2 // **************************************************************************
3 // This file is property of and copyright by the ALICE HLT Project *
4 // ALICE Experiment at CERN, All rights reserved. *
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. *
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 //***************************************************************************
19 #include "AliHLT3DTrackParam.h"
22 ClassImp( AliHLT3DTrackParam )
24 //* Transport utilities
26 double AliHLT3DTrackParam::GetDStoPoint( double Bz, const double xyz[3], const double *T0 ) const
28 //* Get DS = Path/Momentum to a certain space point for Bz field
31 if ( !T0 ) T0 = fParam;
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];
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;
48 void AliHLT3DTrackParam::TransportToDS( double Bz, double DS, double *T0 )
50 //* Transport the particle on DS = Path/Momentum, for Bz field
63 const double kCLight = 0.000299792458;
64 Bz = Bz * T0[6] * kCLight;
66 double s = TMath::Sin( bs ), c = TMath::Cos( bs );
68 if ( TMath::Abs( bs ) > 1.e-10 ) {
72 const Double_t kOvSqr6=1./TMath::Sqrt(6.);
73 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6) * DS;
81 double d[6] = { fParam[0] - T0[0], fParam[1] - T0[1], fParam[2] - T0[2],
82 fParam[3] - T0[3], fParam[4] - T0[4], fParam[5] - T0[5]
85 T0[0] = T0[0] + sB * px + cB * py;
86 T0[1] = T0[1] - cB * px + sB * py;
87 T0[2] = T0[2] + DS * pz ;
88 T0[3] = c * px + s * py;
89 T0[4] = -s * px + c * py;
92 double mJ[6][6] = { {1, 0, 0, sB, cB, 0, },
93 {0, 1, 0, -cB, sB, 0, },
94 {0, 0, 1, 0, 0, DS, },
96 {0, 0, 0, -s, c, 0, },
100 for ( int i = 0; i < 6; i++ ) {
102 for ( int j = 0; j < 6; j++ ) fParam[i] += mJ[i][j] * d[j];
106 for ( int k = 0, i = 0; i < 6; i++ )
107 for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = fCov[k];
110 for ( int i = 0; i < 6; i++ )
111 for ( int j = 0; j < 6; j++ ) {
113 for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j];
116 for ( int k = 0, i = 0; i < 6; i++ )
117 for ( int j = 0; j <= i; j++, k++ ) {
119 for ( int l = 0; l < 6; l++ ) fCov[k] += mJC[i][l] * mJ[j][l];
126 void AliHLT3DTrackParam::InitializeCovarianceMatrix()
128 //* Initialization of covariance matrix
130 for ( int i = 0; i < 21; i++ ) fCov[i] = 0;
132 fCov[0] = fCov[ 2] = fCov[ 5] = 100.;
133 fCov[9] = fCov[14] = fCov[20] = 10000.;
138 void AliHLT3DTrackParam::GetGlueMatrix( const double xyz[3],
139 double G[6], const double *T0 ) const
143 if ( !T0 ) T0 = fParam;
145 double dx = xyz[0] - T0[0], dy = xyz[1] - T0[1], dz = xyz[2] - T0[2];
146 double px2 = T0[3] * T0[3], py2 = T0[4] * T0[4], pz2 = T0[5] * T0[5];
147 double s2 = ( dx * dx + dy * dy + dz * dz );
148 double p2 = px2 + py2 + pz2;
149 if ( p2 > 1.e-4 ) s2 /= p2;
150 double x = T0[3] * s2;
151 double xx = px2 * s2, xy = x * T0[4], xz = x * T0[5], yy = py2 * s2, yz = T0[4] * T0[5] * s2;
153 G[ 1] = xy; G[ 2] = yy;
154 G[ 3] = xz; G[ 4] = yz; G[ 5] = pz2 * s2;
159 void AliHLT3DTrackParam::Filter( const double m[3], const double V[6], const double G[6] )
165 c10 = fCov[ 1], c11 = fCov[ 2],
166 c20 = fCov[ 3], c21 = fCov[ 4], c22 = fCov[ 5],
167 c30 = fCov[ 6], c31 = fCov[ 7], c32 = fCov[ 8],
168 c40 = fCov[10], c41 = fCov[11], c42 = fCov[12],
169 c50 = fCov[15], c51 = fCov[16], c52 = fCov[17];
172 z0 = m[0] - fParam[0],
173 z1 = m[1] - fParam[1],
174 z2 = m[2] - fParam[2];
176 double mS[6] = { c00 + V[0] + G[0], c10 + V[1] + G[1], c11 + V[2] + G[2],
177 c20 + V[3] + G[3], c21 + V[4] + G[4], c22 + V[5] + G[5]
180 mSi[0] = mS[4] * mS[4] - mS[2] * mS[5];
181 mSi[1] = mS[1] * mS[5] - mS[3] * mS[4];
182 mSi[3] = mS[2] * mS[3] - mS[1] * mS[4];
183 double det = 1. / ( mS[0] * mSi[0] + mS[1] * mSi[1] + mS[3] * mSi[3] );
187 mSi[2] = ( mS[3] * mS[3] - mS[0] * mS[5] ) * det;
188 mSi[4] = ( mS[0] * mS[4] - mS[1] * mS[3] ) * det;
189 mSi[5] = ( mS[1] * mS[1] - mS[0] * mS[2] ) * det;
192 fChi2 += ( +( mSi[0] * z0 + mSi[1] * z1 + mSi[3] * z2 ) * z0
193 + ( mSi[1] * z0 + mSi[2] * z1 + mSi[4] * z2 ) * z1
194 + ( mSi[3] * z0 + mSi[4] * z1 + mSi[5] * z2 ) * z2 );
196 double k0, k1, k2 ; // k = CHtS
198 k0 = c00 * mSi[0] + c10 * mSi[1] + c20 * mSi[3];
199 k1 = c00 * mSi[1] + c10 * mSi[2] + c20 * mSi[4];
200 k2 = c00 * mSi[3] + c10 * mSi[4] + c20 * mSi[5];
202 fParam[ 0] += k0 * z0 + k1 * z1 + k2 * z2 ;
203 fCov [ 0] -= k0 * c00 + k1 * c10 + k2 * c20;
205 k0 = c10 * mSi[0] + c11 * mSi[1] + c21 * mSi[3];
206 k1 = c10 * mSi[1] + c11 * mSi[2] + c21 * mSi[4];
207 k2 = c10 * mSi[3] + c11 * mSi[4] + c21 * mSi[5];
209 fParam[ 1] += k0 * z0 + k1 * z1 + k2 * z2 ;
210 fCov [ 1] -= k0 * c00 + k1 * c10 + k2 * c20;
211 fCov [ 2] -= k0 * c10 + k1 * c11 + k2 * c21;
213 k0 = c20 * mSi[0] + c21 * mSi[1] + c22 * mSi[3];
214 k1 = c20 * mSi[1] + c21 * mSi[2] + c22 * mSi[4];
215 k2 = c20 * mSi[3] + c21 * mSi[4] + c22 * mSi[5];
217 fParam[ 2] += k0 * z0 + k1 * z1 + k2 * z2 ;
218 fCov [ 3] -= k0 * c00 + k1 * c10 + k2 * c20;
219 fCov [ 4] -= k0 * c10 + k1 * c11 + k2 * c21;
220 fCov [ 5] -= k0 * c20 + k1 * c21 + k2 * c22;
222 k0 = c30 * mSi[0] + c31 * mSi[1] + c32 * mSi[3];
223 k1 = c30 * mSi[1] + c31 * mSi[2] + c32 * mSi[4];
224 k2 = c30 * mSi[3] + c31 * mSi[4] + c32 * mSi[5];
226 fParam[ 3] += k0 * z0 + k1 * z1 + k2 * z2 ;
227 fCov [ 6] -= k0 * c00 + k1 * c10 + k2 * c20;
228 fCov [ 7] -= k0 * c10 + k1 * c11 + k2 * c21;
229 fCov [ 8] -= k0 * c20 + k1 * c21 + k2 * c22;
230 fCov [ 9] -= k0 * c30 + k1 * c31 + k2 * c32;
232 k0 = c40 * mSi[0] + c41 * mSi[1] + c42 * mSi[3];
233 k1 = c40 * mSi[1] + c41 * mSi[2] + c42 * mSi[4];
234 k2 = c40 * mSi[3] + c41 * mSi[4] + c42 * mSi[5];
236 fParam[ 4] += k0 * z0 + k1 * z1 + k2 * z2 ;
237 fCov [10] -= k0 * c00 + k1 * c10 + k2 * c20;
238 fCov [11] -= k0 * c10 + k1 * c11 + k2 * c21;
239 fCov [12] -= k0 * c20 + k1 * c21 + k2 * c22;
240 fCov [13] -= k0 * c30 + k1 * c31 + k2 * c32;
241 fCov [14] -= k0 * c40 + k1 * c41 + k2 * c42;
243 k0 = c50 * mSi[0] + c51 * mSi[1] + c52 * mSi[3];
244 k1 = c50 * mSi[1] + c51 * mSi[2] + c52 * mSi[4];
245 k2 = c50 * mSi[3] + c51 * mSi[4] + c52 * mSi[5];
247 fParam[ 5] += k0 * z0 + k1 * z1 + k2 * z2 ;
248 fCov [15] -= k0 * c00 + k1 * c10 + k2 * c20;
249 fCov [16] -= k0 * c10 + k1 * c11 + k2 * c21;
250 fCov [17] -= k0 * c20 + k1 * c21 + k2 * c22;
251 fCov [18] -= k0 * c30 + k1 * c31 + k2 * c32;
252 fCov [19] -= k0 * c40 + k1 * c41 + k2 * c42;
253 fCov [20] -= k0 * c50 + k1 * c51 + k2 * c52;
257 double px = fParam[3];
258 double py = fParam[4];
259 double pz = fParam[5];
261 double p = TMath::Sqrt( px * px + py * py + pz * pz );
263 double qp = fSignQ * pi;
264 double qp3 = qp * pi * pi;
266 c60 = qp3 * ( c30 + c40 + c50 ),
267 c61 = qp3 * ( c31 + c41 + c51 ),
268 c62 = qp3 * ( c32 + c42 + c52 );
270 k0 = c60 * mSi[0] + c61 * mSi[1] + c62 * mSi[3];
271 k1 = c60 * mSi[1] + c61 * mSi[2] + c62 * mSi[4];
272 k2 = c60 * mSi[3] + c61 * mSi[4] + c62 * mSi[5];
274 qp += k0 * z0 + k1 * z1 + k2 * z2 ;
275 if ( qp > 0 ) fSignQ = 1;
276 else if ( qp < 0 ) fSignQ = -1;
283 void AliHLT3DTrackParam::SetDirection( double Direction[3] )
285 //* Change track direction
287 if ( fParam[3]*Direction[0] + fParam[4]*Direction[1] + fParam[5]*Direction[2] >= 0 ) return;
289 fParam[3] = -fParam[3];
290 fParam[4] = -fParam[4];
291 fParam[5] = -fParam[5];
294 fCov[ 6] = -fCov[ 6]; fCov[ 7] = -fCov[ 7]; fCov[ 8] = -fCov[ 8];
295 fCov[10] = -fCov[10]; fCov[11] = -fCov[11]; fCov[12] = -fCov[12];
296 fCov[15] = -fCov[15]; fCov[16] = -fCov[16]; fCov[17] = -fCov[17];
300 void AliHLT3DTrackParam::RotateCoordinateSystem( double alpha )
304 double cA = TMath::Cos( alpha );
305 double sA = TMath::Sin( alpha );
306 double x = fParam[0], y = fParam[1], px = fParam[3], py = fParam[4];
307 fParam[0] = x * cA + y * sA;
308 fParam[1] = -x * sA + y * cA;
309 fParam[2] = fParam[2];
310 fParam[3] = px * cA + py * sA;
311 fParam[4] = -px * sA + py * cA;
312 fParam[5] = fParam[5];
314 double mJ[6][6] = { { cA, sA, 0, 0, 0, 0 },
315 { -sA, cA, 0, 0, 0, 0 },
316 { 0, 0, 1, 0, 0, 0 },
317 { 0, 0, 0, cA, sA, 0 },
318 { 0, 0, 0, -sA, cA, 0 },
323 for ( int k = 0, i = 0; i < 6; i++ )
324 for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = fCov[k];
327 for ( int i = 0; i < 6; i++ )
328 for ( int j = 0; j < 6; j++ ) {
330 for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j];
333 for ( int k = 0, i = 0; i < 6; i++ )
334 for ( int j = 0; j <= i; j++, k++ ) {
336 for ( int l = 0; l < 6; l++ ) fCov[k] += mJC[i][l] * mJ[j][l];
341 void AliHLT3DTrackParam::Get5Parameters( double alpha, double T[6], double C[15] ) const
345 AliHLT3DTrackParam t = *this;
346 t.RotateCoordinateSystem( alpha );
348 x = t.fParam[0], y = t.fParam[1], z = t.fParam[2],
349 px = t.fParam[3], py = t.fParam[4], pz = t.fParam[5], q = t.fSignQ;
351 double p2 = px * px + py * py + pz * pz;
352 if ( p2 < 1.e-8 ) p2 = 1;
354 double n = sqrt( n2 );
363 double mJ[5][6] = { { -T[2], 1, 0, 0, 0, 0 },
364 { -T[3], 0, 1, 0, 0, 0 },
365 { 0, 0, 0, -T[2] / px, 1. / px, 0 },
366 { 0, 0, 0, -T[3] / px, 0, 1. / px },
367 { 0, 0, 0, -T[4]*n2*px, -T[4]*n2*py, -T[4]*n2*pz}
371 for ( int k = 0, i = 0; i < 6; i++ )
372 for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = t.fCov[k];
375 for ( int i = 0; i < 5; i++ )
376 for ( int j = 0; j < 6; j++ ) {
378 for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j];
381 for ( int k = 0, i = 0; i < 5; i++ )
382 for ( int j = 0; j <= i; j++, k++ ) {
384 for ( int l = 0; l < 6; l++ ) C[k] += mJC[i][l] * mJ[j][l];