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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 | ||
22 | ClassImp(AliKFParticleBase) | |
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 | ||
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 | ||
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::GetPt( Double_t &pt, Double_t &error ) const | |
127 | { | |
128 | //* Calculate particle transverse momentum | |
129 | ||
130 | Double_t px = fP[3]; | |
131 | Double_t py = fP[4]; | |
132 | Double_t px2 = px*px; | |
133 | Double_t py2 = py*py; | |
134 | Double_t pt2 = px2+py2; | |
135 | pt = TMath::Sqrt(pt2); | |
136 | error = (px2*fC[9] + py2*fC[14] + 2*px*py*fC[13] ); | |
137 | if( error>0 && pt>1.e-4 ){ | |
138 | error = TMath::Sqrt(error)/pt; | |
139 | return 0; | |
140 | } | |
141 | error = 1.e10; | |
142 | return 1; | |
143 | } | |
144 | ||
145 | Int_t AliKFParticleBase::GetEta( Double_t &eta, Double_t &error ) const | |
146 | { | |
147 | //* Calculate particle pseudorapidity | |
148 | ||
149 | Double_t px = fP[3]; | |
150 | Double_t py = fP[4]; | |
151 | Double_t pz = fP[5]; | |
152 | Double_t pt2 = px*px + py*py; | |
153 | Double_t p2 = pt2 + pz*pz; | |
154 | Double_t p = TMath::Sqrt(p2); | |
155 | Double_t a = p + pz; | |
156 | Double_t b = p - pz; | |
157 | eta = 1.e10; | |
158 | if( b > 1.e-8 ){ | |
159 | Double_t c = a/b; | |
160 | if( c>1.e-8 ) eta = 0.5*TMath::Log(a/b); | |
161 | } | |
162 | Double_t h3 = -px*pz; | |
163 | Double_t h4 = -py*pz; | |
164 | Double_t p2pt2 = p2*pt2; | |
165 | ||
166 | error = (h3*h3*fC[9] + h4*h4*fC[14] + pt2*fC[20] + | |
167 | 2*( h3*(h4*fC[13] + fC[18]) + h4*fC[19] ) | |
168 | ); | |
169 | ||
170 | if( error>0 && p2pt2>1.e-4 ){ | |
171 | error = TMath::Sqrt(error/p2pt2); | |
172 | return 0; | |
173 | } | |
174 | error = 1.e10; | |
175 | return 1; | |
176 | } | |
177 | ||
178 | Int_t AliKFParticleBase::GetPhi( Double_t &phi, Double_t &error ) const | |
179 | { | |
180 | //* Calculate particle polar angle | |
181 | ||
182 | Double_t px = fP[3]; | |
183 | Double_t py = fP[4]; | |
184 | Double_t px2 = px*px; | |
185 | Double_t py2 = py*py; | |
186 | Double_t pt2 = px2 + py2; | |
187 | phi = TMath::ATan2(py,px); | |
188 | error = (py2*fC[9] + px2*fC[14] - 2*px*py*fC[13] ); | |
189 | if( error>0 && pt2>1.e-4 ){ | |
190 | error = TMath::Sqrt(error)/pt2; | |
191 | return 0; | |
192 | } | |
193 | error = 1.e10; | |
194 | return 1; | |
195 | } | |
196 | ||
197 | Int_t AliKFParticleBase::GetR( Double_t &r, Double_t &error ) const | |
198 | { | |
199 | //* Calculate distance to the origin | |
200 | ||
201 | Double_t x = fP[0]; | |
202 | Double_t y = fP[1]; | |
203 | Double_t x2 = x*x; | |
204 | Double_t y2 = y*y; | |
205 | r = TMath::Sqrt(x2 + y2); | |
206 | error = (x2*fC[0] + y2*fC[2] - 2*x*y*fC[1] ); | |
207 | if( error>0 && r>1.e-4 ){ | |
208 | error = TMath::Sqrt(error)/r; | |
209 | return 0; | |
210 | } | |
211 | error = 1.e10; | |
212 | return 1; | |
213 | } | |
214 | ||
215 | Int_t AliKFParticleBase::GetMass( Double_t &m, Double_t &error ) const | |
216 | { | |
217 | //* Calculate particle mass | |
218 | ||
219 | // s = sigma^2 of m2/2 | |
220 | ||
221 | Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20] | |
222 | + fP[6]*fP[6]*fC[27] | |
223 | +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19]) | |
224 | - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) ) | |
225 | ); | |
226 | Double_t m2 = TMath::Abs(fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5]); | |
227 | m = TMath::Sqrt(m2); | |
228 | if( m>1.e-10 ){ | |
229 | if( s>=0 ){ | |
230 | error = TMath::Sqrt(s)/m; | |
231 | return 0; | |
232 | } | |
233 | } | |
234 | error = 1.e20; | |
235 | return 1; | |
236 | } | |
237 | ||
238 | ||
239 | Int_t AliKFParticleBase::GetDecayLength( Double_t &l, Double_t &error ) const | |
240 | { | |
241 | //* Calculate particle decay length [cm] | |
242 | ||
243 | Double_t x = fP[3]; | |
244 | Double_t y = fP[4]; | |
245 | Double_t z = fP[5]; | |
246 | Double_t t = fP[7]; | |
247 | Double_t x2 = x*x; | |
248 | Double_t y2 = y*y; | |
249 | Double_t z2 = z*z; | |
250 | Double_t p2 = x2+y2+z2; | |
251 | l = t*TMath::Sqrt(p2); | |
252 | if( p2>1.e-4){ | |
253 | error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20] | |
254 | + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ) | |
255 | + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]); | |
256 | error = TMath::Sqrt(TMath::Abs(error)); | |
257 | return 0; | |
258 | } | |
259 | error = 1.e20; | |
260 | return 1; | |
261 | } | |
262 | ||
263 | Int_t AliKFParticleBase::GetLifeTime( Double_t &tauC, Double_t &error ) const | |
264 | { | |
265 | //* Calculate particle decay time [s] | |
266 | ||
267 | Double_t m, dm; | |
268 | GetMass( m, dm ); | |
269 | Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]); | |
270 | tauC = fP[7]*m; | |
271 | error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm; | |
272 | if( error > 0 ){ | |
273 | error = TMath::Sqrt( error ); | |
274 | return 0; | |
275 | } | |
276 | error = 1.e20; | |
277 | return 1; | |
278 | } | |
279 | ||
280 | ||
281 | void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter ) | |
282 | { | |
283 | //* Add daughter via operator+= | |
284 | ||
285 | AddDaughter( Daughter ); | |
286 | } | |
287 | ||
288 | Double_t AliKFParticleBase::GetSCorrection( const Double_t Part[], const Double_t XYZ[] ) | |
289 | { | |
290 | //* Get big enough correction for S error to let the particle Part be fitted to XYZ point | |
291 | ||
292 | Double_t d[3] = { XYZ[0]-Part[0], XYZ[1]-Part[1], XYZ[2]-Part[2] }; | |
293 | Double_t p2 = Part[3]*Part[3]+Part[4]*Part[4]+Part[5]*Part[5]; | |
294 | Double_t sigmaS = (p2>1.e-4) ? ( .1+3.*TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2]) )/TMath::Sqrt(p2) : 1.; | |
295 | return sigmaS; | |
296 | } | |
297 | ||
298 | void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const | |
299 | { | |
300 | //* Get additional covariances V used during measurement | |
301 | ||
302 | Double_t b[3]; | |
303 | GetFieldValue( XYZ, b ); | |
304 | const Double_t kCLight = 0.000299792458; | |
305 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
306 | ||
307 | Transport( GetDStoPoint(XYZ), m, V ); | |
308 | ||
309 | Double_t sigmaS = GetSCorrection( m, XYZ ); | |
310 | ||
311 | Double_t h[6]; | |
312 | ||
313 | h[0] = m[3]*sigmaS; | |
314 | h[1] = m[4]*sigmaS; | |
315 | h[2] = m[5]*sigmaS; | |
316 | h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); | |
317 | h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); | |
318 | h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); | |
319 | ||
320 | V[ 0]+= h[0]*h[0]; | |
321 | V[ 1]+= h[1]*h[0]; | |
322 | V[ 2]+= h[1]*h[1]; | |
323 | V[ 3]+= h[2]*h[0]; | |
324 | V[ 4]+= h[2]*h[1]; | |
325 | V[ 5]+= h[2]*h[2]; | |
326 | ||
327 | V[ 6]+= h[3]*h[0]; | |
328 | V[ 7]+= h[3]*h[1]; | |
329 | V[ 8]+= h[3]*h[2]; | |
330 | V[ 9]+= h[3]*h[3]; | |
331 | ||
332 | V[10]+= h[4]*h[0]; | |
333 | V[11]+= h[4]*h[1]; | |
334 | V[12]+= h[4]*h[2]; | |
335 | V[13]+= h[4]*h[3]; | |
336 | V[14]+= h[4]*h[4]; | |
337 | ||
338 | V[15]+= h[5]*h[0]; | |
339 | V[16]+= h[5]*h[1]; | |
340 | V[17]+= h[5]*h[2]; | |
341 | V[18]+= h[5]*h[3]; | |
342 | V[19]+= h[5]*h[4]; | |
343 | V[20]+= h[5]*h[5]; | |
344 | } | |
345 | ||
346 | ||
347 | void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter ) | |
348 | { | |
349 | //* Add daughter | |
350 | ||
351 | if( fNDF<-1 ){ // first daughter -> just copy | |
352 | fNDF = -1; | |
353 | fQ = Daughter.GetQ(); | |
354 | for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i]; | |
355 | for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i]; | |
356 | fSFromDecay = 0; | |
357 | return; | |
358 | } | |
359 | ||
360 | TransportToDecayVertex(); | |
361 | ||
362 | Double_t b[3]; | |
363 | Int_t maxIter = 1; | |
364 | ||
365 | if( !fIsLinearized ){ | |
366 | if( fNDF==-1 ){ | |
367 | Double_t ds, ds1; | |
368 | GetDStoParticle(Daughter, ds, ds1); | |
369 | TransportToDS( ds ); | |
370 | Double_t m[8]; | |
371 | Double_t mCd[36]; | |
372 | Daughter.Transport( ds1, m, mCd ); | |
373 | fVtxGuess[0] = .5*( fP[0] + m[0] ); | |
374 | fVtxGuess[1] = .5*( fP[1] + m[1] ); | |
375 | fVtxGuess[2] = .5*( fP[2] + m[2] ); | |
376 | } else { | |
377 | fVtxGuess[0] = fP[0]; | |
378 | fVtxGuess[1] = fP[1]; | |
379 | fVtxGuess[2] = fP[2]; | |
380 | } | |
381 | maxIter = 3; | |
382 | } | |
383 | ||
384 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
385 | ||
386 | { | |
387 | GetFieldValue( fVtxGuess, b ); | |
388 | const Double_t kCLight = 0.000299792458; | |
389 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
390 | } | |
391 | ||
392 | Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36]; | |
393 | if( fNDF==-1 ){ | |
394 | GetMeasurement( fVtxGuess, tmpP, tmpC ); | |
395 | ffP = tmpP; | |
396 | ffC = tmpC; | |
397 | } | |
398 | ||
399 | Double_t m[8], mV[36]; | |
400 | ||
401 | if( Daughter.fC[35]>0 ){ | |
402 | Daughter.GetMeasurement( fVtxGuess, m, mV ); | |
403 | } else { | |
404 | for( Int_t i=0; i<8; i++ ) m[i] = Daughter.fP[i]; | |
405 | for( Int_t i=0; i<36; i++ ) mV[i] = Daughter.fC[i]; | |
406 | } | |
407 | ||
408 | //* | |
409 | ||
410 | Double_t mS[6]; | |
411 | { | |
412 | Double_t mSi[6] = { ffC[0]+mV[0], | |
413 | ffC[1]+mV[1], ffC[2]+mV[2], | |
414 | ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] }; | |
415 | ||
416 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
417 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
418 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
419 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
420 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
421 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
422 | ||
423 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
424 | ||
425 | s = ( s > 1.E-20 ) ?1./s :0; | |
426 | mS[0]*=s; | |
427 | mS[1]*=s; | |
428 | mS[2]*=s; | |
429 | mS[3]*=s; | |
430 | mS[4]*=s; | |
431 | mS[5]*=s; | |
432 | } | |
433 | ||
434 | //* Residual (measured - estimated) | |
435 | ||
436 | Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] }; | |
437 | ||
438 | ||
439 | //* CHt = CH' - D' | |
440 | ||
441 | Double_t mCHt0[7], mCHt1[7], mCHt2[7]; | |
442 | ||
443 | mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ; | |
444 | mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ; | |
445 | mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ; | |
446 | mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8]; | |
447 | mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12]; | |
448 | mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17]; | |
449 | mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23]; | |
450 | ||
451 | //* Kalman gain K = mCH'*S | |
452 | ||
453 | Double_t k0[7], k1[7], k2[7]; | |
454 | ||
455 | for(Int_t i=0;i<7;++i){ | |
456 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
457 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
458 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
459 | } | |
460 | ||
461 | //* New estimation of the vertex position | |
462 | ||
463 | if( iter<maxIter-1 ){ | |
464 | for(Int_t i=0; i<3; ++i) | |
465 | fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2]; | |
466 | continue; | |
467 | } | |
468 | ||
469 | // last itearation -> update the particle | |
470 | ||
471 | //* Add the daughter momentum to the particle momentum | |
472 | ||
473 | ffP[ 3] += m[ 3]; | |
474 | ffP[ 4] += m[ 4]; | |
475 | ffP[ 5] += m[ 5]; | |
476 | ffP[ 6] += m[ 6]; | |
477 | ||
478 | ffC[ 9] += mV[ 9]; | |
479 | ffC[13] += mV[13]; | |
480 | ffC[14] += mV[14]; | |
481 | ffC[18] += mV[18]; | |
482 | ffC[19] += mV[19]; | |
483 | ffC[20] += mV[20]; | |
484 | ffC[24] += mV[24]; | |
485 | ffC[25] += mV[25]; | |
486 | ffC[26] += mV[26]; | |
487 | ffC[27] += mV[27]; | |
488 | ||
489 | ||
490 | //* New estimation of the vertex position r += K*zeta | |
491 | ||
492 | for(Int_t i=0;i<7;++i) | |
493 | fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; | |
494 | ||
495 | //* New covariance matrix C -= K*(mCH')' | |
496 | ||
497 | for(Int_t i=0, k=0;i<7;++i){ | |
498 | for(Int_t j=0;j<=i;++j,++k){ | |
499 | fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] ); | |
500 | } | |
501 | } | |
502 | ||
503 | //* Calculate Chi^2 | |
504 | ||
505 | fNDF += 2; | |
506 | fQ += Daughter.GetQ(); | |
507 | fSFromDecay = 0; | |
508 | fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
509 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
510 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
511 | ||
512 | } | |
513 | } | |
514 | ||
515 | ||
516 | void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx ) | |
517 | { | |
518 | //* Set production vertex for the particle, when the particle was not used in the vertex fit | |
519 | ||
520 | const Double_t *m = Vtx.fP, *mV = Vtx.fC; | |
521 | ||
522 | Bool_t noS = ( fC[35]<=0 ); // no decay length allowed | |
523 | ||
524 | if( noS ){ | |
525 | TransportToDecayVertex(); | |
526 | fP[7] = 0; | |
527 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0; | |
528 | } else { | |
529 | TransportToDS( GetDStoPoint( m ) ); | |
530 | fP[7] = -fSFromDecay; | |
531 | Convert(1); | |
532 | } | |
533 | ||
534 | Double_t mAi[6]; | |
535 | mAi[0] = fC[2]*fC[5] - fC[4]*fC[4]; | |
536 | mAi[1] = fC[3]*fC[4] - fC[1]*fC[5]; | |
537 | mAi[3] = fC[1]*fC[4] - fC[2]*fC[3]; | |
538 | Double_t det = (fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]); | |
539 | if( det>1.e-20 ) det = 1./det; | |
540 | else det = 0; | |
541 | ||
542 | mAi[0] *= det; | |
543 | mAi[1] *= det; | |
544 | mAi[3] *= det; | |
545 | mAi[2] = ( fC[0]*fC[5] - fC[3]*fC[3] )*det; | |
546 | mAi[4] = ( fC[1]*fC[3] - fC[0]*fC[4] )*det; | |
547 | mAi[5] = ( fC[0]*fC[2] - fC[1]*fC[1] )*det; | |
548 | ||
549 | Double_t mB[5][3]; | |
550 | ||
551 | mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3]; | |
552 | mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4]; | |
553 | mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5]; | |
554 | ||
555 | mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3]; | |
556 | mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4]; | |
557 | mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5]; | |
558 | ||
559 | mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3]; | |
560 | mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4]; | |
561 | mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5]; | |
562 | ||
563 | mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3]; | |
564 | mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4]; | |
565 | mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5]; | |
566 | ||
567 | mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3]; | |
568 | mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4]; | |
569 | mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5]; | |
570 | ||
571 | Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] }; | |
572 | ||
573 | { | |
574 | Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2], | |
575 | fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] }; | |
576 | ||
577 | Double_t mAVi[6]; | |
578 | mAVi[0] = mAV[2]*mAV[5] - mAV[4]*mAV[4]; | |
579 | mAVi[1] = mAV[3]*mAV[4] - mAV[1]*mAV[5]; | |
580 | mAVi[2] = mAV[0]*mAV[5] - mAV[3]*mAV[3]; | |
581 | mAVi[3] = mAV[1]*mAV[4] - mAV[2]*mAV[3]; | |
582 | mAVi[4] = mAV[1]*mAV[3] - mAV[0]*mAV[4]; | |
583 | mAVi[5] = mAV[0]*mAV[2] - mAV[1]*mAV[1]; | |
584 | ||
585 | det = ( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] ); | |
586 | ||
587 | if( TMath::Abs(det) > 1.E-20 ){ | |
588 | ||
589 | Double_t dChi2 = ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0] | |
590 | +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1] | |
591 | +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )/det ; | |
592 | ||
593 | // Take Abs(dChi2) here. Negative value of 'det' or 'dChi2' shows that the particle | |
594 | // was not used in the production vertex fit | |
595 | ||
596 | fChi2+= TMath::Abs( dChi2 ); | |
597 | } | |
598 | fNDF += 2; | |
599 | } | |
600 | ||
601 | fP[0] = m[0]; | |
602 | fP[1] = m[1]; | |
603 | fP[2] = m[2]; | |
604 | fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; | |
605 | fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; | |
606 | fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; | |
607 | fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2]; | |
608 | fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2]; | |
609 | ||
610 | Double_t d0, d1, d2; | |
611 | ||
612 | fC[0] = mV[0]; | |
613 | fC[1] = mV[1]; | |
614 | fC[2] = mV[2]; | |
615 | fC[3] = mV[3]; | |
616 | fC[4] = mV[4]; | |
617 | fC[5] = mV[5]; | |
618 | ||
619 | d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6]; | |
620 | d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7]; | |
621 | d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8]; | |
622 | ||
623 | fC[ 6]+= d0; | |
624 | fC[ 7]+= d1; | |
625 | fC[ 8]+= d2; | |
626 | fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
627 | ||
628 | d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10]; | |
629 | d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11]; | |
630 | d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12]; | |
631 | ||
632 | fC[10]+= d0; | |
633 | fC[11]+= d1; | |
634 | fC[12]+= d2; | |
635 | fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
636 | fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
637 | ||
638 | d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15]; | |
639 | d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16]; | |
640 | d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17]; | |
641 | ||
642 | fC[15]+= d0; | |
643 | fC[16]+= d1; | |
644 | fC[17]+= d2; | |
645 | fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
646 | fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
647 | fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
648 | ||
649 | d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21]; | |
650 | d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22]; | |
651 | d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23]; | |
652 | ||
653 | fC[21]+= d0; | |
654 | fC[22]+= d1; | |
655 | fC[23]+= d2; | |
656 | fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
657 | fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
658 | fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
659 | fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
660 | ||
661 | d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28]; | |
662 | d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29]; | |
663 | d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30]; | |
664 | ||
665 | fC[28]+= d0; | |
666 | fC[29]+= d1; | |
667 | fC[30]+= d2; | |
668 | fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
669 | fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
670 | fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
671 | fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
672 | fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2]; | |
673 | ||
674 | if( noS ){ | |
675 | fP[7] = 0; | |
676 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0; | |
677 | } else { | |
678 | TransportToDS( fP[7] ); | |
679 | Convert(0); | |
680 | } | |
681 | ||
682 | fSFromDecay = 0; | |
683 | } | |
684 | ||
685 | ||
686 | ||
687 | void AliKFParticleBase::SetMassConstraint( Double_t Mass, Double_t SigmaMass ) | |
688 | { | |
689 | //* Set hard( SigmaMass=0 ) or soft (SigmaMass>0) mass constraint | |
690 | ||
691 | Double_t m2 = Mass*Mass; // measurement, weighted by Mass | |
692 | Double_t s2 = m2*SigmaMass*SigmaMass; // sigma^2 | |
693 | ||
694 | Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; | |
695 | Double_t e0 = TMath::Sqrt(m2+p2); | |
696 | ||
697 | Double_t mH[8]; | |
698 | mH[0] = mH[1] = mH[2] = 0.; | |
699 | mH[3] = -2*fP[3]; | |
700 | mH[4] = -2*fP[4]; | |
701 | mH[5] = -2*fP[5]; | |
702 | mH[6] = 2*fP[6];//e0; | |
703 | mH[7] = 0; | |
704 | ||
705 | Double_t zeta = e0*e0 - e0*fP[6]; | |
706 | zeta = m2 - (fP[6]*fP[6]-p2); | |
707 | ||
708 | Double_t mCHt[8], s2_est=0; | |
709 | for( Int_t i=0; i<8; ++i ){ | |
710 | mCHt[i] = 0.0; | |
711 | for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j]; | |
712 | s2_est += mH[i]*mCHt[i]; | |
713 | } | |
714 | ||
715 | if( s2_est<1.e-20 ) return; // calculated mass error is already 0, | |
716 | // the particle can not be constrained on mass | |
717 | ||
718 | Double_t w2 = 1./( s2 + s2_est ); | |
719 | fChi2 += zeta*zeta*w2; | |
720 | fNDF += 1; | |
721 | for( Int_t i=0, ii=0; i<8; ++i ){ | |
722 | Double_t ki = mCHt[i]*w2; | |
723 | fP[i]+= ki*zeta; | |
724 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j]; | |
725 | } | |
726 | } | |
727 | ||
728 | ||
729 | void AliKFParticleBase::SetNoDecayLength() | |
730 | { | |
731 | //* Set no decay length for resonances | |
732 | ||
733 | TransportToDecayVertex(); | |
734 | ||
735 | Double_t h[8]; | |
736 | h[0] = h[1] = h[2] = h[3] = h[4] = h[5] = h[6] = 0; | |
737 | h[7] = 1; | |
738 | ||
739 | Double_t zeta = 0 - fP[7]; | |
740 | for(Int_t i=0;i<8;++i) zeta -= h[i]*(fP[i]-fP[i]); | |
741 | ||
742 | Double_t s = fC[35]; | |
743 | if( s>1.e-20 ){ | |
744 | s = 1./s; | |
745 | fChi2 += zeta*zeta*s; | |
746 | fNDF += 1; | |
747 | for( Int_t i=0, ii=0; i<7; ++i ){ | |
748 | Double_t ki = fC[28+i]*s; | |
749 | fP[i]+= ki*zeta; | |
750 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*fC[28+j]; | |
751 | } | |
752 | } | |
753 | fP[7] = 0; | |
754 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0; | |
755 | } | |
756 | ||
757 | ||
758 | void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters, | |
759 | const AliKFParticleBase *Parent, Double_t Mass, Bool_t IsConstrained ) | |
760 | { | |
761 | //* Full reconstruction in one go | |
762 | ||
763 | Int_t maxIter = 1; | |
764 | bool wasLinearized = fIsLinearized; | |
765 | if( !fIsLinearized || IsConstrained ){ | |
766 | //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!! | |
767 | fVtxGuess[0] = GetX(); | |
768 | fVtxGuess[1] = GetY(); | |
769 | fVtxGuess[2] = GetZ(); | |
770 | fIsLinearized = 1; | |
771 | maxIter = 3; | |
772 | } | |
773 | ||
774 | Double_t constraintC[6]; | |
775 | ||
776 | if( IsConstrained ){ | |
777 | for(Int_t i=0;i<6;++i) constraintC[i]=fC[i]; | |
778 | } else { | |
779 | for(Int_t i=0;i<6;++i) constraintC[i]=0.; | |
780 | constraintC[0] = constraintC[2] = constraintC[5] = 100.; | |
781 | } | |
782 | ||
783 | ||
784 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
785 | fAtProductionVertex = 0; | |
786 | fSFromDecay = 0; | |
787 | fP[0] = fVtxGuess[0]; | |
788 | fP[1] = fVtxGuess[1]; | |
789 | fP[2] = fVtxGuess[2]; | |
790 | fP[3] = 0; | |
791 | fP[4] = 0; | |
792 | fP[5] = 0; | |
793 | fP[6] = 0; | |
794 | fP[7] = 0; | |
795 | ||
796 | for(Int_t i=0;i<6; ++i) fC[i]=constraintC[i]; | |
797 | for(Int_t i=6;i<36;++i) fC[i]=0.; | |
798 | fC[35] = 1.; | |
799 | ||
800 | fNDF = IsConstrained ?0 :-3; | |
801 | fChi2 = 0.; | |
802 | fQ = 0; | |
803 | ||
804 | for( Int_t itr =0; itr<NDaughters; itr++ ){ | |
805 | AddDaughter( *vDaughters[itr] ); | |
806 | } | |
807 | if( iter<maxIter-1){ | |
808 | for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i]; | |
809 | } | |
810 | } | |
811 | fIsLinearized = wasLinearized; | |
812 | ||
813 | if( Mass>=0 ) SetMassConstraint( Mass ); | |
814 | if( Parent ) SetProductionVertex( *Parent ); | |
815 | } | |
816 | ||
817 | ||
818 | void AliKFParticleBase::Convert( bool ToProduction ) | |
819 | { | |
820 | //* Tricky function - convert the particle error along its trajectory to | |
821 | //* the value which corresponds to its production/decay vertex | |
822 | //* It is done by combination of the error of decay length with the position errors | |
823 | ||
824 | Double_t fld[3]; | |
825 | { | |
826 | GetFieldValue( fP, fld ); | |
827 | const Double_t kCLight = fQ*0.000299792458; | |
828 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
829 | } | |
830 | ||
831 | Double_t h[6]; | |
832 | ||
833 | h[0] = fP[3]; | |
834 | h[1] = fP[4]; | |
835 | h[2] = fP[5]; | |
836 | if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; } | |
837 | h[3] = h[1]*fld[2]-h[2]*fld[1]; | |
838 | h[4] = h[2]*fld[0]-h[0]*fld[2]; | |
839 | h[5] = h[0]*fld[1]-h[1]*fld[0]; | |
840 | ||
841 | Double_t c; | |
842 | ||
843 | c = fC[28]+h[0]*fC[35]; | |
844 | fC[ 0]+= h[0]*(c+fC[28]); | |
845 | fC[28] = c; | |
846 | ||
847 | fC[ 1]+= h[1]*fC[28] + h[0]*fC[29]; | |
848 | c = fC[29]+h[1]*fC[35]; | |
849 | fC[ 2]+= h[1]*(c+fC[29]); | |
850 | fC[29] = c; | |
851 | ||
852 | fC[ 3]+= h[2]*fC[28] + h[0]*fC[30]; | |
853 | fC[ 4]+= h[2]*fC[29] + h[1]*fC[30]; | |
854 | c = fC[30]+h[2]*fC[35]; | |
855 | fC[ 5]+= h[2]*(c+fC[30]); | |
856 | fC[30] = c; | |
857 | ||
858 | fC[ 6]+= h[3]*fC[28] + h[0]*fC[31]; | |
859 | fC[ 7]+= h[3]*fC[29] + h[1]*fC[31]; | |
860 | fC[ 8]+= h[3]*fC[30] + h[2]*fC[31]; | |
861 | c = fC[31]+h[3]*fC[35]; | |
862 | fC[ 9]+= h[3]*(c+fC[31]); | |
863 | fC[31] = c; | |
864 | ||
865 | fC[10]+= h[4]*fC[28] + h[0]*fC[32]; | |
866 | fC[11]+= h[4]*fC[29] + h[1]*fC[32]; | |
867 | fC[12]+= h[4]*fC[30] + h[2]*fC[32]; | |
868 | fC[13]+= h[4]*fC[31] + h[3]*fC[32]; | |
869 | c = fC[32]+h[4]*fC[35]; | |
870 | fC[14]+= h[4]*(c+fC[32]); | |
871 | fC[32] = c; | |
872 | ||
873 | fC[15]+= h[5]*fC[28] + h[0]*fC[33]; | |
874 | fC[16]+= h[5]*fC[29] + h[1]*fC[33]; | |
875 | fC[17]+= h[5]*fC[30] + h[2]*fC[33]; | |
876 | fC[18]+= h[5]*fC[31] + h[3]*fC[33]; | |
877 | fC[19]+= h[5]*fC[32] + h[4]*fC[33]; | |
878 | c = fC[33]+h[5]*fC[35]; | |
879 | fC[20]+= h[5]*(c+fC[33]); | |
880 | fC[33] = c; | |
881 | ||
882 | fC[21]+= h[0]*fC[34]; | |
883 | fC[22]+= h[1]*fC[34]; | |
884 | fC[23]+= h[2]*fC[34]; | |
885 | fC[24]+= h[3]*fC[34]; | |
886 | fC[25]+= h[4]*fC[34]; | |
887 | fC[26]+= h[5]*fC[34]; | |
888 | } | |
889 | ||
890 | ||
891 | void AliKFParticleBase::TransportToDecayVertex() | |
892 | { | |
893 | //* Transport the particle to its decay vertex | |
894 | ||
895 | if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay ); | |
896 | if( fAtProductionVertex ) Convert(0); | |
897 | fAtProductionVertex = 0; | |
898 | } | |
899 | ||
900 | void AliKFParticleBase::TransportToProductionVertex() | |
901 | { | |
902 | //* Transport the particle to its production vertex | |
903 | ||
904 | if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] ); | |
905 | if( !fAtProductionVertex ) Convert( 1 ); | |
906 | fAtProductionVertex = 1; | |
907 | } | |
908 | ||
909 | ||
910 | void AliKFParticleBase::TransportToDS( Double_t dS ) | |
911 | { | |
912 | //* Transport the particle on dS parameter (SignedPath/Momentum) | |
913 | ||
914 | Transport( dS, fP, fC ); | |
915 | fSFromDecay+= dS; | |
916 | } | |
917 | ||
918 | ||
919 | Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const | |
920 | { | |
921 | //* Get dS to a certain space point without field | |
922 | ||
923 | Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; | |
924 | if( p2<1.e-4 ) p2 = 1; | |
925 | return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2; | |
926 | } | |
927 | ||
928 | ||
929 | Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] ) | |
930 | const | |
931 | { | |
932 | ||
933 | //* Get dS to a certain space point for Bz field | |
934 | const Double_t kCLight = 0.000299792458; | |
935 | Double_t bq = B*fQ*kCLight; | |
936 | Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4]; | |
937 | if( pt2<1.e-4 ) return 0; | |
938 | Double_t dx = xyz[0] - fP[0]; | |
939 | Double_t dy = xyz[1] - fP[1]; | |
940 | Double_t a = dx*fP[3]+dy*fP[4]; | |
941 | Double_t dS; | |
942 | ||
943 | if( TMath::Abs(bq)<1.e-8 ) dS = a/pt2; | |
944 | else dS = TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq; | |
945 | ||
946 | if(0){ | |
947 | ||
948 | Double_t px = fP[3]; | |
949 | Double_t py = fP[4]; | |
950 | Double_t pz = fP[5]; | |
951 | Double_t ss[2], g[2][5]; | |
952 | ||
953 | ss[0] = dS; | |
954 | ss[1] = -dS; | |
955 | for( Int_t i=0; i<2; i++){ | |
956 | Double_t bs = bq*ss[i]; | |
957 | Double_t c = TMath::Cos(bs), s = TMath::Sin(bs); | |
958 | Double_t cB,sB; | |
959 | if( TMath::Abs(bq)>1.e-8){ | |
960 | cB= (1-c)/bq; | |
961 | sB= s/bq; | |
962 | }else{ | |
963 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); | |
964 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i]; | |
965 | cB = .5*sB*bs; | |
966 | } | |
967 | g[i][0] = fP[0] + sB*px + cB*py; | |
968 | g[i][1] = fP[1] - cB*px + sB*py; | |
969 | g[i][2] = fP[2] + ss[i]*pz; | |
970 | g[i][3] = + c*px + s*py; | |
971 | g[i][4] = - s*px + c*py; | |
972 | } | |
973 | ||
974 | Int_t i=0; | |
975 | ||
976 | Double_t dMin = 1.e10; | |
977 | for( Int_t j=0; j<2; j++){ | |
978 | Double_t xx = g[j][0]-xyz[0]; | |
979 | Double_t yy = g[j][1]-xyz[1]; | |
980 | Double_t zz = g[j][2]-xyz[2]; | |
981 | Double_t d = xx*xx + yy*yy + zz*zz; | |
982 | if( d<dMin ){ | |
983 | dMin = d; | |
984 | i = j; | |
985 | } | |
986 | } | |
987 | ||
988 | dS = ss[i]; | |
989 | ||
990 | Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4]; | |
991 | Double_t ddx = x-xyz[0]; | |
992 | Double_t ddy = y-xyz[1]; | |
993 | Double_t ddz = z-xyz[2]; | |
994 | Double_t c = ddx*ppx + ddy*ppy + ddz*pz ; | |
995 | Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz; | |
996 | if( TMath::Abs(pp2)>1.e-8 ){ | |
997 | dS+=c/pp2; | |
998 | } | |
999 | } | |
1000 | return dS; | |
1001 | } | |
1002 | ||
1003 | ||
1004 | void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p, | |
1005 | Double_t &DS, Double_t &DS1 ) | |
1006 | const | |
1007 | { | |
1008 | //* Get dS to another particle for Bz field | |
1009 | Double_t px = fP[3]; | |
1010 | Double_t py = fP[4]; | |
1011 | Double_t pz = fP[5]; | |
1012 | ||
1013 | Double_t px1 = p.fP[3]; | |
1014 | Double_t py1 = p.fP[4]; | |
1015 | Double_t pz1 = p.fP[5]; | |
1016 | ||
1017 | const Double_t kCLight = 0.000299792458; | |
1018 | ||
1019 | Double_t bq = B*fQ*kCLight; | |
1020 | Double_t bq1 = B*p.fQ*kCLight; | |
1021 | Double_t s=0, ds=0, s1=0, ds1=0; | |
1022 | ||
1023 | if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){ | |
1024 | ||
1025 | Double_t dx = (p.fP[0] - fP[0]); | |
1026 | Double_t dy = (p.fP[1] - fP[1]); | |
1027 | Double_t d2 = (dx*dx+dy*dy); | |
1028 | ||
1029 | Double_t p2 = (px *px + py *py); | |
1030 | Double_t p21 = (px1*px1 + py1*py1); | |
1031 | ||
1032 | Double_t a = (px*py1 - py*px1); | |
1033 | Double_t b = (px*px1 + py*py1); | |
1034 | ||
1035 | Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ; | |
1036 | Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ; | |
1037 | Double_t l2 = ldx*ldx + ldy*ldy; | |
1038 | ||
1039 | Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b; | |
1040 | Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b; | |
1041 | ||
1042 | Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ; | |
1043 | Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ; | |
1044 | ||
1045 | Double_t sa = 4*l2*p2 - ca*ca; | |
1046 | Double_t sa1 = 4*l2*p21 - ca1*ca1; | |
1047 | ||
1048 | if(sa<0) sa=0; | |
1049 | if(sa1<0)sa1=0; | |
1050 | ||
1051 | if( TMath::Abs(bq)>1.e-8){ | |
1052 | s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq; | |
1053 | ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq; | |
1054 | } else { | |
1055 | s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2; | |
1056 | ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2; | |
1057 | if( ds<0 ) ds = 0; | |
1058 | ds = TMath::Sqrt(ds); | |
1059 | } | |
1060 | ||
1061 | if( TMath::Abs(bq1)>1.e-8){ | |
1062 | s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1; | |
1063 | ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1; | |
1064 | } else { | |
1065 | s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21; | |
1066 | ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21; | |
1067 | if( ds1<0 ) ds1 = 0; | |
1068 | ds1 = TMath::Sqrt(ds1); | |
1069 | } | |
1070 | } | |
1071 | ||
1072 | Double_t ss[2], ss1[2], g[2][5],g1[2][5]; | |
1073 | ||
1074 | ss[0] = s + ds; | |
1075 | ss[1] = s - ds; | |
1076 | ss1[0] = s1 + ds1; | |
1077 | ss1[1] = s1 - ds1; | |
1078 | for( Int_t i=0; i<2; i++){ | |
1079 | Double_t bs = bq*ss[i]; | |
1080 | Double_t c = TMath::Cos(bs), sss = TMath::Sin(bs); | |
1081 | Double_t cB,sB; | |
1082 | if( TMath::Abs(bq)>1.e-8){ | |
1083 | cB= (1-c)/bq; | |
1084 | sB= sss/bq; | |
1085 | }else{ | |
1086 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); | |
1087 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i]; | |
1088 | cB = .5*sB*bs; | |
1089 | } | |
1090 | g[i][0] = fP[0] + sB*px + cB*py; | |
1091 | g[i][1] = fP[1] - cB*px + sB*py; | |
1092 | g[i][2] = fP[2] + ss[i]*pz; | |
1093 | g[i][3] = + c*px + sss*py; | |
1094 | g[i][4] = - sss*px + c*py; | |
1095 | ||
1096 | bs = bq1*ss1[i]; | |
1097 | c = TMath::Cos(bs); sss = TMath::Sin(bs); | |
1098 | if( TMath::Abs(bq1)>1.e-8){ | |
1099 | cB= (1-c)/bq1; | |
1100 | sB= sss/bq1; | |
1101 | }else{ | |
1102 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); | |
1103 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss1[i]; | |
1104 | cB = .5*sB*bs; | |
1105 | } | |
1106 | ||
1107 | g1[i][0] = p.fP[0] + sB*px1 + cB*py1; | |
1108 | g1[i][1] = p.fP[1] - cB*px1 + sB*py1; | |
1109 | g1[i][2] = p.fP[2] + ss[i]*pz1; | |
1110 | g1[i][3] = + c*px1 + sss*py1; | |
1111 | g1[i][4] = - sss*px1 + c*py1; | |
1112 | } | |
1113 | ||
1114 | Int_t i=0, i1=0; | |
1115 | ||
1116 | Double_t dMin = 1.e10; | |
1117 | for( Int_t j=0; j<2; j++){ | |
1118 | for( Int_t j1=0; j1<2; j1++){ | |
1119 | Double_t xx = g[j][0]-g1[j1][0]; | |
1120 | Double_t yy = g[j][1]-g1[j1][1]; | |
1121 | Double_t zz = g[j][2]-g1[j1][2]; | |
1122 | Double_t d = xx*xx + yy*yy + zz*zz; | |
1123 | if( d<dMin ){ | |
1124 | dMin = d; | |
1125 | i = j; | |
1126 | i1 = j1; | |
1127 | } | |
1128 | } | |
1129 | } | |
1130 | ||
1131 | DS = ss[i]; | |
1132 | DS1 = ss1[i1]; | |
1133 | if(0){ | |
1134 | Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4]; | |
1135 | Double_t x1=g1[i1][0], y1= g1[i1][1], z1= g1[i1][2], ppx1= g1[i1][3], ppy1= g1[i1][4]; | |
1136 | Double_t dx = x1-x; | |
1137 | Double_t dy = y1-y; | |
1138 | Double_t dz = z1-z; | |
1139 | Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1; | |
1140 | Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1; | |
1141 | Double_t c = dx*ppx + dy*ppy + dz*pz ; | |
1142 | Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz; | |
1143 | Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1; | |
1144 | Double_t det = pp2*pp21 - a*a; | |
1145 | if( TMath::Abs(det)>1.e-8 ){ | |
1146 | DS+=(a*b-pp21*c)/det; | |
1147 | DS1+=(a*c-pp2*b)/det; | |
1148 | } | |
1149 | } | |
1150 | } | |
1151 | ||
1152 | ||
1153 | ||
1154 | void AliKFParticleBase::TransportCBM( Double_t dS, | |
1155 | Double_t P[], Double_t C[] ) const | |
1156 | { | |
1157 | //* Transport the particle on dS, output to P[],C[], for CBM field | |
1158 | ||
1159 | if( fQ==0 ){ | |
1160 | TransportLine( dS, P, C ); | |
1161 | return; | |
1162 | } | |
1163 | ||
1164 | const Double_t kCLight = 0.000299792458; | |
1165 | ||
1166 | Double_t c = fQ*kCLight; | |
1167 | ||
1168 | // construct coefficients | |
1169 | ||
1170 | Double_t | |
1171 | px = fP[3], | |
1172 | py = fP[4], | |
1173 | pz = fP[5]; | |
1174 | ||
1175 | Double_t sx=0, sy=0, sz=0, syy=0, syz=0, syyy=0, ssx=0, ssy=0, ssz=0, ssyy=0, ssyz=0, ssyyy=0; | |
1176 | ||
1177 | { // get field integrals | |
1178 | ||
1179 | Double_t fld[3][3]; | |
1180 | Double_t p0[3], p1[3], p2[3]; | |
1181 | ||
1182 | // line track approximation | |
1183 | ||
1184 | p0[0] = fP[0]; | |
1185 | p0[1] = fP[1]; | |
1186 | p0[2] = fP[2]; | |
1187 | ||
1188 | p2[0] = fP[0] + px*dS; | |
1189 | p2[1] = fP[1] + py*dS; | |
1190 | p2[2] = fP[2] + pz*dS; | |
1191 | ||
1192 | p1[0] = 0.5*(p0[0]+p2[0]); | |
1193 | p1[1] = 0.5*(p0[1]+p2[1]); | |
1194 | p1[2] = 0.5*(p0[2]+p2[2]); | |
1195 | ||
1196 | // first order track approximation | |
1197 | { | |
1198 | GetFieldValue( p0, fld[0] ); | |
1199 | GetFieldValue( p1, fld[1] ); | |
1200 | GetFieldValue( p2, fld[2] ); | |
1201 | ||
1202 | Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.; | |
1203 | Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.; | |
1204 | ||
1205 | p1[0] -= ssy1*pz; | |
1206 | p1[2] += ssy1*px; | |
1207 | p2[0] -= ssy2*pz; | |
1208 | p2[2] += ssy2*px; | |
1209 | } | |
1210 | ||
1211 | GetFieldValue( p0, fld[0] ); | |
1212 | GetFieldValue( p1, fld[1] ); | |
1213 | GetFieldValue( p2, fld[2] ); | |
1214 | ||
1215 | sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.; | |
1216 | sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.; | |
1217 | sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.; | |
1218 | ||
1219 | ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.; | |
1220 | ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.; | |
1221 | ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.; | |
1222 | ||
1223 | Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360. | |
1224 | Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520. | |
1225 | for(Int_t n=0; n<3; n++) | |
1226 | for(Int_t m=0; m<3; m++) | |
1227 | { | |
1228 | syz += c2[n][m]*fld[n][1]*fld[m][2]; | |
1229 | ssyz += cc2[n][m]*fld[n][1]*fld[m][2]; | |
1230 | } | |
1231 | ||
1232 | syz *= c*c*dS*dS/360.; | |
1233 | ssyz *= c*c*dS*dS*dS/2520.; | |
1234 | ||
1235 | syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS; | |
1236 | syyy = syy*syy*syy / 1296; | |
1237 | syy = syy*syy/72; | |
1238 | ||
1239 | ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+ | |
1240 | fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+ | |
1241 | fld[2][1]*( 3*fld[2][1] ) | |
1242 | )*dS*dS*dS*c*c/2520.; | |
1243 | ssyyy = | |
1244 | ( | |
1245 | fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+ | |
1246 | fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+ | |
1247 | fld[2][1]*( 19*fld[2][1] ) )+ | |
1248 | fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+ | |
1249 | fld[2][1]*( 62*fld[2][1] ) )+ | |
1250 | fld[2][1]*fld[2][1] *( 3*fld[2][1] ) | |
1251 | )*dS*dS*dS*dS*c*c*c/90720.; | |
1252 | ||
1253 | } | |
1254 | ||
1255 | Double_t mJ[8][8]; | |
1256 | for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0; | |
1257 | ||
1258 | mJ[0][0]=1; mJ[0][1]=0; mJ[0][2]=0; mJ[0][3]=dS-ssyy; mJ[0][4]=ssx; mJ[0][5]=ssyyy-ssy; | |
1259 | mJ[1][0]=0; mJ[1][1]=1; mJ[1][2]=0; mJ[1][3]=-ssz; mJ[1][4]=dS; mJ[1][5]=ssx+ssyz; | |
1260 | mJ[2][0]=0; mJ[2][1]=0; mJ[2][2]=1; mJ[2][3]=ssy-ssyyy; mJ[2][4]=-ssx; mJ[2][5]=dS-ssyy; | |
1261 | ||
1262 | mJ[3][0]=0; mJ[3][1]=0; mJ[3][2]=0; mJ[3][3]=1-syy; mJ[3][4]=sx; mJ[3][5]=syyy-sy; | |
1263 | mJ[4][0]=0; mJ[4][1]=0; mJ[4][2]=0; mJ[4][3]=-sz; mJ[4][4]=1; mJ[4][5]=sx+syz; | |
1264 | mJ[5][0]=0; mJ[5][1]=0; mJ[5][2]=0; mJ[5][3]=sy-syyy; mJ[5][4]=-sx; mJ[5][5]=1-syy; | |
1265 | mJ[6][6] = mJ[7][7] = 1; | |
1266 | ||
1267 | P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz; | |
1268 | P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz; | |
1269 | P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz; | |
1270 | P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz; | |
1271 | P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz; | |
1272 | P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz; | |
1273 | P[6] = fP[6]; | |
1274 | P[7] = fP[7]; | |
1275 | ||
1276 | MultQSQt( mJ[0], fC, C); | |
1277 | ||
1278 | } | |
1279 | ||
1280 | ||
1281 | void AliKFParticleBase::TransportBz( Double_t b, Double_t t, | |
1282 | Double_t p[], Double_t e[] ) const | |
1283 | { | |
1284 | //* Transport the particle on dS, output to P[],C[], for Bz field | |
1285 | ||
1286 | const Double_t kCLight = 0.000299792458; | |
1287 | b = b*fQ*kCLight; | |
1288 | Double_t bs= b*t; | |
1289 | Double_t s = TMath::Sin(bs), c = TMath::Cos(bs); | |
1290 | Double_t sB, cB; | |
1291 | if( TMath::Abs(bs)>1.e-10){ | |
1292 | sB= s/b; | |
1293 | cB= (1-c)/b; | |
1294 | }else{ | |
1295 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); | |
1296 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*t; | |
1297 | cB = .5*sB*bs; | |
1298 | } | |
1299 | ||
1300 | Double_t px = fP[3]; | |
1301 | Double_t py = fP[4]; | |
1302 | Double_t pz = fP[5]; | |
1303 | ||
1304 | p[0] = fP[0] + sB*px + cB*py; | |
1305 | p[1] = fP[1] - cB*px + sB*py; | |
1306 | p[2] = fP[2] + t*pz; | |
1307 | p[3] = c*px + s*py; | |
1308 | p[4] = -s*px + c*py; | |
1309 | p[5] = fP[5]; | |
1310 | p[6] = fP[6]; | |
1311 | p[7] = fP[7]; | |
1312 | ||
1313 | /* | |
1314 | Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 }, | |
1315 | {0,1,0, -cB, sB, 0, 0, 0 }, | |
1316 | {0,0,1, 0, 0, t, 0, 0 }, | |
1317 | {0,0,0, c, s, 0, 0, 0 }, | |
1318 | {0,0,0, -s, c, 0, 0, 0 }, | |
1319 | {0,0,0, 0, 0, 1, 0, 0 }, | |
1320 | {0,0,0, 0, 0, 0, 1, 0 }, | |
1321 | {0,0,0, 0, 0, 0, 0, 1 } }; | |
1322 | Double_t mA[8][8]; | |
1323 | for( Int_t k=0,i=0; i<8; i++) | |
1324 | for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k]; | |
1325 | ||
1326 | Double_t mJC[8][8]; | |
1327 | for( Int_t i=0; i<8; i++ ) | |
1328 | for( Int_t j=0; j<8; j++ ){ | |
1329 | mJC[i][j]=0; | |
1330 | for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j]; | |
1331 | } | |
1332 | ||
1333 | for( Int_t k=0,i=0; i<8; i++) | |
1334 | for( Int_t j=0; j<=i; j++, k++ ){ | |
1335 | e[k] = 0; | |
1336 | for( Int_t l=0; l<8; l++ ) e[k]+=mJC[i][l]*mJ[j][l]; | |
1337 | } | |
1338 | ||
1339 | return; | |
1340 | */ | |
1341 | ||
1342 | Double_t | |
1343 | c6=fC[6], c7=fC[7], c8=fC[8], c17=fC[17], c18=fC[18], | |
1344 | c24 = fC[24], c31 = fC[31]; | |
1345 | ||
1346 | Double_t | |
1347 | cBC13 = cB*fC[13], | |
1348 | mJC13 = c7 - cB*fC[9] + sB*fC[13], | |
1349 | mJC14 = fC[11] - cBC13 + sB*fC[14], | |
1350 | mJC23 = c8 + t*c18, | |
1351 | mJC24 = fC[12] + t*fC[19], | |
1352 | mJC33 = c*fC[9] + s*fC[13], | |
1353 | mJC34 = c*fC[13] + s*fC[14], | |
1354 | mJC43 = -s*fC[9] + c*fC[13], | |
1355 | mJC44 = -s*fC[13] + c*fC[14]; | |
1356 | ||
1357 | ||
1358 | e[0]= fC[0] + 2*(sB*c6 + cB*fC[10]) + (sB*fC[9] + 2*cBC13)*sB + cB*cB*fC[14]; | |
1359 | e[1]= fC[1] - cB*c6 + sB*fC[10] + mJC13*sB + mJC14*cB; | |
1360 | e[2]= fC[2] - cB*c7 + sB*fC[11] - mJC13*cB + mJC14*sB; | |
1361 | e[3]= fC[3] + t*fC[15] + mJC23*sB + mJC24*cB; | |
1362 | e[4]= fC[4] + t*fC[16] - mJC23*cB + mJC24*sB; | |
1363 | ||
1364 | e[15]= fC[15] + c18*sB + fC[19]*cB; | |
1365 | e[16]= fC[16] - c18*cB + fC[19]*sB; | |
1366 | e[17]= c17 + fC[20]*t; | |
1367 | e[18]= c18*c + fC[19]*s; | |
1368 | e[19]= -c18*s + fC[19]*c; | |
1369 | ||
1370 | e[5]= fC[5] + (c17 + e[17] )*t; | |
1371 | ||
1372 | e[6]= c*c6 + s*fC[10] + mJC33*sB + mJC34*cB; | |
1373 | e[7]= c*c7 + s*fC[11] - mJC33*cB + mJC34*sB; | |
1374 | e[8]= c*c8 + s*fC[12] + e[18]*t; | |
1375 | e[9]= mJC33*c + mJC34*s; | |
1376 | e[10]= -s*c6 + c*fC[10] + mJC43*sB + mJC44*cB; | |
1377 | ||
1378 | ||
1379 | e[11]= -s*c7 + c*fC[11] - mJC43*cB + mJC44*sB; | |
1380 | e[12]= -s*c8 + c*fC[12] + e[19]*t; | |
1381 | e[13]= mJC43*c + mJC44*s; | |
1382 | e[14]= -mJC43*s + mJC44*c; | |
1383 | e[20]= fC[20]; | |
1384 | e[21]= fC[21] + fC[25]*cB + c24*sB; | |
1385 | e[22]= fC[22] - c24*cB + fC[25]*sB; | |
1386 | e[23]= fC[23] + fC[26]*t; | |
1387 | e[24]= c*c24 + s*fC[25]; | |
1388 | e[25]= c*fC[25] - c24*s; | |
1389 | e[26]= fC[26]; | |
1390 | e[27]= fC[27]; | |
1391 | e[28]= fC[28] + fC[32]*cB + c31*sB; | |
1392 | e[29]= fC[29] - c31*cB + fC[32]*sB; | |
1393 | e[30]= fC[30] + fC[33]*t; | |
1394 | e[31]= c*c31 + s*fC[32]; | |
1395 | e[32]= c*fC[32] - s*c31; | |
1396 | e[33]= fC[33]; | |
1397 | e[34]= fC[34]; | |
1398 | e[35]= fC[35]; | |
1399 | } | |
1400 | ||
1401 | ||
1402 | Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const | |
1403 | { | |
1404 | //* Calculate distance from vertex [cm] | |
1405 | ||
1406 | return GetDistanceFromVertex( Vtx.fP ); | |
1407 | } | |
1408 | ||
1409 | Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const | |
1410 | { | |
1411 | //* Calculate distance from vertex [cm] | |
1412 | ||
1413 | Double_t mP[8], mC[36]; | |
1414 | Transport( GetDStoPoint(vtx), mP, mC ); | |
1415 | Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]}; | |
1416 | return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] ); | |
1417 | } | |
1418 | ||
1419 | Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p ) | |
1420 | const | |
1421 | { | |
1422 | //* Calculate distance to other particle [cm] | |
1423 | ||
1424 | Double_t dS, dS1; | |
1425 | GetDStoParticle( p, dS, dS1 ); | |
1426 | Double_t mP[8], mC[36], mP1[8], mC1[36]; | |
1427 | Transport( dS, mP, mC ); | |
1428 | p.Transport( dS1, mP1, mC1 ); | |
1429 | Double_t dx = mP[0]-mP1[0]; | |
1430 | Double_t dy = mP[1]-mP1[1]; | |
1431 | Double_t dz = mP[2]-mP1[2]; | |
1432 | return TMath::Sqrt(dx*dx+dy*dy+dz*dz); | |
1433 | } | |
1434 | ||
1435 | Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const | |
1436 | { | |
1437 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1438 | ||
1439 | return GetDeviationFromVertex( Vtx.fP, Vtx.fC ); | |
1440 | } | |
1441 | ||
1442 | ||
1443 | Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const | |
1444 | { | |
1445 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1446 | //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix | |
1447 | ||
1448 | Double_t mP[8]; | |
1449 | Double_t mC[36]; | |
1450 | ||
1451 | Transport( GetDStoPoint(v), mP, mC ); | |
1452 | ||
1453 | Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]}; | |
1454 | ||
1455 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1456 | (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) ); | |
1457 | ||
1458 | ||
1459 | Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS }; | |
1460 | ||
1461 | Double_t mSi[6] = | |
1462 | { mC[0] +h[0]*h[0], | |
1463 | mC[1] +h[1]*h[0], mC[2] +h[1]*h[1], | |
1464 | mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] }; | |
1465 | ||
1466 | if( Cv ){ | |
1467 | mSi[0]+=Cv[0]; | |
1468 | mSi[1]+=Cv[1]; | |
1469 | mSi[2]+=Cv[2]; | |
1470 | mSi[3]+=Cv[3]; | |
1471 | mSi[4]+=Cv[4]; | |
1472 | mSi[5]+=Cv[5]; | |
1473 | } | |
1474 | ||
1475 | Double_t mS[6]; | |
1476 | ||
1477 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1478 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1479 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1480 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1481 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1482 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1483 | ||
1484 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1485 | s = ( s > 1.E-20 ) ?1./s :0; | |
1486 | ||
1487 | return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0] | |
1488 | +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1] | |
1489 | +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2); | |
1490 | } | |
1491 | ||
1492 | ||
1493 | Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p ) | |
1494 | const | |
1495 | { | |
1496 | //* Calculate sqrt(Chi2/ndf) deviation from other particle | |
1497 | ||
1498 | Double_t dS, dS1; | |
1499 | GetDStoParticle( p, dS, dS1 ); | |
1500 | Double_t mP1[8], mC1[36]; | |
1501 | p.Transport( dS1, mP1, mC1 ); | |
1502 | ||
1503 | Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]}; | |
1504 | ||
1505 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1506 | (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) ); | |
1507 | ||
1508 | Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS }; | |
1509 | ||
1510 | mC1[0] +=h[0]*h[0]; | |
1511 | mC1[1] +=h[1]*h[0]; | |
1512 | mC1[2] +=h[1]*h[1]; | |
1513 | mC1[3] +=h[2]*h[0]; | |
1514 | mC1[4] +=h[2]*h[1]; | |
1515 | mC1[5] +=h[2]*h[2]; | |
1516 | ||
1517 | return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.); | |
1518 | } | |
1519 | ||
1520 | ||
1521 | ||
1522 | void AliKFParticleBase::SubtractFromVertex( AliKFParticleBase &Vtx ) const | |
1523 | { | |
1524 | //* Subtract the particle from the vertex | |
1525 | ||
1526 | Double_t fld[3]; | |
1527 | { | |
1528 | GetFieldValue( Vtx.fP, fld ); | |
1529 | const Double_t kCLight = 0.000299792458; | |
1530 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
1531 | } | |
1532 | ||
1533 | Double_t m[8]; | |
1534 | Double_t mCm[36]; | |
1535 | ||
1536 | if( Vtx.fIsLinearized ){ | |
1537 | GetMeasurement( Vtx.fVtxGuess, m, mCm ); | |
1538 | } else { | |
1539 | GetMeasurement( Vtx.fP, m, mCm ); | |
1540 | } | |
1541 | ||
1542 | Double_t mV[6]; | |
1543 | ||
1544 | mV[ 0] = mCm[ 0]; | |
1545 | mV[ 1] = mCm[ 1]; | |
1546 | mV[ 2] = mCm[ 2]; | |
1547 | mV[ 3] = mCm[ 3]; | |
1548 | mV[ 4] = mCm[ 4]; | |
1549 | mV[ 5] = mCm[ 5]; | |
1550 | ||
1551 | //* | |
1552 | ||
1553 | Double_t mS[6]; | |
1554 | { | |
1555 | Double_t mSi[6] = { mV[0]-Vtx.fC[0], | |
1556 | mV[1]-Vtx.fC[1], mV[2]-Vtx.fC[2], | |
1557 | mV[3]-Vtx.fC[3], mV[4]-Vtx.fC[4], mV[5]-Vtx.fC[5] }; | |
1558 | ||
1559 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1560 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1561 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1562 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1563 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1564 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1565 | ||
1566 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1567 | s = ( s > 1.E-20 ) ?1./s :0; | |
1568 | mS[0]*=s; | |
1569 | mS[1]*=s; | |
1570 | mS[2]*=s; | |
1571 | mS[3]*=s; | |
1572 | mS[4]*=s; | |
1573 | mS[5]*=s; | |
1574 | } | |
1575 | ||
1576 | //* Residual (measured - estimated) | |
1577 | ||
1578 | Double_t zeta[3] = { m[0]-Vtx.fP[0], m[1]-Vtx.fP[1], m[2]-Vtx.fP[2] }; | |
1579 | ||
1580 | //* mCHt = mCH' - D' | |
1581 | ||
1582 | Double_t mCHt0[3], mCHt1[3], mCHt2[3]; | |
1583 | ||
1584 | mCHt0[0]=Vtx.fC[ 0] ; mCHt1[0]=Vtx.fC[ 1] ; mCHt2[0]=Vtx.fC[ 3] ; | |
1585 | mCHt0[1]=Vtx.fC[ 1] ; mCHt1[1]=Vtx.fC[ 2] ; mCHt2[1]=Vtx.fC[ 4] ; | |
1586 | mCHt0[2]=Vtx.fC[ 3] ; mCHt1[2]=Vtx.fC[ 4] ; mCHt2[2]=Vtx.fC[ 5] ; | |
1587 | ||
1588 | //* Kalman gain K = mCH'*S | |
1589 | ||
1590 | Double_t k0[3], k1[3], k2[3]; | |
1591 | ||
1592 | for(Int_t i=0;i<3;++i){ | |
1593 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
1594 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
1595 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
1596 | } | |
1597 | ||
1598 | //* New estimation of the vertex position r += K*zeta | |
1599 | ||
1600 | Double_t dChi2 = -(mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
1601 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
1602 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
1603 | ||
1604 | if( Vtx.fChi2 - dChi2 < 0 ) return; | |
1605 | ||
1606 | for(Int_t i=0;i<3;++i) | |
1607 | Vtx.fP[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; | |
1608 | ||
1609 | //* New covariance matrix C -= K*(mCH')' | |
1610 | ||
1611 | for(Int_t i=0, k=0;i<3;++i){ | |
1612 | for(Int_t j=0;j<=i;++j,++k) | |
1613 | Vtx.fC[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j]; | |
1614 | } | |
1615 | ||
1616 | //* Calculate Chi^2 | |
1617 | ||
1618 | Vtx.fNDF -= 2; | |
1619 | Vtx.fChi2 -= dChi2; | |
1620 | } | |
1621 | ||
1622 | ||
1623 | ||
1624 | void AliKFParticleBase::TransportLine( Double_t dS, | |
1625 | Double_t P[], Double_t C[] ) const | |
1626 | { | |
1627 | //* Transport the particle as a straight line | |
1628 | ||
1629 | P[0] = fP[0] + dS*fP[3]; | |
1630 | P[1] = fP[1] + dS*fP[4]; | |
1631 | P[2] = fP[2] + dS*fP[5]; | |
1632 | P[3] = fP[3]; | |
1633 | P[4] = fP[4]; | |
1634 | P[5] = fP[5]; | |
1635 | P[6] = fP[6]; | |
1636 | P[7] = fP[7]; | |
1637 | ||
1638 | Double_t c6 = fC[ 6] + dS*fC[ 9]; | |
1639 | Double_t c11 = fC[11] + dS*fC[14]; | |
1640 | Double_t c17 = fC[17] + dS*fC[20]; | |
1641 | Double_t sc13 = dS*fC[13]; | |
1642 | Double_t sc18 = dS*fC[18]; | |
1643 | Double_t sc19 = dS*fC[19]; | |
1644 | ||
1645 | C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 ); | |
1646 | C[ 2] = fC[ 2] + dS*( fC[11] + c11 ); | |
1647 | C[ 5] = fC[ 5] + dS*( fC[17] + c17 ); | |
1648 | ||
1649 | C[ 7] = fC[ 7] + sc13; | |
1650 | C[ 8] = fC[ 8] + sc18; | |
1651 | C[ 9] = fC[ 9]; | |
1652 | ||
1653 | C[12] = fC[12] + sc19; | |
1654 | ||
1655 | C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] ); | |
1656 | C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] ); | |
1657 | C[ 4] = fC[ 4] + dS*( fC[16] + C[12] ); | |
1658 | C[ 6] = c6; | |
1659 | ||
1660 | C[10] = fC[10] + sc13; | |
1661 | C[11] = c11; | |
1662 | ||
1663 | C[13] = fC[13]; | |
1664 | C[14] = fC[14]; | |
1665 | C[15] = fC[15] + sc18; | |
1666 | C[16] = fC[16] + sc19; | |
1667 | C[17] = c17; | |
1668 | ||
1669 | C[18] = fC[18]; | |
1670 | C[19] = fC[19]; | |
1671 | C[20] = fC[20]; | |
1672 | C[21] = fC[21] + dS*fC[24]; | |
1673 | C[22] = fC[22] + dS*fC[25]; | |
1674 | C[23] = fC[23] + dS*fC[26]; | |
1675 | ||
1676 | C[24] = fC[24]; | |
1677 | C[25] = fC[25]; | |
1678 | C[26] = fC[26]; | |
1679 | C[27] = fC[27]; | |
1680 | C[28] = fC[28] + dS*fC[31]; | |
1681 | C[29] = fC[29] + dS*fC[32]; | |
1682 | C[30] = fC[30] + dS*fC[33]; | |
1683 | ||
1684 | C[31] = fC[31]; | |
1685 | C[32] = fC[32]; | |
1686 | C[33] = fC[33]; | |
1687 | C[34] = fC[34]; | |
1688 | C[35] = fC[35]; | |
1689 | } | |
1690 | ||
1691 | ||
1692 | void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] ) | |
1693 | { | |
1694 | //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric | |
1695 | ||
1696 | const Int_t kN= 8; | |
1697 | Double_t mA[kN*kN]; | |
1698 | ||
1699 | for( Int_t i=0, ij=0; i<kN; i++ ){ | |
1700 | for( Int_t j=0; j<kN; j++, ++ij ){ | |
1701 | mA[ij] = 0 ; | |
1702 | 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]; | |
1703 | } | |
1704 | } | |
1705 | ||
1706 | for( Int_t i=0; i<kN; i++ ){ | |
1707 | for( Int_t j=0; j<=i; j++ ){ | |
1708 | Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i; | |
1709 | SOut[ij] = 0 ; | |
1710 | for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ]; | |
1711 | } | |
1712 | } | |
1713 | } | |
1714 | ||
1715 | ||
1716 | // 72-charachters line to define the printer border | |
1717 | //3456789012345678901234567890123456789012345678901234567890123456789012 | |
1718 |