]>
Commit | Line | Data |
---|---|---|
326c2d4b | 1 | // @(#) $Id$ |
ce565086 | 2 | // ************************************************************************** |
fbb9b71b | 3 | // This file is property of and copyright by the ALICE HLT Project * |
326c2d4b | 4 | // ALICE Experiment at CERN, All rights reserved. * |
5 | // * | |
6 | // Primary Authors: Sergey Gorbunov <sergey.gorbunov@kip.uni-heidelberg.de> * | |
7 | // Ivan Kisel <kisel@kip.uni-heidelberg.de> * | |
8 | // for The ALICE HLT Project. * | |
9 | // * | |
10 | // Permission to use, copy, modify and distribute this software and its * | |
11 | // documentation strictly for non-commercial purposes is hereby granted * | |
12 | // without fee, provided that the above copyright notice appears in all * | |
13 | // copies and that both the copyright notice and this permission notice * | |
14 | // appear in the supporting documentation. The authors make no claims * | |
15 | // about the suitability of this software for any purpose. It is * | |
16 | // provided "as is" without express or implied warranty. * | |
17 | //*************************************************************************** | |
18 | ||
19 | #include "AliHLT3DTrackParam.h" | |
20 | #include "TMath.h" | |
21 | ||
fbb9b71b | 22 | ClassImp( AliHLT3DTrackParam ) |
326c2d4b | 23 | |
24 | //* Transport utilities | |
fbb9b71b | 25 | |
26 | double AliHLT3DTrackParam::GetDStoPoint( double Bz, const double xyz[3], const double *T0 ) const | |
326c2d4b | 27 | { |
28 | //* Get DS = Path/Momentum to a certain space point for Bz field | |
29 | ||
fbb9b71b | 30 | double q = fSignQ; |
31 | if ( !T0 ) T0 = fParam; | |
326c2d4b | 32 | else q = T0[6]; |
33 | ||
fbb9b71b | 34 | const double kCLight = 0.000299792458; |
35 | double bq = Bz * q * kCLight; | |
36 | double pt2 = T0[3] * T0[3] + T0[4] * T0[4]; | |
37 | if ( pt2 < 1.e-4 ) return 0; | |
38 | double dx = xyz[0] - T0[0]; | |
39 | double dy = xyz[1] - T0[1]; | |
40 | double a = dx * T0[3] + dy * T0[4]; | |
41 | double dS = 0; | |
42 | if ( TMath::Abs( bq ) < 1.e-8 ) dS = a / pt2; | |
43 | else dS = TMath::ATan2( bq * a, pt2 + bq * ( dy * T0[3] - dx * T0[4] ) ) / bq; | |
326c2d4b | 44 | return dS; |
45 | } | |
46 | ||
47 | ||
fbb9b71b | 48 | void AliHLT3DTrackParam::TransportToDS( double Bz, double DS, double *T0 ) |
326c2d4b | 49 | { |
fbb9b71b | 50 | //* Transport the particle on DS = Path/Momentum, for Bz field |
326c2d4b | 51 | |
fbb9b71b | 52 | double tmp[7]; |
53 | if ( !T0 ) { | |
326c2d4b | 54 | T0 = tmp; |
55 | T0[0] = fParam[0]; | |
56 | T0[1] = fParam[1]; | |
57 | T0[2] = fParam[2]; | |
58 | T0[3] = fParam[3]; | |
59 | T0[4] = fParam[4]; | |
60 | T0[5] = fParam[5]; | |
61 | T0[6] = fSignQ; | |
62 | } | |
fbb9b71b | 63 | const double kCLight = 0.000299792458; |
64 | Bz = Bz * T0[6] * kCLight; | |
65 | double bs = Bz * DS; | |
66 | double s = TMath::Sin( bs ), c = TMath::Cos( bs ); | |
67 | double sB, cB; | |
68 | if ( TMath::Abs( bs ) > 1.e-10 ) { | |
69 | sB = s / Bz; | |
70 | cB = ( 1 - c ) / Bz; | |
71 | } else { | |
72 | sB = ( 1. - bs * bs / 6. ) * DS; | |
73 | cB = .5 * sB * bs; | |
326c2d4b | 74 | } |
fbb9b71b | 75 | |
76 | double px = T0[3]; | |
77 | double py = T0[4]; | |
78 | double pz = T0[5]; | |
79 | ||
80 | double d[6] = { fParam[0] - T0[0], fParam[1] - T0[1], fParam[2] - T0[2], | |
81 | fParam[3] - T0[3], fParam[4] - T0[4], fParam[5] - T0[5] | |
82 | }; | |
83 | ||
84 | T0[0] = T0[0] + sB * px + cB * py; | |
85 | T0[1] = T0[1] - cB * px + sB * py; | |
86 | T0[2] = T0[2] + DS * pz ; | |
87 | T0[3] = c * px + s * py; | |
88 | T0[4] = -s * px + c * py; | |
326c2d4b | 89 | T0[5] = T0[5]; |
fbb9b71b | 90 | |
91 | double mJ[6][6] = { {1, 0, 0, sB, cB, 0, }, | |
92 | {0, 1, 0, -cB, sB, 0, }, | |
93 | {0, 0, 1, 0, 0, DS, }, | |
94 | {0, 0, 0, c, s, 0, }, | |
95 | {0, 0, 0, -s, c, 0, }, | |
96 | {0, 0, 0, 0, 0, 1, } | |
97 | }; | |
98 | ||
99 | for ( int i = 0; i < 6; i++ ) { | |
326c2d4b | 100 | fParam[i] = T0[i]; |
fbb9b71b | 101 | for ( int j = 0; j < 6; j++ ) fParam[i] += mJ[i][j] * d[j]; |
326c2d4b | 102 | } |
103 | ||
fbb9b71b | 104 | double mA[6][6]; |
105 | for ( int k = 0, i = 0; i < 6; i++ ) | |
106 | for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = fCov[k]; | |
326c2d4b | 107 | |
fbb9b71b | 108 | double mJC[6][6]; |
109 | for ( int i = 0; i < 6; i++ ) | |
110 | for ( int j = 0; j < 6; j++ ) { | |
111 | mJC[i][j] = 0; | |
112 | for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j]; | |
326c2d4b | 113 | } |
fbb9b71b | 114 | |
115 | for ( int k = 0, i = 0; i < 6; i++ ) | |
116 | for ( int j = 0; j <= i; j++, k++ ) { | |
326c2d4b | 117 | fCov[k] = 0; |
fbb9b71b | 118 | for ( int l = 0; l < 6; l++ ) fCov[k] += mJC[i][l] * mJ[j][l]; |
326c2d4b | 119 | } |
120 | } | |
121 | ||
122 | ||
fbb9b71b | 123 | //* Fit utilities |
326c2d4b | 124 | |
125 | void AliHLT3DTrackParam::InitializeCovarianceMatrix() | |
126 | { | |
127 | //* Initialization of covariance matrix | |
128 | ||
fbb9b71b | 129 | for ( int i = 0; i < 21; i++ ) fCov[i] = 0; |
326c2d4b | 130 | fSignQ = 0; |
131 | fCov[0] = fCov[ 2] = fCov[ 5] = 100.; | |
132 | fCov[9] = fCov[14] = fCov[20] = 10000.; | |
133 | fChi2 = 0; | |
134 | fNDF = -5; | |
135 | } | |
136 | ||
fbb9b71b | 137 | void AliHLT3DTrackParam::GetGlueMatrix( const double xyz[3], |
138 | double G[6], const double *T0 ) const | |
326c2d4b | 139 | { |
140 | //* ! | |
141 | ||
fbb9b71b | 142 | if ( !T0 ) T0 = fParam; |
143 | ||
144 | double dx = xyz[0] - T0[0], dy = xyz[1] - T0[1], dz = xyz[2] - T0[2]; | |
145 | double px2 = T0[3] * T0[3], py2 = T0[4] * T0[4], pz2 = T0[5] * T0[5]; | |
146 | double s2 = ( dx * dx + dy * dy + dz * dz ); | |
147 | double p2 = px2 + py2 + pz2; | |
148 | if ( p2 > 1.e-4 ) s2 /= p2; | |
149 | double x = T0[3] * s2; | |
150 | double xx = px2 * s2, xy = x * T0[4], xz = x * T0[5], yy = py2 * s2, yz = T0[4] * T0[5] * s2; | |
151 | G[ 0] = xx; | |
152 | G[ 1] = xy; G[ 2] = yy; | |
153 | G[ 3] = xz; G[ 4] = yz; G[ 5] = pz2 * s2; | |
326c2d4b | 154 | } |
155 | ||
156 | ||
157 | ||
fbb9b71b | 158 | void AliHLT3DTrackParam::Filter( const double m[3], const double V[6], const double G[6] ) |
159 | { | |
326c2d4b | 160 | //* ! |
fbb9b71b | 161 | |
326c2d4b | 162 | double |
fbb9b71b | 163 | c00 = fCov[ 0], |
164 | c10 = fCov[ 1], c11 = fCov[ 2], | |
165 | c20 = fCov[ 3], c21 = fCov[ 4], c22 = fCov[ 5], | |
166 | c30 = fCov[ 6], c31 = fCov[ 7], c32 = fCov[ 8], | |
167 | c40 = fCov[10], c41 = fCov[11], c42 = fCov[12], | |
168 | c50 = fCov[15], c51 = fCov[16], c52 = fCov[17]; | |
169 | ||
170 | double | |
171 | z0 = m[0] - fParam[0], | |
172 | z1 = m[1] - fParam[1], | |
173 | z2 = m[2] - fParam[2]; | |
174 | ||
175 | double mS[6] = { c00 + V[0] + G[0], c10 + V[1] + G[1], c11 + V[2] + G[2], | |
176 | c20 + V[3] + G[3], c21 + V[4] + G[4], c22 + V[5] + G[5] | |
177 | }; | |
178 | double mSi[6]; | |
179 | mSi[0] = mS[4] * mS[4] - mS[2] * mS[5]; | |
180 | mSi[1] = mS[1] * mS[5] - mS[3] * mS[4]; | |
181 | mSi[3] = mS[2] * mS[3] - mS[1] * mS[4]; | |
182 | double det = 1. / ( mS[0] * mSi[0] + mS[1] * mSi[1] + mS[3] * mSi[3] ); | |
326c2d4b | 183 | mSi[0] *= det; |
184 | mSi[1] *= det; | |
185 | mSi[3] *= det; | |
fbb9b71b | 186 | mSi[2] = ( mS[3] * mS[3] - mS[0] * mS[5] ) * det; |
187 | mSi[4] = ( mS[0] * mS[4] - mS[1] * mS[3] ) * det; | |
188 | mSi[5] = ( mS[1] * mS[1] - mS[0] * mS[2] ) * det; | |
189 | ||
326c2d4b | 190 | fNDF += 2; |
fbb9b71b | 191 | fChi2 += ( +( mSi[0] * z0 + mSi[1] * z1 + mSi[3] * z2 ) * z0 |
192 | + ( mSi[1] * z0 + mSi[2] * z1 + mSi[4] * z2 ) * z1 | |
193 | + ( mSi[3] * z0 + mSi[4] * z1 + mSi[5] * z2 ) * z2 ); | |
194 | ||
195 | double k0, k1, k2 ; // k = CHtS | |
196 | ||
197 | k0 = c00 * mSi[0] + c10 * mSi[1] + c20 * mSi[3]; | |
198 | k1 = c00 * mSi[1] + c10 * mSi[2] + c20 * mSi[4]; | |
199 | k2 = c00 * mSi[3] + c10 * mSi[4] + c20 * mSi[5]; | |
200 | ||
201 | fParam[ 0] += k0 * z0 + k1 * z1 + k2 * z2 ; | |
202 | fCov [ 0] -= k0 * c00 + k1 * c10 + k2 * c20; | |
203 | ||
204 | k0 = c10 * mSi[0] + c11 * mSi[1] + c21 * mSi[3]; | |
205 | k1 = c10 * mSi[1] + c11 * mSi[2] + c21 * mSi[4]; | |
206 | k2 = c10 * mSi[3] + c11 * mSi[4] + c21 * mSi[5]; | |
207 | ||
208 | fParam[ 1] += k0 * z0 + k1 * z1 + k2 * z2 ; | |
209 | fCov [ 1] -= k0 * c00 + k1 * c10 + k2 * c20; | |
210 | fCov [ 2] -= k0 * c10 + k1 * c11 + k2 * c21; | |
211 | ||
212 | k0 = c20 * mSi[0] + c21 * mSi[1] + c22 * mSi[3]; | |
213 | k1 = c20 * mSi[1] + c21 * mSi[2] + c22 * mSi[4]; | |
214 | k2 = c20 * mSi[3] + c21 * mSi[4] + c22 * mSi[5]; | |
215 | ||
216 | fParam[ 2] += k0 * z0 + k1 * z1 + k2 * z2 ; | |
217 | fCov [ 3] -= k0 * c00 + k1 * c10 + k2 * c20; | |
218 | fCov [ 4] -= k0 * c10 + k1 * c11 + k2 * c21; | |
219 | fCov [ 5] -= k0 * c20 + k1 * c21 + k2 * c22; | |
220 | ||
221 | k0 = c30 * mSi[0] + c31 * mSi[1] + c32 * mSi[3]; | |
222 | k1 = c30 * mSi[1] + c31 * mSi[2] + c32 * mSi[4]; | |
223 | k2 = c30 * mSi[3] + c31 * mSi[4] + c32 * mSi[5]; | |
224 | ||
225 | fParam[ 3] += k0 * z0 + k1 * z1 + k2 * z2 ; | |
226 | fCov [ 6] -= k0 * c00 + k1 * c10 + k2 * c20; | |
227 | fCov [ 7] -= k0 * c10 + k1 * c11 + k2 * c21; | |
228 | fCov [ 8] -= k0 * c20 + k1 * c21 + k2 * c22; | |
229 | fCov [ 9] -= k0 * c30 + k1 * c31 + k2 * c32; | |
230 | ||
231 | k0 = c40 * mSi[0] + c41 * mSi[1] + c42 * mSi[3]; | |
232 | k1 = c40 * mSi[1] + c41 * mSi[2] + c42 * mSi[4]; | |
233 | k2 = c40 * mSi[3] + c41 * mSi[4] + c42 * mSi[5]; | |
234 | ||
235 | fParam[ 4] += k0 * z0 + k1 * z1 + k2 * z2 ; | |
236 | fCov [10] -= k0 * c00 + k1 * c10 + k2 * c20; | |
237 | fCov [11] -= k0 * c10 + k1 * c11 + k2 * c21; | |
238 | fCov [12] -= k0 * c20 + k1 * c21 + k2 * c22; | |
239 | fCov [13] -= k0 * c30 + k1 * c31 + k2 * c32; | |
240 | fCov [14] -= k0 * c40 + k1 * c41 + k2 * c42; | |
241 | ||
242 | k0 = c50 * mSi[0] + c51 * mSi[1] + c52 * mSi[3]; | |
243 | k1 = c50 * mSi[1] + c51 * mSi[2] + c52 * mSi[4]; | |
244 | k2 = c50 * mSi[3] + c51 * mSi[4] + c52 * mSi[5]; | |
245 | ||
246 | fParam[ 5] += k0 * z0 + k1 * z1 + k2 * z2 ; | |
247 | fCov [15] -= k0 * c00 + k1 * c10 + k2 * c20; | |
248 | fCov [16] -= k0 * c10 + k1 * c11 + k2 * c21; | |
249 | fCov [17] -= k0 * c20 + k1 * c21 + k2 * c22; | |
250 | fCov [18] -= k0 * c30 + k1 * c31 + k2 * c32; | |
251 | fCov [19] -= k0 * c40 + k1 * c41 + k2 * c42; | |
252 | fCov [20] -= k0 * c50 + k1 * c51 + k2 * c52; | |
326c2d4b | 253 | |
254 | // fit charge | |
255 | ||
fbb9b71b | 256 | double px = fParam[3]; |
257 | double py = fParam[4]; | |
258 | double pz = fParam[5]; | |
259 | ||
260 | double p = TMath::Sqrt( px * px + py * py + pz * pz ); | |
261 | double pi = 1. / p; | |
262 | double qp = fSignQ * pi; | |
263 | double qp3 = qp * pi * pi; | |
264 | double | |
265 | c60 = qp3 * ( c30 + c40 + c50 ), | |
266 | c61 = qp3 * ( c31 + c41 + c51 ), | |
267 | c62 = qp3 * ( c32 + c42 + c52 ); | |
268 | ||
269 | k0 = c60 * mSi[0] + c61 * mSi[1] + c62 * mSi[3]; | |
270 | k1 = c60 * mSi[1] + c61 * mSi[2] + c62 * mSi[4]; | |
271 | k2 = c60 * mSi[3] + c61 * mSi[4] + c62 * mSi[5]; | |
272 | ||
273 | qp += k0 * z0 + k1 * z1 + k2 * z2 ; | |
274 | if ( qp > 0 ) fSignQ = 1; | |
275 | else if ( qp < 0 ) fSignQ = -1; | |
326c2d4b | 276 | else fSignQ = 0; |
277 | } | |
278 | ||
279 | ||
280 | //* Other utilities | |
281 | ||
fbb9b71b | 282 | void AliHLT3DTrackParam::SetDirection( double Direction[3] ) |
326c2d4b | 283 | { |
fbb9b71b | 284 | //* Change track direction |
326c2d4b | 285 | |
fbb9b71b | 286 | if ( fParam[3]*Direction[0] + fParam[4]*Direction[1] + fParam[5]*Direction[2] >= 0 ) return; |
326c2d4b | 287 | |
288 | fParam[3] = -fParam[3]; | |
289 | fParam[4] = -fParam[4]; | |
290 | fParam[5] = -fParam[5]; | |
291 | fSignQ = -fSignQ; | |
292 | ||
fbb9b71b | 293 | fCov[ 6] = -fCov[ 6]; fCov[ 7] = -fCov[ 7]; fCov[ 8] = -fCov[ 8]; |
294 | fCov[10] = -fCov[10]; fCov[11] = -fCov[11]; fCov[12] = -fCov[12]; | |
295 | fCov[15] = -fCov[15]; fCov[16] = -fCov[16]; fCov[17] = -fCov[17]; | |
326c2d4b | 296 | } |
297 | ||
298 | ||
fbb9b71b | 299 | void AliHLT3DTrackParam::RotateCoordinateSystem( double alpha ) |
326c2d4b | 300 | { |
301 | //* ! | |
302 | ||
fbb9b71b | 303 | double cA = TMath::Cos( alpha ); |
304 | double sA = TMath::Sin( alpha ); | |
305 | double x = fParam[0], y = fParam[1], px = fParam[3], py = fParam[4]; | |
306 | fParam[0] = x * cA + y * sA; | |
307 | fParam[1] = -x * sA + y * cA; | |
326c2d4b | 308 | fParam[2] = fParam[2]; |
fbb9b71b | 309 | fParam[3] = px * cA + py * sA; |
310 | fParam[4] = -px * sA + py * cA; | |
311 | fParam[5] = fParam[5]; | |
312 | ||
313 | double mJ[6][6] = { { cA, sA, 0, 0, 0, 0 }, | |
314 | { -sA, cA, 0, 0, 0, 0 }, | |
315 | { 0, 0, 1, 0, 0, 0 }, | |
316 | { 0, 0, 0, cA, sA, 0 }, | |
317 | { 0, 0, 0, -sA, cA, 0 }, | |
318 | { 0, 0, 0, 0, 0, 1 } | |
319 | }; | |
320 | ||
321 | double mA[6][6]; | |
322 | for ( int k = 0, i = 0; i < 6; i++ ) | |
323 | for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = fCov[k]; | |
324 | ||
325 | double mJC[6][6]; | |
326 | for ( int i = 0; i < 6; i++ ) | |
327 | for ( int j = 0; j < 6; j++ ) { | |
328 | mJC[i][j] = 0; | |
329 | for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j]; | |
326c2d4b | 330 | } |
fbb9b71b | 331 | |
332 | for ( int k = 0, i = 0; i < 6; i++ ) | |
333 | for ( int j = 0; j <= i; j++, k++ ) { | |
326c2d4b | 334 | fCov[k] = 0; |
fbb9b71b | 335 | for ( int l = 0; l < 6; l++ ) fCov[k] += mJC[i][l] * mJ[j][l]; |
326c2d4b | 336 | } |
337 | } | |
338 | ||
339 | ||
fbb9b71b | 340 | void AliHLT3DTrackParam::Get5Parameters( double alpha, double T[6], double C[15] ) const |
326c2d4b | 341 | { |
342 | //* ! | |
343 | ||
344 | AliHLT3DTrackParam t = *this; | |
fbb9b71b | 345 | t.RotateCoordinateSystem( alpha ); |
346 | double | |
347 | x = t.fParam[0], y = t.fParam[1], z = t.fParam[2], | |
348 | px = t.fParam[3], py = t.fParam[4], pz = t.fParam[5], q = t.fSignQ; | |
326c2d4b | 349 | |
fbb9b71b | 350 | double p2 = px * px + py * py + pz * pz; |
351 | if ( p2 < 1.e-8 ) p2 = 1; | |
352 | double n2 = 1. / p2; | |
353 | double n = sqrt( n2 ); | |
326c2d4b | 354 | |
355 | T[5] = x; | |
356 | T[0] = y; | |
357 | T[1] = z; | |
fbb9b71b | 358 | T[2] = py / px; |
359 | T[3] = pz / px; | |
360 | T[4] = q * n; | |
361 | ||
362 | double mJ[5][6] = { { -T[2], 1, 0, 0, 0, 0 }, | |
363 | { -T[3], 0, 1, 0, 0, 0 }, | |
364 | { 0, 0, 0, -T[2] / px, 1. / px, 0 }, | |
365 | { 0, 0, 0, -T[3] / px, 0, 1. / px }, | |
366 | { 0, 0, 0, -T[4]*n2*px, -T[4]*n2*py, -T[4]*n2*pz} | |
367 | }; | |
368 | ||
369 | double mA[6][6]; | |
370 | for ( int k = 0, i = 0; i < 6; i++ ) | |
371 | for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = t.fCov[k]; | |
372 | ||
373 | double mJC[5][6]; | |
374 | for ( int i = 0; i < 5; i++ ) | |
375 | for ( int j = 0; j < 6; j++ ) { | |
376 | mJC[i][j] = 0; | |
377 | for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j]; | |
326c2d4b | 378 | } |
fbb9b71b | 379 | |
380 | for ( int k = 0, i = 0; i < 5; i++ ) | |
381 | for ( int j = 0; j <= i; j++, k++ ) { | |
326c2d4b | 382 | C[k] = 0; |
fbb9b71b | 383 | for ( int l = 0; l < 6; l++ ) C[k] += mJC[i][l] * mJ[j][l]; |
326c2d4b | 384 | } |
385 | } |