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f826d409 | 1 | //--------------------------------------------------------------------------------- |
2 | // Implementation of the AliKFParticleBase class | |
3 | // . | |
4 | // @author S.Gorbunov, I.Kisel | |
5 | // @version 1.0 | |
6 | // @since 13.05.07 | |
7 | // | |
8 | // Class to reconstruct and store the decayed particle parameters. | |
9 | // The method is described in CBM-SOFT note 2007-003, | |
10 | // ``Reconstruction of decayed particles based on the Kalman filter'', | |
11 | // http://www.gsi.de/documents/DOC-2007-May-14-1.pdf | |
12 | // | |
13 | // This class describes general mathematics which is used by AliKFParticle class | |
14 | // | |
15 | // -= Copyright © ALICE HLT Group =- | |
16 | //_________________________________________________________________________________ | |
17 | ||
18 | ||
19 | #include "AliKFParticleBase.h" | |
20 | #include "TMath.h" | |
21 | ||
effa6338 | 22 | ClassImp(AliKFParticleBase) |
f826d409 | 23 | |
24 | ||
25 | AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0) | |
26 | { | |
27 | //* Constructor | |
28 | ||
29 | Initialize(); | |
30 | } | |
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]; | |
706952f5 | 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] ) ); | |
e7b09c95 | 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 | ||
5fc72f28 | 105 | Int_t AliKFParticleBase::GetMomentum( Double_t &p, Double_t &error ) const |
f826d409 | 106 | { |
107 | //* Calculate particle momentum | |
108 | ||
109 | Double_t x = fP[3]; | |
110 | Double_t y = fP[4]; | |
111 | Double_t z = fP[5]; | |
55ac3e1e | 112 | |
f826d409 | 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; | |
5fc72f28 | 117 | p = TMath::Sqrt(p2); |
55ac3e1e | 118 | |
5fc72f28 | 119 | error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ); |
55ac3e1e | 120 | if( error>1.e-16 && p>1.e-4 ){ |
5fc72f28 | 121 | error = TMath::Sqrt(error)/p; |
f826d409 | 122 | return 0; |
123 | } | |
55ac3e1e | 124 | error = 1.e8; |
f826d409 | 125 | return 1; |
126 | } | |
127 | ||
5fc72f28 | 128 | Int_t AliKFParticleBase::GetPt( Double_t &pt, Double_t &error ) const |
706952f5 | 129 | { |
130 | //* Calculate particle transverse momentum | |
131 | ||
132 | Double_t px = fP[3]; | |
133 | Double_t py = fP[4]; | |
134 | Double_t px2 = px*px; | |
135 | Double_t py2 = py*py; | |
136 | Double_t pt2 = px2+py2; | |
5fc72f28 | 137 | pt = TMath::Sqrt(pt2); |
138 | error = (px2*fC[9] + py2*fC[14] + 2*px*py*fC[13] ); | |
139 | if( error>0 && pt>1.e-4 ){ | |
140 | error = TMath::Sqrt(error)/pt; | |
706952f5 | 141 | return 0; |
142 | } | |
5fc72f28 | 143 | error = 1.e10; |
706952f5 | 144 | return 1; |
145 | } | |
146 | ||
5fc72f28 | 147 | Int_t AliKFParticleBase::GetEta( Double_t &eta, Double_t &error ) const |
706952f5 | 148 | { |
149 | //* Calculate particle pseudorapidity | |
150 | ||
151 | Double_t px = fP[3]; | |
152 | Double_t py = fP[4]; | |
153 | Double_t pz = fP[5]; | |
154 | Double_t pt2 = px*px + py*py; | |
155 | Double_t p2 = pt2 + pz*pz; | |
156 | Double_t p = TMath::Sqrt(p2); | |
157 | Double_t a = p + pz; | |
158 | Double_t b = p - pz; | |
5fc72f28 | 159 | eta = 1.e10; |
706952f5 | 160 | if( b > 1.e-8 ){ |
161 | Double_t c = a/b; | |
a65041d0 | 162 | if( c>1.e-8 ) eta = 0.5*TMath::Log(c); |
706952f5 | 163 | } |
164 | Double_t h3 = -px*pz; | |
a65041d0 | 165 | Double_t h4 = -py*pz; |
166 | Double_t pt4 = pt2*pt2; | |
167 | Double_t p2pt4 = p2*pt4; | |
168 | error = (h3*h3*fC[9] + h4*h4*fC[14] + pt4*fC[20] + 2*( h3*(h4*fC[13] + fC[18]*pt2) + pt2*h4*fC[19] ) ); | |
706952f5 | 169 | |
a65041d0 | 170 | if( error>0 && p2pt4>1.e-10 ){ |
171 | error = TMath::Sqrt(error/p2pt4); | |
706952f5 | 172 | return 0; |
173 | } | |
a65041d0 | 174 | |
5fc72f28 | 175 | error = 1.e10; |
706952f5 | 176 | return 1; |
177 | } | |
178 | ||
5fc72f28 | 179 | Int_t AliKFParticleBase::GetPhi( Double_t &phi, Double_t &error ) const |
706952f5 | 180 | { |
181 | //* Calculate particle polar angle | |
182 | ||
183 | Double_t px = fP[3]; | |
184 | Double_t py = fP[4]; | |
185 | Double_t px2 = px*px; | |
186 | Double_t py2 = py*py; | |
187 | Double_t pt2 = px2 + py2; | |
5fc72f28 | 188 | phi = TMath::ATan2(py,px); |
189 | error = (py2*fC[9] + px2*fC[14] - 2*px*py*fC[13] ); | |
190 | if( error>0 && pt2>1.e-4 ){ | |
191 | error = TMath::Sqrt(error)/pt2; | |
706952f5 | 192 | return 0; |
193 | } | |
5fc72f28 | 194 | error = 1.e10; |
706952f5 | 195 | return 1; |
196 | } | |
197 | ||
5fc72f28 | 198 | Int_t AliKFParticleBase::GetR( Double_t &r, Double_t &error ) const |
706952f5 | 199 | { |
200 | //* Calculate distance to the origin | |
201 | ||
202 | Double_t x = fP[0]; | |
203 | Double_t y = fP[1]; | |
204 | Double_t x2 = x*x; | |
205 | Double_t y2 = y*y; | |
5fc72f28 | 206 | r = TMath::Sqrt(x2 + y2); |
207 | error = (x2*fC[0] + y2*fC[2] - 2*x*y*fC[1] ); | |
208 | if( error>0 && r>1.e-4 ){ | |
209 | error = TMath::Sqrt(error)/r; | |
706952f5 | 210 | return 0; |
211 | } | |
5fc72f28 | 212 | error = 1.e10; |
706952f5 | 213 | return 1; |
214 | } | |
215 | ||
5fc72f28 | 216 | Int_t AliKFParticleBase::GetMass( Double_t &m, Double_t &error ) const |
f826d409 | 217 | { |
218 | //* Calculate particle mass | |
219 | ||
220 | // s = sigma^2 of m2/2 | |
221 | ||
222 | Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20] | |
223 | + fP[6]*fP[6]*fC[27] | |
224 | +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19]) | |
225 | - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) ) | |
226 | ); | |
706952f5 | 227 | Double_t m2 = TMath::Abs(fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5]); |
5fc72f28 | 228 | m = TMath::Sqrt(m2); |
229 | if( m>1.e-10 ){ | |
616ffc76 | 230 | if( s>=0 ){ |
5fc72f28 | 231 | error = TMath::Sqrt(s)/m; |
616ffc76 | 232 | return 0; |
233 | } | |
f826d409 | 234 | } |
5fc72f28 | 235 | error = 1.e20; |
f826d409 | 236 | return 1; |
237 | } | |
238 | ||
239 | ||
5fc72f28 | 240 | Int_t AliKFParticleBase::GetDecayLength( Double_t &l, Double_t &error ) const |
f826d409 | 241 | { |
242 | //* Calculate particle decay length [cm] | |
243 | ||
244 | Double_t x = fP[3]; | |
245 | Double_t y = fP[4]; | |
246 | Double_t z = fP[5]; | |
247 | Double_t t = fP[7]; | |
248 | Double_t x2 = x*x; | |
249 | Double_t y2 = y*y; | |
250 | Double_t z2 = z*z; | |
251 | Double_t p2 = x2+y2+z2; | |
5fc72f28 | 252 | l = t*TMath::Sqrt(p2); |
f826d409 | 253 | if( p2>1.e-4){ |
5fc72f28 | 254 | error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20] |
f826d409 | 255 | + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ) |
256 | + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]); | |
5fc72f28 | 257 | error = TMath::Sqrt(TMath::Abs(error)); |
f826d409 | 258 | return 0; |
259 | } | |
5fc72f28 | 260 | error = 1.e20; |
f826d409 | 261 | return 1; |
262 | } | |
263 | ||
446ce366 | 264 | Int_t AliKFParticleBase::GetDecayLengthXY( Double_t &l, Double_t &error ) const |
265 | { | |
266 | //* Calculate particle decay length in XY projection [cm] | |
267 | ||
268 | Double_t x = fP[3]; | |
269 | Double_t y = fP[4]; | |
270 | Double_t t = fP[7]; | |
271 | Double_t x2 = x*x; | |
272 | Double_t y2 = y*y; | |
273 | Double_t pt2 = x2+y2; | |
274 | l = t*TMath::Sqrt(pt2); | |
275 | if( pt2>1.e-4){ | |
276 | error = pt2*fC[35] + t*t/pt2*(x2*fC[9]+y2*fC[14] + 2*x*y*fC[13] ) | |
277 | + 2*t*(x*fC[31]+y*fC[32]); | |
278 | error = TMath::Sqrt(TMath::Abs(error)); | |
279 | return 0; | |
280 | } | |
281 | error = 1.e20; | |
282 | return 1; | |
283 | } | |
284 | ||
285 | ||
5fc72f28 | 286 | Int_t AliKFParticleBase::GetLifeTime( Double_t &tauC, Double_t &error ) const |
f826d409 | 287 | { |
288 | //* Calculate particle decay time [s] | |
289 | ||
290 | Double_t m, dm; | |
291 | GetMass( m, dm ); | |
292 | Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]); | |
5fc72f28 | 293 | tauC = fP[7]*m; |
294 | error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm; | |
295 | if( error > 0 ){ | |
296 | error = TMath::Sqrt( error ); | |
f826d409 | 297 | return 0; |
298 | } | |
5fc72f28 | 299 | error = 1.e20; |
f826d409 | 300 | return 1; |
301 | } | |
302 | ||
303 | ||
304 | void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter ) | |
305 | { | |
306 | //* Add daughter via operator+= | |
307 | ||
308 | AddDaughter( Daughter ); | |
309 | } | |
310 | ||
706952f5 | 311 | Double_t AliKFParticleBase::GetSCorrection( const Double_t Part[], const Double_t XYZ[] ) |
312 | { | |
313 | //* Get big enough correction for S error to let the particle Part be fitted to XYZ point | |
314 | ||
315 | Double_t d[3] = { XYZ[0]-Part[0], XYZ[1]-Part[1], XYZ[2]-Part[2] }; | |
316 | Double_t p2 = Part[3]*Part[3]+Part[4]*Part[4]+Part[5]*Part[5]; | |
a65041d0 | 317 | Double_t sigmaS = (p2>1.e-4) ? ( 10.1+3.*TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2]) )/TMath::Sqrt(p2) : 1.; |
706952f5 | 318 | return sigmaS; |
319 | } | |
616ffc76 | 320 | |
321 | void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const | |
322 | { | |
e7b09c95 | 323 | //* Get additional covariances V used during measurement |
324 | ||
616ffc76 | 325 | Double_t b[3]; |
326 | GetFieldValue( XYZ, b ); | |
327 | const Double_t kCLight = 0.000299792458; | |
328 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
329 | ||
330 | Transport( GetDStoPoint(XYZ), m, V ); | |
331 | ||
706952f5 | 332 | Double_t sigmaS = GetSCorrection( m, XYZ ); |
616ffc76 | 333 | |
334 | Double_t h[6]; | |
335 | ||
336 | h[0] = m[3]*sigmaS; | |
337 | h[1] = m[4]*sigmaS; | |
338 | h[2] = m[5]*sigmaS; | |
339 | h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); | |
340 | h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); | |
341 | h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); | |
342 | ||
616ffc76 | 343 | V[ 0]+= h[0]*h[0]; |
344 | V[ 1]+= h[1]*h[0]; | |
345 | V[ 2]+= h[1]*h[1]; | |
346 | V[ 3]+= h[2]*h[0]; | |
347 | V[ 4]+= h[2]*h[1]; | |
348 | V[ 5]+= h[2]*h[2]; | |
349 | ||
350 | V[ 6]+= h[3]*h[0]; | |
351 | V[ 7]+= h[3]*h[1]; | |
352 | V[ 8]+= h[3]*h[2]; | |
353 | V[ 9]+= h[3]*h[3]; | |
354 | ||
355 | V[10]+= h[4]*h[0]; | |
356 | V[11]+= h[4]*h[1]; | |
357 | V[12]+= h[4]*h[2]; | |
358 | V[13]+= h[4]*h[3]; | |
359 | V[14]+= h[4]*h[4]; | |
360 | ||
361 | V[15]+= h[5]*h[0]; | |
362 | V[16]+= h[5]*h[1]; | |
363 | V[17]+= h[5]*h[2]; | |
364 | V[18]+= h[5]*h[3]; | |
365 | V[19]+= h[5]*h[4]; | |
366 | V[20]+= h[5]*h[5]; | |
367 | } | |
368 | ||
616ffc76 | 369 | |
f826d409 | 370 | void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter ) |
371 | { | |
372 | //* Add daughter | |
373 | ||
616ffc76 | 374 | if( fNDF<-1 ){ // first daughter -> just copy |
375 | fNDF = -1; | |
376 | fQ = Daughter.GetQ(); | |
377 | for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i]; | |
378 | for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i]; | |
379 | fSFromDecay = 0; | |
380 | return; | |
381 | } | |
382 | ||
f826d409 | 383 | TransportToDecayVertex(); |
384 | ||
385 | Double_t b[3]; | |
386 | Int_t maxIter = 1; | |
387 | ||
388 | if( !fIsLinearized ){ | |
389 | if( fNDF==-1 ){ | |
390 | Double_t ds, ds1; | |
616ffc76 | 391 | GetDStoParticle(Daughter, ds, ds1); |
f826d409 | 392 | TransportToDS( ds ); |
616ffc76 | 393 | Double_t m[8]; |
394 | Double_t mCd[36]; | |
395 | Daughter.Transport( ds1, m, mCd ); | |
396 | fVtxGuess[0] = .5*( fP[0] + m[0] ); | |
397 | fVtxGuess[1] = .5*( fP[1] + m[1] ); | |
398 | fVtxGuess[2] = .5*( fP[2] + m[2] ); | |
399 | } else { | |
400 | fVtxGuess[0] = fP[0]; | |
401 | fVtxGuess[1] = fP[1]; | |
402 | fVtxGuess[2] = fP[2]; | |
f826d409 | 403 | } |
f826d409 | 404 | maxIter = 3; |
405 | } | |
406 | ||
407 | for( Int_t iter=0; iter<maxIter; iter++ ){ | |
408 | ||
409 | { | |
410 | GetFieldValue( fVtxGuess, b ); | |
411 | const Double_t kCLight = 0.000299792458; | |
412 | b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; | |
413 | } | |
f826d409 | 414 | |
616ffc76 | 415 | Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36]; |
de0d0ceb | 416 | if( fNDF==-1 ){ |
616ffc76 | 417 | GetMeasurement( fVtxGuess, tmpP, tmpC ); |
418 | ffP = tmpP; | |
419 | ffC = tmpC; | |
f826d409 | 420 | } |
421 | ||
e7b09c95 | 422 | Double_t m[8], mV[36]; |
de0d0ceb | 423 | |
e7b09c95 | 424 | if( Daughter.fC[35]>0 ){ |
425 | Daughter.GetMeasurement( fVtxGuess, m, mV ); | |
426 | } else { | |
427 | for( Int_t i=0; i<8; i++ ) m[i] = Daughter.fP[i]; | |
428 | for( Int_t i=0; i<36; i++ ) mV[i] = Daughter.fC[i]; | |
429 | } | |
de0d0ceb | 430 | |
f826d409 | 431 | //* |
432 | ||
433 | Double_t mS[6]; | |
434 | { | |
616ffc76 | 435 | Double_t mSi[6] = { ffC[0]+mV[0], |
436 | ffC[1]+mV[1], ffC[2]+mV[2], | |
437 | ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] }; | |
de0d0ceb | 438 | |
f826d409 | 439 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; |
440 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
441 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
442 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
443 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
444 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
445 | ||
706952f5 | 446 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); |
447 | ||
f826d409 | 448 | s = ( s > 1.E-20 ) ?1./s :0; |
449 | mS[0]*=s; | |
450 | mS[1]*=s; | |
451 | mS[2]*=s; | |
452 | mS[3]*=s; | |
453 | mS[4]*=s; | |
454 | mS[5]*=s; | |
455 | } | |
456 | ||
457 | //* Residual (measured - estimated) | |
458 | ||
616ffc76 | 459 | Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] }; |
de0d0ceb | 460 | |
f826d409 | 461 | |
462 | //* CHt = CH' - D' | |
463 | ||
464 | Double_t mCHt0[7], mCHt1[7], mCHt2[7]; | |
465 | ||
616ffc76 | 466 | mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ; |
467 | mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ; | |
468 | mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ; | |
469 | mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8]; | |
470 | mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12]; | |
471 | mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17]; | |
472 | mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23]; | |
f826d409 | 473 | |
474 | //* Kalman gain K = mCH'*S | |
475 | ||
476 | Double_t k0[7], k1[7], k2[7]; | |
477 | ||
478 | for(Int_t i=0;i<7;++i){ | |
479 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
480 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
481 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
482 | } | |
483 | ||
4bbc290d | 484 | //* New estimation of the vertex position |
f826d409 | 485 | |
486 | if( iter<maxIter-1 ){ | |
487 | for(Int_t i=0; i<3; ++i) | |
616ffc76 | 488 | fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2]; |
f826d409 | 489 | continue; |
490 | } | |
491 | ||
492 | // last itearation -> update the particle | |
493 | ||
494 | //* Add the daughter momentum to the particle momentum | |
495 | ||
616ffc76 | 496 | ffP[ 3] += m[ 3]; |
497 | ffP[ 4] += m[ 4]; | |
498 | ffP[ 5] += m[ 5]; | |
499 | ffP[ 6] += m[ 6]; | |
f826d409 | 500 | |
616ffc76 | 501 | ffC[ 9] += mV[ 9]; |
502 | ffC[13] += mV[13]; | |
503 | ffC[14] += mV[14]; | |
504 | ffC[18] += mV[18]; | |
505 | ffC[19] += mV[19]; | |
506 | ffC[20] += mV[20]; | |
507 | ffC[24] += mV[24]; | |
508 | ffC[25] += mV[25]; | |
509 | ffC[26] += mV[26]; | |
510 | ffC[27] += mV[27]; | |
f826d409 | 511 | |
de0d0ceb | 512 | |
513 | //* New estimation of the vertex position r += K*zeta | |
f826d409 | 514 | |
515 | for(Int_t i=0;i<7;++i) | |
616ffc76 | 516 | fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; |
f826d409 | 517 | |
518 | //* New covariance matrix C -= K*(mCH')' | |
de0d0ceb | 519 | |
f826d409 | 520 | for(Int_t i=0, k=0;i<7;++i){ |
de0d0ceb | 521 | for(Int_t j=0;j<=i;++j,++k){ |
616ffc76 | 522 | fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] ); |
de0d0ceb | 523 | } |
f826d409 | 524 | } |
de0d0ceb | 525 | |
f826d409 | 526 | //* Calculate Chi^2 |
527 | ||
528 | fNDF += 2; | |
529 | fQ += Daughter.GetQ(); | |
530 | fSFromDecay = 0; | |
531 | fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] | |
532 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
706952f5 | 533 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; |
de0d0ceb | 534 | |
f826d409 | 535 | } |
536 | } | |
537 | ||
f826d409 | 538 | void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx ) |
539 | { | |
706952f5 | 540 | //* Set production vertex for the particle, when the particle was not used in the vertex fit |
f826d409 | 541 | |
542 | const Double_t *m = Vtx.fP, *mV = Vtx.fC; | |
543 | ||
e7b09c95 | 544 | Bool_t noS = ( fC[35]<=0 ); // no decay length allowed |
545 | ||
546 | if( noS ){ | |
547 | TransportToDecayVertex(); | |
548 | fP[7] = 0; | |
55ac3e1e | 549 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[34] = fC[35] = 0; |
e7b09c95 | 550 | } else { |
55ac3e1e | 551 | TransportToDS( GetDStoPoint( m ) ); |
e7b09c95 | 552 | fP[7] = -fSFromDecay; |
55ac3e1e | 553 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[34] = 0; |
554 | fC[35] = 1000.; | |
555 | ||
e7b09c95 | 556 | Convert(1); |
557 | } | |
558 | ||
f826d409 | 559 | Double_t mAi[6]; |
706952f5 | 560 | |
446ce366 | 561 | InvertSym3( fC, mAi ); |
f826d409 | 562 | |
563 | Double_t mB[5][3]; | |
564 | ||
565 | mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3]; | |
566 | mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4]; | |
567 | mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5]; | |
568 | ||
569 | mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3]; | |
570 | mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4]; | |
571 | mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5]; | |
572 | ||
573 | mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3]; | |
574 | mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4]; | |
575 | mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5]; | |
576 | ||
577 | mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3]; | |
578 | mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4]; | |
579 | mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5]; | |
580 | ||
581 | mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3]; | |
582 | mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4]; | |
583 | mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5]; | |
584 | ||
585 | Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] }; | |
586 | ||
587 | { | |
a65041d0 | 588 | Double_t mAVi[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2], |
f826d409 | 589 | fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] }; |
706952f5 | 590 | |
a65041d0 | 591 | if( !InvertSym3( mAVi, mAVi ) ){ |
706952f5 | 592 | |
593 | Double_t dChi2 = ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0] | |
594 | +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1] | |
a65041d0 | 595 | +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] ); |
706952f5 | 596 | |
597 | // Take Abs(dChi2) here. Negative value of 'det' or 'dChi2' shows that the particle | |
598 | // was not used in the production vertex fit | |
599 | ||
600 | fChi2+= TMath::Abs( dChi2 ); | |
601 | } | |
f826d409 | 602 | fNDF += 2; |
f826d409 | 603 | } |
604 | ||
605 | fP[0] = m[0]; | |
606 | fP[1] = m[1]; | |
607 | fP[2] = m[2]; | |
608 | fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; | |
609 | fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; | |
610 | fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; | |
611 | fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2]; | |
612 | fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2]; | |
613 | ||
614 | Double_t d0, d1, d2; | |
615 | ||
616 | fC[0] = mV[0]; | |
617 | fC[1] = mV[1]; | |
618 | fC[2] = mV[2]; | |
619 | fC[3] = mV[3]; | |
620 | fC[4] = mV[4]; | |
621 | fC[5] = mV[5]; | |
622 | ||
623 | d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6]; | |
624 | d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7]; | |
625 | d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8]; | |
626 | ||
627 | fC[ 6]+= d0; | |
628 | fC[ 7]+= d1; | |
629 | fC[ 8]+= d2; | |
630 | fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
631 | ||
632 | d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10]; | |
633 | d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11]; | |
634 | d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12]; | |
635 | ||
636 | fC[10]+= d0; | |
637 | fC[11]+= d1; | |
638 | fC[12]+= d2; | |
639 | fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
640 | fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
641 | ||
642 | d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15]; | |
643 | d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16]; | |
644 | d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17]; | |
645 | ||
646 | fC[15]+= d0; | |
647 | fC[16]+= d1; | |
648 | fC[17]+= d2; | |
649 | fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
650 | fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
651 | fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
652 | ||
653 | d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21]; | |
654 | d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22]; | |
655 | d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23]; | |
656 | ||
657 | fC[21]+= d0; | |
658 | fC[22]+= d1; | |
659 | fC[23]+= d2; | |
660 | fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
661 | fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
662 | fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
663 | fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
664 | ||
665 | d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28]; | |
666 | d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29]; | |
667 | d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30]; | |
668 | ||
669 | fC[28]+= d0; | |
670 | fC[29]+= d1; | |
671 | fC[30]+= d2; | |
672 | fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
673 | fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
674 | fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
675 | fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
676 | fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2]; | |
677 | ||
e7b09c95 | 678 | if( noS ){ |
679 | fP[7] = 0; | |
55ac3e1e | 680 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[34] = fC[35] = 0; |
e7b09c95 | 681 | } else { |
682 | TransportToDS( fP[7] ); | |
683 | Convert(0); | |
684 | } | |
685 | ||
f826d409 | 686 | fSFromDecay = 0; |
f826d409 | 687 | } |
688 | ||
689 | ||
690 | ||
e7b09c95 | 691 | void AliKFParticleBase::SetMassConstraint( Double_t Mass, Double_t SigmaMass ) |
f826d409 | 692 | { |
706952f5 | 693 | //* Set hard( SigmaMass=0 ) or soft (SigmaMass>0) mass constraint |
694 | ||
695 | Double_t m2 = Mass*Mass; // measurement, weighted by Mass | |
696 | Double_t s2 = m2*SigmaMass*SigmaMass; // sigma^2 | |
697 | ||
698 | Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; | |
699 | Double_t e0 = TMath::Sqrt(m2+p2); | |
f826d409 | 700 | |
701 | Double_t mH[8]; | |
702 | mH[0] = mH[1] = mH[2] = 0.; | |
703 | mH[3] = -2*fP[3]; | |
704 | mH[4] = -2*fP[4]; | |
705 | mH[5] = -2*fP[5]; | |
706952f5 | 706 | mH[6] = 2*fP[6];//e0; |
f826d409 | 707 | mH[7] = 0; |
f826d409 | 708 | |
706952f5 | 709 | Double_t zeta = e0*e0 - e0*fP[6]; |
710 | zeta = m2 - (fP[6]*fP[6]-p2); | |
f826d409 | 711 | |
706952f5 | 712 | Double_t mCHt[8], s2_est=0; |
713 | for( Int_t i=0; i<8; ++i ){ | |
f826d409 | 714 | mCHt[i] = 0.0; |
715 | for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j]; | |
706952f5 | 716 | s2_est += mH[i]*mCHt[i]; |
f826d409 | 717 | } |
718 | ||
706952f5 | 719 | if( s2_est<1.e-20 ) return; // calculated mass error is already 0, |
720 | // the particle can not be constrained on mass | |
721 | ||
722 | Double_t w2 = 1./( s2 + s2_est ); | |
723 | fChi2 += zeta*zeta*w2; | |
f826d409 | 724 | fNDF += 1; |
725 | for( Int_t i=0, ii=0; i<8; ++i ){ | |
706952f5 | 726 | Double_t ki = mCHt[i]*w2; |
f826d409 | 727 | fP[i]+= ki*zeta; |
728 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j]; | |
729 | } | |
730 | } | |
731 | ||
732 | ||
e7b09c95 | 733 | void AliKFParticleBase::SetNoDecayLength() |
734 | { | |
735 | //* Set no decay length for resonances | |
736 | ||
737 | TransportToDecayVertex(); | |
738 | ||
739 | Double_t h[8]; | |
740 | h[0] = h[1] = h[2] = h[3] = h[4] = h[5] = h[6] = 0; | |
741 | h[7] = 1; | |
742 | ||
743 | Double_t zeta = 0 - fP[7]; | |
744 | for(Int_t i=0;i<8;++i) zeta -= h[i]*(fP[i]-fP[i]); | |
745 | ||
746 | Double_t s = fC[35]; | |
747 | if( s>1.e-20 ){ | |
748 | s = 1./s; | |
749 | fChi2 += zeta*zeta*s; | |
750 | fNDF += 1; | |
751 | for( Int_t i=0, ii=0; i<7; ++i ){ | |
752 | Double_t ki = fC[28+i]*s; | |
753 | fP[i]+= ki*zeta; | |
754 | for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*fC[28+j]; | |
755 | } | |
756 | } | |
757 | fP[7] = 0; | |
55ac3e1e | 758 | fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[34] = fC[35] = 0; |
e7b09c95 | 759 | } |
760 | ||
761 | ||
f826d409 | 762 | void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters, |
706952f5 | 763 | const AliKFParticleBase *Parent, Double_t Mass, Bool_t IsConstrained ) |
f826d409 | 764 | { |
765 | //* Full reconstruction in one go | |
766 | ||
767 | Int_t maxIter = 1; | |
768 | bool wasLinearized = fIsLinearized; | |
706952f5 | 769 | if( !fIsLinearized || IsConstrained ){ |
616ffc76 | 770 | //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!! |
771 | fVtxGuess[0] = GetX(); | |
772 | fVtxGuess[1] = GetY(); | |
773 | fVtxGuess[2] = GetZ(); | |
f826d409 | 774 | fIsLinearized = 1; |
775 | maxIter = 3; | |
776 | } | |
777 | ||
706952f5 | 778 | Double_t constraintC[6]; |
779 | ||
780 | if( IsConstrained ){ | |
781 | for(Int_t i=0;i<6;++i) constraintC[i]=fC[i]; | |
782 | } else { | |
783 | for(Int_t i=0;i<6;++i) constraintC[i]=0.; | |
784 | constraintC[0] = constraintC[2] = constraintC[5] = 100.; | |
785 | } | |
786 | ||
787 | ||
f826d409 | 788 | for( Int_t iter=0; iter<maxIter; iter++ ){ |
f826d409 | 789 | fAtProductionVertex = 0; |
790 | fSFromDecay = 0; | |
791 | fP[0] = fVtxGuess[0]; | |
792 | fP[1] = fVtxGuess[1]; | |
793 | fP[2] = fVtxGuess[2]; | |
794 | fP[3] = 0; | |
795 | fP[4] = 0; | |
796 | fP[5] = 0; | |
797 | fP[6] = 0; | |
798 | fP[7] = 0; | |
706952f5 | 799 | |
800 | for(Int_t i=0;i<6; ++i) fC[i]=constraintC[i]; | |
801 | for(Int_t i=6;i<36;++i) fC[i]=0.; | |
f826d409 | 802 | fC[35] = 1.; |
803 | ||
706952f5 | 804 | fNDF = IsConstrained ?0 :-3; |
f826d409 | 805 | fChi2 = 0.; |
806 | fQ = 0; | |
807 | ||
4bbc290d | 808 | for( Int_t itr =0; itr<NDaughters; itr++ ){ |
809 | AddDaughter( *vDaughters[itr] ); | |
810 | } | |
f826d409 | 811 | if( iter<maxIter-1){ |
812 | for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i]; | |
813 | } | |
814 | } | |
815 | fIsLinearized = wasLinearized; | |
816 | ||
817 | if( Mass>=0 ) SetMassConstraint( Mass ); | |
818 | if( Parent ) SetProductionVertex( *Parent ); | |
819 | } | |
820 | ||
821 | ||
822 | void AliKFParticleBase::Convert( bool ToProduction ) | |
823 | { | |
824 | //* Tricky function - convert the particle error along its trajectory to | |
825 | //* the value which corresponds to its production/decay vertex | |
826 | //* It is done by combination of the error of decay length with the position errors | |
827 | ||
828 | Double_t fld[3]; | |
829 | { | |
830 | GetFieldValue( fP, fld ); | |
831 | const Double_t kCLight = fQ*0.000299792458; | |
832 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
833 | } | |
834 | ||
835 | Double_t h[6]; | |
836 | ||
837 | h[0] = fP[3]; | |
838 | h[1] = fP[4]; | |
839 | h[2] = fP[5]; | |
840 | if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; } | |
841 | h[3] = h[1]*fld[2]-h[2]*fld[1]; | |
842 | h[4] = h[2]*fld[0]-h[0]*fld[2]; | |
843 | h[5] = h[0]*fld[1]-h[1]*fld[0]; | |
844 | ||
845 | Double_t c; | |
846 | ||
847 | c = fC[28]+h[0]*fC[35]; | |
848 | fC[ 0]+= h[0]*(c+fC[28]); | |
849 | fC[28] = c; | |
850 | ||
851 | fC[ 1]+= h[1]*fC[28] + h[0]*fC[29]; | |
852 | c = fC[29]+h[1]*fC[35]; | |
853 | fC[ 2]+= h[1]*(c+fC[29]); | |
854 | fC[29] = c; | |
855 | ||
856 | fC[ 3]+= h[2]*fC[28] + h[0]*fC[30]; | |
857 | fC[ 4]+= h[2]*fC[29] + h[1]*fC[30]; | |
858 | c = fC[30]+h[2]*fC[35]; | |
859 | fC[ 5]+= h[2]*(c+fC[30]); | |
860 | fC[30] = c; | |
861 | ||
862 | fC[ 6]+= h[3]*fC[28] + h[0]*fC[31]; | |
863 | fC[ 7]+= h[3]*fC[29] + h[1]*fC[31]; | |
864 | fC[ 8]+= h[3]*fC[30] + h[2]*fC[31]; | |
865 | c = fC[31]+h[3]*fC[35]; | |
866 | fC[ 9]+= h[3]*(c+fC[31]); | |
867 | fC[31] = c; | |
868 | ||
869 | fC[10]+= h[4]*fC[28] + h[0]*fC[32]; | |
870 | fC[11]+= h[4]*fC[29] + h[1]*fC[32]; | |
871 | fC[12]+= h[4]*fC[30] + h[2]*fC[32]; | |
872 | fC[13]+= h[4]*fC[31] + h[3]*fC[32]; | |
873 | c = fC[32]+h[4]*fC[35]; | |
874 | fC[14]+= h[4]*(c+fC[32]); | |
875 | fC[32] = c; | |
876 | ||
877 | fC[15]+= h[5]*fC[28] + h[0]*fC[33]; | |
878 | fC[16]+= h[5]*fC[29] + h[1]*fC[33]; | |
879 | fC[17]+= h[5]*fC[30] + h[2]*fC[33]; | |
880 | fC[18]+= h[5]*fC[31] + h[3]*fC[33]; | |
881 | fC[19]+= h[5]*fC[32] + h[4]*fC[33]; | |
882 | c = fC[33]+h[5]*fC[35]; | |
883 | fC[20]+= h[5]*(c+fC[33]); | |
884 | fC[33] = c; | |
885 | ||
886 | fC[21]+= h[0]*fC[34]; | |
887 | fC[22]+= h[1]*fC[34]; | |
888 | fC[23]+= h[2]*fC[34]; | |
889 | fC[24]+= h[3]*fC[34]; | |
890 | fC[25]+= h[4]*fC[34]; | |
891 | fC[26]+= h[5]*fC[34]; | |
892 | } | |
893 | ||
894 | ||
895 | void AliKFParticleBase::TransportToDecayVertex() | |
896 | { | |
897 | //* Transport the particle to its decay vertex | |
898 | ||
899 | if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay ); | |
900 | if( fAtProductionVertex ) Convert(0); | |
901 | fAtProductionVertex = 0; | |
902 | } | |
903 | ||
904 | void AliKFParticleBase::TransportToProductionVertex() | |
905 | { | |
906 | //* Transport the particle to its production vertex | |
616ffc76 | 907 | |
f826d409 | 908 | if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] ); |
909 | if( !fAtProductionVertex ) Convert( 1 ); | |
910 | fAtProductionVertex = 1; | |
911 | } | |
912 | ||
913 | ||
914 | void AliKFParticleBase::TransportToDS( Double_t dS ) | |
915 | { | |
916 | //* Transport the particle on dS parameter (SignedPath/Momentum) | |
616ffc76 | 917 | |
f826d409 | 918 | Transport( dS, fP, fC ); |
919 | fSFromDecay+= dS; | |
920 | } | |
921 | ||
922 | ||
923 | Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const | |
924 | { | |
925 | //* Get dS to a certain space point without field | |
926 | ||
927 | Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; | |
928 | if( p2<1.e-4 ) p2 = 1; | |
929 | return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2; | |
930 | } | |
931 | ||
932 | ||
933 | Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] ) | |
934 | const | |
935 | { | |
616ffc76 | 936 | |
f826d409 | 937 | //* Get dS to a certain space point for Bz field |
f826d409 | 938 | const Double_t kCLight = 0.000299792458; |
939 | Double_t bq = B*fQ*kCLight; | |
940 | Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4]; | |
941 | if( pt2<1.e-4 ) return 0; | |
942 | Double_t dx = xyz[0] - fP[0]; | |
943 | Double_t dy = xyz[1] - fP[1]; | |
944 | Double_t a = dx*fP[3]+dy*fP[4]; | |
706952f5 | 945 | Double_t dS; |
946 | ||
947 | if( TMath::Abs(bq)<1.e-8 ) dS = a/pt2; | |
948 | else dS = TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq; | |
949 | ||
950 | if(0){ | |
951 | ||
952 | Double_t px = fP[3]; | |
953 | Double_t py = fP[4]; | |
954 | Double_t pz = fP[5]; | |
955 | Double_t ss[2], g[2][5]; | |
956 | ||
957 | ss[0] = dS; | |
958 | ss[1] = -dS; | |
959 | for( Int_t i=0; i<2; i++){ | |
960 | Double_t bs = bq*ss[i]; | |
961 | Double_t c = TMath::Cos(bs), s = TMath::Sin(bs); | |
962 | Double_t cB,sB; | |
963 | if( TMath::Abs(bq)>1.e-8){ | |
964 | cB= (1-c)/bq; | |
965 | sB= s/bq; | |
966 | }else{ | |
bfd20868 | 967 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); |
968 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i]; | |
706952f5 | 969 | cB = .5*sB*bs; |
970 | } | |
971 | g[i][0] = fP[0] + sB*px + cB*py; | |
972 | g[i][1] = fP[1] - cB*px + sB*py; | |
973 | g[i][2] = fP[2] + ss[i]*pz; | |
974 | g[i][3] = + c*px + s*py; | |
975 | g[i][4] = - s*px + c*py; | |
976 | } | |
977 | ||
978 | Int_t i=0; | |
979 | ||
980 | Double_t dMin = 1.e10; | |
981 | for( Int_t j=0; j<2; j++){ | |
982 | Double_t xx = g[j][0]-xyz[0]; | |
983 | Double_t yy = g[j][1]-xyz[1]; | |
984 | Double_t zz = g[j][2]-xyz[2]; | |
985 | Double_t d = xx*xx + yy*yy + zz*zz; | |
986 | if( d<dMin ){ | |
987 | dMin = d; | |
988 | i = j; | |
989 | } | |
990 | } | |
991 | ||
992 | dS = ss[i]; | |
993 | ||
994 | Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4]; | |
5fc72f28 | 995 | Double_t ddx = x-xyz[0]; |
996 | Double_t ddy = y-xyz[1]; | |
997 | Double_t ddz = z-xyz[2]; | |
998 | Double_t c = ddx*ppx + ddy*ppy + ddz*pz ; | |
706952f5 | 999 | Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz; |
1000 | if( TMath::Abs(pp2)>1.e-8 ){ | |
1001 | dS+=c/pp2; | |
1002 | } | |
1003 | } | |
1004 | return dS; | |
f826d409 | 1005 | } |
1006 | ||
1007 | ||
1008 | void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p, | |
616ffc76 | 1009 | Double_t &DS, Double_t &DS1 ) |
f826d409 | 1010 | const |
1011 | { | |
1012 | //* Get dS to another particle for Bz field | |
f826d409 | 1013 | Double_t px = fP[3]; |
1014 | Double_t py = fP[4]; | |
1015 | Double_t pz = fP[5]; | |
1016 | ||
1017 | Double_t px1 = p.fP[3]; | |
1018 | Double_t py1 = p.fP[4]; | |
1019 | Double_t pz1 = p.fP[5]; | |
1020 | ||
1021 | const Double_t kCLight = 0.000299792458; | |
1022 | ||
1023 | Double_t bq = B*fQ*kCLight; | |
1024 | Double_t bq1 = B*p.fQ*kCLight; | |
f826d409 | 1025 | Double_t s=0, ds=0, s1=0, ds1=0; |
1026 | ||
1027 | if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){ | |
4bbc290d | 1028 | |
f826d409 | 1029 | Double_t dx = (p.fP[0] - fP[0]); |
1030 | Double_t dy = (p.fP[1] - fP[1]); | |
1031 | Double_t d2 = (dx*dx+dy*dy); | |
1032 | ||
1033 | Double_t p2 = (px *px + py *py); | |
1034 | Double_t p21 = (px1*px1 + py1*py1); | |
1035 | ||
1036 | Double_t a = (px*py1 - py*px1); | |
1037 | Double_t b = (px*px1 + py*py1); | |
1038 | ||
1039 | Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ; | |
1040 | Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ; | |
1041 | Double_t l2 = ldx*ldx + ldy*ldy; | |
1042 | ||
1043 | Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b; | |
1044 | Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b; | |
1045 | ||
1046 | Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ; | |
1047 | Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ; | |
1048 | ||
1049 | Double_t sa = 4*l2*p2 - ca*ca; | |
1050 | Double_t sa1 = 4*l2*p21 - ca1*ca1; | |
e7b09c95 | 1051 | |
f826d409 | 1052 | if(sa<0) sa=0; |
1053 | if(sa1<0)sa1=0; | |
1054 | ||
1055 | if( TMath::Abs(bq)>1.e-8){ | |
1056 | s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq; | |
1057 | ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq; | |
1058 | } else { | |
1059 | s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2; | |
1060 | ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2; | |
1061 | if( ds<0 ) ds = 0; | |
1062 | ds = TMath::Sqrt(ds); | |
1063 | } | |
1064 | ||
1065 | if( TMath::Abs(bq1)>1.e-8){ | |
1066 | s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1; | |
1067 | ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1; | |
1068 | } else { | |
1069 | s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21; | |
1070 | ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21; | |
1071 | if( ds1<0 ) ds1 = 0; | |
1072 | ds1 = TMath::Sqrt(ds1); | |
1073 | } | |
1074 | } | |
1075 | ||
f826d409 | 1076 | Double_t ss[2], ss1[2], g[2][5],g1[2][5]; |
1077 | ||
1078 | ss[0] = s + ds; | |
1079 | ss[1] = s - ds; | |
1080 | ss1[0] = s1 + ds1; | |
1081 | ss1[1] = s1 - ds1; | |
1082 | for( Int_t i=0; i<2; i++){ | |
1083 | Double_t bs = bq*ss[i]; | |
5fc72f28 | 1084 | Double_t c = TMath::Cos(bs), sss = TMath::Sin(bs); |
f826d409 | 1085 | Double_t cB,sB; |
1086 | if( TMath::Abs(bq)>1.e-8){ | |
1087 | cB= (1-c)/bq; | |
5fc72f28 | 1088 | sB= sss/bq; |
f826d409 | 1089 | }else{ |
bfd20868 | 1090 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); |
1091 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i]; | |
f826d409 | 1092 | cB = .5*sB*bs; |
1093 | } | |
1094 | g[i][0] = fP[0] + sB*px + cB*py; | |
1095 | g[i][1] = fP[1] - cB*px + sB*py; | |
1096 | g[i][2] = fP[2] + ss[i]*pz; | |
5fc72f28 | 1097 | g[i][3] = + c*px + sss*py; |
1098 | g[i][4] = - sss*px + c*py; | |
f826d409 | 1099 | |
1100 | bs = bq1*ss1[i]; | |
5fc72f28 | 1101 | c = TMath::Cos(bs); sss = TMath::Sin(bs); |
f826d409 | 1102 | if( TMath::Abs(bq1)>1.e-8){ |
1103 | cB= (1-c)/bq1; | |
5fc72f28 | 1104 | sB= sss/bq1; |
f826d409 | 1105 | }else{ |
bfd20868 | 1106 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); |
1107 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss1[i]; | |
f826d409 | 1108 | cB = .5*sB*bs; |
1109 | } | |
1110 | ||
e7b09c95 | 1111 | g1[i][0] = p.fP[0] + sB*px1 + cB*py1; |
1112 | g1[i][1] = p.fP[1] - cB*px1 + sB*py1; | |
1113 | g1[i][2] = p.fP[2] + ss[i]*pz1; | |
5fc72f28 | 1114 | g1[i][3] = + c*px1 + sss*py1; |
1115 | g1[i][4] = - sss*px1 + c*py1; | |
f826d409 | 1116 | } |
1117 | ||
1118 | Int_t i=0, i1=0; | |
1119 | ||
1120 | Double_t dMin = 1.e10; | |
1121 | for( Int_t j=0; j<2; j++){ | |
1122 | for( Int_t j1=0; j1<2; j1++){ | |
1123 | Double_t xx = g[j][0]-g1[j1][0]; | |
1124 | Double_t yy = g[j][1]-g1[j1][1]; | |
1125 | Double_t zz = g[j][2]-g1[j1][2]; | |
1126 | Double_t d = xx*xx + yy*yy + zz*zz; | |
1127 | if( d<dMin ){ | |
1128 | dMin = d; | |
1129 | i = j; | |
1130 | i1 = j1; | |
1131 | } | |
1132 | } | |
1133 | } | |
1134 | ||
1135 | DS = ss[i]; | |
1136 | DS1 = ss1[i1]; | |
91468b27 | 1137 | if(0){ |
1138 | Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4]; | |
1139 | Double_t x1=g1[i1][0], y1= g1[i1][1], z1= g1[i1][2], ppx1= g1[i1][3], ppy1= g1[i1][4]; | |
1140 | Double_t dx = x1-x; | |
1141 | Double_t dy = y1-y; | |
1142 | Double_t dz = z1-z; | |
1143 | Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1; | |
1144 | Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1; | |
1145 | Double_t c = dx*ppx + dy*ppy + dz*pz ; | |
1146 | Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz; | |
1147 | Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1; | |
706952f5 | 1148 | Double_t det = pp2*pp21 - a*a; |
91468b27 | 1149 | if( TMath::Abs(det)>1.e-8 ){ |
1150 | DS+=(a*b-pp21*c)/det; | |
1151 | DS1+=(a*c-pp2*b)/det; | |
1152 | } | |
f826d409 | 1153 | } |
1154 | } | |
1155 | ||
1156 | ||
1157 | ||
1158 | void AliKFParticleBase::TransportCBM( Double_t dS, | |
1159 | Double_t P[], Double_t C[] ) const | |
1160 | { | |
1161 | //* Transport the particle on dS, output to P[],C[], for CBM field | |
1162 | ||
1163 | if( fQ==0 ){ | |
1164 | TransportLine( dS, P, C ); | |
1165 | return; | |
1166 | } | |
1167 | ||
1168 | const Double_t kCLight = 0.000299792458; | |
1169 | ||
1170 | Double_t c = fQ*kCLight; | |
1171 | ||
1172 | // construct coefficients | |
1173 | ||
1174 | Double_t | |
1175 | px = fP[3], | |
1176 | py = fP[4], | |
1177 | pz = fP[5]; | |
1178 | ||
1179 | 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; | |
1180 | ||
1181 | { // get field integrals | |
1182 | ||
1183 | Double_t fld[3][3]; | |
1184 | Double_t p0[3], p1[3], p2[3]; | |
1185 | ||
1186 | // line track approximation | |
1187 | ||
1188 | p0[0] = fP[0]; | |
1189 | p0[1] = fP[1]; | |
1190 | p0[2] = fP[2]; | |
1191 | ||
1192 | p2[0] = fP[0] + px*dS; | |
1193 | p2[1] = fP[1] + py*dS; | |
1194 | p2[2] = fP[2] + pz*dS; | |
1195 | ||
1196 | p1[0] = 0.5*(p0[0]+p2[0]); | |
1197 | p1[1] = 0.5*(p0[1]+p2[1]); | |
1198 | p1[2] = 0.5*(p0[2]+p2[2]); | |
1199 | ||
1200 | // first order track approximation | |
1201 | { | |
1202 | GetFieldValue( p0, fld[0] ); | |
1203 | GetFieldValue( p1, fld[1] ); | |
1204 | GetFieldValue( p2, fld[2] ); | |
1205 | ||
1206 | Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.; | |
1207 | Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.; | |
1208 | ||
1209 | p1[0] -= ssy1*pz; | |
1210 | p1[2] += ssy1*px; | |
1211 | p2[0] -= ssy2*pz; | |
1212 | p2[2] += ssy2*px; | |
1213 | } | |
1214 | ||
1215 | GetFieldValue( p0, fld[0] ); | |
1216 | GetFieldValue( p1, fld[1] ); | |
1217 | GetFieldValue( p2, fld[2] ); | |
1218 | ||
1219 | sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.; | |
1220 | sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.; | |
1221 | sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.; | |
1222 | ||
1223 | ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.; | |
1224 | ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.; | |
1225 | ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.; | |
1226 | ||
1227 | Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360. | |
1228 | Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520. | |
1229 | for(Int_t n=0; n<3; n++) | |
1230 | for(Int_t m=0; m<3; m++) | |
1231 | { | |
1232 | syz += c2[n][m]*fld[n][1]*fld[m][2]; | |
1233 | ssyz += cc2[n][m]*fld[n][1]*fld[m][2]; | |
1234 | } | |
1235 | ||
1236 | syz *= c*c*dS*dS/360.; | |
1237 | ssyz *= c*c*dS*dS*dS/2520.; | |
1238 | ||
1239 | syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS; | |
1240 | syyy = syy*syy*syy / 1296; | |
1241 | syy = syy*syy/72; | |
1242 | ||
1243 | ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+ | |
1244 | fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+ | |
1245 | fld[2][1]*( 3*fld[2][1] ) | |
1246 | )*dS*dS*dS*c*c/2520.; | |
1247 | ssyyy = | |
1248 | ( | |
1249 | fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+ | |
1250 | fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+ | |
1251 | fld[2][1]*( 19*fld[2][1] ) )+ | |
1252 | fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+ | |
1253 | fld[2][1]*( 62*fld[2][1] ) )+ | |
1254 | fld[2][1]*fld[2][1] *( 3*fld[2][1] ) | |
1255 | )*dS*dS*dS*dS*c*c*c/90720.; | |
1256 | ||
1257 | } | |
1258 | ||
1259 | Double_t mJ[8][8]; | |
1260 | for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0; | |
1261 | ||
1262 | 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; | |
1263 | 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; | |
1264 | 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; | |
1265 | ||
1266 | 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; | |
1267 | 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; | |
1268 | 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; | |
1269 | mJ[6][6] = mJ[7][7] = 1; | |
1270 | ||
1271 | P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz; | |
1272 | P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz; | |
1273 | P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz; | |
1274 | P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz; | |
1275 | P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz; | |
1276 | P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz; | |
1277 | P[6] = fP[6]; | |
1278 | P[7] = fP[7]; | |
1279 | ||
1280 | MultQSQt( mJ[0], fC, C); | |
1281 | ||
1282 | } | |
1283 | ||
1284 | ||
0d14829a | 1285 | void AliKFParticleBase::TransportBz( Double_t b, Double_t t, |
1286 | Double_t p[], Double_t e[] ) const | |
f826d409 | 1287 | { |
1288 | //* Transport the particle on dS, output to P[],C[], for Bz field | |
616ffc76 | 1289 | |
f826d409 | 1290 | const Double_t kCLight = 0.000299792458; |
5fc72f28 | 1291 | b = b*fQ*kCLight; |
0d14829a | 1292 | Double_t bs= b*t; |
f826d409 | 1293 | Double_t s = TMath::Sin(bs), c = TMath::Cos(bs); |
1294 | Double_t sB, cB; | |
616ffc76 | 1295 | if( TMath::Abs(bs)>1.e-10){ |
5fc72f28 | 1296 | sB= s/b; |
1297 | cB= (1-c)/b; | |
f826d409 | 1298 | }else{ |
bfd20868 | 1299 | const Double_t kOvSqr6 = 1./TMath::Sqrt(6.); |
0d14829a | 1300 | sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*t; |
f826d409 | 1301 | cB = .5*sB*bs; |
1302 | } | |
1303 | ||
1304 | Double_t px = fP[3]; | |
1305 | Double_t py = fP[4]; | |
1306 | Double_t pz = fP[5]; | |
1307 | ||
5fc72f28 | 1308 | p[0] = fP[0] + sB*px + cB*py; |
1309 | p[1] = fP[1] - cB*px + sB*py; | |
0d14829a | 1310 | p[2] = fP[2] + t*pz; |
5fc72f28 | 1311 | p[3] = c*px + s*py; |
1312 | p[4] = -s*px + c*py; | |
1313 | p[5] = fP[5]; | |
1314 | p[6] = fP[6]; | |
1315 | p[7] = fP[7]; | |
0d14829a | 1316 | |
1317 | /* | |
f826d409 | 1318 | Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 }, |
616ffc76 | 1319 | {0,1,0, -cB, sB, 0, 0, 0 }, |
0d14829a | 1320 | {0,0,1, 0, 0, t, 0, 0 }, |
616ffc76 | 1321 | {0,0,0, c, s, 0, 0, 0 }, |
1322 | {0,0,0, -s, c, 0, 0, 0 }, | |
1323 | {0,0,0, 0, 0, 1, 0, 0 }, | |
1324 | {0,0,0, 0, 0, 0, 1, 0 }, | |
1325 | {0,0,0, 0, 0, 0, 0, 1 } }; | |
f826d409 | 1326 | Double_t mA[8][8]; |
1327 | for( Int_t k=0,i=0; i<8; i++) | |
1328 | for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k]; | |
1329 | ||
1330 | Double_t mJC[8][8]; | |
1331 | for( Int_t i=0; i<8; i++ ) | |
1332 | for( Int_t j=0; j<8; j++ ){ | |
1333 | mJC[i][j]=0; | |
1334 | for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j]; | |
1335 | } | |
1336 | ||
1337 | for( Int_t k=0,i=0; i<8; i++) | |
1338 | for( Int_t j=0; j<=i; j++, k++ ){ | |
0d14829a | 1339 | e[k] = 0; |
1340 | for( Int_t l=0; l<8; l++ ) e[k]+=mJC[i][l]*mJ[j][l]; | |
f826d409 | 1341 | } |
1342 | ||
1343 | return; | |
f826d409 | 1344 | */ |
0d14829a | 1345 | |
1346 | Double_t | |
1347 | c6=fC[6], c7=fC[7], c8=fC[8], c17=fC[17], c18=fC[18], | |
1348 | c24 = fC[24], c31 = fC[31]; | |
1349 | ||
1350 | Double_t | |
1351 | cBC13 = cB*fC[13], | |
1352 | mJC13 = c7 - cB*fC[9] + sB*fC[13], | |
1353 | mJC14 = fC[11] - cBC13 + sB*fC[14], | |
1354 | mJC23 = c8 + t*c18, | |
1355 | mJC24 = fC[12] + t*fC[19], | |
1356 | mJC33 = c*fC[9] + s*fC[13], | |
1357 | mJC34 = c*fC[13] + s*fC[14], | |
1358 | mJC43 = -s*fC[9] + c*fC[13], | |
1359 | mJC44 = -s*fC[13] + c*fC[14]; | |
1360 | ||
1361 | ||
1362 | e[0]= fC[0] + 2*(sB*c6 + cB*fC[10]) + (sB*fC[9] + 2*cBC13)*sB + cB*cB*fC[14]; | |
1363 | e[1]= fC[1] - cB*c6 + sB*fC[10] + mJC13*sB + mJC14*cB; | |
1364 | e[2]= fC[2] - cB*c7 + sB*fC[11] - mJC13*cB + mJC14*sB; | |
1365 | e[3]= fC[3] + t*fC[15] + mJC23*sB + mJC24*cB; | |
1366 | e[4]= fC[4] + t*fC[16] - mJC23*cB + mJC24*sB; | |
1367 | ||
1368 | e[15]= fC[15] + c18*sB + fC[19]*cB; | |
1369 | e[16]= fC[16] - c18*cB + fC[19]*sB; | |
1370 | e[17]= c17 + fC[20]*t; | |
1371 | e[18]= c18*c + fC[19]*s; | |
1372 | e[19]= -c18*s + fC[19]*c; | |
1373 | ||
1374 | e[5]= fC[5] + (c17 + e[17] )*t; | |
1375 | ||
1376 | e[6]= c*c6 + s*fC[10] + mJC33*sB + mJC34*cB; | |
1377 | e[7]= c*c7 + s*fC[11] - mJC33*cB + mJC34*sB; | |
1378 | e[8]= c*c8 + s*fC[12] + e[18]*t; | |
1379 | e[9]= mJC33*c + mJC34*s; | |
1380 | e[10]= -s*c6 + c*fC[10] + mJC43*sB + mJC44*cB; | |
1381 | ||
1382 | ||
1383 | e[11]= -s*c7 + c*fC[11] - mJC43*cB + mJC44*sB; | |
1384 | e[12]= -s*c8 + c*fC[12] + e[19]*t; | |
1385 | e[13]= mJC43*c + mJC44*s; | |
1386 | e[14]= -mJC43*s + mJC44*c; | |
1387 | e[20]= fC[20]; | |
1388 | e[21]= fC[21] + fC[25]*cB + c24*sB; | |
1389 | e[22]= fC[22] - c24*cB + fC[25]*sB; | |
1390 | e[23]= fC[23] + fC[26]*t; | |
1391 | e[24]= c*c24 + s*fC[25]; | |
1392 | e[25]= c*fC[25] - c24*s; | |
1393 | e[26]= fC[26]; | |
1394 | e[27]= fC[27]; | |
1395 | e[28]= fC[28] + fC[32]*cB + c31*sB; | |
1396 | e[29]= fC[29] - c31*cB + fC[32]*sB; | |
1397 | e[30]= fC[30] + fC[33]*t; | |
1398 | e[31]= c*c31 + s*fC[32]; | |
1399 | e[32]= c*fC[32] - s*c31; | |
1400 | e[33]= fC[33]; | |
1401 | e[34]= fC[34]; | |
1402 | e[35]= fC[35]; | |
f826d409 | 1403 | } |
1404 | ||
1405 | ||
1406 | Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const | |
1407 | { | |
1408 | //* Calculate distance from vertex [cm] | |
1409 | ||
1410 | return GetDistanceFromVertex( Vtx.fP ); | |
1411 | } | |
1412 | ||
1413 | Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const | |
1414 | { | |
1415 | //* Calculate distance from vertex [cm] | |
1416 | ||
1417 | Double_t mP[8], mC[36]; | |
1418 | Transport( GetDStoPoint(vtx), mP, mC ); | |
1419 | Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]}; | |
1420 | return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] ); | |
1421 | } | |
1422 | ||
616ffc76 | 1423 | Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p ) |
f826d409 | 1424 | const |
1425 | { | |
616ffc76 | 1426 | //* Calculate distance to other particle [cm] |
f826d409 | 1427 | |
1428 | Double_t dS, dS1; | |
616ffc76 | 1429 | GetDStoParticle( p, dS, dS1 ); |
f826d409 | 1430 | Double_t mP[8], mC[36], mP1[8], mC1[36]; |
616ffc76 | 1431 | Transport( dS, mP, mC ); |
1432 | p.Transport( dS1, mP1, mC1 ); | |
f826d409 | 1433 | Double_t dx = mP[0]-mP1[0]; |
1434 | Double_t dy = mP[1]-mP1[1]; | |
1435 | Double_t dz = mP[2]-mP1[2]; | |
55ac3e1e | 1436 | dz = 0; |
f826d409 | 1437 | return TMath::Sqrt(dx*dx+dy*dy+dz*dz); |
1438 | } | |
1439 | ||
1440 | Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const | |
1441 | { | |
1442 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1443 | ||
1444 | return GetDeviationFromVertex( Vtx.fP, Vtx.fC ); | |
1445 | } | |
1446 | ||
1447 | ||
1448 | Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const | |
1449 | { | |
1450 | //* Calculate sqrt(Chi2/ndf) deviation from vertex | |
1451 | //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix | |
1452 | ||
1453 | Double_t mP[8]; | |
1454 | Double_t mC[36]; | |
1455 | ||
1456 | Transport( GetDStoPoint(v), mP, mC ); | |
1457 | ||
1458 | Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]}; | |
1459 | ||
1460 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
1461 | (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) ); | |
1462 | ||
1463 | ||
1464 | Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS }; | |
1465 | ||
1466 | Double_t mSi[6] = | |
1467 | { mC[0] +h[0]*h[0], | |
1468 | mC[1] +h[1]*h[0], mC[2] +h[1]*h[1], | |
1469 | mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] }; | |
1470 | ||
1471 | if( Cv ){ | |
1472 | mSi[0]+=Cv[0]; | |
1473 | mSi[1]+=Cv[1]; | |
1474 | mSi[2]+=Cv[2]; | |
1475 | mSi[3]+=Cv[3]; | |
1476 | mSi[4]+=Cv[4]; | |
1477 | mSi[5]+=Cv[5]; | |
1478 | } | |
1479 | ||
1480 | Double_t mS[6]; | |
1481 | ||
1482 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1483 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1484 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1485 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1486 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1487 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1488 | ||
1489 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1490 | s = ( s > 1.E-20 ) ?1./s :0; | |
1491 | ||
1492 | return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0] | |
1493 | +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1] | |
1494 | +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2); | |
1495 | } | |
1496 | ||
1497 | ||
616ffc76 | 1498 | Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p ) |
f826d409 | 1499 | const |
1500 | { | |
616ffc76 | 1501 | //* Calculate sqrt(Chi2/ndf) deviation from other particle |
f826d409 | 1502 | |
1503 | Double_t dS, dS1; | |
616ffc76 | 1504 | GetDStoParticle( p, dS, dS1 ); |
f826d409 | 1505 | Double_t mP1[8], mC1[36]; |
616ffc76 | 1506 | p.Transport( dS1, mP1, mC1 ); |
f826d409 | 1507 | |
1508 | Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]}; | |
1509 | ||
1510 | Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ | |
616ffc76 | 1511 | (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) ); |
f826d409 | 1512 | |
1513 | Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS }; | |
1514 | ||
1515 | mC1[0] +=h[0]*h[0]; | |
1516 | mC1[1] +=h[1]*h[0]; | |
1517 | mC1[2] +=h[1]*h[1]; | |
1518 | mC1[3] +=h[2]*h[0]; | |
1519 | mC1[4] +=h[2]*h[1]; | |
1520 | mC1[5] +=h[2]*h[2]; | |
1521 | ||
1522 | return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.); | |
1523 | } | |
1524 | ||
1525 | ||
1526 | ||
de0d0ceb | 1527 | void AliKFParticleBase::SubtractFromVertex( AliKFParticleBase &Vtx ) const |
f826d409 | 1528 | { |
1529 | //* Subtract the particle from the vertex | |
de0d0ceb | 1530 | |
f826d409 | 1531 | Double_t fld[3]; |
1532 | { | |
de0d0ceb | 1533 | GetFieldValue( Vtx.fP, fld ); |
f826d409 | 1534 | const Double_t kCLight = 0.000299792458; |
1535 | fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; | |
1536 | } | |
1537 | ||
1538 | Double_t m[8]; | |
1539 | Double_t mCm[36]; | |
f826d409 | 1540 | |
de0d0ceb | 1541 | if( Vtx.fIsLinearized ){ |
1542 | GetMeasurement( Vtx.fVtxGuess, m, mCm ); | |
1543 | } else { | |
1544 | GetMeasurement( Vtx.fP, m, mCm ); | |
f826d409 | 1545 | } |
de0d0ceb | 1546 | |
f826d409 | 1547 | Double_t mV[6]; |
1548 | ||
de0d0ceb | 1549 | mV[ 0] = mCm[ 0]; |
1550 | mV[ 1] = mCm[ 1]; | |
1551 | mV[ 2] = mCm[ 2]; | |
1552 | mV[ 3] = mCm[ 3]; | |
1553 | mV[ 4] = mCm[ 4]; | |
1554 | mV[ 5] = mCm[ 5]; | |
f826d409 | 1555 | |
1556 | //* | |
1557 | ||
1558 | Double_t mS[6]; | |
1559 | { | |
de0d0ceb | 1560 | Double_t mSi[6] = { mV[0]-Vtx.fC[0], |
1561 | mV[1]-Vtx.fC[1], mV[2]-Vtx.fC[2], | |
1562 | mV[3]-Vtx.fC[3], mV[4]-Vtx.fC[4], mV[5]-Vtx.fC[5] }; | |
f826d409 | 1563 | |
1564 | mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; | |
1565 | mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; | |
1566 | mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; | |
1567 | mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; | |
1568 | mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; | |
1569 | mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; | |
1570 | ||
1571 | Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); | |
1572 | s = ( s > 1.E-20 ) ?1./s :0; | |
1573 | mS[0]*=s; | |
1574 | mS[1]*=s; | |
1575 | mS[2]*=s; | |
1576 | mS[3]*=s; | |
1577 | mS[4]*=s; | |
1578 | mS[5]*=s; | |
1579 | } | |
1580 | ||
1581 | //* Residual (measured - estimated) | |
1582 | ||
de0d0ceb | 1583 | Double_t zeta[3] = { m[0]-Vtx.fP[0], m[1]-Vtx.fP[1], m[2]-Vtx.fP[2] }; |
f826d409 | 1584 | |
1585 | //* mCHt = mCH' - D' | |
1586 | ||
1587 | Double_t mCHt0[3], mCHt1[3], mCHt2[3]; | |
1588 | ||
de0d0ceb | 1589 | mCHt0[0]=Vtx.fC[ 0] ; mCHt1[0]=Vtx.fC[ 1] ; mCHt2[0]=Vtx.fC[ 3] ; |
1590 | mCHt0[1]=Vtx.fC[ 1] ; mCHt1[1]=Vtx.fC[ 2] ; mCHt2[1]=Vtx.fC[ 4] ; | |
1591 | mCHt0[2]=Vtx.fC[ 3] ; mCHt1[2]=Vtx.fC[ 4] ; mCHt2[2]=Vtx.fC[ 5] ; | |
f826d409 | 1592 | |
1593 | //* Kalman gain K = mCH'*S | |
1594 | ||
1595 | Double_t k0[3], k1[3], k2[3]; | |
1596 | ||
1597 | for(Int_t i=0;i<3;++i){ | |
1598 | k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; | |
1599 | k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; | |
1600 | k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; | |
1601 | } | |
1602 | ||
1603 | //* New estimation of the vertex position r += K*zeta | |
1604 | ||
de0d0ceb | 1605 | Double_t dChi2 = -(mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] |
1606 | + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] | |
1607 | + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; | |
1608 | ||
1609 | if( Vtx.fChi2 - dChi2 < 0 ) return; | |
1610 | ||
f826d409 | 1611 | for(Int_t i=0;i<3;++i) |
de0d0ceb | 1612 | Vtx.fP[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; |
f826d409 | 1613 | |
1614 | //* New covariance matrix C -= K*(mCH')' | |
1615 | ||
1616 | for(Int_t i=0, k=0;i<3;++i){ | |
1617 | for(Int_t j=0;j<=i;++j,++k) | |
de0d0ceb | 1618 | Vtx.fC[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j]; |
f826d409 | 1619 | } |
1620 | ||
1621 | //* Calculate Chi^2 | |
de0d0ceb | 1622 | |
1623 | Vtx.fNDF -= 2; | |
1624 | Vtx.fChi2 -= dChi2; | |
f826d409 | 1625 | } |
1626 | ||
1627 | ||
1628 | ||
1629 | void AliKFParticleBase::TransportLine( Double_t dS, | |
1630 | Double_t P[], Double_t C[] ) const | |
1631 | { | |
1632 | //* Transport the particle as a straight line | |
1633 | ||
1634 | P[0] = fP[0] + dS*fP[3]; | |
1635 | P[1] = fP[1] + dS*fP[4]; | |
1636 | P[2] = fP[2] + dS*fP[5]; | |
1637 | P[3] = fP[3]; | |
1638 | P[4] = fP[4]; | |
1639 | P[5] = fP[5]; | |
1640 | P[6] = fP[6]; | |
1641 | P[7] = fP[7]; | |
1642 | ||
1643 | Double_t c6 = fC[ 6] + dS*fC[ 9]; | |
1644 | Double_t c11 = fC[11] + dS*fC[14]; | |
1645 | Double_t c17 = fC[17] + dS*fC[20]; | |
1646 | Double_t sc13 = dS*fC[13]; | |
1647 | Double_t sc18 = dS*fC[18]; | |
1648 | Double_t sc19 = dS*fC[19]; | |
1649 | ||
1650 | C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 ); | |
1651 | C[ 2] = fC[ 2] + dS*( fC[11] + c11 ); | |
1652 | C[ 5] = fC[ 5] + dS*( fC[17] + c17 ); | |
1653 | ||
1654 | C[ 7] = fC[ 7] + sc13; | |
1655 | C[ 8] = fC[ 8] + sc18; | |
1656 | C[ 9] = fC[ 9]; | |
1657 | ||
1658 | C[12] = fC[12] + sc19; | |
1659 | ||
1660 | C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] ); | |
1661 | C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] ); | |
1662 | C[ 4] = fC[ 4] + dS*( fC[16] + C[12] ); | |
1663 | C[ 6] = c6; | |
1664 | ||
1665 | C[10] = fC[10] + sc13; | |
1666 | C[11] = c11; | |
1667 | ||
1668 | C[13] = fC[13]; | |
1669 | C[14] = fC[14]; | |
1670 | C[15] = fC[15] + sc18; | |
1671 | C[16] = fC[16] + sc19; | |
1672 | C[17] = c17; | |
1673 | ||
1674 | C[18] = fC[18]; | |
1675 | C[19] = fC[19]; | |
1676 | C[20] = fC[20]; | |
1677 | C[21] = fC[21] + dS*fC[24]; | |
1678 | C[22] = fC[22] + dS*fC[25]; | |
1679 | C[23] = fC[23] + dS*fC[26]; | |
1680 | ||
1681 | C[24] = fC[24]; | |
1682 | C[25] = fC[25]; | |
1683 | C[26] = fC[26]; | |
1684 | C[27] = fC[27]; | |
1685 | C[28] = fC[28] + dS*fC[31]; | |
1686 | C[29] = fC[29] + dS*fC[32]; | |
1687 | C[30] = fC[30] + dS*fC[33]; | |
1688 | ||
1689 | C[31] = fC[31]; | |
1690 | C[32] = fC[32]; | |
1691 | C[33] = fC[33]; | |
1692 | C[34] = fC[34]; | |
1693 | C[35] = fC[35]; | |
1694 | } | |
1695 | ||
1696 | ||
a65041d0 | 1697 | void AliKFParticleBase::ConstructGammaBz( const AliKFParticleBase &daughter1, |
1698 | const AliKFParticleBase &daughter2, double Bz ) | |
1699 | { | |
1700 | //* Create gamma | |
1701 | ||
1702 | const AliKFParticleBase *daughters[2] = { &daughter1, &daughter2}; | |
1703 | ||
1704 | double v0[3]; | |
1705 | ||
1706 | if( !fIsLinearized ){ | |
1707 | Double_t ds, ds1; | |
1708 | Double_t m[8]; | |
1709 | Double_t mCd[36]; | |
1710 | daughter1.GetDStoParticle(daughter2, ds, ds1); | |
1711 | daughter1.Transport( ds, m, mCd ); | |
55ac3e1e | 1712 | fP[0] = m[0]; |
1713 | fP[1] = m[1]; | |
1714 | fP[2] = m[2]; | |
a65041d0 | 1715 | daughter2.Transport( ds1, m, mCd ); |
55ac3e1e | 1716 | fP[0] = .5*( fP[0] + m[0] ); |
1717 | fP[1] = .5*( fP[1] + m[1] ); | |
1718 | fP[2] = .5*( fP[2] + m[2] ); | |
a65041d0 | 1719 | } else { |
55ac3e1e | 1720 | fP[0] = fVtxGuess[0]; |
1721 | fP[1] = fVtxGuess[1]; | |
1722 | fP[2] = fVtxGuess[2]; | |
a65041d0 | 1723 | } |
1724 | ||
a65041d0 | 1725 | double daughterP[2][8], daughterC[2][36]; |
1726 | double vtxMom[2][3]; | |
1727 | ||
55ac3e1e | 1728 | int nIter = fIsLinearized ?1 :2; |
a65041d0 | 1729 | |
55ac3e1e | 1730 | for( int iter=0; iter<nIter; iter++){ |
a65041d0 | 1731 | |
55ac3e1e | 1732 | v0[0] = fP[0]; |
1733 | v0[1] = fP[1]; | |
1734 | v0[2] = fP[2]; | |
a65041d0 | 1735 | |
55ac3e1e | 1736 | fAtProductionVertex = 0; |
1737 | fSFromDecay = 0; | |
1738 | fP[0] = v0[0]; | |
1739 | fP[1] = v0[1]; | |
1740 | fP[2] = v0[2]; | |
1741 | fP[3] = 0; | |
1742 | fP[4] = 0; | |
1743 | fP[5] = 0; | |
1744 | fP[6] = 0; | |
1745 | fP[7] = 0; | |
1746 | ||
1747 | ||
1748 | // fit daughters to the vertex guess | |
a65041d0 | 1749 | |
55ac3e1e | 1750 | { |
1751 | for( int id=0; id<2; id++ ){ | |
1752 | ||
1753 | double *p = daughterP[id]; | |
1754 | double *mC = daughterC[id]; | |
1755 | ||
1756 | daughters[id]->GetMeasurement( v0, p, mC ); | |
1757 | ||
1758 | Double_t mAi[6]; | |
1759 | InvertSym3(mC, mAi ); | |
1760 | ||
1761 | Double_t mB[3][3]; | |
1762 | ||
1763 | mB[0][0] = mC[ 6]*mAi[0] + mC[ 7]*mAi[1] + mC[ 8]*mAi[3]; | |
1764 | mB[0][1] = mC[ 6]*mAi[1] + mC[ 7]*mAi[2] + mC[ 8]*mAi[4]; | |
1765 | mB[0][2] = mC[ 6]*mAi[3] + mC[ 7]*mAi[4] + mC[ 8]*mAi[5]; | |
1766 | ||
1767 | mB[1][0] = mC[10]*mAi[0] + mC[11]*mAi[1] + mC[12]*mAi[3]; | |
1768 | mB[1][1] = mC[10]*mAi[1] + mC[11]*mAi[2] + mC[12]*mAi[4]; | |
1769 | mB[1][2] = mC[10]*mAi[3] + mC[11]*mAi[4] + mC[12]*mAi[5]; | |
1770 | ||
1771 | mB[2][0] = mC[15]*mAi[0] + mC[16]*mAi[1] + mC[17]*mAi[3]; | |
1772 | mB[2][1] = mC[15]*mAi[1] + mC[16]*mAi[2] + mC[17]*mAi[4]; | |
1773 | mB[2][2] = mC[15]*mAi[3] + mC[16]*mAi[4] + mC[17]*mAi[5]; | |
1774 | ||
1775 | Double_t z[3] = { v0[0]-p[0], v0[1]-p[1], v0[2]-p[2] }; | |
1776 | ||
1777 | vtxMom[id][0] = p[3] + mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; | |
1778 | vtxMom[id][1] = p[4] + mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; | |
1779 | vtxMom[id][2] = p[5] + mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; | |
1780 | ||
1781 | daughters[id]->Transport( daughters[id]->GetDStoPoint(v0), p, mC ); | |
a65041d0 | 1782 | |
55ac3e1e | 1783 | } |
a65041d0 | 1784 | |
55ac3e1e | 1785 | } // fit daughters to guess |
1786 | ||
1787 | ||
1788 | // fit new vertex | |
1789 | { | |
a65041d0 | 1790 | |
55ac3e1e | 1791 | double mpx0 = vtxMom[0][0]+vtxMom[1][0]; |
1792 | double mpy0 = vtxMom[0][1]+vtxMom[1][1]; | |
1793 | double mpt0 = TMath::Sqrt(mpx0*mpx0 + mpy0*mpy0); | |
1794 | // double a0 = TMath::ATan2(mpy0,mpx0); | |
a65041d0 | 1795 | |
55ac3e1e | 1796 | double ca0 = mpx0/mpt0; |
1797 | double sa0 = mpy0/mpt0; | |
1798 | double r[3] = { v0[0], v0[1], v0[2] }; | |
1799 | double mC[3][3] = {{10000., 0 , 0 }, | |
1800 | {0, 10000., 0 }, | |
1801 | {0, 0, 10000. } }; | |
1802 | double chi2=0; | |
a65041d0 | 1803 | |
55ac3e1e | 1804 | for( int id=0; id<2; id++ ){ |
1805 | const Double_t kCLight = 0.000299792458; | |
1806 | Double_t q = Bz*daughters[id]->GetQ()*kCLight; | |
1807 | Double_t px0 = vtxMom[id][0]; | |
1808 | Double_t py0 = vtxMom[id][1]; | |
1809 | Double_t pz0 = vtxMom[id][2]; | |
1810 | Double_t pt0 = TMath::Sqrt(px0*px0+py0*py0); | |
1811 | Double_t mG[3][6], mB[3], mH[3][3]; | |
1812 | // r = {vx,vy,vz}; | |
1813 | // m = {x,y,z,Px,Py,Pz}; | |
1814 | // V = daughter.C | |
1815 | // G*m + B = H*r; | |
1816 | // q*x + Py - q*vx - sin(a)*Pt = 0 | |
1817 | // q*y - Px - q*vy + cos(a)*Pt = 0 | |
1818 | // (Px*cos(a) + Py*sin(a) ) (vz -z) - Pz( cos(a)*(vx-x) + sin(a)*(vy-y)) = 0 | |
1819 | ||
1820 | mG[0][0] = q; | |
1821 | mG[0][1] = 0; | |
1822 | mG[0][2] = 0; | |
1823 | mG[0][3] = -sa0*px0/pt0; | |
1824 | mG[0][4] = 1 -sa0*py0/pt0; | |
1825 | mG[0][5] = 0; | |
1826 | mH[0][0] = q; | |
1827 | mH[0][1] = 0; | |
1828 | mH[0][2] = 0; | |
1829 | mB[0] = py0 - sa0*pt0 - mG[0][3]*px0 - mG[0][4]*py0 ; | |
1830 | ||
1831 | // q*y - Px - q*vy + cos(a)*Pt = 0 | |
1832 | ||
1833 | mG[1][0] = 0; | |
1834 | mG[1][1] = q; | |
1835 | mG[1][2] = 0; | |
1836 | mG[1][3] = -1 + ca0*px0/pt0; | |
1837 | mG[1][4] = + ca0*py0/pt0; | |
1838 | mG[1][5] = 0; | |
1839 | mH[1][0] = 0; | |
1840 | mH[1][1] = q; | |
1841 | mH[1][2] = 0; | |
1842 | mB[1] = -px0 + ca0*pt0 - mG[1][3]*px0 - mG[1][4]*py0 ; | |
1843 | ||
1844 | // (Px*cos(a) + Py*sin(a) ) (z -vz) - Pz( cos(a)*(x-vx) + sin(a)*(y-vy)) = 0 | |
a65041d0 | 1845 | |
55ac3e1e | 1846 | mG[2][0] = -pz0*ca0; |
1847 | mG[2][1] = -pz0*sa0; | |
1848 | mG[2][2] = px0*ca0 + py0*sa0; | |
1849 | mG[2][3] = 0; | |
1850 | mG[2][4] = 0; | |
1851 | mG[2][5] = 0; | |
1852 | ||
1853 | mH[2][0] = mG[2][0]; | |
1854 | mH[2][1] = mG[2][1]; | |
1855 | mH[2][2] = mG[2][2]; | |
1856 | ||
1857 | mB[2] = 0; | |
1858 | ||
1859 | // fit the vertex | |
a65041d0 | 1860 | |
55ac3e1e | 1861 | // V = GVGt |
a65041d0 | 1862 | |
55ac3e1e | 1863 | double mGV[3][6]; |
1864 | double mV[6]; | |
1865 | double m[3]; | |
1866 | for( int i=0; i<3; i++ ){ | |
1867 | m[i] = mB[i]; | |
1868 | for( int k=0; k<6; k++ ) m[i]+=mG[i][k]*daughterP[id][k]; | |
a65041d0 | 1869 | } |
55ac3e1e | 1870 | for( int i=0; i<3; i++ ){ |
1871 | for( int j=0; j<6; j++ ){ | |
1872 | mGV[i][j] = 0; | |
1873 | for( int k=0; k<6; k++ ) mGV[i][j]+=mG[i][k]*daughterC[id][ IJ(k,j) ]; | |
1874 | } | |
a65041d0 | 1875 | } |
55ac3e1e | 1876 | for( int i=0, k=0; i<3; i++ ){ |
1877 | for( int j=0; j<=i; j++,k++ ){ | |
1878 | mV[k] = 0; | |
1879 | for( int l=0; l<6; l++ ) mV[k]+=mGV[i][l]*mG[j][l]; | |
1880 | } | |
1881 | } | |
1882 | ||
a65041d0 | 1883 | |
55ac3e1e | 1884 | //* CHt |
1885 | ||
1886 | Double_t mCHt[3][3]; | |
1887 | Double_t mHCHt[6]; | |
1888 | Double_t mHr[3]; | |
1889 | for( int i=0; i<3; i++ ){ | |
1890 | mHr[i] = 0; | |
1891 | for( int k=0; k<3; k++ ) mHr[i]+= mH[i][k]*r[k]; | |
1892 | } | |
a65041d0 | 1893 | |
55ac3e1e | 1894 | for( int i=0; i<3; i++ ){ |
1895 | for( int j=0; j<3; j++){ | |
1896 | mCHt[i][j] = 0; | |
1897 | for( int k=0; k<3; k++ ) mCHt[i][j]+= mC[i][k]*mH[j][k]; | |
1898 | } | |
a65041d0 | 1899 | } |
a65041d0 | 1900 | |
55ac3e1e | 1901 | for( int i=0, k=0; i<3; i++ ){ |
1902 | for( int j=0; j<=i; j++, k++ ){ | |
1903 | mHCHt[k] = 0; | |
1904 | for( int l=0; l<3; l++ ) mHCHt[k]+= mH[i][l]*mCHt[l][j]; | |
1905 | } | |
a65041d0 | 1906 | } |
a65041d0 | 1907 | |
55ac3e1e | 1908 | Double_t mS[6] = { mHCHt[0]+mV[0], |
1909 | mHCHt[1]+mV[1], mHCHt[2]+mV[2], | |
1910 | mHCHt[3]+mV[3], mHCHt[4]+mV[4], mHCHt[5]+mV[5] }; | |
a65041d0 | 1911 | |
1912 | ||
55ac3e1e | 1913 | InvertSym3(mS,mS); |
a65041d0 | 1914 | |
55ac3e1e | 1915 | //* Residual (measured - estimated) |
a65041d0 | 1916 | |
55ac3e1e | 1917 | Double_t zeta[3] = { m[0]-mHr[0], m[1]-mHr[1], m[2]-mHr[2] }; |
a65041d0 | 1918 | |
55ac3e1e | 1919 | //* Kalman gain K = mCH'*S |
a65041d0 | 1920 | |
55ac3e1e | 1921 | Double_t k[3][3]; |
a65041d0 | 1922 | |
55ac3e1e | 1923 | for(Int_t i=0;i<3;++i){ |
1924 | k[i][0] = mCHt[i][0]*mS[0] + mCHt[i][1]*mS[1] + mCHt[i][2]*mS[3]; | |
1925 | k[i][1] = mCHt[i][0]*mS[1] + mCHt[i][1]*mS[2] + mCHt[i][2]*mS[4]; | |
1926 | k[i][2] = mCHt[i][0]*mS[3] + mCHt[i][1]*mS[4] + mCHt[i][2]*mS[5]; | |
1927 | } | |
a65041d0 | 1928 | |
55ac3e1e | 1929 | //* New estimation of the vertex position r += K*zeta |
a65041d0 | 1930 | |
55ac3e1e | 1931 | for(Int_t i=0;i<3;++i) |
1932 | r[i] = r[i] + k[i][0]*zeta[0] + k[i][1]*zeta[1] + k[i][2]*zeta[2]; | |
a65041d0 | 1933 | |
55ac3e1e | 1934 | //* New covariance matrix C -= K*(mCH')' |
a65041d0 | 1935 | |
55ac3e1e | 1936 | for(Int_t i=0;i<3;++i){ |
1937 | for(Int_t j=0;j<=i;++j){ | |
1938 | mC[i][j] = mC[i][j] - (k[i][0]*mCHt[j][0] + k[i][1]*mCHt[j][1] + k[i][2]*mCHt[j][2]); | |
1939 | mC[j][i] = mC[i][j]; | |
1940 | } | |
a65041d0 | 1941 | } |
a65041d0 | 1942 | |
1943 | ||
55ac3e1e | 1944 | //* Calculate Chi^2 |
a65041d0 | 1945 | |
55ac3e1e | 1946 | chi2 += ( ( mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2] )*zeta[0] |
1947 | +(mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2] )*zeta[1] | |
1948 | +(mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2] )*zeta[2] ); | |
1949 | } | |
a65041d0 | 1950 | |
55ac3e1e | 1951 | // store vertex |
a65041d0 | 1952 | |
55ac3e1e | 1953 | fNDF = 2; |
1954 | fChi2 = chi2; | |
1955 | for( int i=0; i<3; i++ ) fP[i] = r[i]; | |
1956 | for( int i=0,k=0; i<3; i++ ){ | |
1957 | for( int j=0; j<=i; j++,k++ ){ | |
1958 | fC[k] = mC[i][j]; | |
1959 | } | |
a65041d0 | 1960 | } |
1961 | } | |
55ac3e1e | 1962 | |
1963 | } // iterations | |
a65041d0 | 1964 | |
1965 | // now fit daughters to the vertex | |
1966 | ||
1967 | fQ = 0; | |
1968 | fSFromDecay = 0; | |
1969 | ||
1970 | for(Int_t i=3;i<8;++i) fP[i]=0.; | |
55ac3e1e | 1971 | for(Int_t i=6;i<35;++i) fC[i]=0.; |
1972 | fC[35] = 100.; | |
a65041d0 | 1973 | |
1974 | for( int id=0; id<2; id++ ){ | |
1975 | ||
1976 | double *p = daughterP[id]; | |
1977 | double *mC = daughterC[id]; | |
1978 | daughters[id]->GetMeasurement( v0, p, mC ); | |
1979 | ||
1980 | const Double_t *m = fP, *mV = fC; | |
1981 | ||
1982 | Double_t mAi[6]; | |
1983 | InvertSym3(mC, mAi ); | |
1984 | ||
1985 | Double_t mB[4][3]; | |
1986 | ||
1987 | mB[0][0] = mC[ 6]*mAi[0] + mC[ 7]*mAi[1] + mC[ 8]*mAi[3]; | |
1988 | mB[0][1] = mC[ 6]*mAi[1] + mC[ 7]*mAi[2] + mC[ 8]*mAi[4]; | |
1989 | mB[0][2] = mC[ 6]*mAi[3] + mC[ 7]*mAi[4] + mC[ 8]*mAi[5]; | |
1990 | ||
1991 | mB[1][0] = mC[10]*mAi[0] + mC[11]*mAi[1] + mC[12]*mAi[3]; | |
1992 | mB[1][1] = mC[10]*mAi[1] + mC[11]*mAi[2] + mC[12]*mAi[4]; | |
1993 | mB[1][2] = mC[10]*mAi[3] + mC[11]*mAi[4] + mC[12]*mAi[5]; | |
1994 | ||
1995 | mB[2][0] = mC[15]*mAi[0] + mC[16]*mAi[1] + mC[17]*mAi[3]; | |
1996 | mB[2][1] = mC[15]*mAi[1] + mC[16]*mAi[2] + mC[17]*mAi[4]; | |
1997 | mB[2][2] = mC[15]*mAi[3] + mC[16]*mAi[4] + mC[17]*mAi[5]; | |
1998 | ||
1999 | mB[3][0] = mC[21]*mAi[0] + mC[22]*mAi[1] + mC[23]*mAi[3]; | |
2000 | mB[3][1] = mC[21]*mAi[1] + mC[22]*mAi[2] + mC[23]*mAi[4]; | |
2001 | mB[3][2] = mC[21]*mAi[3] + mC[22]*mAi[4] + mC[23]*mAi[5]; | |
2002 | ||
2003 | ||
2004 | Double_t z[3] = { m[0]-p[0], m[1]-p[1], m[2]-p[2] }; | |
2005 | ||
2006 | { | |
2007 | Double_t mAV[6] = { mC[0]-mV[0], mC[1]-mV[1], mC[2]-mV[2], | |
2008 | mC[3]-mV[3], mC[4]-mV[4], mC[5]-mV[5] }; | |
2009 | ||
2010 | Double_t mAVi[6]; | |
2011 | if( !InvertSym3(mAV, mAVi) ){ | |
2012 | Double_t dChi2 = ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0] | |
2013 | +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1] | |
2014 | +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] ); | |
2015 | fChi2+= TMath::Abs( dChi2 ); | |
2016 | } | |
2017 | fNDF += 2; | |
2018 | } | |
2019 | ||
2020 | //* Add the daughter momentum to the particle momentum | |
2021 | ||
2022 | fP[3]+= p[3] + mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; | |
2023 | fP[4]+= p[4] + mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; | |
2024 | fP[5]+= p[5] + mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; | |
2025 | fP[6]+= p[6] + mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2]; | |
2026 | ||
2027 | Double_t d0, d1, d2; | |
2028 | ||
2029 | d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - mC[ 6]; | |
2030 | d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - mC[ 7]; | |
2031 | d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - mC[ 8]; | |
2032 | ||
2033 | //fC[6]+= mC[ 6] + d0; | |
2034 | //fC[7]+= mC[ 7] + d1; | |
2035 | //fC[8]+= mC[ 8] + d2; | |
2036 | fC[9]+= mC[ 9] + d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
2037 | ||
2038 | d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - mC[10]; | |
2039 | d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - mC[11]; | |
2040 | d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - mC[12]; | |
2041 | ||
2042 | //fC[10]+= mC[10]+ d0; | |
2043 | //fC[11]+= mC[11]+ d1; | |
2044 | //fC[12]+= mC[12]+ d2; | |
2045 | fC[13]+= mC[13]+ d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
2046 | fC[14]+= mC[14]+ d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
2047 | ||
2048 | d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - mC[15]; | |
2049 | d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - mC[16]; | |
2050 | d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - mC[17]; | |
2051 | ||
2052 | //fC[15]+= mC[15]+ d0; | |
2053 | //fC[16]+= mC[16]+ d1; | |
2054 | //fC[17]+= mC[17]+ d2; | |
2055 | fC[18]+= mC[18]+ d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
2056 | fC[19]+= mC[19]+ d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
2057 | fC[20]+= mC[20]+ d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
2058 | ||
2059 | d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - mC[21]; | |
2060 | d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - mC[22]; | |
2061 | d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - mC[23]; | |
2062 | ||
2063 | //fC[21]+= mC[21] + d0; | |
2064 | //fC[22]+= mC[22] + d1; | |
2065 | //fC[23]+= mC[23] + d2; | |
2066 | fC[24]+= mC[24] + d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; | |
2067 | fC[25]+= mC[25] + d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; | |
2068 | fC[26]+= mC[26] + d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; | |
2069 | fC[27]+= mC[27] + d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; | |
2070 | } | |
2071 | ||
55ac3e1e | 2072 | SetMassConstraint(0,0); |
a65041d0 | 2073 | } |
2074 | ||
2075 | Bool_t AliKFParticleBase::InvertSym3( const Double_t A[], Double_t Ai[] ) | |
2076 | { | |
2077 | //* Invert symmetric matric stored in low-triagonal form | |
2078 | ||
2079 | bool ret = 0; | |
2080 | double a0 = A[0], a1 = A[1], a2 = A[2], a3 = A[3]; | |
2081 | ||
2082 | Ai[0] = a2*A[5] - A[4]*A[4]; | |
2083 | Ai[1] = a3*A[4] - a1*A[5]; | |
2084 | Ai[3] = a1*A[4] - a2*a3; | |
2085 | Double_t det = (a0*Ai[0] + a1*Ai[1] + a3*Ai[3]); | |
2086 | if( det>1.e-20 ) det = 1./det; | |
2087 | else{ | |
2088 | det = 0; | |
2089 | ret = 1; | |
2090 | } | |
2091 | Ai[0] *= det; | |
2092 | Ai[1] *= det; | |
2093 | Ai[3] *= det; | |
2094 | Ai[2] = ( a0*A[5] - a3*a3 )*det; | |
2095 | Ai[4] = ( a1*a3 - a0*A[4] )*det; | |
2096 | Ai[5] = ( a0*a2 - a1*a1 )*det; | |
2097 | return ret; | |
2098 | } | |
2099 | ||
f826d409 | 2100 | void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] ) |
2101 | { | |
2102 | //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric | |
2103 | ||
2104 | const Int_t kN= 8; | |
2105 | Double_t mA[kN*kN]; | |
2106 | ||
2107 | for( Int_t i=0, ij=0; i<kN; i++ ){ | |
2108 | for( Int_t j=0; j<kN; j++, ++ij ){ | |
2109 | mA[ij] = 0 ; | |
2110 | 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]; | |
2111 | } | |
2112 | } | |
2113 | ||
2114 | for( Int_t i=0; i<kN; i++ ){ | |
2115 | for( Int_t j=0; j<=i; j++ ){ | |
2116 | Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i; | |
2117 | SOut[ij] = 0 ; | |
2118 | for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ]; | |
2119 | } | |
2120 | } | |
2121 | } | |
2122 | ||
2123 | ||
2124 | // 72-charachters line to define the printer border | |
2125 | //3456789012345678901234567890123456789012345678901234567890123456789012 | |
446ce366 | 2126 |