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Introducing a new set of classes for secondary vertex fitting based on Kalman filter...
[u/mrichter/AliRoot.git] / STEER / AliKFParticleBase.cxx
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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
22
23ClassImp(AliKFParticleBase)
24
25
26AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0)
27{
28 //* Constructor
29
30 Initialize();
31}
32
33
34void AliKFParticleBase::Initialize()
35{
36 //* Initialise covariance matrix and set current parameters to 0.0
37
38 for( Int_t i=0; i<8; i++) fP[i] = 0;
39 for(Int_t i=0;i<36;++i) fC[i]=0.;
40 fC[0] = fC[2] = fC[5] = 100.;
41 fC[35] = 1.;
42 fNDF = -3;
43 fChi2 = 0.;
44 fQ = 0;
45 fSFromDecay = 0;
46 fAtProductionVertex = 0;
47 fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.;
48 fIsLinearized = 0;
49}
50
51void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z )
52{
53 //* Set decay vertex parameters for linearisation
54
55 fVtxGuess[0] = x;
56 fVtxGuess[1] = y;
57 fVtxGuess[2] = z;
58 fIsLinearized = 1;
59}
60
61
62Int_t AliKFParticleBase::GetMomentum( Double_t &P, Double_t &Error ) const
63{
64 //* Calculate particle momentum
65
66 Double_t x = fP[3];
67 Double_t y = fP[4];
68 Double_t z = fP[5];
69 Double_t x2 = x*x;
70 Double_t y2 = y*y;
71 Double_t z2 = z*z;
72 Double_t p2 = x2+y2+z2;
73 P = TMath::Sqrt(p2);
74 Error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) );
75 if( Error>0 && P>1.e-4 ){
76 Error = TMath::Sqrt(Error)/P;
77 return 0;
78 }
79 return 1;
80}
81
82Int_t AliKFParticleBase::GetMass( Double_t &M, Double_t &Error ) const
83{
84 //* Calculate particle mass
85
86 // s = sigma^2 of m2/2
87
88 Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20]
89 + fP[6]*fP[6]*fC[27]
90 +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19])
91 - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) )
92 );
93 Double_t m2 = fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5];
94 if( s>=0 && m2>1.e-20 ){
95 M = TMath::Sqrt(m2);
96 Error = TMath::Sqrt(s/m2);
97 return 0;
98 }
99 M = 0;
100 Error = 0;
101 return 1;
102}
103
104
105Int_t AliKFParticleBase::GetDecayLength( Double_t &L, Double_t &Error ) const
106{
107 //* Calculate particle decay length [cm]
108
109 Double_t x = fP[3];
110 Double_t y = fP[4];
111 Double_t z = fP[5];
112 Double_t t = fP[7];
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;
117 L = t*TMath::Sqrt(p2);
118 if( p2>1.e-4){
119 Error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20]
120 + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) )
121 + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]);
122 Error = TMath::Sqrt(TMath::Abs(Error));
123 return 0;
124 }
125 Error = 0;
126 return 1;
127}
128
129Int_t AliKFParticleBase::GetLifeTime( Double_t &TauC, Double_t &Error ) const
130{
131 //* Calculate particle decay time [s]
132
133 Double_t m, dm;
134 GetMass( m, dm );
135 Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]);
136 TauC = fP[7]*m;
137 Error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm;
138 if( Error > 0 ){
139 Error = TMath::Sqrt( Error );
140 return 0;
141 }
142 Error = 0;
143 return 1;
144}
145
146
147void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter )
148{
149 //* Add daughter via operator+=
150
151 AddDaughter( Daughter );
152}
153
154
155void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter )
156{
157 //* Add daughter
158
159 TransportToDecayVertex();
160
161 Double_t b[3];
162 Int_t maxIter = 1;
163
164 if( !fIsLinearized ){
165 if( fNDF==-1 ){
166 Double_t ds, ds1;
167 GetDStoParticle(Daughter, ds, ds1);
168 TransportToDS( ds );
169 }
170 fVtxGuess[0] = fP[0];
171 fVtxGuess[1] = fP[1];
172 fVtxGuess[2] = fP[2];
173 maxIter = 3;
174 }
175
176 for( Int_t iter=0; iter<maxIter; iter++ ){
177
178 {
179 GetFieldValue( fVtxGuess, b );
180 const Double_t kCLight = 0.000299792458;
181 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
182 }
183 if( fNDF==-1 ){
184 TransportToDS( GetDStoPoint(fVtxGuess) );
185 }
186 fSFromDecay = 0;
187
188 Double_t m[8];
189 Double_t mCd[36];
190
191 Daughter.Transport( Daughter.GetDStoPoint(fVtxGuess), m, mCd );
192
193 Double_t d[3] = { fVtxGuess[0]-m[0], fVtxGuess[1]-m[1], fVtxGuess[2]-m[2] };
194 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
195 (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) );
196
197 Double_t h[6];
198
199 h[0] = m[3]*sigmaS;
200 h[1] = m[4]*sigmaS;
201 h[2] = m[5]*sigmaS;
202 h[3] = ( h[1]*b[2]-h[2]*b[1] )*Daughter.GetQ();
203 h[4] = ( h[2]*b[0]-h[0]*b[2] )*Daughter.GetQ();
204 h[5] = ( h[0]*b[1]-h[1]*b[0] )*Daughter.GetQ();
205
206 //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex
207 {
208 Double_t zeta[3] = { fVtxGuess[0]-m[0], fVtxGuess[1]-m[1], fVtxGuess[2]-m[2] };
209
210 Double_t mVv[6] =
211 { mCd[ 0] + h[0]*h[0],
212 mCd[ 1] + h[1]*h[0], mCd[ 2] + h[1]*h[1],
213 mCd[ 3] + h[2]*h[0], mCd[ 4] + h[2]*h[1], mCd[ 5] + h[2]*h[2] };
214
215 Double_t mVvp[9]=
216 { mCd[ 6] + h[0]*h[3], mCd[ 7] + h[1]*h[3], mCd[ 8] + h[2]*h[3],
217 mCd[10] + h[0]*h[4], mCd[11] + h[1]*h[4], mCd[12] + h[2]*h[4],
218 mCd[15] + h[0]*h[5], mCd[16] + h[1]*h[5], mCd[17] + h[2]*h[5] };
219
220 Double_t mS[6] =
221 { mVv[2]*mVv[5] - mVv[4]*mVv[4],
222 mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3],
223 mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4],
224 mVv[0]*mVv[2] - mVv[1]*mVv[1] };
225
226 Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] );
227 s = ( s > 1.E-20 ) ?1./s :0;
228
229 mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s;
230
231 Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]),
232 (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]),
233 (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) };
234
235 Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2];
236 Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2];
237 Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2];
238
239 h[0] = px*sigmaS;
240 h[1] = py*sigmaS;
241 h[2] = pz*sigmaS;
242 h[3] = ( h[1]*b[2]-h[2]*b[1] )*Daughter.GetQ();
243 h[4] = ( h[2]*b[0]-h[0]*b[2] )*Daughter.GetQ();
244 h[5] = ( h[0]*b[1]-h[1]*b[0] )*Daughter.GetQ();
245 }
246
247 Double_t mV[28];
248
249 mV[ 0] = mCd[ 0] + h[0]*h[0];
250 mV[ 1] = mCd[ 1] + h[1]*h[0];
251 mV[ 2] = mCd[ 2] + h[1]*h[1];
252 mV[ 3] = mCd[ 3] + h[2]*h[0];
253 mV[ 4] = mCd[ 4] + h[2]*h[1];
254 mV[ 5] = mCd[ 5] + h[2]*h[2];
255
256 mV[ 6] = mCd[ 6] + h[3]*h[0];
257 mV[ 7] = mCd[ 7] + h[3]*h[1];
258 mV[ 8] = mCd[ 8] + h[3]*h[2];
259 mV[ 9] = mCd[ 9] + h[3]*h[3];
260
261 mV[10] = mCd[10] + h[4]*h[0];
262 mV[11] = mCd[11] + h[4]*h[1];
263 mV[12] = mCd[12] + h[4]*h[2];
264 mV[13] = mCd[13] + h[4]*h[3];
265 mV[14] = mCd[14] + h[4]*h[4];
266
267 mV[15] = mCd[15] + h[5]*h[0];
268 mV[16] = mCd[16] + h[5]*h[1];
269 mV[17] = mCd[17] + h[5]*h[2];
270 mV[18] = mCd[18] + h[5]*h[3];
271 mV[19] = mCd[19] + h[5]*h[4];
272 mV[20] = mCd[20] + h[5]*h[5];
273
274 mV[21] = mCd[21];
275 mV[22] = mCd[22];
276 mV[23] = mCd[23];
277 mV[24] = mCd[24];
278 mV[25] = mCd[25];
279 mV[26] = mCd[26];
280 mV[27] = mCd[27];
281
282 //*
283
284 if( fNDF<-1 ){ // first daughter -> just copy
285 fNDF = -1;
286 fQ = Daughter.GetQ();
287 for( Int_t i=0; i<7; i++) fP[i] = m[i];
288 for( Int_t i=0; i<28; i++) fC[i] = mV[i];
289 fSFromDecay = 0;
290 return;
291 }
292
293 //*
294
295 Double_t mS[6];
296 {
297 Double_t mSi[6] = { fC[0]+mV[0],
298 fC[1]+mV[1], fC[2]+mV[2],
299 fC[3]+mV[3], fC[4]+mV[4], fC[5]+mV[5] };
300
301 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
302 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
303 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
304 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
305 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
306 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
307
308 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
309 s = ( s > 1.E-20 ) ?1./s :0;
310 mS[0]*=s;
311 mS[1]*=s;
312 mS[2]*=s;
313 mS[3]*=s;
314 mS[4]*=s;
315 mS[5]*=s;
316 }
317
318 //* Residual (measured - estimated)
319
320 Double_t zeta[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
321
322
323 //* CHt = CH' - D'
324
325 Double_t mCHt0[7], mCHt1[7], mCHt2[7];
326
327 mCHt0[0]=fC[ 0] ; mCHt1[0]=fC[ 1] ; mCHt2[0]=fC[ 3] ;
328 mCHt0[1]=fC[ 1] ; mCHt1[1]=fC[ 2] ; mCHt2[1]=fC[ 4] ;
329 mCHt0[2]=fC[ 3] ; mCHt1[2]=fC[ 4] ; mCHt2[2]=fC[ 5] ;
330 mCHt0[3]=fC[ 6]-mV[ 6]; mCHt1[3]=fC[ 7]-mV[ 7]; mCHt2[3]=fC[ 8]-mV[ 8];
331 mCHt0[4]=fC[10]-mV[10]; mCHt1[4]=fC[11]-mV[11]; mCHt2[4]=fC[12]-mV[12];
332 mCHt0[5]=fC[15]-mV[15]; mCHt1[5]=fC[16]-mV[16]; mCHt2[5]=fC[17]-mV[17];
333 mCHt0[6]=fC[21]-mV[21]; mCHt1[6]=fC[22]-mV[22]; mCHt2[6]=fC[23]-mV[23];
334
335 //* Kalman gain K = mCH'*S
336
337 Double_t k0[7], k1[7], k2[7];
338
339 for(Int_t i=0;i<7;++i){
340 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
341 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
342 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
343 }
344
345 //* New estimation of the vertex position
346
347 if( iter<maxIter-1 ){
348 for(Int_t i=0; i<3; ++i)
349 fVtxGuess[i]= fP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2];
350 continue;
351 }
352
353 // last itearation -> update the particle
354
355 //* Add the daughter momentum to the particle momentum
356
357 fP[ 3] += m[ 3];
358 fP[ 4] += m[ 4];
359 fP[ 5] += m[ 5];
360 fP[ 6] += m[ 6];
361
362 fC[ 9] += mV[ 9];
363 fC[13] += mV[13];
364 fC[14] += mV[14];
365 fC[18] += mV[18];
366 fC[19] += mV[19];
367 fC[20] += mV[20];
368 fC[24] += mV[24];
369 fC[25] += mV[25];
370 fC[26] += mV[26];
371 fC[27] += mV[27];
372
373 //* New estimation of the vertex position r += K*zeta
374
375 for(Int_t i=0;i<7;++i)
376 fP[i] += k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
377
378 //* New covariance matrix C -= K*(mCH')'
379
380 for(Int_t i=0, k=0;i<7;++i){
381 for(Int_t j=0;j<=i;++j,++k)
382 fC[k] -= k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
383 }
384
385 //* Calculate Chi^2
386
387 fNDF += 2;
388 fQ += Daughter.GetQ();
389 fSFromDecay = 0;
390 fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
391 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
392 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
393 }
394}
395
396
397void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx )
398{
399 //* Set production vertex for the particle
400
401 const Double_t *m = Vtx.fP, *mV = Vtx.fC;
402
403 TransportToDS( GetDStoPoint( m ) );
404 fP[7] = -fSFromDecay;
405 Convert(1);
406
407 Double_t mAi[6];
408 mAi[0] = fC[4]*fC[4] - fC[2]*fC[5];
409 mAi[1] = fC[1]*fC[5] - fC[3]*fC[4];
410 mAi[3] = fC[2]*fC[3] - fC[1]*fC[4];
411 Double_t det = 1./(fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]);
412 mAi[0] *= det;
413 mAi[1] *= det;
414 mAi[3] *= det;
415 mAi[2] = ( fC[3]*fC[3] - fC[0]*fC[5] )*det;
416 mAi[4] = ( fC[0]*fC[4] - fC[1]*fC[3] )*det;
417 mAi[5] = ( fC[1]*fC[1] - fC[0]*fC[2] )*det;
418
419 Double_t mB[5][3];
420
421 mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3];
422 mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4];
423 mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5];
424
425 mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3];
426 mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4];
427 mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5];
428
429 mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3];
430 mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4];
431 mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5];
432
433 mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3];
434 mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4];
435 mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5];
436
437 mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3];
438 mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4];
439 mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5];
440
441 Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
442
443 {
444 Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2],
445 fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] };
446 Double_t mAVi[6];
447 mAVi[0] = mAV[4]*mAV[4] - mAV[2]*mAV[5];
448 mAVi[1] = mAV[1]*mAV[5] - mAV[3]*mAV[4];
449 mAVi[2] = mAV[3]*mAV[3] - mAV[0]*mAV[5] ;
450 mAVi[3] = mAV[2]*mAV[3] - mAV[1]*mAV[4];
451 mAVi[4] = mAV[0]*mAV[4] - mAV[1]*mAV[3] ;
452 mAVi[5] = mAV[1]*mAV[1] - mAV[0]*mAV[2] ;
453
454 det = 1./( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] );
455
456 fNDF += 2;
457 fChi2 +=
458 ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0]
459 +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1]
460 +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )*det;
461 }
462
463 fP[0] = m[0];
464 fP[1] = m[1];
465 fP[2] = m[2];
466 fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
467 fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
468 fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
469 fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2];
470 fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2];
471
472 Double_t d0, d1, d2;
473
474 fC[0] = mV[0];
475 fC[1] = mV[1];
476 fC[2] = mV[2];
477 fC[3] = mV[3];
478 fC[4] = mV[4];
479 fC[5] = mV[5];
480
481 d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6];
482 d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7];
483 d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8];
484
485 fC[ 6]+= d0;
486 fC[ 7]+= d1;
487 fC[ 8]+= d2;
488 fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
489
490 d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10];
491 d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11];
492 d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12];
493
494 fC[10]+= d0;
495 fC[11]+= d1;
496 fC[12]+= d2;
497 fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
498 fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
499
500 d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15];
501 d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16];
502 d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17];
503
504 fC[15]+= d0;
505 fC[16]+= d1;
506 fC[17]+= d2;
507 fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
508 fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
509 fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
510
511 d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21];
512 d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22];
513 d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23];
514
515 fC[21]+= d0;
516 fC[22]+= d1;
517 fC[23]+= d2;
518 fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
519 fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
520 fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
521 fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
522
523 d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28];
524 d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29];
525 d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30];
526
527 fC[28]+= d0;
528 fC[29]+= d1;
529 fC[30]+= d2;
530 fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
531 fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
532 fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
533 fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
534 fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2];
535
536 TransportToDS( fP[7] );
537 fSFromDecay = 0;
538 Convert(0);
539}
540
541
542
543
544void AliKFParticleBase::SetMassConstraint( Double_t Mass )
545{
546 //* Set hard mass constraint
547
548 Double_t mH[8];
549 mH[0] = mH[1] = mH[2] = 0.;
550 mH[3] = -2*fP[3];
551 mH[4] = -2*fP[4];
552 mH[5] = -2*fP[5];
553 mH[6] = 2*fP[6];
554 mH[7] = 0;
555 Double_t m2 = ( fP[6]*fP[6]
556 - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5] );
557
558 Double_t zeta = Mass*Mass - m2;
559 for(Int_t i=0;i<8;++i) zeta -= mH[i]*(fP[i]-fP[i]);
560
561 Double_t s = 0.;
562 Double_t mCHt[8];
563 for (Int_t i=0;i<8;++i ){
564 mCHt[i] = 0.0;
565 for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j];
566 s += mH[i]*mCHt[i];
567 }
568
569 if( s<1.e-20 ) return;
570 s = 1./s;
571 fChi2 += zeta*zeta*s;
572 fNDF += 1;
573 for( Int_t i=0, ii=0; i<8; ++i ){
574 Double_t ki = mCHt[i]*s;
575 fP[i]+= ki*zeta;
576 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j];
577 }
578}
579
580
581void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters,
582 const AliKFParticleBase *Parent, Double_t Mass )
583{
584 //* Full reconstruction in one go
585
586 Int_t maxIter = 1;
587 bool wasLinearized = fIsLinearized;
588 if( !fIsLinearized ){
589 fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0;
590 fIsLinearized = 1;
591 maxIter = 3;
592 }
593
594 for( Int_t iter=0; iter<maxIter; iter++ ){
595
596 fAtProductionVertex = 0;
597 fSFromDecay = 0;
598 fP[0] = fVtxGuess[0];
599 fP[1] = fVtxGuess[1];
600 fP[2] = fVtxGuess[2];
601 fP[3] = 0;
602 fP[4] = 0;
603 fP[5] = 0;
604 fP[6] = 0;
605 fP[7] = 0;
606
607 for(Int_t i=0;i<36;++i) fC[i]=0.;
608
609 fC[0] = fC[2] = fC[5] = 100.;
610 fC[35] = 1.;
611
612 fNDF = -3;
613 fChi2 = 0.;
614 fQ = 0;
615
616 for( Int_t itr =0; itr<NDaughters; itr++ ) AddDaughter( *vDaughters[itr] );
617 if( iter<maxIter-1){
618 for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i];
619 }
620 }
621 fIsLinearized = wasLinearized;
622
623 if( Mass>=0 ) SetMassConstraint( Mass );
624 if( Parent ) SetProductionVertex( *Parent );
625}
626
627
628void AliKFParticleBase::Convert( bool ToProduction )
629{
630 //* Tricky function - convert the particle error along its trajectory to
631 //* the value which corresponds to its production/decay vertex
632 //* It is done by combination of the error of decay length with the position errors
633
634 Double_t fld[3];
635 {
636 GetFieldValue( fP, fld );
637 const Double_t kCLight = fQ*0.000299792458;
638 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
639 }
640
641 Double_t h[6];
642
643 h[0] = fP[3];
644 h[1] = fP[4];
645 h[2] = fP[5];
646 if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; }
647 h[3] = h[1]*fld[2]-h[2]*fld[1];
648 h[4] = h[2]*fld[0]-h[0]*fld[2];
649 h[5] = h[0]*fld[1]-h[1]*fld[0];
650
651 Double_t c;
652
653 c = fC[28]+h[0]*fC[35];
654 fC[ 0]+= h[0]*(c+fC[28]);
655 fC[28] = c;
656
657 fC[ 1]+= h[1]*fC[28] + h[0]*fC[29];
658 c = fC[29]+h[1]*fC[35];
659 fC[ 2]+= h[1]*(c+fC[29]);
660 fC[29] = c;
661
662 fC[ 3]+= h[2]*fC[28] + h[0]*fC[30];
663 fC[ 4]+= h[2]*fC[29] + h[1]*fC[30];
664 c = fC[30]+h[2]*fC[35];
665 fC[ 5]+= h[2]*(c+fC[30]);
666 fC[30] = c;
667
668 fC[ 6]+= h[3]*fC[28] + h[0]*fC[31];
669 fC[ 7]+= h[3]*fC[29] + h[1]*fC[31];
670 fC[ 8]+= h[3]*fC[30] + h[2]*fC[31];
671 c = fC[31]+h[3]*fC[35];
672 fC[ 9]+= h[3]*(c+fC[31]);
673 fC[31] = c;
674
675 fC[10]+= h[4]*fC[28] + h[0]*fC[32];
676 fC[11]+= h[4]*fC[29] + h[1]*fC[32];
677 fC[12]+= h[4]*fC[30] + h[2]*fC[32];
678 fC[13]+= h[4]*fC[31] + h[3]*fC[32];
679 c = fC[32]+h[4]*fC[35];
680 fC[14]+= h[4]*(c+fC[32]);
681 fC[32] = c;
682
683 fC[15]+= h[5]*fC[28] + h[0]*fC[33];
684 fC[16]+= h[5]*fC[29] + h[1]*fC[33];
685 fC[17]+= h[5]*fC[30] + h[2]*fC[33];
686 fC[18]+= h[5]*fC[31] + h[3]*fC[33];
687 fC[19]+= h[5]*fC[32] + h[4]*fC[33];
688 c = fC[33]+h[5]*fC[35];
689 fC[20]+= h[5]*(c+fC[33]);
690 fC[33] = c;
691
692 fC[21]+= h[0]*fC[34];
693 fC[22]+= h[1]*fC[34];
694 fC[23]+= h[2]*fC[34];
695 fC[24]+= h[3]*fC[34];
696 fC[25]+= h[4]*fC[34];
697 fC[26]+= h[5]*fC[34];
698}
699
700
701void AliKFParticleBase::TransportToDecayVertex()
702{
703 //* Transport the particle to its decay vertex
704
705 if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay );
706 if( fAtProductionVertex ) Convert(0);
707 fAtProductionVertex = 0;
708}
709
710void AliKFParticleBase::TransportToProductionVertex()
711{
712 //* Transport the particle to its production vertex
713
714 if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] );
715 if( !fAtProductionVertex ) Convert( 1 );
716 fAtProductionVertex = 1;
717}
718
719
720void AliKFParticleBase::TransportToDS( Double_t dS )
721{
722 //* Transport the particle on dS parameter (SignedPath/Momentum)
723
724 Transport( dS, fP, fC );
725 fSFromDecay+= dS;
726}
727
728
729Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const
730{
731 //* Get dS to a certain space point without field
732
733 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
734 if( p2<1.e-4 ) p2 = 1;
735 return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2;
736}
737
738
739Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] )
740 const
741{
742 //* Get dS to a certain space point for Bz field
743
744 const Double_t kCLight = 0.000299792458;
745 Double_t bq = B*fQ*kCLight;
746 Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4];
747 if( pt2<1.e-4 ) return 0;
748 Double_t dx = xyz[0] - fP[0];
749 Double_t dy = xyz[1] - fP[1];
750 Double_t a = dx*fP[3]+dy*fP[4];
751 if( TMath::Abs(bq)<1.e-8 ) return a/pt2;
752 return TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq;
753}
754
755
756void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p,
757 Double_t &DS, Double_t &DS1 )
758 const
759{
760 //* Get dS to another particle for Bz field
761
762 Double_t px = fP[3];
763 Double_t py = fP[4];
764 Double_t pz = fP[5];
765
766 Double_t px1 = p.fP[3];
767 Double_t py1 = p.fP[4];
768 Double_t pz1 = p.fP[5];
769
770 const Double_t kCLight = 0.000299792458;
771
772 Double_t bq = B*fQ*kCLight;
773 Double_t bq1 = B*p.fQ*kCLight;
774
775 Double_t s=0, ds=0, s1=0, ds1=0;
776
777 if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){
778 Double_t dx = (p.fP[0] - fP[0]);
779 Double_t dy = (p.fP[1] - fP[1]);
780 Double_t d2 = (dx*dx+dy*dy);
781
782 Double_t p2 = (px *px + py *py);
783 Double_t p21 = (px1*px1 + py1*py1);
784
785 Double_t a = (px*py1 - py*px1);
786 Double_t b = (px*px1 + py*py1);
787
788 Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ;
789 Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ;
790 Double_t l2 = ldx*ldx + ldy*ldy;
791
792 Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b;
793 Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b;
794
795 Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ;
796 Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ;
797
798 Double_t sa = 4*l2*p2 - ca*ca;
799 Double_t sa1 = 4*l2*p21 - ca1*ca1;
800 if(sa<0) sa=0;
801 if(sa1<0)sa1=0;
802
803 if( TMath::Abs(bq)>1.e-8){
804 s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq;
805 ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq;
806 } else {
807 s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2;
808 ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2;
809 if( ds<0 ) ds = 0;
810 ds = TMath::Sqrt(ds);
811 }
812
813 if( TMath::Abs(bq1)>1.e-8){
814 s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1;
815 ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1;
816 } else {
817 s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21;
818 ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21;
819 if( ds1<0 ) ds1 = 0;
820 ds1 = TMath::Sqrt(ds1);
821 }
822 }
823
824
825 Double_t ss[2], ss1[2], g[2][5],g1[2][5];
826
827 ss[0] = s + ds;
828 ss[1] = s - ds;
829 ss1[0] = s1 + ds1;
830 ss1[1] = s1 - ds1;
831 for( Int_t i=0; i<2; i++){
832 Double_t bs = bq*ss[i];
833 Double_t c = TMath::Cos(bs), s = TMath::Sin(bs);
834 Double_t cB,sB;
835 if( TMath::Abs(bq)>1.e-8){
836 cB= (1-c)/bq;
837 sB= s/bq;
838 }else{
839 sB = (1. - bs*bs/6.)*ss[i];
840 cB = .5*sB*bs;
841 }
842 g[i][0] = fP[0] + sB*px + cB*py;
843 g[i][1] = fP[1] - cB*px + sB*py;
844 g[i][2] = fP[2] + ss[i]*pz;
845 g[i][3] = + c*px + s*py;
846 g[i][4] = - s*px + c*py;
847
848 bs = bq1*ss1[i];
849 c = TMath::Cos(bs); s = TMath::Sin(bs);
850 if( TMath::Abs(bq1)>1.e-8){
851 cB= (1-c)/bq1;
852 sB= s/bq1;
853 }else{
854 sB = (1. - bs*bs/6.)*ss1[i];
855 cB = .5*sB*bs;
856 }
857
858 g[i][0] = p.fP[0] + sB*px1 + cB*py1;
859 g[i][1] = p.fP[1] - cB*px1 + sB*py1;
860 g[i][2] = p.fP[2] + ss[i]*pz1;
861 g[i][3] = + c*px1 + s*py1;
862 g[i][4] = - s*px1 + c*py1;
863 }
864
865 Int_t i=0, i1=0;
866
867 Double_t dMin = 1.e10;
868 for( Int_t j=0; j<2; j++){
869 for( Int_t j1=0; j1<2; j1++){
870 Double_t xx = g[j][0]-g1[j1][0];
871 Double_t yy = g[j][1]-g1[j1][1];
872 Double_t zz = g[j][2]-g1[j1][2];
873 Double_t d = xx*xx + yy*yy + zz*zz;
874 if( d<dMin ){
875 dMin = d;
876 i = j;
877 i1 = j1;
878 }
879 }
880 }
881
882 DS = ss[i];
883 DS1 = ss1[i1];
884
885 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
886 Double_t x1=g[i1][0], y1= g[i1][1], z1= g[i1][2], ppx1= g[i1][3], ppy1= g[i1][4];
887 Double_t dx = x1-x;
888 Double_t dy = y1-y;
889 Double_t dz = z1-z;
890 Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1;
891 Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1;
892 Double_t c = dx*ppx + dy*ppy + dz*pz ;
893 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
894 Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1;
895 Double_t det = pp2*pp21 - a*a;
896 if( TMath::Abs(det)>1.e-8 ){
897 DS+=(a*b-pp21*c)/det;
898 DS1+=(a*c-pp2*b)/det;
899 }
900}
901
902
903
904void AliKFParticleBase::TransportCBM( Double_t dS,
905 Double_t P[], Double_t C[] ) const
906{
907 //* Transport the particle on dS, output to P[],C[], for CBM field
908
909 if( fQ==0 ){
910 TransportLine( dS, P, C );
911 return;
912 }
913
914 const Double_t kCLight = 0.000299792458;
915
916 Double_t c = fQ*kCLight;
917
918 // construct coefficients
919
920 Double_t
921 px = fP[3],
922 py = fP[4],
923 pz = fP[5];
924
925 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;
926
927 { // get field integrals
928
929 Double_t fld[3][3];
930 Double_t p0[3], p1[3], p2[3];
931
932 // line track approximation
933
934 p0[0] = fP[0];
935 p0[1] = fP[1];
936 p0[2] = fP[2];
937
938 p2[0] = fP[0] + px*dS;
939 p2[1] = fP[1] + py*dS;
940 p2[2] = fP[2] + pz*dS;
941
942 p1[0] = 0.5*(p0[0]+p2[0]);
943 p1[1] = 0.5*(p0[1]+p2[1]);
944 p1[2] = 0.5*(p0[2]+p2[2]);
945
946 // first order track approximation
947 {
948 GetFieldValue( p0, fld[0] );
949 GetFieldValue( p1, fld[1] );
950 GetFieldValue( p2, fld[2] );
951
952 Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.;
953 Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.;
954
955 p1[0] -= ssy1*pz;
956 p1[2] += ssy1*px;
957 p2[0] -= ssy2*pz;
958 p2[2] += ssy2*px;
959 }
960
961 GetFieldValue( p0, fld[0] );
962 GetFieldValue( p1, fld[1] );
963 GetFieldValue( p2, fld[2] );
964
965 sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.;
966 sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.;
967 sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.;
968
969 ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.;
970 ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.;
971 ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.;
972
973 Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360.
974 Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520.
975 for(Int_t n=0; n<3; n++)
976 for(Int_t m=0; m<3; m++)
977 {
978 syz += c2[n][m]*fld[n][1]*fld[m][2];
979 ssyz += cc2[n][m]*fld[n][1]*fld[m][2];
980 }
981
982 syz *= c*c*dS*dS/360.;
983 ssyz *= c*c*dS*dS*dS/2520.;
984
985 syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS;
986 syyy = syy*syy*syy / 1296;
987 syy = syy*syy/72;
988
989 ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+
990 fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+
991 fld[2][1]*( 3*fld[2][1] )
992 )*dS*dS*dS*c*c/2520.;
993 ssyyy =
994 (
995 fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+
996 fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+
997 fld[2][1]*( 19*fld[2][1] ) )+
998 fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+
999 fld[2][1]*( 62*fld[2][1] ) )+
1000 fld[2][1]*fld[2][1] *( 3*fld[2][1] )
1001 )*dS*dS*dS*dS*c*c*c/90720.;
1002
1003 }
1004
1005 Double_t mJ[8][8];
1006 for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0;
1007
1008 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;
1009 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;
1010 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;
1011
1012 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;
1013 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;
1014 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;
1015 mJ[6][6] = mJ[7][7] = 1;
1016
1017 P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz;
1018 P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz;
1019 P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz;
1020 P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz;
1021 P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz;
1022 P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz;
1023 P[6] = fP[6];
1024 P[7] = fP[7];
1025
1026 MultQSQt( mJ[0], fC, C);
1027
1028}
1029
1030
1031void AliKFParticleBase::TransportBz( Double_t B, Double_t S,
1032 Double_t P[], Double_t C[] ) const
1033{
1034 //* Transport the particle on dS, output to P[],C[], for Bz field
1035
1036 const Double_t kCLight = 0.000299792458;
1037 B = B*fQ*kCLight;
1038 Double_t bs= B*S;
1039 Double_t s = TMath::Sin(bs), c = TMath::Cos(bs);
1040 Double_t sB, cB;
1041 if( TMath::Abs(bs)>1.e-8){
1042 sB= s/B;
1043 cB= (1-c)/B;
1044 }else{
1045 sB = (1. - bs*bs/6.)*S;
1046 cB = .5*sB*bs;
1047 }
1048
1049 Double_t px = fP[3];
1050 Double_t py = fP[4];
1051 Double_t pz = fP[5];
1052
1053 P[0] = fP[0] + sB*px + cB*py;
1054 P[1] = fP[1] - cB*px + sB*py;
1055 P[2] = fP[2] + S*pz;
1056 P[3] = c*px + s*py;
1057 P[4] = -s*px + c*py;
1058 P[5] = fP[5];
1059 P[6] = fP[6];
1060 P[7] = fP[7];
1061
1062 Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 },
1063 {0,1,0, -cB, sB, 0, 0, 0 },
1064 {0,0,1, 0, 0, S, 0, 0 },
1065 {0,0,0, c, s, 0, 0, 0 },
1066 {0,0,0, -s, c, 0, 0, 0 },
1067 {0,0,0, 0, 0, 1, 0, 0 },
1068 {0,0,0, 0, 0, 0, 1, 0 },
1069 {0,0,0, 0, 0, 0, 0, 1 } };
1070 Double_t mA[8][8];
1071 for( Int_t k=0,i=0; i<8; i++)
1072 for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k];
1073
1074 Double_t mJC[8][8];
1075 for( Int_t i=0; i<8; i++ )
1076 for( Int_t j=0; j<8; j++ ){
1077 mJC[i][j]=0;
1078 for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j];
1079 }
1080
1081 for( Int_t k=0,i=0; i<8; i++)
1082 for( Int_t j=0; j<=i; j++, k++ ){
1083 C[k] = 0;
1084 for( Int_t l=0; l<8; l++ ) C[k]+=mJC[i][l]*mJ[j][l];
1085 }
1086
1087 return;
1088 /*
1089 Double_t cBC13 = cB*fC[13];
1090 Double_t C17 = fC[17];
1091 Double_t C18 = fC[18];
1092 fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14];
1093
1094 Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13];
1095 Double_t mJC14= fC[11] - cBC13 + sB*fC[14];
1096
1097 fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB;
1098 fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB;
1099
1100 Double_t mJC23= fC[ 8] + S*fC[18];
1101 Double_t mJC24= fC[12] + S*fC[19];
1102 fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB;
1103 fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB;
1104
1105 fC[15]+= C18*sB + fC[19]*cB;
1106 fC[16]+= -C18*cB + fC[19]*sB;
1107 fC[17]+= fC[20]*S;
1108 fC[18] = C18*c + fC[19]*s;
1109 fC[19] = -C18*s + fC[19]*c;
1110
1111 fC[ 5]+= (C17 + C17 + fC[17])*S;
1112
1113 Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14];
1114 Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14];
1115 Double_t C6= fC[6], C7= fC[7], C8= fC[8];
1116
1117 fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB;
1118 fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB;
1119 fC[ 8]= c*C8 + s*fC[12] +fC[18]*S;
1120 fC[ 9]= mJC33*c +mJC34*s;
1121
1122 fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB;
1123 fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB;
1124 fC[12]= -s*C8 + c*fC[12] +fC[19]*S;
1125 fC[13]= mJC43*c +mJC44*s;
1126 fC[14]=-mJC43*s +mJC44*c;
1127 */
1128}
1129
1130
1131Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const
1132{
1133 //* Calculate distance from vertex [cm]
1134
1135 return GetDistanceFromVertex( Vtx.fP );
1136}
1137
1138Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const
1139{
1140 //* Calculate distance from vertex [cm]
1141
1142 Double_t mP[8], mC[36];
1143 Transport( GetDStoPoint(vtx), mP, mC );
1144 Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]};
1145 return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] );
1146}
1147
1148Double_t AliKFParticleBase::GetDistanceFromParticleBz( Double_t B,
1149 const AliKFParticleBase &p )
1150 const
1151{
1152 //* Calculate distance other particle [cm] for Bz field
1153
1154 Double_t dS, dS1;
1155 GetDStoParticleBz( B, p, dS, dS1 );
1156 Double_t mP[8], mC[36], mP1[8], mC1[36];
1157 TransportBz( B, dS, mP, mC );
1158 p.TransportBz( B, dS1, mP1, mC1 );
1159 Double_t dx = mP[0]-mP1[0];
1160 Double_t dy = mP[1]-mP1[1];
1161 Double_t dz = mP[2]-mP1[2];
1162 return TMath::Sqrt(dx*dx+dy*dy+dz*dz);
1163}
1164
1165Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const
1166{
1167 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1168
1169 return GetDeviationFromVertex( Vtx.fP, Vtx.fC );
1170}
1171
1172
1173Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const
1174{
1175 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1176 //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix
1177
1178 Double_t mP[8];
1179 Double_t mC[36];
1180
1181 Transport( GetDStoPoint(v), mP, mC );
1182
1183 Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]};
1184
1185 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1186 (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) );
1187
1188
1189 Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS };
1190
1191 Double_t mSi[6] =
1192 { mC[0] +h[0]*h[0],
1193 mC[1] +h[1]*h[0], mC[2] +h[1]*h[1],
1194 mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] };
1195
1196 if( Cv ){
1197 mSi[0]+=Cv[0];
1198 mSi[1]+=Cv[1];
1199 mSi[2]+=Cv[2];
1200 mSi[3]+=Cv[3];
1201 mSi[4]+=Cv[4];
1202 mSi[5]+=Cv[5];
1203 }
1204
1205 Double_t mS[6];
1206
1207 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1208 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1209 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1210 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1211 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1212 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1213
1214 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1215 s = ( s > 1.E-20 ) ?1./s :0;
1216
1217 return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0]
1218 +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1]
1219 +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2);
1220}
1221
1222
1223Double_t AliKFParticleBase::GetDeviationFromParticleBz( Double_t B,
1224 const AliKFParticleBase &p )
1225 const
1226{
1227 //* Calculate sqrt(Chi2/ndf) deviation from other particle, for Bz field
1228
1229 Double_t dS, dS1;
1230 GetDStoParticleBz( B, p, dS, dS1 );
1231 Double_t mP1[8], mC1[36];
1232 p.TransportBz( B, dS1, mP1, mC1 );
1233
1234 Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]};
1235
1236 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1237 (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) );
1238
1239 Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS };
1240
1241 mC1[0] +=h[0]*h[0];
1242 mC1[1] +=h[1]*h[0];
1243 mC1[2] +=h[1]*h[1];
1244 mC1[3] +=h[2]*h[0];
1245 mC1[4] +=h[2]*h[1];
1246 mC1[5] +=h[2]*h[2];
1247
1248 return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.);
1249}
1250
1251
1252
1253void AliKFParticleBase::SubtractFromVertex( Double_t v[], Double_t Cv[],
1254 Double_t &vChi2, Int_t vNDF ) const
1255{
1256 //* Subtract the particle from the vertex
1257
1258 Double_t fld[3];
1259 {
1260 GetFieldValue( v, fld );
1261 const Double_t kCLight = 0.000299792458;
1262 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
1263 }
1264
1265 Double_t m[8];
1266 Double_t mCm[36];
1267
1268 Transport( GetDStoPoint(v), m, mCm );
1269
1270 Double_t d[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] };
1271 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1272 (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) );
1273
1274 Double_t h[6];
1275
1276 h[0] = m[3]*sigmaS;
1277 h[1] = m[4]*sigmaS;
1278 h[2] = m[5]*sigmaS;
1279 h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ();
1280 h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ();
1281 h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ();
1282
1283 //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex
1284 {
1285 Double_t zeta[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] };
1286
1287 Double_t mVv[6] =
1288 { mCm[ 0] + h[0]*h[0],
1289 mCm[ 1] + h[1]*h[0], mCm[ 2] + h[1]*h[1],
1290 mCm[ 3] + h[2]*h[0], mCm[ 4] + h[2]*h[1], mCm[ 5] + h[2]*h[2] };
1291
1292 Double_t mVvp[9]=
1293 { mCm[ 6] + h[0]*h[3], mCm[ 7] + h[1]*h[3], mCm[ 8] + h[2]*h[3],
1294 mCm[10] + h[0]*h[4], mCm[11] + h[1]*h[4], mCm[12] + h[2]*h[4],
1295 mCm[15] + h[0]*h[5], mCm[16] + h[1]*h[5], mCm[17] + h[2]*h[5] };
1296
1297 Double_t mS[6] =
1298 { mVv[2]*mVv[5] - mVv[4]*mVv[4],
1299 mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3],
1300 mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4],
1301 mVv[0]*mVv[2] - mVv[1]*mVv[1] };
1302
1303 Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] );
1304 s = ( s > 1.E-20 ) ?1./s :0;
1305
1306 mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s;
1307
1308 Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]),
1309 (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]),
1310 (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) };
1311
1312 Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2];
1313 Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2];
1314 Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2];
1315
1316 h[0] = px*sigmaS;
1317 h[1] = py*sigmaS;
1318 h[2] = pz*sigmaS;
1319 h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ();
1320 h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ();
1321 h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ();
1322 }
1323
1324 Double_t mV[6];
1325
1326 mV[ 0] = mCm[ 0] + h[0]*h[0];
1327 mV[ 1] = mCm[ 1] + h[1]*h[0];
1328 mV[ 2] = mCm[ 2] + h[1]*h[1];
1329 mV[ 3] = mCm[ 3] + h[2]*h[0];
1330 mV[ 4] = mCm[ 4] + h[2]*h[1];
1331 mV[ 5] = mCm[ 5] + h[2]*h[2];
1332
1333 //*
1334
1335 Double_t mS[6];
1336 {
1337 Double_t mSi[6] = { mV[0]-Cv[0],
1338 mV[1]-Cv[1], mV[2]-Cv[2],
1339 mV[3]-Cv[3], mV[4]-Cv[4], mV[5]-Cv[5] };
1340
1341 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1342 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1343 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1344 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1345 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1346 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1347
1348 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1349 s = ( s > 1.E-20 ) ?1./s :0;
1350 mS[0]*=s;
1351 mS[1]*=s;
1352 mS[2]*=s;
1353 mS[3]*=s;
1354 mS[4]*=s;
1355 mS[5]*=s;
1356 }
1357
1358 //* Residual (measured - estimated)
1359
1360 Double_t zeta[3] = { m[0]-v[0], m[1]-v[1], m[2]-v[2] };
1361
1362 //* mCHt = mCH' - D'
1363
1364 Double_t mCHt0[3], mCHt1[3], mCHt2[3];
1365
1366 mCHt0[0]=Cv[ 0] ; mCHt1[0]=Cv[ 1] ; mCHt2[0]=Cv[ 3] ;
1367 mCHt0[1]=Cv[ 1] ; mCHt1[1]=Cv[ 2] ; mCHt2[1]=Cv[ 4] ;
1368 mCHt0[2]=Cv[ 3] ; mCHt1[2]=Cv[ 4] ; mCHt2[2]=Cv[ 5] ;
1369
1370 //* Kalman gain K = mCH'*S
1371
1372 Double_t k0[3], k1[3], k2[3];
1373
1374 for(Int_t i=0;i<3;++i){
1375 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
1376 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
1377 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
1378 }
1379
1380 //* New estimation of the vertex position r += K*zeta
1381
1382 for(Int_t i=0;i<3;++i)
1383 v[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
1384
1385 //* New covariance matrix C -= K*(mCH')'
1386
1387 for(Int_t i=0, k=0;i<3;++i){
1388 for(Int_t j=0;j<=i;++j,++k)
1389 Cv[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
1390 }
1391
1392 //* Calculate Chi^2
1393
1394 vNDF -= 2;
1395 vChi2 -= (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
1396 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
1397 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
1398}
1399
1400
1401
1402void AliKFParticleBase::TransportLine( Double_t dS,
1403 Double_t P[], Double_t C[] ) const
1404{
1405 //* Transport the particle as a straight line
1406
1407 P[0] = fP[0] + dS*fP[3];
1408 P[1] = fP[1] + dS*fP[4];
1409 P[2] = fP[2] + dS*fP[5];
1410 P[3] = fP[3];
1411 P[4] = fP[4];
1412 P[5] = fP[5];
1413 P[6] = fP[6];
1414 P[7] = fP[7];
1415
1416 Double_t c6 = fC[ 6] + dS*fC[ 9];
1417 Double_t c11 = fC[11] + dS*fC[14];
1418 Double_t c17 = fC[17] + dS*fC[20];
1419 Double_t sc13 = dS*fC[13];
1420 Double_t sc18 = dS*fC[18];
1421 Double_t sc19 = dS*fC[19];
1422
1423 C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 );
1424 C[ 2] = fC[ 2] + dS*( fC[11] + c11 );
1425 C[ 5] = fC[ 5] + dS*( fC[17] + c17 );
1426
1427 C[ 7] = fC[ 7] + sc13;
1428 C[ 8] = fC[ 8] + sc18;
1429 C[ 9] = fC[ 9];
1430
1431 C[12] = fC[12] + sc19;
1432
1433 C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] );
1434 C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] );
1435 C[ 4] = fC[ 4] + dS*( fC[16] + C[12] );
1436 C[ 6] = c6;
1437
1438 C[10] = fC[10] + sc13;
1439 C[11] = c11;
1440
1441 C[13] = fC[13];
1442 C[14] = fC[14];
1443 C[15] = fC[15] + sc18;
1444 C[16] = fC[16] + sc19;
1445 C[17] = c17;
1446
1447 C[18] = fC[18];
1448 C[19] = fC[19];
1449 C[20] = fC[20];
1450 C[21] = fC[21] + dS*fC[24];
1451 C[22] = fC[22] + dS*fC[25];
1452 C[23] = fC[23] + dS*fC[26];
1453
1454 C[24] = fC[24];
1455 C[25] = fC[25];
1456 C[26] = fC[26];
1457 C[27] = fC[27];
1458 C[28] = fC[28] + dS*fC[31];
1459 C[29] = fC[29] + dS*fC[32];
1460 C[30] = fC[30] + dS*fC[33];
1461
1462 C[31] = fC[31];
1463 C[32] = fC[32];
1464 C[33] = fC[33];
1465 C[34] = fC[34];
1466 C[35] = fC[35];
1467}
1468
1469
1470void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] )
1471{
1472 //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric
1473
1474 const Int_t kN= 8;
1475 Double_t mA[kN*kN];
1476
1477 for( Int_t i=0, ij=0; i<kN; i++ ){
1478 for( Int_t j=0; j<kN; j++, ++ij ){
1479 mA[ij] = 0 ;
1480 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];
1481 }
1482 }
1483
1484 for( Int_t i=0; i<kN; i++ ){
1485 for( Int_t j=0; j<=i; j++ ){
1486 Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i;
1487 SOut[ij] = 0 ;
1488 for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ];
1489 }
1490 }
1491}
1492
1493
1494// 72-charachters line to define the printer border
1495//3456789012345678901234567890123456789012345678901234567890123456789012