( Double_t B,
1220 const AliKFParticleBase &p )
1221 const
1222{
1223 //* Calculate sqrt(Chi2/ndf) deviation from other particle, for Bz field
1224
1225 Double_t dS, dS1;
1226 GetDStoParticleBz( B, p, dS, dS1 );
1227 Double_t mP1[8], mC1[36];
1228 p.TransportBz( B, dS1, mP1, mC1 );
1229
1230 Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]};
1231
1232 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1233 (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) );
1234
1235 Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS };
1236
1237 mC1[0] +=h[0]*h[0];
1238 mC1[1] +=h[1]*h[0];
1239 mC1[2] +=h[1]*h[1];
1240 mC1[3] +=h[2]*h[0];
1241 mC1[4] +=h[2]*h[1];
1242 mC1[5] +=h[2]*h[2];
1243
1244 return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.);
1245}
1246
1247
1248
1249void AliKFParticleBase::SubtractFromVertex( Double_t v[], Double_t Cv[],
1250 Double_t &vChi2, Int_t vNDF ) const
1251{
1252 //* Subtract the particle from the vertex
1253
1254 Double_t fld[3];
1255 {
1256 GetFieldValue( v, fld );
1257 const Double_t kCLight = 0.000299792458;
1258 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
1259 }
1260
1261 Double_t m[8];
1262 Double_t mCm[36];
1263
1264 Transport( GetDStoPoint(v), m, mCm );
1265
1266 Double_t d[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] };
1267 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1268 (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) );
1269
1270 Double_t h[6];
1271
1272 h[0] = m[3]*sigmaS;
1273 h[1] = m[4]*sigmaS;
1274 h[2] = m[5]*sigmaS;
1275 h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ();
1276 h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ();
1277 h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ();
1278
1279 //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex
1280 {
1281 Double_t zeta[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] };
1282
1283 Double_t mVv[6] =
1284 { mCm[ 0] + h[0]*h[0],
1285 mCm[ 1] + h[1]*h[0], mCm[ 2] + h[1]*h[1],
1286 mCm[ 3] + h[2]*h[0], mCm[ 4] + h[2]*h[1], mCm[ 5] + h[2]*h[2] };
1287
1288 Double_t mVvp[9]=
1289 { mCm[ 6] + h[0]*h[3], mCm[ 7] + h[1]*h[3], mCm[ 8] + h[2]*h[3],
1290 mCm[10] + h[0]*h[4], mCm[11] + h[1]*h[4], mCm[12] + h[2]*h[4],
1291 mCm[15] + h[0]*h[5], mCm[16] + h[1]*h[5], mCm[17] + h[2]*h[5] };
1292
1293 Double_t mS[6] =
1294 { mVv[2]*mVv[5] - mVv[4]*mVv[4],
1295 mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3],
1296 mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4],
1297 mVv[0]*mVv[2] - mVv[1]*mVv[1] };
1298
1299 Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] );
1300 s = ( s > 1.E-20 ) ?1./s :0;
1301
1302 mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s;
1303
1304 Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]),
1305 (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]),
1306 (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) };
1307
1308 Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2];
1309 Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2];
1310 Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2];
1311
1312 h[0] = px*sigmaS;
1313 h[1] = py*sigmaS;
1314 h[2] = pz*sigmaS;
1315 h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ();
1316 h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ();
1317 h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ();
1318 }
1319
1320 Double_t mV[6];
1321
1322 mV[ 0] = mCm[ 0] + h[0]*h[0];
1323 mV[ 1] = mCm[ 1] + h[1]*h[0];
1324 mV[ 2] = mCm[ 2] + h[1]*h[1];
1325 mV[ 3] = mCm[ 3] + h[2]*h[0];
1326 mV[ 4] = mCm[ 4] + h[2]*h[1];
1327 mV[ 5] = mCm[ 5] + h[2]*h[2];
1328
1329 //*
1330
1331 Double_t mS[6];
1332 {
1333 Double_t mSi[6] = { mV[0]-Cv[0],
1334 mV[1]-Cv[1], mV[2]-Cv[2],
1335 mV[3]-Cv[3], mV[4]-Cv[4], mV[5]-Cv[5] };
1336
1337 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1338 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1339 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1340 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1341 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1342 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1343
1344 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1345 s = ( s > 1.E-20 ) ?1./s :0;
1346 mS[0]*=s;
1347 mS[1]*=s;
1348 mS[2]*=s;
1349 mS[3]*=s;
1350 mS[4]*=s;
1351 mS[5]*=s;
1352 }
1353
1354 //* Residual (measured - estimated)
1355
1356 Double_t zeta[3] = { m[0]-v[0], m[1]-v[1], m[2]-v[2] };
1357
1358 //* mCHt = mCH' - D'
1359
1360 Double_t mCHt0[3], mCHt1[3], mCHt2[3];
1361
1362 mCHt0[0]=Cv[ 0] ; mCHt1[0]=Cv[ 1] ; mCHt2[0]=Cv[ 3] ;
1363 mCHt0[1]=Cv[ 1] ; mCHt1[1]=Cv[ 2] ; mCHt2[1]=Cv[ 4] ;
1364 mCHt0[2]=Cv[ 3] ; mCHt1[2]=Cv[ 4] ; mCHt2[2]=Cv[ 5] ;
1365
1366 //* Kalman gain K = mCH'*S
1367
1368 Double_t k0[3], k1[3], k2[3];
1369
1370 for(Int_t i=0;i<3;++i){
1371 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
1372 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
1373 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
1374 }
1375
1376 //* New estimation of the vertex position r += K*zeta
1377
1378 for(Int_t i=0;i<3;++i)
1379 v[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
1380
1381 //* New covariance matrix C -= K*(mCH')'
1382
1383 for(Int_t i=0, k=0;i<3;++i){
1384 for(Int_t j=0;j<=i;++j,++k)
1385 Cv[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
1386 }
1387
1388 //* Calculate Chi^2
1389
1390 vNDF -= 2;
1391 vChi2 -= (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
1392 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
1393 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
1394}
1395
1396
1397
1398void AliKFParticleBase::TransportLine( Double_t dS,
1399 Double_t P[], Double_t C[] ) const
1400{
1401 //* Transport the particle as a straight line
1402
1403 P[0] = fP[0] + dS*fP[3];
1404 P[1] = fP[1] + dS*fP[4];
1405 P[2] = fP[2] + dS*fP[5];
1406 P[3] = fP[3];
1407 P[4] = fP[4];
1408 P[5] = fP[5];
1409 P[6] = fP[6];
1410 P[7] = fP[7];
1411
1412 Double_t c6 = fC[ 6] + dS*fC[ 9];
1413 Double_t c11 = fC[11] + dS*fC[14];
1414 Double_t c17 = fC[17] + dS*fC[20];
1415 Double_t sc13 = dS*fC[13];
1416 Double_t sc18 = dS*fC[18];
1417 Double_t sc19 = dS*fC[19];
1418
1419 C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 );
1420 C[ 2] = fC[ 2] + dS*( fC[11] + c11 );
1421 C[ 5] = fC[ 5] + dS*( fC[17] + c17 );
1422
1423 C[ 7] = fC[ 7] + sc13;
1424 C[ 8] = fC[ 8] + sc18;
1425 C[ 9] = fC[ 9];
1426
1427 C[12] = fC[12] + sc19;
1428
1429 C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] );
1430 C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] );
1431 C[ 4] = fC[ 4] + dS*( fC[16] + C[12] );
1432 C[ 6] = c6;
1433
1434 C[10] = fC[10] + sc13;
1435 C[11] = c11;
1436
1437 C[13] = fC[13];
1438 C[14] = fC[14];
1439 C[15] = fC[15] + sc18;
1440 C[16] = fC[16] + sc19;
1441 C[17] = c17;
1442
1443 C[18] = fC[18];
1444 C[19] = fC[19];
1445 C[20] = fC[20];
1446 C[21] = fC[21] + dS*fC[24];
1447 C[22] = fC[22] + dS*fC[25];
1448 C[23] = fC[23] + dS*fC[26];
1449
1450 C[24] = fC[24];
1451 C[25] = fC[25];
1452 C[26] = fC[26];
1453 C[27] = fC[27];
1454 C[28] = fC[28] + dS*fC[31];
1455 C[29] = fC[29] + dS*fC[32];
1456 C[30] = fC[30] + dS*fC[33];
1457
1458 C[31] = fC[31];
1459 C[32] = fC[32];
1460 C[33] = fC[33];
1461 C[34] = fC[34];
1462 C[35] = fC[35];
1463}
1464
1465
1466void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] )
1467{
1468 //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric
1469
1470 const Int_t kN= 8;
1471 Double_t mA[kN*kN];
1472
1473 for( Int_t i=0, ij=0; i<kN; i++ ){
1474 for( Int_t j=0; j<kN; j++, ++ij ){
1475 mA[ij] = 0 ;
1476 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];
1477 }
1478 }
1479
1480 for( Int_t i=0; i<kN; i++ ){
1481 for( Int_t j=0; j<=i; j++ ){
1482 Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i;
1483 SOut[ij] = 0 ;
1484 for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ];
1485 }
1486 }
1487}
1488
1489
1490// 72-charachters line to define the printer border
1491//3456789012345678901234567890123456789012345678901234567890123456789012