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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 © ALICE HLT Group =- | |
16 | //_________________________________________________________________________________ | |
17 | ||
18 | ||
19 | #include "AliKFParticleBase.h" | |
20 | #include "TMath.h" | |
21 | ||
effa6338 | 22 | ClassImp(AliKFParticleBase) |
f826d409 | 23 | |
24 | ||
25 | AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0) | |
26 | { | |
27 | //* Constructor | |
28 | ||
29 | Initialize(); | |
30 | } | |
31 | ||
f826d409 | 32 | void 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 | ||
49 | void 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 | ||
60 | Int_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 | ||
80 | Int_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]; | |
616ffc76 | 92 | M = 0; |
93 | if( m2>1.e-20 ){ | |
f826d409 | 94 | M = TMath::Sqrt(m2); |
616ffc76 | 95 | if( s>=0 ){ |
96 | Error = TMath::Sqrt(s/m2); | |
97 | return 0; | |
98 | } | |
f826d409 | 99 | } |
4bbc290d | 100 | Error = 1.e20; |
f826d409 | 101 | return 1; |
102 | } | |
103 | ||
104 | ||
105 | Int_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 | } | |
4bbc290d | 125 | Error = 1.e20; |
f826d409 | 126 | return 1; |
127 | } | |
128 | ||
129 | Int_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 | } | |
4bbc290d | 142 | Error = 1.e20; |
f826d409 | 143 | return 1; |
144 | } | |
145 | ||
146 | ||
147 | void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter ) | |
148 | { | |
149 | //* Add daughter via operator+= | |
150 | ||
151 | AddDaughter( Daughter ); | |
152 | } | |
153 | ||
616ffc76 | 154 | |
155 | void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const | |
156 | { | |
157 | Double_t b[3]; | |
158 | GetFieldValue( XYZ, b ); | |
159 | const Double_t kCLight = 0.000299792458; | |
160 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
161 | ||
162 | Transport( GetDStoPoint(XYZ), m, V ); | |
163 | ||
164 | Double_t d[3] = { XYZ[0]-m[0], XYZ[1]-m[1], XYZ[2]-m[2] }; | |
165 | Double_t sigmaS = 1.+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
166 | (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) ); | |
167 | ||
168 | Double_t h[6]; | |
169 | ||
170 | h[0] = m[3]*sigmaS; | |
171 | h[1] = m[4]*sigmaS; | |
172 | h[2] = m[5]*sigmaS; | |
173 | h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); | |
174 | h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); | |
175 | h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); | |
176 | ||
177 | //* Fit of momentum (Px,Py,Pz) to XYZ point | |
178 | if(0){ | |
179 | Double_t mVv[6] = | |
180 | { V[ 0] + h[0]*h[0], | |
181 | V[ 1] + h[0]*h[1], V[ 2] + h[1]*h[1], | |
182 | V[ 3] + h[0]*h[2], V[ 4] + h[1]*h[2], V[ 5] + h[2]*h[2] }; | |
183 | ||
184 | Double_t mVvp[9]= | |
185 | { V[ 6] + h[0]*h[3], V[ 7] + h[1]*h[3], V[ 8] + h[2]*h[3], | |
186 | V[10] + h[0]*h[4], V[11] + h[1]*h[4], V[12] + h[2]*h[4], | |
187 | V[15] + h[0]*h[5], V[16] + h[1]*h[5], V[17] + h[2]*h[5] }; | |
188 | ||
189 | Double_t mS[6] = | |
190 | { mVv[2]*mVv[5] - mVv[4]*mVv[4], | |
191 | mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3], | |
192 | mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4], | |
193 | mVv[0]*mVv[2] - mVv[1]*mVv[1] }; | |
194 | ||
195 | Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] ); | |
196 | s = ( s > 1.E-20 ) ?1./s :0; | |
197 | ||
198 | Double_t mSz[3] = { mS[0]*d[0]+mS[1]*d[1]+mS[3]*d[2], | |
199 | mS[1]*d[0]+mS[2]*d[1]+mS[4]*d[2], | |
200 | mS[3]*d[0]+mS[4]*d[1]+mS[5]*d[2] }; | |
201 | ||
202 | Double_t px = m[3] + s*( mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2] ); | |
203 | Double_t py = m[4] + s*( mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2] ); | |
204 | Double_t pz = m[5] + s*( mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2] ); | |
205 | ||
206 | h[0] = px*sigmaS; | |
207 | h[1] = py*sigmaS; | |
208 | h[2] = pz*sigmaS; | |
209 | h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); | |
210 | h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); | |
211 | h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); | |
212 | } | |
213 | ||
214 | V[ 0]+= h[0]*h[0]; | |
215 | V[ 1]+= h[1]*h[0]; | |
216 | V[ 2]+= h[1]*h[1]; | |
217 | V[ 3]+= h[2]*h[0]; | |
218 | V[ 4]+= h[2]*h[1]; | |
219 | V[ 5]+= h[2]*h[2]; | |
220 | ||
221 | V[ 6]+= h[3]*h[0]; | |
222 | V[ 7]+= h[3]*h[1]; | |
223 | V[ 8]+= h[3]*h[2]; | |
224 | V[ 9]+= h[3]*h[3]; | |
225 | ||
226 | V[10]+= h[4]*h[0]; | |
227 | V[11]+= h[4]*h[1]; | |
228 | V[12]+= h[4]*h[2]; | |
229 | V[13]+= h[4]*h[3]; | |
230 | V[14]+= h[4]*h[4]; | |
231 | ||
232 | V[15]+= h[5]*h[0]; | |
233 | V[16]+= h[5]*h[1]; | |
234 | V[17]+= h[5]*h[2]; | |
235 | V[18]+= h[5]*h[3]; | |
236 | V[19]+= h[5]*h[4]; | |
237 | V[20]+= h[5]*h[5]; | |
238 | } | |
239 | ||
240 | ||
241 | ||
f826d409 | 242 | void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter ) |
243 | { | |
244 | //* Add daughter | |
245 | ||
616ffc76 | 246 | if( fNDF<-1 ){ // first daughter -> just copy |
247 | fNDF = -1; | |
248 | fQ = Daughter.GetQ(); | |
249 | for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i]; | |
250 | for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i]; | |
251 | fSFromDecay = 0; | |
252 | return; | |
253 | } | |
254 | ||
f826d409 | 255 | TransportToDecayVertex(); |
256 | ||
257 | Double_t b[3]; | |
258 | Int_t maxIter = 1; | |
259 | ||
260 | if( !fIsLinearized ){ | |
261 | if( fNDF==-1 ){ | |
262 | Double_t ds, ds1; | |
616ffc76 | 263 | GetDStoParticle(Daughter, ds, ds1); |
f826d409 | 264 | TransportToDS( ds ); |
616ffc76 | 265 | Double_t m[8]; |
266 | Double_t mCd[36]; | |
267 | Daughter.Transport( ds1, m, mCd ); | |
268 | fVtxGuess[0] = .5*( fP[0] + m[0] ); | |
269 | fVtxGuess[1] = .5*( fP[1] + m[1] ); | |
270 | fVtxGuess[2] = .5*( fP[2] + m[2] ); | |
271 | } else { | |
272 | fVtxGuess[0] = fP[0]; | |
273 | fVtxGuess[1] = fP[1]; | |
274 | fVtxGuess[2] = fP[2]; | |
f826d409 | 275 | } |
f826d409 | 276 | maxIter = 3; |
277 | } | |
278 | ||
279 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
280 | ||
281 | { | |
282 | GetFieldValue( fVtxGuess, b ); | |
283 | const Double_t kCLight = 0.000299792458; | |
284 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
285 | } | |
f826d409 | 286 | |
616ffc76 | 287 | Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36]; |
288 | if( fNDF==-1 ){ | |
289 | GetMeasurement( fVtxGuess, tmpP, tmpC ); | |
290 | ffP = tmpP; | |
291 | ffC = tmpC; | |
f826d409 | 292 | } |
293 | ||
616ffc76 | 294 | Double_t m[8], mV[36]; |
295 | Daughter.GetMeasurement( fVtxGuess, m, mV ); | |
296 | ||
f826d409 | 297 | //* |
298 | ||
299 | Double_t mS[6]; | |
300 | { | |
616ffc76 | 301 | Double_t mSi[6] = { ffC[0]+mV[0], |
302 | ffC[1]+mV[1], ffC[2]+mV[2], | |
303 | ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] }; | |
f826d409 | 304 | |
305 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
306 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
307 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
308 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
309 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
310 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
311 | ||
312 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
313 | s = ( s > 1.E-20 ) ?1./s :0; | |
314 | mS[0]*=s; | |
315 | mS[1]*=s; | |
316 | mS[2]*=s; | |
317 | mS[3]*=s; | |
318 | mS[4]*=s; | |
319 | mS[5]*=s; | |
320 | } | |
321 | ||
322 | //* Residual (measured - estimated) | |
323 | ||
616ffc76 | 324 | Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] }; |
f826d409 | 325 | |
326 | //* CHt = CH' - D' | |
327 | ||
328 | Double_t mCHt0[7], mCHt1[7], mCHt2[7]; | |
329 | ||
616ffc76 | 330 | mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ; |
331 | mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ; | |
332 | mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ; | |
333 | mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8]; | |
334 | mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12]; | |
335 | mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17]; | |
336 | mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23]; | |
f826d409 | 337 | |
338 | //* Kalman gain K = mCH'*S | |
339 | ||
340 | Double_t k0[7], k1[7], k2[7]; | |
341 | ||
342 | for(Int_t i=0;i<7;++i){ | |
343 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
344 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
345 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
346 | } | |
347 | ||
4bbc290d | 348 | //* New estimation of the vertex position |
f826d409 | 349 | |
350 | if( iter<maxIter-1 ){ | |
351 | for(Int_t i=0; i<3; ++i) | |
616ffc76 | 352 | fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2]; |
f826d409 | 353 | continue; |
354 | } | |
355 | ||
356 | // last itearation -> update the particle | |
357 | ||
358 | //* Add the daughter momentum to the particle momentum | |
359 | ||
616ffc76 | 360 | ffP[ 3] += m[ 3]; |
361 | ffP[ 4] += m[ 4]; | |
362 | ffP[ 5] += m[ 5]; | |
363 | ffP[ 6] += m[ 6]; | |
f826d409 | 364 | |
616ffc76 | 365 | ffC[ 9] += mV[ 9]; |
366 | ffC[13] += mV[13]; | |
367 | ffC[14] += mV[14]; | |
368 | ffC[18] += mV[18]; | |
369 | ffC[19] += mV[19]; | |
370 | ffC[20] += mV[20]; | |
371 | ffC[24] += mV[24]; | |
372 | ffC[25] += mV[25]; | |
373 | ffC[26] += mV[26]; | |
374 | ffC[27] += mV[27]; | |
f826d409 | 375 | |
376 | //* New estimation of the vertex position r += K*zeta | |
377 | ||
378 | for(Int_t i=0;i<7;++i) | |
616ffc76 | 379 | fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; |
f826d409 | 380 | |
381 | //* New covariance matrix C -= K*(mCH')' | |
4bbc290d | 382 | |
f826d409 | 383 | for(Int_t i=0, k=0;i<7;++i){ |
384 | for(Int_t j=0;j<=i;++j,++k) | |
616ffc76 | 385 | fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] ); |
f826d409 | 386 | } |
387 | ||
388 | //* Calculate Chi^2 | |
389 | ||
390 | fNDF += 2; | |
391 | fQ += Daughter.GetQ(); | |
392 | fSFromDecay = 0; | |
393 | fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
394 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
395 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
396 | } | |
397 | } | |
398 | ||
399 | ||
400 | void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx ) | |
401 | { | |
402 | //* Set production vertex for the particle | |
403 | ||
404 | const Double_t *m = Vtx.fP, *mV = Vtx.fC; | |
405 | ||
406 | TransportToDS( GetDStoPoint( m ) ); | |
407 | fP[7] = -fSFromDecay; | |
408 | Convert(1); | |
409 | ||
410 | Double_t mAi[6]; | |
411 | mAi[0] = fC[4]*fC[4] - fC[2]*fC[5]; | |
412 | mAi[1] = fC[1]*fC[5] - fC[3]*fC[4]; | |
413 | mAi[3] = fC[2]*fC[3] - fC[1]*fC[4]; | |
414 | Double_t det = 1./(fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]); | |
415 | mAi[0] *= det; | |
416 | mAi[1] *= det; | |
417 | mAi[3] *= det; | |
418 | mAi[2] = ( fC[3]*fC[3] - fC[0]*fC[5] )*det; | |
419 | mAi[4] = ( fC[0]*fC[4] - fC[1]*fC[3] )*det; | |
420 | mAi[5] = ( fC[1]*fC[1] - fC[0]*fC[2] )*det; | |
421 | ||
422 | Double_t mB[5][3]; | |
423 | ||
424 | mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3]; | |
425 | mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4]; | |
426 | mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5]; | |
427 | ||
428 | mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3]; | |
429 | mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4]; | |
430 | mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5]; | |
431 | ||
432 | mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3]; | |
433 | mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4]; | |
434 | mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5]; | |
435 | ||
436 | mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3]; | |
437 | mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4]; | |
438 | mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5]; | |
439 | ||
440 | mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3]; | |
441 | mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4]; | |
442 | mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5]; | |
443 | ||
444 | Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] }; | |
445 | ||
446 | { | |
447 | Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2], | |
448 | fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] }; | |
449 | Double_t mAVi[6]; | |
450 | mAVi[0] = mAV[4]*mAV[4] - mAV[2]*mAV[5]; | |
451 | mAVi[1] = mAV[1]*mAV[5] - mAV[3]*mAV[4]; | |
452 | mAVi[2] = mAV[3]*mAV[3] - mAV[0]*mAV[5] ; | |
453 | mAVi[3] = mAV[2]*mAV[3] - mAV[1]*mAV[4]; | |
454 | mAVi[4] = mAV[0]*mAV[4] - mAV[1]*mAV[3] ; | |
455 | mAVi[5] = mAV[1]*mAV[1] - mAV[0]*mAV[2] ; | |
456 | ||
457 | det = 1./( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] ); | |
458 | ||
459 | fNDF += 2; | |
460 | fChi2 += | |
461 | ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0] | |
462 | +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1] | |
463 | +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )*det; | |
464 | } | |
465 | ||
466 | fP[0] = m[0]; | |
467 | fP[1] = m[1]; | |
468 | fP[2] = m[2]; | |
469 | fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; | |
470 | fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; | |
471 | fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; | |
472 | fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2]; | |
473 | fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2]; | |
474 | ||
475 | Double_t d0, d1, d2; | |
476 | ||
477 | fC[0] = mV[0]; | |
478 | fC[1] = mV[1]; | |
479 | fC[2] = mV[2]; | |
480 | fC[3] = mV[3]; | |
481 | fC[4] = mV[4]; | |
482 | fC[5] = mV[5]; | |
483 | ||
484 | d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6]; | |
485 | d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7]; | |
486 | d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8]; | |
487 | ||
488 | fC[ 6]+= d0; | |
489 | fC[ 7]+= d1; | |
490 | fC[ 8]+= d2; | |
491 | fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
492 | ||
493 | d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10]; | |
494 | d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11]; | |
495 | d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12]; | |
496 | ||
497 | fC[10]+= d0; | |
498 | fC[11]+= d1; | |
499 | fC[12]+= d2; | |
500 | fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
501 | fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
502 | ||
503 | d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15]; | |
504 | d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16]; | |
505 | d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17]; | |
506 | ||
507 | fC[15]+= d0; | |
508 | fC[16]+= d1; | |
509 | fC[17]+= d2; | |
510 | fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
511 | fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
512 | fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
513 | ||
514 | d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21]; | |
515 | d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22]; | |
516 | d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23]; | |
517 | ||
518 | fC[21]+= d0; | |
519 | fC[22]+= d1; | |
520 | fC[23]+= d2; | |
521 | fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
522 | fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
523 | fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
524 | fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
525 | ||
526 | d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28]; | |
527 | d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29]; | |
528 | d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30]; | |
529 | ||
530 | fC[28]+= d0; | |
531 | fC[29]+= d1; | |
532 | fC[30]+= d2; | |
533 | fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
534 | fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
535 | fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
536 | fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
537 | fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2]; | |
538 | ||
539 | TransportToDS( fP[7] ); | |
540 | fSFromDecay = 0; | |
541 | Convert(0); | |
542 | } | |
543 | ||
544 | ||
545 | ||
546 | ||
547 | void AliKFParticleBase::SetMassConstraint( Double_t Mass ) | |
548 | { | |
549 | //* Set hard mass constraint | |
550 | ||
551 | Double_t mH[8]; | |
552 | mH[0] = mH[1] = mH[2] = 0.; | |
553 | mH[3] = -2*fP[3]; | |
554 | mH[4] = -2*fP[4]; | |
555 | mH[5] = -2*fP[5]; | |
556 | mH[6] = 2*fP[6]; | |
557 | mH[7] = 0; | |
558 | Double_t m2 = ( fP[6]*fP[6] | |
559 | - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5] ); | |
560 | ||
561 | Double_t zeta = Mass*Mass - m2; | |
562 | for(Int_t i=0;i<8;++i) zeta -= mH[i]*(fP[i]-fP[i]); | |
563 | ||
564 | Double_t s = 0.; | |
565 | Double_t mCHt[8]; | |
566 | for (Int_t i=0;i<8;++i ){ | |
567 | mCHt[i] = 0.0; | |
568 | for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j]; | |
569 | s += mH[i]*mCHt[i]; | |
570 | } | |
571 | ||
572 | if( s<1.e-20 ) return; | |
573 | s = 1./s; | |
574 | fChi2 += zeta*zeta*s; | |
575 | fNDF += 1; | |
576 | for( Int_t i=0, ii=0; i<8; ++i ){ | |
577 | Double_t ki = mCHt[i]*s; | |
578 | fP[i]+= ki*zeta; | |
579 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j]; | |
580 | } | |
581 | } | |
582 | ||
583 | ||
584 | void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters, | |
4bbc290d | 585 | const AliKFParticleBase *Parent, Double_t Mass ) |
f826d409 | 586 | { |
587 | //* Full reconstruction in one go | |
588 | ||
589 | Int_t maxIter = 1; | |
590 | bool wasLinearized = fIsLinearized; | |
591 | if( !fIsLinearized ){ | |
616ffc76 | 592 | //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!! |
593 | fVtxGuess[0] = GetX(); | |
594 | fVtxGuess[1] = GetY(); | |
595 | fVtxGuess[2] = GetZ(); | |
f826d409 | 596 | fIsLinearized = 1; |
597 | maxIter = 3; | |
598 | } | |
599 | ||
600 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
f826d409 | 601 | fAtProductionVertex = 0; |
602 | fSFromDecay = 0; | |
603 | fP[0] = fVtxGuess[0]; | |
604 | fP[1] = fVtxGuess[1]; | |
605 | fP[2] = fVtxGuess[2]; | |
606 | fP[3] = 0; | |
607 | fP[4] = 0; | |
608 | fP[5] = 0; | |
609 | fP[6] = 0; | |
610 | fP[7] = 0; | |
611 | ||
612 | for(Int_t i=0;i<36;++i) fC[i]=0.; | |
613 | ||
614 | fC[0] = fC[2] = fC[5] = 100.; | |
615 | fC[35] = 1.; | |
616 | ||
617 | fNDF = -3; | |
618 | fChi2 = 0.; | |
619 | fQ = 0; | |
620 | ||
4bbc290d | 621 | for( Int_t itr =0; itr<NDaughters; itr++ ){ |
622 | AddDaughter( *vDaughters[itr] ); | |
623 | } | |
f826d409 | 624 | if( iter<maxIter-1){ |
625 | for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i]; | |
626 | } | |
627 | } | |
628 | fIsLinearized = wasLinearized; | |
629 | ||
630 | if( Mass>=0 ) SetMassConstraint( Mass ); | |
631 | if( Parent ) SetProductionVertex( *Parent ); | |
632 | } | |
633 | ||
634 | ||
635 | void AliKFParticleBase::Convert( bool ToProduction ) | |
636 | { | |
637 | //* Tricky function - convert the particle error along its trajectory to | |
638 | //* the value which corresponds to its production/decay vertex | |
639 | //* It is done by combination of the error of decay length with the position errors | |
640 | ||
641 | Double_t fld[3]; | |
642 | { | |
643 | GetFieldValue( fP, fld ); | |
644 | const Double_t kCLight = fQ*0.000299792458; | |
645 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
646 | } | |
647 | ||
648 | Double_t h[6]; | |
649 | ||
650 | h[0] = fP[3]; | |
651 | h[1] = fP[4]; | |
652 | h[2] = fP[5]; | |
653 | if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; } | |
654 | h[3] = h[1]*fld[2]-h[2]*fld[1]; | |
655 | h[4] = h[2]*fld[0]-h[0]*fld[2]; | |
656 | h[5] = h[0]*fld[1]-h[1]*fld[0]; | |
657 | ||
658 | Double_t c; | |
659 | ||
660 | c = fC[28]+h[0]*fC[35]; | |
661 | fC[ 0]+= h[0]*(c+fC[28]); | |
662 | fC[28] = c; | |
663 | ||
664 | fC[ 1]+= h[1]*fC[28] + h[0]*fC[29]; | |
665 | c = fC[29]+h[1]*fC[35]; | |
666 | fC[ 2]+= h[1]*(c+fC[29]); | |
667 | fC[29] = c; | |
668 | ||
669 | fC[ 3]+= h[2]*fC[28] + h[0]*fC[30]; | |
670 | fC[ 4]+= h[2]*fC[29] + h[1]*fC[30]; | |
671 | c = fC[30]+h[2]*fC[35]; | |
672 | fC[ 5]+= h[2]*(c+fC[30]); | |
673 | fC[30] = c; | |
674 | ||
675 | fC[ 6]+= h[3]*fC[28] + h[0]*fC[31]; | |
676 | fC[ 7]+= h[3]*fC[29] + h[1]*fC[31]; | |
677 | fC[ 8]+= h[3]*fC[30] + h[2]*fC[31]; | |
678 | c = fC[31]+h[3]*fC[35]; | |
679 | fC[ 9]+= h[3]*(c+fC[31]); | |
680 | fC[31] = c; | |
681 | ||
682 | fC[10]+= h[4]*fC[28] + h[0]*fC[32]; | |
683 | fC[11]+= h[4]*fC[29] + h[1]*fC[32]; | |
684 | fC[12]+= h[4]*fC[30] + h[2]*fC[32]; | |
685 | fC[13]+= h[4]*fC[31] + h[3]*fC[32]; | |
686 | c = fC[32]+h[4]*fC[35]; | |
687 | fC[14]+= h[4]*(c+fC[32]); | |
688 | fC[32] = c; | |
689 | ||
690 | fC[15]+= h[5]*fC[28] + h[0]*fC[33]; | |
691 | fC[16]+= h[5]*fC[29] + h[1]*fC[33]; | |
692 | fC[17]+= h[5]*fC[30] + h[2]*fC[33]; | |
693 | fC[18]+= h[5]*fC[31] + h[3]*fC[33]; | |
694 | fC[19]+= h[5]*fC[32] + h[4]*fC[33]; | |
695 | c = fC[33]+h[5]*fC[35]; | |
696 | fC[20]+= h[5]*(c+fC[33]); | |
697 | fC[33] = c; | |
698 | ||
699 | fC[21]+= h[0]*fC[34]; | |
700 | fC[22]+= h[1]*fC[34]; | |
701 | fC[23]+= h[2]*fC[34]; | |
702 | fC[24]+= h[3]*fC[34]; | |
703 | fC[25]+= h[4]*fC[34]; | |
704 | fC[26]+= h[5]*fC[34]; | |
705 | } | |
706 | ||
707 | ||
708 | void AliKFParticleBase::TransportToDecayVertex() | |
709 | { | |
710 | //* Transport the particle to its decay vertex | |
711 | ||
712 | if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay ); | |
713 | if( fAtProductionVertex ) Convert(0); | |
714 | fAtProductionVertex = 0; | |
715 | } | |
716 | ||
717 | void AliKFParticleBase::TransportToProductionVertex() | |
718 | { | |
719 | //* Transport the particle to its production vertex | |
616ffc76 | 720 | |
f826d409 | 721 | if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] ); |
722 | if( !fAtProductionVertex ) Convert( 1 ); | |
723 | fAtProductionVertex = 1; | |
724 | } | |
725 | ||
726 | ||
727 | void AliKFParticleBase::TransportToDS( Double_t dS ) | |
728 | { | |
729 | //* Transport the particle on dS parameter (SignedPath/Momentum) | |
616ffc76 | 730 | |
f826d409 | 731 | Transport( dS, fP, fC ); |
732 | fSFromDecay+= dS; | |
733 | } | |
734 | ||
735 | ||
736 | Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const | |
737 | { | |
738 | //* Get dS to a certain space point without field | |
739 | ||
740 | Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; | |
741 | if( p2<1.e-4 ) p2 = 1; | |
742 | return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2; | |
743 | } | |
744 | ||
745 | ||
746 | Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] ) | |
747 | const | |
748 | { | |
616ffc76 | 749 | |
f826d409 | 750 | //* Get dS to a certain space point for Bz field |
f826d409 | 751 | const Double_t kCLight = 0.000299792458; |
752 | Double_t bq = B*fQ*kCLight; | |
753 | Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4]; | |
754 | if( pt2<1.e-4 ) return 0; | |
755 | Double_t dx = xyz[0] - fP[0]; | |
756 | Double_t dy = xyz[1] - fP[1]; | |
757 | Double_t a = dx*fP[3]+dy*fP[4]; | |
616ffc76 | 758 | if( TMath::Abs(bq)<1.e-8 ) return a/pt2; |
f826d409 | 759 | return TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq; |
760 | } | |
761 | ||
762 | ||
763 | void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p, | |
616ffc76 | 764 | Double_t &DS, Double_t &DS1 ) |
f826d409 | 765 | const |
766 | { | |
767 | //* Get dS to another particle for Bz field | |
f826d409 | 768 | Double_t px = fP[3]; |
769 | Double_t py = fP[4]; | |
770 | Double_t pz = fP[5]; | |
771 | ||
772 | Double_t px1 = p.fP[3]; | |
773 | Double_t py1 = p.fP[4]; | |
774 | Double_t pz1 = p.fP[5]; | |
775 | ||
776 | const Double_t kCLight = 0.000299792458; | |
777 | ||
778 | Double_t bq = B*fQ*kCLight; | |
779 | Double_t bq1 = B*p.fQ*kCLight; | |
f826d409 | 780 | Double_t s=0, ds=0, s1=0, ds1=0; |
781 | ||
782 | if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){ | |
4bbc290d | 783 | |
f826d409 | 784 | Double_t dx = (p.fP[0] - fP[0]); |
785 | Double_t dy = (p.fP[1] - fP[1]); | |
786 | Double_t d2 = (dx*dx+dy*dy); | |
787 | ||
788 | Double_t p2 = (px *px + py *py); | |
789 | Double_t p21 = (px1*px1 + py1*py1); | |
790 | ||
791 | Double_t a = (px*py1 - py*px1); | |
792 | Double_t b = (px*px1 + py*py1); | |
793 | ||
794 | Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ; | |
795 | Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ; | |
796 | Double_t l2 = ldx*ldx + ldy*ldy; | |
797 | ||
798 | Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b; | |
799 | Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b; | |
800 | ||
801 | Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ; | |
802 | Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ; | |
803 | ||
804 | Double_t sa = 4*l2*p2 - ca*ca; | |
805 | Double_t sa1 = 4*l2*p21 - ca1*ca1; | |
806 | if(sa<0) sa=0; | |
807 | if(sa1<0)sa1=0; | |
808 | ||
809 | if( TMath::Abs(bq)>1.e-8){ | |
810 | s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq; | |
811 | ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq; | |
812 | } else { | |
813 | s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2; | |
814 | ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2; | |
815 | if( ds<0 ) ds = 0; | |
816 | ds = TMath::Sqrt(ds); | |
817 | } | |
818 | ||
819 | if( TMath::Abs(bq1)>1.e-8){ | |
820 | s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1; | |
821 | ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1; | |
822 | } else { | |
823 | s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21; | |
824 | ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21; | |
825 | if( ds1<0 ) ds1 = 0; | |
826 | ds1 = TMath::Sqrt(ds1); | |
827 | } | |
828 | } | |
829 | ||
f826d409 | 830 | Double_t ss[2], ss1[2], g[2][5],g1[2][5]; |
831 | ||
832 | ss[0] = s + ds; | |
833 | ss[1] = s - ds; | |
834 | ss1[0] = s1 + ds1; | |
835 | ss1[1] = s1 - ds1; | |
836 | for( Int_t i=0; i<2; i++){ | |
837 | Double_t bs = bq*ss[i]; | |
838 | Double_t c = TMath::Cos(bs), s = TMath::Sin(bs); | |
839 | Double_t cB,sB; | |
840 | if( TMath::Abs(bq)>1.e-8){ | |
841 | cB= (1-c)/bq; | |
842 | sB= s/bq; | |
843 | }else{ | |
844 | sB = (1. - bs*bs/6.)*ss[i]; | |
845 | cB = .5*sB*bs; | |
846 | } | |
847 | g[i][0] = fP[0] + sB*px + cB*py; | |
848 | g[i][1] = fP[1] - cB*px + sB*py; | |
849 | g[i][2] = fP[2] + ss[i]*pz; | |
850 | g[i][3] = + c*px + s*py; | |
851 | g[i][4] = - s*px + c*py; | |
852 | ||
853 | bs = bq1*ss1[i]; | |
854 | c = TMath::Cos(bs); s = TMath::Sin(bs); | |
855 | if( TMath::Abs(bq1)>1.e-8){ | |
856 | cB= (1-c)/bq1; | |
857 | sB= s/bq1; | |
858 | }else{ | |
859 | sB = (1. - bs*bs/6.)*ss1[i]; | |
860 | cB = .5*sB*bs; | |
861 | } | |
862 | ||
863 | g[i][0] = p.fP[0] + sB*px1 + cB*py1; | |
864 | g[i][1] = p.fP[1] - cB*px1 + sB*py1; | |
865 | g[i][2] = p.fP[2] + ss[i]*pz1; | |
866 | g[i][3] = + c*px1 + s*py1; | |
867 | g[i][4] = - s*px1 + c*py1; | |
868 | } | |
869 | ||
870 | Int_t i=0, i1=0; | |
871 | ||
872 | Double_t dMin = 1.e10; | |
873 | for( Int_t j=0; j<2; j++){ | |
874 | for( Int_t j1=0; j1<2; j1++){ | |
875 | Double_t xx = g[j][0]-g1[j1][0]; | |
876 | Double_t yy = g[j][1]-g1[j1][1]; | |
877 | Double_t zz = g[j][2]-g1[j1][2]; | |
878 | Double_t d = xx*xx + yy*yy + zz*zz; | |
879 | if( d<dMin ){ | |
880 | dMin = d; | |
881 | i = j; | |
882 | i1 = j1; | |
883 | } | |
884 | } | |
885 | } | |
886 | ||
887 | DS = ss[i]; | |
888 | DS1 = ss1[i1]; | |
889 | ||
890 | Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4]; | |
891 | Double_t x1=g[i1][0], y1= g[i1][1], z1= g[i1][2], ppx1= g[i1][3], ppy1= g[i1][4]; | |
892 | Double_t dx = x1-x; | |
893 | Double_t dy = y1-y; | |
894 | Double_t dz = z1-z; | |
895 | Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1; | |
896 | Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1; | |
897 | Double_t c = dx*ppx + dy*ppy + dz*pz ; | |
898 | Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz; | |
899 | Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1; | |
900 | Double_t det = pp2*pp21 - a*a; | |
901 | if( TMath::Abs(det)>1.e-8 ){ | |
902 | DS+=(a*b-pp21*c)/det; | |
903 | DS1+=(a*c-pp2*b)/det; | |
904 | } | |
905 | } | |
906 | ||
907 | ||
908 | ||
909 | void AliKFParticleBase::TransportCBM( Double_t dS, | |
910 | Double_t P[], Double_t C[] ) const | |
911 | { | |
912 | //* Transport the particle on dS, output to P[],C[], for CBM field | |
913 | ||
914 | if( fQ==0 ){ | |
915 | TransportLine( dS, P, C ); | |
916 | return; | |
917 | } | |
918 | ||
919 | const Double_t kCLight = 0.000299792458; | |
920 | ||
921 | Double_t c = fQ*kCLight; | |
922 | ||
923 | // construct coefficients | |
924 | ||
925 | Double_t | |
926 | px = fP[3], | |
927 | py = fP[4], | |
928 | pz = fP[5]; | |
929 | ||
930 | 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; | |
931 | ||
932 | { // get field integrals | |
933 | ||
934 | Double_t fld[3][3]; | |
935 | Double_t p0[3], p1[3], p2[3]; | |
936 | ||
937 | // line track approximation | |
938 | ||
939 | p0[0] = fP[0]; | |
940 | p0[1] = fP[1]; | |
941 | p0[2] = fP[2]; | |
942 | ||
943 | p2[0] = fP[0] + px*dS; | |
944 | p2[1] = fP[1] + py*dS; | |
945 | p2[2] = fP[2] + pz*dS; | |
946 | ||
947 | p1[0] = 0.5*(p0[0]+p2[0]); | |
948 | p1[1] = 0.5*(p0[1]+p2[1]); | |
949 | p1[2] = 0.5*(p0[2]+p2[2]); | |
950 | ||
951 | // first order track approximation | |
952 | { | |
953 | GetFieldValue( p0, fld[0] ); | |
954 | GetFieldValue( p1, fld[1] ); | |
955 | GetFieldValue( p2, fld[2] ); | |
956 | ||
957 | Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.; | |
958 | Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.; | |
959 | ||
960 | p1[0] -= ssy1*pz; | |
961 | p1[2] += ssy1*px; | |
962 | p2[0] -= ssy2*pz; | |
963 | p2[2] += ssy2*px; | |
964 | } | |
965 | ||
966 | GetFieldValue( p0, fld[0] ); | |
967 | GetFieldValue( p1, fld[1] ); | |
968 | GetFieldValue( p2, fld[2] ); | |
969 | ||
970 | sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.; | |
971 | sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.; | |
972 | sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.; | |
973 | ||
974 | ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.; | |
975 | ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.; | |
976 | ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.; | |
977 | ||
978 | Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360. | |
979 | Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520. | |
980 | for(Int_t n=0; n<3; n++) | |
981 | for(Int_t m=0; m<3; m++) | |
982 | { | |
983 | syz += c2[n][m]*fld[n][1]*fld[m][2]; | |
984 | ssyz += cc2[n][m]*fld[n][1]*fld[m][2]; | |
985 | } | |
986 | ||
987 | syz *= c*c*dS*dS/360.; | |
988 | ssyz *= c*c*dS*dS*dS/2520.; | |
989 | ||
990 | syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS; | |
991 | syyy = syy*syy*syy / 1296; | |
992 | syy = syy*syy/72; | |
993 | ||
994 | ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+ | |
995 | fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+ | |
996 | fld[2][1]*( 3*fld[2][1] ) | |
997 | )*dS*dS*dS*c*c/2520.; | |
998 | ssyyy = | |
999 | ( | |
1000 | fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+ | |
1001 | fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+ | |
1002 | fld[2][1]*( 19*fld[2][1] ) )+ | |
1003 | fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+ | |
1004 | fld[2][1]*( 62*fld[2][1] ) )+ | |
1005 | fld[2][1]*fld[2][1] *( 3*fld[2][1] ) | |
1006 | )*dS*dS*dS*dS*c*c*c/90720.; | |
1007 | ||
1008 | } | |
1009 | ||
1010 | Double_t mJ[8][8]; | |
1011 | for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0; | |
1012 | ||
1013 | 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; | |
1014 | 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; | |
1015 | 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; | |
1016 | ||
1017 | 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; | |
1018 | 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; | |
1019 | 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; | |
1020 | mJ[6][6] = mJ[7][7] = 1; | |
1021 | ||
1022 | P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz; | |
1023 | P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz; | |
1024 | P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz; | |
1025 | P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz; | |
1026 | P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz; | |
1027 | P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz; | |
1028 | P[6] = fP[6]; | |
1029 | P[7] = fP[7]; | |
1030 | ||
1031 | MultQSQt( mJ[0], fC, C); | |
1032 | ||
1033 | } | |
1034 | ||
1035 | ||
1036 | void AliKFParticleBase::TransportBz( Double_t B, Double_t S, | |
616ffc76 | 1037 | Double_t P[], Double_t C[] ) const |
f826d409 | 1038 | { |
1039 | //* Transport the particle on dS, output to P[],C[], for Bz field | |
616ffc76 | 1040 | |
f826d409 | 1041 | const Double_t kCLight = 0.000299792458; |
1042 | B = B*fQ*kCLight; | |
1043 | Double_t bs= B*S; | |
1044 | Double_t s = TMath::Sin(bs), c = TMath::Cos(bs); | |
1045 | Double_t sB, cB; | |
616ffc76 | 1046 | if( TMath::Abs(bs)>1.e-10){ |
f826d409 | 1047 | sB= s/B; |
1048 | cB= (1-c)/B; | |
1049 | }else{ | |
1050 | sB = (1. - bs*bs/6.)*S; | |
1051 | cB = .5*sB*bs; | |
1052 | } | |
1053 | ||
1054 | Double_t px = fP[3]; | |
1055 | Double_t py = fP[4]; | |
1056 | Double_t pz = fP[5]; | |
1057 | ||
1058 | P[0] = fP[0] + sB*px + cB*py; | |
1059 | P[1] = fP[1] - cB*px + sB*py; | |
1060 | P[2] = fP[2] + S*pz; | |
1061 | P[3] = c*px + s*py; | |
1062 | P[4] = -s*px + c*py; | |
1063 | P[5] = fP[5]; | |
1064 | P[6] = fP[6]; | |
1065 | P[7] = fP[7]; | |
1066 | ||
1067 | Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 }, | |
616ffc76 | 1068 | {0,1,0, -cB, sB, 0, 0, 0 }, |
1069 | {0,0,1, 0, 0, S, 0, 0 }, | |
1070 | {0,0,0, c, s, 0, 0, 0 }, | |
1071 | {0,0,0, -s, c, 0, 0, 0 }, | |
1072 | {0,0,0, 0, 0, 1, 0, 0 }, | |
1073 | {0,0,0, 0, 0, 0, 1, 0 }, | |
1074 | {0,0,0, 0, 0, 0, 0, 1 } }; | |
f826d409 | 1075 | Double_t mA[8][8]; |
1076 | for( Int_t k=0,i=0; i<8; i++) | |
1077 | for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k]; | |
1078 | ||
1079 | Double_t mJC[8][8]; | |
1080 | for( Int_t i=0; i<8; i++ ) | |
1081 | for( Int_t j=0; j<8; j++ ){ | |
1082 | mJC[i][j]=0; | |
1083 | for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j]; | |
1084 | } | |
1085 | ||
1086 | for( Int_t k=0,i=0; i<8; i++) | |
1087 | for( Int_t j=0; j<=i; j++, k++ ){ | |
1088 | C[k] = 0; | |
1089 | for( Int_t l=0; l<8; l++ ) C[k]+=mJC[i][l]*mJ[j][l]; | |
1090 | } | |
1091 | ||
1092 | return; | |
1093 | /* | |
1094 | Double_t cBC13 = cB*fC[13]; | |
1095 | Double_t C17 = fC[17]; | |
1096 | Double_t C18 = fC[18]; | |
1097 | fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14]; | |
1098 | ||
1099 | Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13]; | |
1100 | Double_t mJC14= fC[11] - cBC13 + sB*fC[14]; | |
1101 | ||
1102 | fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB; | |
1103 | fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB; | |
1104 | ||
1105 | Double_t mJC23= fC[ 8] + S*fC[18]; | |
1106 | Double_t mJC24= fC[12] + S*fC[19]; | |
1107 | fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB; | |
1108 | fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB; | |
1109 | ||
1110 | fC[15]+= C18*sB + fC[19]*cB; | |
1111 | fC[16]+= -C18*cB + fC[19]*sB; | |
1112 | fC[17]+= fC[20]*S; | |
1113 | fC[18] = C18*c + fC[19]*s; | |
1114 | fC[19] = -C18*s + fC[19]*c; | |
1115 | ||
1116 | fC[ 5]+= (C17 + C17 + fC[17])*S; | |
1117 | ||
1118 | Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14]; | |
1119 | Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14]; | |
1120 | Double_t C6= fC[6], C7= fC[7], C8= fC[8]; | |
1121 | ||
1122 | fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB; | |
1123 | fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB; | |
1124 | fC[ 8]= c*C8 + s*fC[12] +fC[18]*S; | |
1125 | fC[ 9]= mJC33*c +mJC34*s; | |
1126 | ||
1127 | fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB; | |
1128 | fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB; | |
1129 | fC[12]= -s*C8 + c*fC[12] +fC[19]*S; | |
1130 | fC[13]= mJC43*c +mJC44*s; | |
1131 | fC[14]=-mJC43*s +mJC44*c; | |
1132 | */ | |
1133 | } | |
1134 | ||
1135 | ||
1136 | Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const | |
1137 | { | |
1138 | //* Calculate distance from vertex [cm] | |
1139 | ||
1140 | return GetDistanceFromVertex( Vtx.fP ); | |
1141 | } | |
1142 | ||
1143 | Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const | |
1144 | { | |
1145 | //* Calculate distance from vertex [cm] | |
1146 | ||
1147 | Double_t mP[8], mC[36]; | |
1148 | Transport( GetDStoPoint(vtx), mP, mC ); | |
1149 | Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]}; | |
1150 | return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] ); | |
1151 | } | |
1152 | ||
616ffc76 | 1153 | Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p ) |
f826d409 | 1154 | const |
1155 | { | |
616ffc76 | 1156 | //* Calculate distance to other particle [cm] |
f826d409 | 1157 | |
1158 | Double_t dS, dS1; | |
616ffc76 | 1159 | GetDStoParticle( p, dS, dS1 ); |
f826d409 | 1160 | Double_t mP[8], mC[36], mP1[8], mC1[36]; |
616ffc76 | 1161 | Transport( dS, mP, mC ); |
1162 | p.Transport( dS1, mP1, mC1 ); | |
f826d409 | 1163 | Double_t dx = mP[0]-mP1[0]; |
1164 | Double_t dy = mP[1]-mP1[1]; | |
1165 | Double_t dz = mP[2]-mP1[2]; | |
1166 | return TMath::Sqrt(dx*dx+dy*dy+dz*dz); | |
1167 | } | |
1168 | ||
1169 | Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const | |
1170 | { | |
1171 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1172 | ||
1173 | return GetDeviationFromVertex( Vtx.fP, Vtx.fC ); | |
1174 | } | |
1175 | ||
1176 | ||
1177 | Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const | |
1178 | { | |
1179 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1180 | //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix | |
1181 | ||
1182 | Double_t mP[8]; | |
1183 | Double_t mC[36]; | |
1184 | ||
1185 | Transport( GetDStoPoint(v), mP, mC ); | |
1186 | ||
1187 | Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]}; | |
1188 | ||
1189 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1190 | (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) ); | |
1191 | ||
1192 | ||
1193 | Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS }; | |
1194 | ||
1195 | Double_t mSi[6] = | |
1196 | { mC[0] +h[0]*h[0], | |
1197 | mC[1] +h[1]*h[0], mC[2] +h[1]*h[1], | |
1198 | mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] }; | |
1199 | ||
1200 | if( Cv ){ | |
1201 | mSi[0]+=Cv[0]; | |
1202 | mSi[1]+=Cv[1]; | |
1203 | mSi[2]+=Cv[2]; | |
1204 | mSi[3]+=Cv[3]; | |
1205 | mSi[4]+=Cv[4]; | |
1206 | mSi[5]+=Cv[5]; | |
1207 | } | |
1208 | ||
1209 | Double_t mS[6]; | |
1210 | ||
1211 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1212 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1213 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1214 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1215 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1216 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1217 | ||
1218 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1219 | s = ( s > 1.E-20 ) ?1./s :0; | |
1220 | ||
1221 | return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0] | |
1222 | +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1] | |
1223 | +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2); | |
1224 | } | |
1225 | ||
1226 | ||
616ffc76 | 1227 | Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p ) |
f826d409 | 1228 | const |
1229 | { | |
616ffc76 | 1230 | //* Calculate sqrt(Chi2/ndf) deviation from other particle |
f826d409 | 1231 | |
1232 | Double_t dS, dS1; | |
616ffc76 | 1233 | GetDStoParticle( p, dS, dS1 ); |
f826d409 | 1234 | Double_t mP1[8], mC1[36]; |
616ffc76 | 1235 | p.Transport( dS1, mP1, mC1 ); |
f826d409 | 1236 | |
1237 | Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]}; | |
1238 | ||
1239 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
616ffc76 | 1240 | (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) ); |
f826d409 | 1241 | |
1242 | Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS }; | |
1243 | ||
1244 | mC1[0] +=h[0]*h[0]; | |
1245 | mC1[1] +=h[1]*h[0]; | |
1246 | mC1[2] +=h[1]*h[1]; | |
1247 | mC1[3] +=h[2]*h[0]; | |
1248 | mC1[4] +=h[2]*h[1]; | |
1249 | mC1[5] +=h[2]*h[2]; | |
1250 | ||
1251 | return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.); | |
1252 | } | |
1253 | ||
1254 | ||
1255 | ||
1256 | void AliKFParticleBase::SubtractFromVertex( Double_t v[], Double_t Cv[], | |
1257 | Double_t &vChi2, Int_t vNDF ) const | |
1258 | { | |
1259 | //* Subtract the particle from the vertex | |
1260 | ||
1261 | Double_t fld[3]; | |
1262 | { | |
1263 | GetFieldValue( v, fld ); | |
1264 | const Double_t kCLight = 0.000299792458; | |
1265 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
1266 | } | |
1267 | ||
1268 | Double_t m[8]; | |
1269 | Double_t mCm[36]; | |
1270 | ||
1271 | Transport( GetDStoPoint(v), m, mCm ); | |
1272 | ||
1273 | Double_t d[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] }; | |
1274 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1275 | (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) ); | |
1276 | ||
1277 | Double_t h[6]; | |
1278 | ||
1279 | h[0] = m[3]*sigmaS; | |
1280 | h[1] = m[4]*sigmaS; | |
1281 | h[2] = m[5]*sigmaS; | |
1282 | h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ(); | |
1283 | h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ(); | |
1284 | h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ(); | |
1285 | ||
1286 | //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex | |
1287 | { | |
1288 | Double_t zeta[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] }; | |
1289 | ||
1290 | Double_t mVv[6] = | |
1291 | { mCm[ 0] + h[0]*h[0], | |
1292 | mCm[ 1] + h[1]*h[0], mCm[ 2] + h[1]*h[1], | |
1293 | mCm[ 3] + h[2]*h[0], mCm[ 4] + h[2]*h[1], mCm[ 5] + h[2]*h[2] }; | |
1294 | ||
1295 | Double_t mVvp[9]= | |
1296 | { mCm[ 6] + h[0]*h[3], mCm[ 7] + h[1]*h[3], mCm[ 8] + h[2]*h[3], | |
1297 | mCm[10] + h[0]*h[4], mCm[11] + h[1]*h[4], mCm[12] + h[2]*h[4], | |
1298 | mCm[15] + h[0]*h[5], mCm[16] + h[1]*h[5], mCm[17] + h[2]*h[5] }; | |
1299 | ||
1300 | Double_t mS[6] = | |
1301 | { mVv[2]*mVv[5] - mVv[4]*mVv[4], | |
1302 | mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3], | |
1303 | mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4], | |
1304 | mVv[0]*mVv[2] - mVv[1]*mVv[1] }; | |
1305 | ||
1306 | Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] ); | |
1307 | s = ( s > 1.E-20 ) ?1./s :0; | |
1308 | ||
1309 | mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s; | |
1310 | ||
1311 | Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]), | |
1312 | (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]), | |
1313 | (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) }; | |
1314 | ||
1315 | Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2]; | |
1316 | Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2]; | |
1317 | Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2]; | |
1318 | ||
1319 | h[0] = px*sigmaS; | |
1320 | h[1] = py*sigmaS; | |
1321 | h[2] = pz*sigmaS; | |
1322 | h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ(); | |
1323 | h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ(); | |
1324 | h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ(); | |
1325 | } | |
1326 | ||
1327 | Double_t mV[6]; | |
1328 | ||
1329 | mV[ 0] = mCm[ 0] + h[0]*h[0]; | |
1330 | mV[ 1] = mCm[ 1] + h[1]*h[0]; | |
1331 | mV[ 2] = mCm[ 2] + h[1]*h[1]; | |
1332 | mV[ 3] = mCm[ 3] + h[2]*h[0]; | |
1333 | mV[ 4] = mCm[ 4] + h[2]*h[1]; | |
1334 | mV[ 5] = mCm[ 5] + h[2]*h[2]; | |
1335 | ||
1336 | //* | |
1337 | ||
1338 | Double_t mS[6]; | |
1339 | { | |
1340 | Double_t mSi[6] = { mV[0]-Cv[0], | |
1341 | mV[1]-Cv[1], mV[2]-Cv[2], | |
1342 | mV[3]-Cv[3], mV[4]-Cv[4], mV[5]-Cv[5] }; | |
1343 | ||
1344 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1345 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1346 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1347 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1348 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1349 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1350 | ||
1351 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1352 | s = ( s > 1.E-20 ) ?1./s :0; | |
1353 | mS[0]*=s; | |
1354 | mS[1]*=s; | |
1355 | mS[2]*=s; | |
1356 | mS[3]*=s; | |
1357 | mS[4]*=s; | |
1358 | mS[5]*=s; | |
1359 | } | |
1360 | ||
1361 | //* Residual (measured - estimated) | |
1362 | ||
1363 | Double_t zeta[3] = { m[0]-v[0], m[1]-v[1], m[2]-v[2] }; | |
1364 | ||
1365 | //* mCHt = mCH' - D' | |
1366 | ||
1367 | Double_t mCHt0[3], mCHt1[3], mCHt2[3]; | |
1368 | ||
1369 | mCHt0[0]=Cv[ 0] ; mCHt1[0]=Cv[ 1] ; mCHt2[0]=Cv[ 3] ; | |
1370 | mCHt0[1]=Cv[ 1] ; mCHt1[1]=Cv[ 2] ; mCHt2[1]=Cv[ 4] ; | |
1371 | mCHt0[2]=Cv[ 3] ; mCHt1[2]=Cv[ 4] ; mCHt2[2]=Cv[ 5] ; | |
1372 | ||
1373 | //* Kalman gain K = mCH'*S | |
1374 | ||
1375 | Double_t k0[3], k1[3], k2[3]; | |
1376 | ||
1377 | for(Int_t i=0;i<3;++i){ | |
1378 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
1379 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
1380 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
1381 | } | |
1382 | ||
1383 | //* New estimation of the vertex position r += K*zeta | |
1384 | ||
1385 | for(Int_t i=0;i<3;++i) | |
1386 | v[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; | |
1387 | ||
1388 | //* New covariance matrix C -= K*(mCH')' | |
1389 | ||
1390 | for(Int_t i=0, k=0;i<3;++i){ | |
1391 | for(Int_t j=0;j<=i;++j,++k) | |
1392 | Cv[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j]; | |
1393 | } | |
1394 | ||
1395 | //* Calculate Chi^2 | |
1396 | ||
1397 | vNDF -= 2; | |
1398 | vChi2 -= (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
1399 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
1400 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
1401 | } | |
1402 | ||
1403 | ||
1404 | ||
1405 | void AliKFParticleBase::TransportLine( Double_t dS, | |
1406 | Double_t P[], Double_t C[] ) const | |
1407 | { | |
1408 | //* Transport the particle as a straight line | |
1409 | ||
1410 | P[0] = fP[0] + dS*fP[3]; | |
1411 | P[1] = fP[1] + dS*fP[4]; | |
1412 | P[2] = fP[2] + dS*fP[5]; | |
1413 | P[3] = fP[3]; | |
1414 | P[4] = fP[4]; | |
1415 | P[5] = fP[5]; | |
1416 | P[6] = fP[6]; | |
1417 | P[7] = fP[7]; | |
1418 | ||
1419 | Double_t c6 = fC[ 6] + dS*fC[ 9]; | |
1420 | Double_t c11 = fC[11] + dS*fC[14]; | |
1421 | Double_t c17 = fC[17] + dS*fC[20]; | |
1422 | Double_t sc13 = dS*fC[13]; | |
1423 | Double_t sc18 = dS*fC[18]; | |
1424 | Double_t sc19 = dS*fC[19]; | |
1425 | ||
1426 | C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 ); | |
1427 | C[ 2] = fC[ 2] + dS*( fC[11] + c11 ); | |
1428 | C[ 5] = fC[ 5] + dS*( fC[17] + c17 ); | |
1429 | ||
1430 | C[ 7] = fC[ 7] + sc13; | |
1431 | C[ 8] = fC[ 8] + sc18; | |
1432 | C[ 9] = fC[ 9]; | |
1433 | ||
1434 | C[12] = fC[12] + sc19; | |
1435 | ||
1436 | C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] ); | |
1437 | C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] ); | |
1438 | C[ 4] = fC[ 4] + dS*( fC[16] + C[12] ); | |
1439 | C[ 6] = c6; | |
1440 | ||
1441 | C[10] = fC[10] + sc13; | |
1442 | C[11] = c11; | |
1443 | ||
1444 | C[13] = fC[13]; | |
1445 | C[14] = fC[14]; | |
1446 | C[15] = fC[15] + sc18; | |
1447 | C[16] = fC[16] + sc19; | |
1448 | C[17] = c17; | |
1449 | ||
1450 | C[18] = fC[18]; | |
1451 | C[19] = fC[19]; | |
1452 | C[20] = fC[20]; | |
1453 | C[21] = fC[21] + dS*fC[24]; | |
1454 | C[22] = fC[22] + dS*fC[25]; | |
1455 | C[23] = fC[23] + dS*fC[26]; | |
1456 | ||
1457 | C[24] = fC[24]; | |
1458 | C[25] = fC[25]; | |
1459 | C[26] = fC[26]; | |
1460 | C[27] = fC[27]; | |
1461 | C[28] = fC[28] + dS*fC[31]; | |
1462 | C[29] = fC[29] + dS*fC[32]; | |
1463 | C[30] = fC[30] + dS*fC[33]; | |
1464 | ||
1465 | C[31] = fC[31]; | |
1466 | C[32] = fC[32]; | |
1467 | C[33] = fC[33]; | |
1468 | C[34] = fC[34]; | |
1469 | C[35] = fC[35]; | |
1470 | } | |
1471 | ||
1472 | ||
1473 | void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] ) | |
1474 | { | |
1475 | //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric | |
1476 | ||
1477 | const Int_t kN= 8; | |
1478 | Double_t mA[kN*kN]; | |
1479 | ||
1480 | for( Int_t i=0, ij=0; i<kN; i++ ){ | |
1481 | for( Int_t j=0; j<kN; j++, ++ij ){ | |
1482 | mA[ij] = 0 ; | |
1483 | 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]; | |
1484 | } | |
1485 | } | |
1486 | ||
1487 | for( Int_t i=0; i<kN; i++ ){ | |
1488 | for( Int_t j=0; j<=i; j++ ){ | |
1489 | Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i; | |
1490 | SOut[ij] = 0 ; | |
1491 | for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ]; | |
1492 | } | |
1493 | } | |
1494 | } | |
1495 | ||
1496 | ||
1497 | // 72-charachters line to define the printer border | |
1498 | //3456789012345678901234567890123456789012345678901234567890123456789012 |