]>
Commit | Line | Data |
---|---|---|
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 | } | |
e7b09c95 | 31 | |
32 | void AliKFParticleBase::Initialize( const Double_t Param[], const Double_t Cov[], Int_t Charge, Double_t Mass ) | |
33 | { | |
34 | // Constructor from "cartesian" track, particle mass hypothesis should be provided | |
35 | // | |
36 | // Param[6] = { X, Y, Z, Px, Py, Pz } - position and momentum | |
37 | // Cov [21] = lower-triangular part of the covariance matrix: | |
38 | // | |
39 | // ( 0 . . . . . ) | |
40 | // ( 1 2 . . . . ) | |
41 | // Cov. matrix = ( 3 4 5 . . . ) - numbering of covariance elements in Cov[] | |
42 | // ( 6 7 8 9 . . ) | |
43 | // ( 10 11 12 13 14 . ) | |
44 | // ( 15 16 17 18 19 20 ) | |
45 | ||
46 | ||
47 | for( Int_t i=0; i<6 ; i++ ) fP[i] = Param[i]; | |
48 | for( Int_t i=0; i<21; i++ ) fC[i] = Cov[i]; | |
49 | ||
50 | Double_t energy = TMath::Sqrt( Mass*Mass + fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]); | |
51 | fP[6] = energy; | |
52 | fP[7] = 0; | |
53 | fQ = Charge; | |
54 | fNDF = 0; | |
55 | fChi2 = 0; | |
56 | fAtProductionVertex = 0; | |
57 | fIsLinearized = 0; | |
58 | fSFromDecay = 0; | |
59 | ||
60 | Double_t energyInv = 1./energy; | |
61 | Double_t | |
62 | h0 = fP[3]*energyInv, | |
63 | h1 = fP[4]*energyInv, | |
64 | h2 = fP[5]*energyInv; | |
65 | ||
66 | fC[21] = h0*fC[ 6] + h1*fC[10] + h2*fC[15]; | |
67 | fC[22] = h0*fC[ 7] + h1*fC[11] + h2*fC[16]; | |
68 | fC[23] = h0*fC[ 8] + h1*fC[12] + h2*fC[17]; | |
69 | fC[24] = h0*fC[ 9] + h1*fC[13] + h2*fC[18]; | |
70 | fC[25] = h0*fC[13] + h1*fC[14] + h2*fC[19]; | |
71 | fC[26] = h0*fC[18] + h1*fC[19] + h2*fC[20]; | |
72 | fC[27] = h0*h0*fC[ 9] + h1*h1*fC[14] + h2*h2*fC[20] | |
73 | + 2*(h0*h1*fC[13] + h0*h2*fC[18] + h1*h2*fC[19] ); | |
74 | for( Int_t i=28; i<36; i++ ) fC[i] = 0; | |
75 | fC[35] = 1.; | |
76 | } | |
77 | ||
f826d409 | 78 | void AliKFParticleBase::Initialize() |
79 | { | |
80 | //* Initialise covariance matrix and set current parameters to 0.0 | |
81 | ||
82 | for( Int_t i=0; i<8; i++) fP[i] = 0; | |
83 | for(Int_t i=0;i<36;++i) fC[i]=0.; | |
84 | fC[0] = fC[2] = fC[5] = 100.; | |
85 | fC[35] = 1.; | |
86 | fNDF = -3; | |
87 | fChi2 = 0.; | |
88 | fQ = 0; | |
89 | fSFromDecay = 0; | |
90 | fAtProductionVertex = 0; | |
91 | fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.; | |
92 | fIsLinearized = 0; | |
93 | } | |
94 | ||
95 | void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z ) | |
96 | { | |
97 | //* Set decay vertex parameters for linearisation | |
98 | ||
99 | fVtxGuess[0] = x; | |
100 | fVtxGuess[1] = y; | |
101 | fVtxGuess[2] = z; | |
102 | fIsLinearized = 1; | |
103 | } | |
104 | ||
105 | ||
106 | Int_t AliKFParticleBase::GetMomentum( Double_t &P, Double_t &Error ) const | |
107 | { | |
108 | //* Calculate particle momentum | |
109 | ||
110 | Double_t x = fP[3]; | |
111 | Double_t y = fP[4]; | |
112 | Double_t z = fP[5]; | |
113 | Double_t x2 = x*x; | |
114 | Double_t y2 = y*y; | |
115 | Double_t z2 = z*z; | |
116 | Double_t p2 = x2+y2+z2; | |
117 | P = TMath::Sqrt(p2); | |
118 | Error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ); | |
119 | if( Error>0 && P>1.e-4 ){ | |
120 | Error = TMath::Sqrt(Error)/P; | |
121 | return 0; | |
122 | } | |
123 | return 1; | |
124 | } | |
125 | ||
126 | Int_t AliKFParticleBase::GetMass( Double_t &M, Double_t &Error ) const | |
127 | { | |
128 | //* Calculate particle mass | |
129 | ||
130 | // s = sigma^2 of m2/2 | |
131 | ||
132 | Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20] | |
133 | + fP[6]*fP[6]*fC[27] | |
134 | +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19]) | |
135 | - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) ) | |
136 | ); | |
137 | Double_t m2 = fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5]; | |
616ffc76 | 138 | M = 0; |
139 | if( m2>1.e-20 ){ | |
f826d409 | 140 | M = TMath::Sqrt(m2); |
616ffc76 | 141 | if( s>=0 ){ |
142 | Error = TMath::Sqrt(s/m2); | |
143 | return 0; | |
144 | } | |
f826d409 | 145 | } |
4bbc290d | 146 | Error = 1.e20; |
f826d409 | 147 | return 1; |
148 | } | |
149 | ||
150 | ||
151 | Int_t AliKFParticleBase::GetDecayLength( Double_t &L, Double_t &Error ) const | |
152 | { | |
153 | //* Calculate particle decay length [cm] | |
154 | ||
155 | Double_t x = fP[3]; | |
156 | Double_t y = fP[4]; | |
157 | Double_t z = fP[5]; | |
158 | Double_t t = fP[7]; | |
159 | Double_t x2 = x*x; | |
160 | Double_t y2 = y*y; | |
161 | Double_t z2 = z*z; | |
162 | Double_t p2 = x2+y2+z2; | |
163 | L = t*TMath::Sqrt(p2); | |
164 | if( p2>1.e-4){ | |
165 | Error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20] | |
166 | + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ) | |
167 | + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]); | |
168 | Error = TMath::Sqrt(TMath::Abs(Error)); | |
169 | return 0; | |
170 | } | |
4bbc290d | 171 | Error = 1.e20; |
f826d409 | 172 | return 1; |
173 | } | |
174 | ||
175 | Int_t AliKFParticleBase::GetLifeTime( Double_t &TauC, Double_t &Error ) const | |
176 | { | |
177 | //* Calculate particle decay time [s] | |
178 | ||
179 | Double_t m, dm; | |
180 | GetMass( m, dm ); | |
181 | Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]); | |
182 | TauC = fP[7]*m; | |
183 | Error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm; | |
184 | if( Error > 0 ){ | |
185 | Error = TMath::Sqrt( Error ); | |
186 | return 0; | |
187 | } | |
4bbc290d | 188 | Error = 1.e20; |
f826d409 | 189 | return 1; |
190 | } | |
191 | ||
192 | ||
193 | void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter ) | |
194 | { | |
195 | //* Add daughter via operator+= | |
196 | ||
197 | AddDaughter( Daughter ); | |
198 | } | |
199 | ||
616ffc76 | 200 | |
201 | void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const | |
202 | { | |
e7b09c95 | 203 | //* Get additional covariances V used during measurement |
204 | ||
616ffc76 | 205 | Double_t b[3]; |
206 | GetFieldValue( XYZ, b ); | |
207 | const Double_t kCLight = 0.000299792458; | |
208 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
209 | ||
210 | Transport( GetDStoPoint(XYZ), m, V ); | |
211 | ||
212 | Double_t d[3] = { XYZ[0]-m[0], XYZ[1]-m[1], XYZ[2]-m[2] }; | |
e7b09c95 | 213 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ |
616ffc76 | 214 | (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) ); |
215 | ||
216 | Double_t h[6]; | |
217 | ||
218 | h[0] = m[3]*sigmaS; | |
219 | h[1] = m[4]*sigmaS; | |
220 | h[2] = m[5]*sigmaS; | |
221 | h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); | |
222 | h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); | |
223 | h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); | |
224 | ||
225 | //* Fit of momentum (Px,Py,Pz) to XYZ point | |
226 | if(0){ | |
227 | Double_t mVv[6] = | |
228 | { V[ 0] + h[0]*h[0], | |
229 | V[ 1] + h[0]*h[1], V[ 2] + h[1]*h[1], | |
230 | V[ 3] + h[0]*h[2], V[ 4] + h[1]*h[2], V[ 5] + h[2]*h[2] }; | |
231 | ||
232 | Double_t mVvp[9]= | |
233 | { V[ 6] + h[0]*h[3], V[ 7] + h[1]*h[3], V[ 8] + h[2]*h[3], | |
234 | V[10] + h[0]*h[4], V[11] + h[1]*h[4], V[12] + h[2]*h[4], | |
235 | V[15] + h[0]*h[5], V[16] + h[1]*h[5], V[17] + h[2]*h[5] }; | |
236 | ||
237 | Double_t mS[6] = | |
238 | { mVv[2]*mVv[5] - mVv[4]*mVv[4], | |
239 | mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3], | |
240 | mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4], | |
241 | mVv[0]*mVv[2] - mVv[1]*mVv[1] }; | |
242 | ||
243 | Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] ); | |
244 | s = ( s > 1.E-20 ) ?1./s :0; | |
245 | ||
246 | Double_t mSz[3] = { mS[0]*d[0]+mS[1]*d[1]+mS[3]*d[2], | |
247 | mS[1]*d[0]+mS[2]*d[1]+mS[4]*d[2], | |
248 | mS[3]*d[0]+mS[4]*d[1]+mS[5]*d[2] }; | |
249 | ||
250 | Double_t px = m[3] + s*( mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2] ); | |
251 | Double_t py = m[4] + s*( mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2] ); | |
252 | Double_t pz = m[5] + s*( mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2] ); | |
253 | ||
254 | h[0] = px*sigmaS; | |
255 | h[1] = py*sigmaS; | |
256 | h[2] = pz*sigmaS; | |
257 | h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); | |
258 | h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); | |
259 | h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); | |
260 | } | |
261 | ||
262 | V[ 0]+= h[0]*h[0]; | |
263 | V[ 1]+= h[1]*h[0]; | |
264 | V[ 2]+= h[1]*h[1]; | |
265 | V[ 3]+= h[2]*h[0]; | |
266 | V[ 4]+= h[2]*h[1]; | |
267 | V[ 5]+= h[2]*h[2]; | |
268 | ||
269 | V[ 6]+= h[3]*h[0]; | |
270 | V[ 7]+= h[3]*h[1]; | |
271 | V[ 8]+= h[3]*h[2]; | |
272 | V[ 9]+= h[3]*h[3]; | |
273 | ||
274 | V[10]+= h[4]*h[0]; | |
275 | V[11]+= h[4]*h[1]; | |
276 | V[12]+= h[4]*h[2]; | |
277 | V[13]+= h[4]*h[3]; | |
278 | V[14]+= h[4]*h[4]; | |
279 | ||
280 | V[15]+= h[5]*h[0]; | |
281 | V[16]+= h[5]*h[1]; | |
282 | V[17]+= h[5]*h[2]; | |
283 | V[18]+= h[5]*h[3]; | |
284 | V[19]+= h[5]*h[4]; | |
285 | V[20]+= h[5]*h[5]; | |
286 | } | |
287 | ||
616ffc76 | 288 | |
f826d409 | 289 | void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter ) |
290 | { | |
291 | //* Add daughter | |
292 | ||
616ffc76 | 293 | if( fNDF<-1 ){ // first daughter -> just copy |
294 | fNDF = -1; | |
295 | fQ = Daughter.GetQ(); | |
296 | for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i]; | |
297 | for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i]; | |
298 | fSFromDecay = 0; | |
299 | return; | |
300 | } | |
301 | ||
f826d409 | 302 | TransportToDecayVertex(); |
303 | ||
304 | Double_t b[3]; | |
305 | Int_t maxIter = 1; | |
306 | ||
307 | if( !fIsLinearized ){ | |
308 | if( fNDF==-1 ){ | |
309 | Double_t ds, ds1; | |
616ffc76 | 310 | GetDStoParticle(Daughter, ds, ds1); |
f826d409 | 311 | TransportToDS( ds ); |
616ffc76 | 312 | Double_t m[8]; |
313 | Double_t mCd[36]; | |
314 | Daughter.Transport( ds1, m, mCd ); | |
315 | fVtxGuess[0] = .5*( fP[0] + m[0] ); | |
316 | fVtxGuess[1] = .5*( fP[1] + m[1] ); | |
317 | fVtxGuess[2] = .5*( fP[2] + m[2] ); | |
318 | } else { | |
319 | fVtxGuess[0] = fP[0]; | |
320 | fVtxGuess[1] = fP[1]; | |
321 | fVtxGuess[2] = fP[2]; | |
f826d409 | 322 | } |
f826d409 | 323 | maxIter = 3; |
324 | } | |
325 | ||
326 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
327 | ||
328 | { | |
329 | GetFieldValue( fVtxGuess, b ); | |
330 | const Double_t kCLight = 0.000299792458; | |
331 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
332 | } | |
f826d409 | 333 | |
616ffc76 | 334 | Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36]; |
335 | if( fNDF==-1 ){ | |
336 | GetMeasurement( fVtxGuess, tmpP, tmpC ); | |
337 | ffP = tmpP; | |
338 | ffC = tmpC; | |
f826d409 | 339 | } |
340 | ||
e7b09c95 | 341 | Double_t m[8], mV[36]; |
342 | if( Daughter.fC[35]>0 ){ | |
343 | Daughter.GetMeasurement( fVtxGuess, m, mV ); | |
344 | } else { | |
345 | for( Int_t i=0; i<8; i++ ) m[i] = Daughter.fP[i]; | |
346 | for( Int_t i=0; i<36; i++ ) mV[i] = Daughter.fC[i]; | |
347 | } | |
348 | ||
f826d409 | 349 | //* |
350 | ||
351 | Double_t mS[6]; | |
352 | { | |
616ffc76 | 353 | Double_t mSi[6] = { ffC[0]+mV[0], |
354 | ffC[1]+mV[1], ffC[2]+mV[2], | |
355 | ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] }; | |
f826d409 | 356 | |
357 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
358 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
359 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
360 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
361 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
362 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
363 | ||
364 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
365 | s = ( s > 1.E-20 ) ?1./s :0; | |
366 | mS[0]*=s; | |
367 | mS[1]*=s; | |
368 | mS[2]*=s; | |
369 | mS[3]*=s; | |
370 | mS[4]*=s; | |
371 | mS[5]*=s; | |
372 | } | |
373 | ||
374 | //* Residual (measured - estimated) | |
375 | ||
616ffc76 | 376 | Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] }; |
f826d409 | 377 | |
378 | //* CHt = CH' - D' | |
379 | ||
380 | Double_t mCHt0[7], mCHt1[7], mCHt2[7]; | |
381 | ||
616ffc76 | 382 | mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ; |
383 | mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ; | |
384 | mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ; | |
385 | mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8]; | |
386 | mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12]; | |
387 | mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17]; | |
388 | mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23]; | |
f826d409 | 389 | |
390 | //* Kalman gain K = mCH'*S | |
391 | ||
392 | Double_t k0[7], k1[7], k2[7]; | |
393 | ||
394 | for(Int_t i=0;i<7;++i){ | |
395 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
396 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
397 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
398 | } | |
399 | ||
4bbc290d | 400 | //* New estimation of the vertex position |
f826d409 | 401 | |
402 | if( iter<maxIter-1 ){ | |
403 | for(Int_t i=0; i<3; ++i) | |
616ffc76 | 404 | fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2]; |
f826d409 | 405 | continue; |
406 | } | |
407 | ||
408 | // last itearation -> update the particle | |
409 | ||
410 | //* Add the daughter momentum to the particle momentum | |
411 | ||
616ffc76 | 412 | ffP[ 3] += m[ 3]; |
413 | ffP[ 4] += m[ 4]; | |
414 | ffP[ 5] += m[ 5]; | |
415 | ffP[ 6] += m[ 6]; | |
f826d409 | 416 | |
616ffc76 | 417 | ffC[ 9] += mV[ 9]; |
418 | ffC[13] += mV[13]; | |
419 | ffC[14] += mV[14]; | |
420 | ffC[18] += mV[18]; | |
421 | ffC[19] += mV[19]; | |
422 | ffC[20] += mV[20]; | |
423 | ffC[24] += mV[24]; | |
424 | ffC[25] += mV[25]; | |
425 | ffC[26] += mV[26]; | |
426 | ffC[27] += mV[27]; | |
f826d409 | 427 | |
428 | //* New estimation of the vertex position r += K*zeta | |
429 | ||
430 | for(Int_t i=0;i<7;++i) | |
616ffc76 | 431 | fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; |
f826d409 | 432 | |
433 | //* New covariance matrix C -= K*(mCH')' | |
4bbc290d | 434 | |
f826d409 | 435 | for(Int_t i=0, k=0;i<7;++i){ |
436 | for(Int_t j=0;j<=i;++j,++k) | |
616ffc76 | 437 | fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] ); |
f826d409 | 438 | } |
439 | ||
440 | //* Calculate Chi^2 | |
441 | ||
442 | fNDF += 2; | |
443 | fQ += Daughter.GetQ(); | |
444 | fSFromDecay = 0; | |
445 | fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
446 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
447 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
448 | } | |
449 | } | |
450 | ||
f826d409 | 451 | void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx ) |
452 | { | |
453 | //* Set production vertex for the particle | |
454 | ||
455 | const Double_t *m = Vtx.fP, *mV = Vtx.fC; | |
456 | ||
e7b09c95 | 457 | Bool_t noS = ( fC[35]<=0 ); // no decay length allowed |
458 | ||
459 | if( noS ){ | |
460 | TransportToDecayVertex(); | |
461 | fP[7] = 0; | |
462 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0; | |
463 | } else { | |
464 | TransportToDS( GetDStoPoint( m ) ); | |
465 | fP[7] = -fSFromDecay; | |
466 | Convert(1); | |
467 | } | |
468 | ||
f826d409 | 469 | |
470 | Double_t mAi[6]; | |
471 | mAi[0] = fC[4]*fC[4] - fC[2]*fC[5]; | |
472 | mAi[1] = fC[1]*fC[5] - fC[3]*fC[4]; | |
473 | mAi[3] = fC[2]*fC[3] - fC[1]*fC[4]; | |
474 | Double_t det = 1./(fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]); | |
475 | mAi[0] *= det; | |
476 | mAi[1] *= det; | |
477 | mAi[3] *= det; | |
478 | mAi[2] = ( fC[3]*fC[3] - fC[0]*fC[5] )*det; | |
479 | mAi[4] = ( fC[0]*fC[4] - fC[1]*fC[3] )*det; | |
480 | mAi[5] = ( fC[1]*fC[1] - fC[0]*fC[2] )*det; | |
481 | ||
482 | Double_t mB[5][3]; | |
483 | ||
484 | mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3]; | |
485 | mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4]; | |
486 | mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5]; | |
487 | ||
488 | mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3]; | |
489 | mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4]; | |
490 | mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5]; | |
491 | ||
492 | mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3]; | |
493 | mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4]; | |
494 | mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5]; | |
495 | ||
496 | mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3]; | |
497 | mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4]; | |
498 | mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5]; | |
499 | ||
500 | mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3]; | |
501 | mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4]; | |
502 | mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5]; | |
503 | ||
504 | Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] }; | |
505 | ||
506 | { | |
507 | Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2], | |
508 | fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] }; | |
509 | Double_t mAVi[6]; | |
510 | mAVi[0] = mAV[4]*mAV[4] - mAV[2]*mAV[5]; | |
511 | mAVi[1] = mAV[1]*mAV[5] - mAV[3]*mAV[4]; | |
512 | mAVi[2] = mAV[3]*mAV[3] - mAV[0]*mAV[5] ; | |
513 | mAVi[3] = mAV[2]*mAV[3] - mAV[1]*mAV[4]; | |
514 | mAVi[4] = mAV[0]*mAV[4] - mAV[1]*mAV[3] ; | |
515 | mAVi[5] = mAV[1]*mAV[1] - mAV[0]*mAV[2] ; | |
516 | ||
e7b09c95 | 517 | det = ( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] ); |
518 | if( det>1.e-8 ) det = 1./det; | |
f826d409 | 519 | |
520 | fNDF += 2; | |
521 | fChi2 += | |
522 | ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0] | |
523 | +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1] | |
524 | +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )*det; | |
525 | } | |
526 | ||
527 | fP[0] = m[0]; | |
528 | fP[1] = m[1]; | |
529 | fP[2] = m[2]; | |
530 | fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; | |
531 | fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; | |
532 | fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; | |
533 | fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2]; | |
534 | fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2]; | |
535 | ||
536 | Double_t d0, d1, d2; | |
537 | ||
538 | fC[0] = mV[0]; | |
539 | fC[1] = mV[1]; | |
540 | fC[2] = mV[2]; | |
541 | fC[3] = mV[3]; | |
542 | fC[4] = mV[4]; | |
543 | fC[5] = mV[5]; | |
544 | ||
545 | d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6]; | |
546 | d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7]; | |
547 | d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8]; | |
548 | ||
549 | fC[ 6]+= d0; | |
550 | fC[ 7]+= d1; | |
551 | fC[ 8]+= d2; | |
552 | fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
553 | ||
554 | d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10]; | |
555 | d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11]; | |
556 | d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12]; | |
557 | ||
558 | fC[10]+= d0; | |
559 | fC[11]+= d1; | |
560 | fC[12]+= d2; | |
561 | fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
562 | fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
563 | ||
564 | d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15]; | |
565 | d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16]; | |
566 | d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17]; | |
567 | ||
568 | fC[15]+= d0; | |
569 | fC[16]+= d1; | |
570 | fC[17]+= d2; | |
571 | fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
572 | fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
573 | fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
574 | ||
575 | d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21]; | |
576 | d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22]; | |
577 | d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23]; | |
578 | ||
579 | fC[21]+= d0; | |
580 | fC[22]+= d1; | |
581 | fC[23]+= d2; | |
582 | fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
583 | fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
584 | fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
585 | fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
586 | ||
587 | d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28]; | |
588 | d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29]; | |
589 | d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30]; | |
590 | ||
591 | fC[28]+= d0; | |
592 | fC[29]+= d1; | |
593 | fC[30]+= d2; | |
594 | fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
595 | fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
596 | fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
597 | fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
598 | fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2]; | |
599 | ||
e7b09c95 | 600 | if( noS ){ |
601 | fP[7] = 0; | |
602 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0; | |
603 | } else { | |
604 | TransportToDS( fP[7] ); | |
605 | Convert(0); | |
606 | } | |
607 | ||
f826d409 | 608 | fSFromDecay = 0; |
f826d409 | 609 | } |
610 | ||
611 | ||
612 | ||
613 | ||
e7b09c95 | 614 | void AliKFParticleBase::SetMassConstraint( Double_t Mass, Double_t SigmaMass ) |
f826d409 | 615 | { |
616 | //* Set hard mass constraint | |
617 | ||
618 | Double_t mH[8]; | |
619 | mH[0] = mH[1] = mH[2] = 0.; | |
620 | mH[3] = -2*fP[3]; | |
621 | mH[4] = -2*fP[4]; | |
622 | mH[5] = -2*fP[5]; | |
623 | mH[6] = 2*fP[6]; | |
624 | mH[7] = 0; | |
625 | Double_t m2 = ( fP[6]*fP[6] | |
626 | - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5] ); | |
627 | ||
628 | Double_t zeta = Mass*Mass - m2; | |
629 | for(Int_t i=0;i<8;++i) zeta -= mH[i]*(fP[i]-fP[i]); | |
630 | ||
e7b09c95 | 631 | Double_t s = 4*Mass*Mass*SigmaMass*SigmaMass; |
f826d409 | 632 | Double_t mCHt[8]; |
633 | for (Int_t i=0;i<8;++i ){ | |
634 | mCHt[i] = 0.0; | |
635 | for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j]; | |
636 | s += mH[i]*mCHt[i]; | |
637 | } | |
638 | ||
639 | if( s<1.e-20 ) return; | |
640 | s = 1./s; | |
641 | fChi2 += zeta*zeta*s; | |
642 | fNDF += 1; | |
643 | for( Int_t i=0, ii=0; i<8; ++i ){ | |
644 | Double_t ki = mCHt[i]*s; | |
645 | fP[i]+= ki*zeta; | |
646 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j]; | |
647 | } | |
648 | } | |
649 | ||
650 | ||
e7b09c95 | 651 | void AliKFParticleBase::SetNoDecayLength() |
652 | { | |
653 | //* Set no decay length for resonances | |
654 | ||
655 | TransportToDecayVertex(); | |
656 | ||
657 | Double_t h[8]; | |
658 | h[0] = h[1] = h[2] = h[3] = h[4] = h[5] = h[6] = 0; | |
659 | h[7] = 1; | |
660 | ||
661 | Double_t zeta = 0 - fP[7]; | |
662 | for(Int_t i=0;i<8;++i) zeta -= h[i]*(fP[i]-fP[i]); | |
663 | ||
664 | Double_t s = fC[35]; | |
665 | if( s>1.e-20 ){ | |
666 | s = 1./s; | |
667 | fChi2 += zeta*zeta*s; | |
668 | fNDF += 1; | |
669 | for( Int_t i=0, ii=0; i<7; ++i ){ | |
670 | Double_t ki = fC[28+i]*s; | |
671 | fP[i]+= ki*zeta; | |
672 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*fC[28+j]; | |
673 | } | |
674 | } | |
675 | fP[7] = 0; | |
676 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0; | |
677 | } | |
678 | ||
679 | ||
f826d409 | 680 | void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters, |
4bbc290d | 681 | const AliKFParticleBase *Parent, Double_t Mass ) |
f826d409 | 682 | { |
683 | //* Full reconstruction in one go | |
684 | ||
685 | Int_t maxIter = 1; | |
686 | bool wasLinearized = fIsLinearized; | |
687 | if( !fIsLinearized ){ | |
616ffc76 | 688 | //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!! |
689 | fVtxGuess[0] = GetX(); | |
690 | fVtxGuess[1] = GetY(); | |
691 | fVtxGuess[2] = GetZ(); | |
f826d409 | 692 | fIsLinearized = 1; |
693 | maxIter = 3; | |
694 | } | |
695 | ||
696 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
f826d409 | 697 | fAtProductionVertex = 0; |
698 | fSFromDecay = 0; | |
699 | fP[0] = fVtxGuess[0]; | |
700 | fP[1] = fVtxGuess[1]; | |
701 | fP[2] = fVtxGuess[2]; | |
702 | fP[3] = 0; | |
703 | fP[4] = 0; | |
704 | fP[5] = 0; | |
705 | fP[6] = 0; | |
706 | fP[7] = 0; | |
707 | ||
708 | for(Int_t i=0;i<36;++i) fC[i]=0.; | |
709 | ||
710 | fC[0] = fC[2] = fC[5] = 100.; | |
711 | fC[35] = 1.; | |
712 | ||
713 | fNDF = -3; | |
714 | fChi2 = 0.; | |
715 | fQ = 0; | |
716 | ||
4bbc290d | 717 | for( Int_t itr =0; itr<NDaughters; itr++ ){ |
718 | AddDaughter( *vDaughters[itr] ); | |
719 | } | |
f826d409 | 720 | if( iter<maxIter-1){ |
721 | for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i]; | |
722 | } | |
723 | } | |
724 | fIsLinearized = wasLinearized; | |
725 | ||
726 | if( Mass>=0 ) SetMassConstraint( Mass ); | |
727 | if( Parent ) SetProductionVertex( *Parent ); | |
728 | } | |
729 | ||
730 | ||
731 | void AliKFParticleBase::Convert( bool ToProduction ) | |
732 | { | |
733 | //* Tricky function - convert the particle error along its trajectory to | |
734 | //* the value which corresponds to its production/decay vertex | |
735 | //* It is done by combination of the error of decay length with the position errors | |
736 | ||
737 | Double_t fld[3]; | |
738 | { | |
739 | GetFieldValue( fP, fld ); | |
740 | const Double_t kCLight = fQ*0.000299792458; | |
741 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
742 | } | |
743 | ||
744 | Double_t h[6]; | |
745 | ||
746 | h[0] = fP[3]; | |
747 | h[1] = fP[4]; | |
748 | h[2] = fP[5]; | |
749 | if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; } | |
750 | h[3] = h[1]*fld[2]-h[2]*fld[1]; | |
751 | h[4] = h[2]*fld[0]-h[0]*fld[2]; | |
752 | h[5] = h[0]*fld[1]-h[1]*fld[0]; | |
753 | ||
754 | Double_t c; | |
755 | ||
756 | c = fC[28]+h[0]*fC[35]; | |
757 | fC[ 0]+= h[0]*(c+fC[28]); | |
758 | fC[28] = c; | |
759 | ||
760 | fC[ 1]+= h[1]*fC[28] + h[0]*fC[29]; | |
761 | c = fC[29]+h[1]*fC[35]; | |
762 | fC[ 2]+= h[1]*(c+fC[29]); | |
763 | fC[29] = c; | |
764 | ||
765 | fC[ 3]+= h[2]*fC[28] + h[0]*fC[30]; | |
766 | fC[ 4]+= h[2]*fC[29] + h[1]*fC[30]; | |
767 | c = fC[30]+h[2]*fC[35]; | |
768 | fC[ 5]+= h[2]*(c+fC[30]); | |
769 | fC[30] = c; | |
770 | ||
771 | fC[ 6]+= h[3]*fC[28] + h[0]*fC[31]; | |
772 | fC[ 7]+= h[3]*fC[29] + h[1]*fC[31]; | |
773 | fC[ 8]+= h[3]*fC[30] + h[2]*fC[31]; | |
774 | c = fC[31]+h[3]*fC[35]; | |
775 | fC[ 9]+= h[3]*(c+fC[31]); | |
776 | fC[31] = c; | |
777 | ||
778 | fC[10]+= h[4]*fC[28] + h[0]*fC[32]; | |
779 | fC[11]+= h[4]*fC[29] + h[1]*fC[32]; | |
780 | fC[12]+= h[4]*fC[30] + h[2]*fC[32]; | |
781 | fC[13]+= h[4]*fC[31] + h[3]*fC[32]; | |
782 | c = fC[32]+h[4]*fC[35]; | |
783 | fC[14]+= h[4]*(c+fC[32]); | |
784 | fC[32] = c; | |
785 | ||
786 | fC[15]+= h[5]*fC[28] + h[0]*fC[33]; | |
787 | fC[16]+= h[5]*fC[29] + h[1]*fC[33]; | |
788 | fC[17]+= h[5]*fC[30] + h[2]*fC[33]; | |
789 | fC[18]+= h[5]*fC[31] + h[3]*fC[33]; | |
790 | fC[19]+= h[5]*fC[32] + h[4]*fC[33]; | |
791 | c = fC[33]+h[5]*fC[35]; | |
792 | fC[20]+= h[5]*(c+fC[33]); | |
793 | fC[33] = c; | |
794 | ||
795 | fC[21]+= h[0]*fC[34]; | |
796 | fC[22]+= h[1]*fC[34]; | |
797 | fC[23]+= h[2]*fC[34]; | |
798 | fC[24]+= h[3]*fC[34]; | |
799 | fC[25]+= h[4]*fC[34]; | |
800 | fC[26]+= h[5]*fC[34]; | |
801 | } | |
802 | ||
803 | ||
804 | void AliKFParticleBase::TransportToDecayVertex() | |
805 | { | |
806 | //* Transport the particle to its decay vertex | |
807 | ||
808 | if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay ); | |
809 | if( fAtProductionVertex ) Convert(0); | |
810 | fAtProductionVertex = 0; | |
811 | } | |
812 | ||
813 | void AliKFParticleBase::TransportToProductionVertex() | |
814 | { | |
815 | //* Transport the particle to its production vertex | |
616ffc76 | 816 | |
f826d409 | 817 | if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] ); |
818 | if( !fAtProductionVertex ) Convert( 1 ); | |
819 | fAtProductionVertex = 1; | |
820 | } | |
821 | ||
822 | ||
823 | void AliKFParticleBase::TransportToDS( Double_t dS ) | |
824 | { | |
825 | //* Transport the particle on dS parameter (SignedPath/Momentum) | |
616ffc76 | 826 | |
f826d409 | 827 | Transport( dS, fP, fC ); |
828 | fSFromDecay+= dS; | |
829 | } | |
830 | ||
831 | ||
832 | Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const | |
833 | { | |
834 | //* Get dS to a certain space point without field | |
835 | ||
836 | Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; | |
837 | if( p2<1.e-4 ) p2 = 1; | |
838 | return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2; | |
839 | } | |
840 | ||
841 | ||
842 | Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] ) | |
843 | const | |
844 | { | |
616ffc76 | 845 | |
f826d409 | 846 | //* Get dS to a certain space point for Bz field |
f826d409 | 847 | const Double_t kCLight = 0.000299792458; |
848 | Double_t bq = B*fQ*kCLight; | |
849 | Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4]; | |
850 | if( pt2<1.e-4 ) return 0; | |
851 | Double_t dx = xyz[0] - fP[0]; | |
852 | Double_t dy = xyz[1] - fP[1]; | |
853 | Double_t a = dx*fP[3]+dy*fP[4]; | |
616ffc76 | 854 | if( TMath::Abs(bq)<1.e-8 ) return a/pt2; |
f826d409 | 855 | return TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq; |
856 | } | |
857 | ||
858 | ||
859 | void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p, | |
616ffc76 | 860 | Double_t &DS, Double_t &DS1 ) |
f826d409 | 861 | const |
862 | { | |
863 | //* Get dS to another particle for Bz field | |
f826d409 | 864 | Double_t px = fP[3]; |
865 | Double_t py = fP[4]; | |
866 | Double_t pz = fP[5]; | |
867 | ||
868 | Double_t px1 = p.fP[3]; | |
869 | Double_t py1 = p.fP[4]; | |
870 | Double_t pz1 = p.fP[5]; | |
871 | ||
872 | const Double_t kCLight = 0.000299792458; | |
873 | ||
874 | Double_t bq = B*fQ*kCLight; | |
875 | Double_t bq1 = B*p.fQ*kCLight; | |
f826d409 | 876 | Double_t s=0, ds=0, s1=0, ds1=0; |
877 | ||
878 | if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){ | |
4bbc290d | 879 | |
f826d409 | 880 | Double_t dx = (p.fP[0] - fP[0]); |
881 | Double_t dy = (p.fP[1] - fP[1]); | |
882 | Double_t d2 = (dx*dx+dy*dy); | |
883 | ||
884 | Double_t p2 = (px *px + py *py); | |
885 | Double_t p21 = (px1*px1 + py1*py1); | |
886 | ||
887 | Double_t a = (px*py1 - py*px1); | |
888 | Double_t b = (px*px1 + py*py1); | |
889 | ||
890 | Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ; | |
891 | Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ; | |
892 | Double_t l2 = ldx*ldx + ldy*ldy; | |
893 | ||
894 | Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b; | |
895 | Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b; | |
896 | ||
897 | Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ; | |
898 | Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ; | |
899 | ||
900 | Double_t sa = 4*l2*p2 - ca*ca; | |
901 | Double_t sa1 = 4*l2*p21 - ca1*ca1; | |
e7b09c95 | 902 | |
f826d409 | 903 | if(sa<0) sa=0; |
904 | if(sa1<0)sa1=0; | |
905 | ||
906 | if( TMath::Abs(bq)>1.e-8){ | |
907 | s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq; | |
908 | ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq; | |
909 | } else { | |
910 | s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2; | |
911 | ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2; | |
912 | if( ds<0 ) ds = 0; | |
913 | ds = TMath::Sqrt(ds); | |
914 | } | |
915 | ||
916 | if( TMath::Abs(bq1)>1.e-8){ | |
917 | s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1; | |
918 | ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1; | |
919 | } else { | |
920 | s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21; | |
921 | ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21; | |
922 | if( ds1<0 ) ds1 = 0; | |
923 | ds1 = TMath::Sqrt(ds1); | |
924 | } | |
925 | } | |
926 | ||
f826d409 | 927 | Double_t ss[2], ss1[2], g[2][5],g1[2][5]; |
928 | ||
929 | ss[0] = s + ds; | |
930 | ss[1] = s - ds; | |
931 | ss1[0] = s1 + ds1; | |
932 | ss1[1] = s1 - ds1; | |
933 | for( Int_t i=0; i<2; i++){ | |
934 | Double_t bs = bq*ss[i]; | |
935 | Double_t c = TMath::Cos(bs), s = TMath::Sin(bs); | |
936 | Double_t cB,sB; | |
937 | if( TMath::Abs(bq)>1.e-8){ | |
938 | cB= (1-c)/bq; | |
939 | sB= s/bq; | |
940 | }else{ | |
941 | sB = (1. - bs*bs/6.)*ss[i]; | |
942 | cB = .5*sB*bs; | |
943 | } | |
944 | g[i][0] = fP[0] + sB*px + cB*py; | |
945 | g[i][1] = fP[1] - cB*px + sB*py; | |
946 | g[i][2] = fP[2] + ss[i]*pz; | |
947 | g[i][3] = + c*px + s*py; | |
948 | g[i][4] = - s*px + c*py; | |
949 | ||
950 | bs = bq1*ss1[i]; | |
951 | c = TMath::Cos(bs); s = TMath::Sin(bs); | |
952 | if( TMath::Abs(bq1)>1.e-8){ | |
953 | cB= (1-c)/bq1; | |
954 | sB= s/bq1; | |
955 | }else{ | |
956 | sB = (1. - bs*bs/6.)*ss1[i]; | |
957 | cB = .5*sB*bs; | |
958 | } | |
959 | ||
e7b09c95 | 960 | g1[i][0] = p.fP[0] + sB*px1 + cB*py1; |
961 | g1[i][1] = p.fP[1] - cB*px1 + sB*py1; | |
962 | g1[i][2] = p.fP[2] + ss[i]*pz1; | |
963 | g1[i][3] = + c*px1 + s*py1; | |
964 | g1[i][4] = - s*px1 + c*py1; | |
f826d409 | 965 | } |
966 | ||
967 | Int_t i=0, i1=0; | |
968 | ||
969 | Double_t dMin = 1.e10; | |
970 | for( Int_t j=0; j<2; j++){ | |
971 | for( Int_t j1=0; j1<2; j1++){ | |
972 | Double_t xx = g[j][0]-g1[j1][0]; | |
973 | Double_t yy = g[j][1]-g1[j1][1]; | |
974 | Double_t zz = g[j][2]-g1[j1][2]; | |
975 | Double_t d = xx*xx + yy*yy + zz*zz; | |
976 | if( d<dMin ){ | |
977 | dMin = d; | |
978 | i = j; | |
979 | i1 = j1; | |
980 | } | |
981 | } | |
982 | } | |
983 | ||
984 | DS = ss[i]; | |
985 | DS1 = ss1[i1]; | |
986 | ||
987 | Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4]; | |
e7b09c95 | 988 | Double_t x1=g1[i1][0], y1= g1[i1][1], z1= g1[i1][2], ppx1= g1[i1][3], ppy1= g1[i1][4]; |
f826d409 | 989 | Double_t dx = x1-x; |
990 | Double_t dy = y1-y; | |
991 | Double_t dz = z1-z; | |
992 | Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1; | |
993 | Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1; | |
994 | Double_t c = dx*ppx + dy*ppy + dz*pz ; | |
995 | Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz; | |
996 | Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1; | |
997 | Double_t det = pp2*pp21 - a*a; | |
998 | if( TMath::Abs(det)>1.e-8 ){ | |
999 | DS+=(a*b-pp21*c)/det; | |
1000 | DS1+=(a*c-pp2*b)/det; | |
1001 | } | |
1002 | } | |
1003 | ||
1004 | ||
1005 | ||
1006 | void AliKFParticleBase::TransportCBM( Double_t dS, | |
1007 | Double_t P[], Double_t C[] ) const | |
1008 | { | |
1009 | //* Transport the particle on dS, output to P[],C[], for CBM field | |
1010 | ||
1011 | if( fQ==0 ){ | |
1012 | TransportLine( dS, P, C ); | |
1013 | return; | |
1014 | } | |
1015 | ||
1016 | const Double_t kCLight = 0.000299792458; | |
1017 | ||
1018 | Double_t c = fQ*kCLight; | |
1019 | ||
1020 | // construct coefficients | |
1021 | ||
1022 | Double_t | |
1023 | px = fP[3], | |
1024 | py = fP[4], | |
1025 | pz = fP[5]; | |
1026 | ||
1027 | 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; | |
1028 | ||
1029 | { // get field integrals | |
1030 | ||
1031 | Double_t fld[3][3]; | |
1032 | Double_t p0[3], p1[3], p2[3]; | |
1033 | ||
1034 | // line track approximation | |
1035 | ||
1036 | p0[0] = fP[0]; | |
1037 | p0[1] = fP[1]; | |
1038 | p0[2] = fP[2]; | |
1039 | ||
1040 | p2[0] = fP[0] + px*dS; | |
1041 | p2[1] = fP[1] + py*dS; | |
1042 | p2[2] = fP[2] + pz*dS; | |
1043 | ||
1044 | p1[0] = 0.5*(p0[0]+p2[0]); | |
1045 | p1[1] = 0.5*(p0[1]+p2[1]); | |
1046 | p1[2] = 0.5*(p0[2]+p2[2]); | |
1047 | ||
1048 | // first order track approximation | |
1049 | { | |
1050 | GetFieldValue( p0, fld[0] ); | |
1051 | GetFieldValue( p1, fld[1] ); | |
1052 | GetFieldValue( p2, fld[2] ); | |
1053 | ||
1054 | Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.; | |
1055 | Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.; | |
1056 | ||
1057 | p1[0] -= ssy1*pz; | |
1058 | p1[2] += ssy1*px; | |
1059 | p2[0] -= ssy2*pz; | |
1060 | p2[2] += ssy2*px; | |
1061 | } | |
1062 | ||
1063 | GetFieldValue( p0, fld[0] ); | |
1064 | GetFieldValue( p1, fld[1] ); | |
1065 | GetFieldValue( p2, fld[2] ); | |
1066 | ||
1067 | sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.; | |
1068 | sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.; | |
1069 | sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.; | |
1070 | ||
1071 | ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.; | |
1072 | ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.; | |
1073 | ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.; | |
1074 | ||
1075 | Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360. | |
1076 | Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520. | |
1077 | for(Int_t n=0; n<3; n++) | |
1078 | for(Int_t m=0; m<3; m++) | |
1079 | { | |
1080 | syz += c2[n][m]*fld[n][1]*fld[m][2]; | |
1081 | ssyz += cc2[n][m]*fld[n][1]*fld[m][2]; | |
1082 | } | |
1083 | ||
1084 | syz *= c*c*dS*dS/360.; | |
1085 | ssyz *= c*c*dS*dS*dS/2520.; | |
1086 | ||
1087 | syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS; | |
1088 | syyy = syy*syy*syy / 1296; | |
1089 | syy = syy*syy/72; | |
1090 | ||
1091 | ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+ | |
1092 | fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+ | |
1093 | fld[2][1]*( 3*fld[2][1] ) | |
1094 | )*dS*dS*dS*c*c/2520.; | |
1095 | ssyyy = | |
1096 | ( | |
1097 | fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+ | |
1098 | fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+ | |
1099 | fld[2][1]*( 19*fld[2][1] ) )+ | |
1100 | fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+ | |
1101 | fld[2][1]*( 62*fld[2][1] ) )+ | |
1102 | fld[2][1]*fld[2][1] *( 3*fld[2][1] ) | |
1103 | )*dS*dS*dS*dS*c*c*c/90720.; | |
1104 | ||
1105 | } | |
1106 | ||
1107 | Double_t mJ[8][8]; | |
1108 | for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0; | |
1109 | ||
1110 | 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; | |
1111 | 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; | |
1112 | 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; | |
1113 | ||
1114 | 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; | |
1115 | 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; | |
1116 | 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; | |
1117 | mJ[6][6] = mJ[7][7] = 1; | |
1118 | ||
1119 | P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz; | |
1120 | P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz; | |
1121 | P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz; | |
1122 | P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz; | |
1123 | P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz; | |
1124 | P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz; | |
1125 | P[6] = fP[6]; | |
1126 | P[7] = fP[7]; | |
1127 | ||
1128 | MultQSQt( mJ[0], fC, C); | |
1129 | ||
1130 | } | |
1131 | ||
1132 | ||
1133 | void AliKFParticleBase::TransportBz( Double_t B, Double_t S, | |
616ffc76 | 1134 | Double_t P[], Double_t C[] ) const |
f826d409 | 1135 | { |
1136 | //* Transport the particle on dS, output to P[],C[], for Bz field | |
616ffc76 | 1137 | |
f826d409 | 1138 | const Double_t kCLight = 0.000299792458; |
1139 | B = B*fQ*kCLight; | |
1140 | Double_t bs= B*S; | |
1141 | Double_t s = TMath::Sin(bs), c = TMath::Cos(bs); | |
1142 | Double_t sB, cB; | |
616ffc76 | 1143 | if( TMath::Abs(bs)>1.e-10){ |
f826d409 | 1144 | sB= s/B; |
1145 | cB= (1-c)/B; | |
1146 | }else{ | |
1147 | sB = (1. - bs*bs/6.)*S; | |
1148 | cB = .5*sB*bs; | |
1149 | } | |
1150 | ||
1151 | Double_t px = fP[3]; | |
1152 | Double_t py = fP[4]; | |
1153 | Double_t pz = fP[5]; | |
1154 | ||
1155 | P[0] = fP[0] + sB*px + cB*py; | |
1156 | P[1] = fP[1] - cB*px + sB*py; | |
1157 | P[2] = fP[2] + S*pz; | |
1158 | P[3] = c*px + s*py; | |
1159 | P[4] = -s*px + c*py; | |
1160 | P[5] = fP[5]; | |
1161 | P[6] = fP[6]; | |
1162 | P[7] = fP[7]; | |
1163 | ||
1164 | Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 }, | |
616ffc76 | 1165 | {0,1,0, -cB, sB, 0, 0, 0 }, |
1166 | {0,0,1, 0, 0, S, 0, 0 }, | |
1167 | {0,0,0, c, s, 0, 0, 0 }, | |
1168 | {0,0,0, -s, c, 0, 0, 0 }, | |
1169 | {0,0,0, 0, 0, 1, 0, 0 }, | |
1170 | {0,0,0, 0, 0, 0, 1, 0 }, | |
1171 | {0,0,0, 0, 0, 0, 0, 1 } }; | |
f826d409 | 1172 | Double_t mA[8][8]; |
1173 | for( Int_t k=0,i=0; i<8; i++) | |
1174 | for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k]; | |
1175 | ||
1176 | Double_t mJC[8][8]; | |
1177 | for( Int_t i=0; i<8; i++ ) | |
1178 | for( Int_t j=0; j<8; j++ ){ | |
1179 | mJC[i][j]=0; | |
1180 | for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j]; | |
1181 | } | |
1182 | ||
1183 | for( Int_t k=0,i=0; i<8; i++) | |
1184 | for( Int_t j=0; j<=i; j++, k++ ){ | |
1185 | C[k] = 0; | |
1186 | for( Int_t l=0; l<8; l++ ) C[k]+=mJC[i][l]*mJ[j][l]; | |
1187 | } | |
1188 | ||
1189 | return; | |
1190 | /* | |
1191 | Double_t cBC13 = cB*fC[13]; | |
1192 | Double_t C17 = fC[17]; | |
1193 | Double_t C18 = fC[18]; | |
1194 | fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14]; | |
1195 | ||
1196 | Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13]; | |
1197 | Double_t mJC14= fC[11] - cBC13 + sB*fC[14]; | |
1198 | ||
1199 | fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB; | |
1200 | fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB; | |
1201 | ||
1202 | Double_t mJC23= fC[ 8] + S*fC[18]; | |
1203 | Double_t mJC24= fC[12] + S*fC[19]; | |
1204 | fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB; | |
1205 | fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB; | |
1206 | ||
1207 | fC[15]+= C18*sB + fC[19]*cB; | |
1208 | fC[16]+= -C18*cB + fC[19]*sB; | |
1209 | fC[17]+= fC[20]*S; | |
1210 | fC[18] = C18*c + fC[19]*s; | |
1211 | fC[19] = -C18*s + fC[19]*c; | |
1212 | ||
1213 | fC[ 5]+= (C17 + C17 + fC[17])*S; | |
1214 | ||
1215 | Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14]; | |
1216 | Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14]; | |
1217 | Double_t C6= fC[6], C7= fC[7], C8= fC[8]; | |
1218 | ||
1219 | fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB; | |
1220 | fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB; | |
1221 | fC[ 8]= c*C8 + s*fC[12] +fC[18]*S; | |
1222 | fC[ 9]= mJC33*c +mJC34*s; | |
1223 | ||
1224 | fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB; | |
1225 | fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB; | |
1226 | fC[12]= -s*C8 + c*fC[12] +fC[19]*S; | |
1227 | fC[13]= mJC43*c +mJC44*s; | |
1228 | fC[14]=-mJC43*s +mJC44*c; | |
1229 | */ | |
1230 | } | |
1231 | ||
1232 | ||
1233 | Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const | |
1234 | { | |
1235 | //* Calculate distance from vertex [cm] | |
1236 | ||
1237 | return GetDistanceFromVertex( Vtx.fP ); | |
1238 | } | |
1239 | ||
1240 | Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const | |
1241 | { | |
1242 | //* Calculate distance from vertex [cm] | |
1243 | ||
1244 | Double_t mP[8], mC[36]; | |
1245 | Transport( GetDStoPoint(vtx), mP, mC ); | |
1246 | Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]}; | |
1247 | return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] ); | |
1248 | } | |
1249 | ||
616ffc76 | 1250 | Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p ) |
f826d409 | 1251 | const |
1252 | { | |
616ffc76 | 1253 | //* Calculate distance to other particle [cm] |
f826d409 | 1254 | |
1255 | Double_t dS, dS1; | |
616ffc76 | 1256 | GetDStoParticle( p, dS, dS1 ); |
f826d409 | 1257 | Double_t mP[8], mC[36], mP1[8], mC1[36]; |
616ffc76 | 1258 | Transport( dS, mP, mC ); |
1259 | p.Transport( dS1, mP1, mC1 ); | |
f826d409 | 1260 | Double_t dx = mP[0]-mP1[0]; |
1261 | Double_t dy = mP[1]-mP1[1]; | |
1262 | Double_t dz = mP[2]-mP1[2]; | |
1263 | return TMath::Sqrt(dx*dx+dy*dy+dz*dz); | |
1264 | } | |
1265 | ||
1266 | Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const | |
1267 | { | |
1268 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1269 | ||
1270 | return GetDeviationFromVertex( Vtx.fP, Vtx.fC ); | |
1271 | } | |
1272 | ||
1273 | ||
1274 | Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const | |
1275 | { | |
1276 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1277 | //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix | |
1278 | ||
1279 | Double_t mP[8]; | |
1280 | Double_t mC[36]; | |
1281 | ||
1282 | Transport( GetDStoPoint(v), mP, mC ); | |
1283 | ||
1284 | Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]}; | |
1285 | ||
1286 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1287 | (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) ); | |
1288 | ||
1289 | ||
1290 | Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS }; | |
1291 | ||
1292 | Double_t mSi[6] = | |
1293 | { mC[0] +h[0]*h[0], | |
1294 | mC[1] +h[1]*h[0], mC[2] +h[1]*h[1], | |
1295 | mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] }; | |
1296 | ||
1297 | if( Cv ){ | |
1298 | mSi[0]+=Cv[0]; | |
1299 | mSi[1]+=Cv[1]; | |
1300 | mSi[2]+=Cv[2]; | |
1301 | mSi[3]+=Cv[3]; | |
1302 | mSi[4]+=Cv[4]; | |
1303 | mSi[5]+=Cv[5]; | |
1304 | } | |
1305 | ||
1306 | Double_t mS[6]; | |
1307 | ||
1308 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1309 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1310 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1311 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1312 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1313 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1314 | ||
1315 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1316 | s = ( s > 1.E-20 ) ?1./s :0; | |
1317 | ||
1318 | return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0] | |
1319 | +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1] | |
1320 | +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2); | |
1321 | } | |
1322 | ||
1323 | ||
616ffc76 | 1324 | Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p ) |
f826d409 | 1325 | const |
1326 | { | |
616ffc76 | 1327 | //* Calculate sqrt(Chi2/ndf) deviation from other particle |
f826d409 | 1328 | |
1329 | Double_t dS, dS1; | |
616ffc76 | 1330 | GetDStoParticle( p, dS, dS1 ); |
f826d409 | 1331 | Double_t mP1[8], mC1[36]; |
616ffc76 | 1332 | p.Transport( dS1, mP1, mC1 ); |
f826d409 | 1333 | |
1334 | Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]}; | |
1335 | ||
1336 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
616ffc76 | 1337 | (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) ); |
f826d409 | 1338 | |
1339 | Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS }; | |
1340 | ||
1341 | mC1[0] +=h[0]*h[0]; | |
1342 | mC1[1] +=h[1]*h[0]; | |
1343 | mC1[2] +=h[1]*h[1]; | |
1344 | mC1[3] +=h[2]*h[0]; | |
1345 | mC1[4] +=h[2]*h[1]; | |
1346 | mC1[5] +=h[2]*h[2]; | |
1347 | ||
1348 | return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.); | |
1349 | } | |
1350 | ||
1351 | ||
1352 | ||
1353 | void AliKFParticleBase::SubtractFromVertex( Double_t v[], Double_t Cv[], | |
1354 | Double_t &vChi2, Int_t vNDF ) const | |
1355 | { | |
1356 | //* Subtract the particle from the vertex | |
1357 | ||
1358 | Double_t fld[3]; | |
1359 | { | |
1360 | GetFieldValue( v, fld ); | |
1361 | const Double_t kCLight = 0.000299792458; | |
1362 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
1363 | } | |
1364 | ||
1365 | Double_t m[8]; | |
1366 | Double_t mCm[36]; | |
1367 | ||
1368 | Transport( GetDStoPoint(v), m, mCm ); | |
1369 | ||
1370 | Double_t d[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] }; | |
1371 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1372 | (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) ); | |
1373 | ||
1374 | Double_t h[6]; | |
1375 | ||
1376 | h[0] = m[3]*sigmaS; | |
1377 | h[1] = m[4]*sigmaS; | |
1378 | h[2] = m[5]*sigmaS; | |
1379 | h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ(); | |
1380 | h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ(); | |
1381 | h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ(); | |
1382 | ||
1383 | //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex | |
1384 | { | |
1385 | Double_t zeta[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] }; | |
1386 | ||
1387 | Double_t mVv[6] = | |
1388 | { mCm[ 0] + h[0]*h[0], | |
1389 | mCm[ 1] + h[1]*h[0], mCm[ 2] + h[1]*h[1], | |
1390 | mCm[ 3] + h[2]*h[0], mCm[ 4] + h[2]*h[1], mCm[ 5] + h[2]*h[2] }; | |
1391 | ||
1392 | Double_t mVvp[9]= | |
1393 | { mCm[ 6] + h[0]*h[3], mCm[ 7] + h[1]*h[3], mCm[ 8] + h[2]*h[3], | |
1394 | mCm[10] + h[0]*h[4], mCm[11] + h[1]*h[4], mCm[12] + h[2]*h[4], | |
1395 | mCm[15] + h[0]*h[5], mCm[16] + h[1]*h[5], mCm[17] + h[2]*h[5] }; | |
1396 | ||
1397 | Double_t mS[6] = | |
1398 | { mVv[2]*mVv[5] - mVv[4]*mVv[4], | |
1399 | mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3], | |
1400 | mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4], | |
1401 | mVv[0]*mVv[2] - mVv[1]*mVv[1] }; | |
1402 | ||
1403 | Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] ); | |
1404 | s = ( s > 1.E-20 ) ?1./s :0; | |
1405 | ||
1406 | mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s; | |
1407 | ||
1408 | Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]), | |
1409 | (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]), | |
1410 | (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) }; | |
1411 | ||
1412 | Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2]; | |
1413 | Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2]; | |
1414 | Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2]; | |
1415 | ||
1416 | h[0] = px*sigmaS; | |
1417 | h[1] = py*sigmaS; | |
1418 | h[2] = pz*sigmaS; | |
1419 | h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ(); | |
1420 | h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ(); | |
1421 | h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ(); | |
1422 | } | |
1423 | ||
1424 | Double_t mV[6]; | |
1425 | ||
1426 | mV[ 0] = mCm[ 0] + h[0]*h[0]; | |
1427 | mV[ 1] = mCm[ 1] + h[1]*h[0]; | |
1428 | mV[ 2] = mCm[ 2] + h[1]*h[1]; | |
1429 | mV[ 3] = mCm[ 3] + h[2]*h[0]; | |
1430 | mV[ 4] = mCm[ 4] + h[2]*h[1]; | |
1431 | mV[ 5] = mCm[ 5] + h[2]*h[2]; | |
1432 | ||
1433 | //* | |
1434 | ||
1435 | Double_t mS[6]; | |
1436 | { | |
1437 | Double_t mSi[6] = { mV[0]-Cv[0], | |
1438 | mV[1]-Cv[1], mV[2]-Cv[2], | |
1439 | mV[3]-Cv[3], mV[4]-Cv[4], mV[5]-Cv[5] }; | |
1440 | ||
1441 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1442 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1443 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1444 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1445 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1446 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1447 | ||
1448 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1449 | s = ( s > 1.E-20 ) ?1./s :0; | |
1450 | mS[0]*=s; | |
1451 | mS[1]*=s; | |
1452 | mS[2]*=s; | |
1453 | mS[3]*=s; | |
1454 | mS[4]*=s; | |
1455 | mS[5]*=s; | |
1456 | } | |
1457 | ||
1458 | //* Residual (measured - estimated) | |
1459 | ||
1460 | Double_t zeta[3] = { m[0]-v[0], m[1]-v[1], m[2]-v[2] }; | |
1461 | ||
1462 | //* mCHt = mCH' - D' | |
1463 | ||
1464 | Double_t mCHt0[3], mCHt1[3], mCHt2[3]; | |
1465 | ||
1466 | mCHt0[0]=Cv[ 0] ; mCHt1[0]=Cv[ 1] ; mCHt2[0]=Cv[ 3] ; | |
1467 | mCHt0[1]=Cv[ 1] ; mCHt1[1]=Cv[ 2] ; mCHt2[1]=Cv[ 4] ; | |
1468 | mCHt0[2]=Cv[ 3] ; mCHt1[2]=Cv[ 4] ; mCHt2[2]=Cv[ 5] ; | |
1469 | ||
1470 | //* Kalman gain K = mCH'*S | |
1471 | ||
1472 | Double_t k0[3], k1[3], k2[3]; | |
1473 | ||
1474 | for(Int_t i=0;i<3;++i){ | |
1475 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
1476 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
1477 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
1478 | } | |
1479 | ||
1480 | //* New estimation of the vertex position r += K*zeta | |
1481 | ||
1482 | for(Int_t i=0;i<3;++i) | |
1483 | v[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; | |
1484 | ||
1485 | //* New covariance matrix C -= K*(mCH')' | |
1486 | ||
1487 | for(Int_t i=0, k=0;i<3;++i){ | |
1488 | for(Int_t j=0;j<=i;++j,++k) | |
1489 | Cv[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j]; | |
1490 | } | |
1491 | ||
1492 | //* Calculate Chi^2 | |
1493 | ||
1494 | vNDF -= 2; | |
1495 | vChi2 -= (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
1496 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
1497 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
1498 | } | |
1499 | ||
1500 | ||
1501 | ||
1502 | void AliKFParticleBase::TransportLine( Double_t dS, | |
1503 | Double_t P[], Double_t C[] ) const | |
1504 | { | |
1505 | //* Transport the particle as a straight line | |
1506 | ||
1507 | P[0] = fP[0] + dS*fP[3]; | |
1508 | P[1] = fP[1] + dS*fP[4]; | |
1509 | P[2] = fP[2] + dS*fP[5]; | |
1510 | P[3] = fP[3]; | |
1511 | P[4] = fP[4]; | |
1512 | P[5] = fP[5]; | |
1513 | P[6] = fP[6]; | |
1514 | P[7] = fP[7]; | |
1515 | ||
1516 | Double_t c6 = fC[ 6] + dS*fC[ 9]; | |
1517 | Double_t c11 = fC[11] + dS*fC[14]; | |
1518 | Double_t c17 = fC[17] + dS*fC[20]; | |
1519 | Double_t sc13 = dS*fC[13]; | |
1520 | Double_t sc18 = dS*fC[18]; | |
1521 | Double_t sc19 = dS*fC[19]; | |
1522 | ||
1523 | C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 ); | |
1524 | C[ 2] = fC[ 2] + dS*( fC[11] + c11 ); | |
1525 | C[ 5] = fC[ 5] + dS*( fC[17] + c17 ); | |
1526 | ||
1527 | C[ 7] = fC[ 7] + sc13; | |
1528 | C[ 8] = fC[ 8] + sc18; | |
1529 | C[ 9] = fC[ 9]; | |
1530 | ||
1531 | C[12] = fC[12] + sc19; | |
1532 | ||
1533 | C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] ); | |
1534 | C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] ); | |
1535 | C[ 4] = fC[ 4] + dS*( fC[16] + C[12] ); | |
1536 | C[ 6] = c6; | |
1537 | ||
1538 | C[10] = fC[10] + sc13; | |
1539 | C[11] = c11; | |
1540 | ||
1541 | C[13] = fC[13]; | |
1542 | C[14] = fC[14]; | |
1543 | C[15] = fC[15] + sc18; | |
1544 | C[16] = fC[16] + sc19; | |
1545 | C[17] = c17; | |
1546 | ||
1547 | C[18] = fC[18]; | |
1548 | C[19] = fC[19]; | |
1549 | C[20] = fC[20]; | |
1550 | C[21] = fC[21] + dS*fC[24]; | |
1551 | C[22] = fC[22] + dS*fC[25]; | |
1552 | C[23] = fC[23] + dS*fC[26]; | |
1553 | ||
1554 | C[24] = fC[24]; | |
1555 | C[25] = fC[25]; | |
1556 | C[26] = fC[26]; | |
1557 | C[27] = fC[27]; | |
1558 | C[28] = fC[28] + dS*fC[31]; | |
1559 | C[29] = fC[29] + dS*fC[32]; | |
1560 | C[30] = fC[30] + dS*fC[33]; | |
1561 | ||
1562 | C[31] = fC[31]; | |
1563 | C[32] = fC[32]; | |
1564 | C[33] = fC[33]; | |
1565 | C[34] = fC[34]; | |
1566 | C[35] = fC[35]; | |
1567 | } | |
1568 | ||
1569 | ||
1570 | void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] ) | |
1571 | { | |
1572 | //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric | |
1573 | ||
1574 | const Int_t kN= 8; | |
1575 | Double_t mA[kN*kN]; | |
1576 | ||
1577 | for( Int_t i=0, ij=0; i<kN; i++ ){ | |
1578 | for( Int_t j=0; j<kN; j++, ++ij ){ | |
1579 | mA[ij] = 0 ; | |
1580 | 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]; | |
1581 | } | |
1582 | } | |
1583 | ||
1584 | for( Int_t i=0; i<kN; i++ ){ | |
1585 | for( Int_t j=0; j<=i; j++ ){ | |
1586 | Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i; | |
1587 | SOut[ij] = 0 ; | |
1588 | for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ]; | |
1589 | } | |
1590 | } | |
1591 | } | |
1592 | ||
1593 | ||
1594 | // 72-charachters line to define the printer border | |
1595 | //3456789012345678901234567890123456789012345678901234567890123456789012 |