// @(#) $Id$ // ************************************************************************** // This file is property of and copyright by the ALICE HLT Project * // ALICE Experiment at CERN, All rights reserved. * // * // Primary Authors: Sergey Gorbunov * // Ivan Kisel * // for The ALICE HLT Project. * // * // Permission to use, copy, modify and distribute this software and its * // documentation strictly for non-commercial purposes is hereby granted * // without fee, provided that the above copyright notice appears in all * // copies and that both the copyright notice and this permission notice * // appear in the supporting documentation. The authors make no claims * // about the suitability of this software for any purpose. It is * // provided "as is" without express or implied warranty. * //*************************************************************************** #include "AliHLT3DTrackParam.h" #include "TMath.h" ClassImp( AliHLT3DTrackParam ) //* Transport utilities double AliHLT3DTrackParam::GetDStoPoint( double Bz, const double xyz[3], const double *T0 ) const { //* Get DS = Path/Momentum to a certain space point for Bz field double q = fSignQ; if ( !T0 ) T0 = fParam; else q = T0[6]; const double kCLight = 0.000299792458; double bq = Bz * q * kCLight; double pt2 = T0[3] * T0[3] + T0[4] * T0[4]; if ( pt2 < 1.e-4 ) return 0; double dx = xyz[0] - T0[0]; double dy = xyz[1] - T0[1]; double a = dx * T0[3] + dy * T0[4]; double dS = 0; if ( TMath::Abs( bq ) < 1.e-8 ) dS = a / pt2; else dS = TMath::ATan2( bq * a, pt2 + bq * ( dy * T0[3] - dx * T0[4] ) ) / bq; return dS; } void AliHLT3DTrackParam::TransportToDS( double Bz, double DS, double *T0 ) { //* Transport the particle on DS = Path/Momentum, for Bz field double tmp[7]; if ( !T0 ) { T0 = tmp; T0[0] = fParam[0]; T0[1] = fParam[1]; T0[2] = fParam[2]; T0[3] = fParam[3]; T0[4] = fParam[4]; T0[5] = fParam[5]; T0[6] = fSignQ; } const double kCLight = 0.000299792458; Bz = Bz * T0[6] * kCLight; double bs = Bz * DS; double s = TMath::Sin( bs ), c = TMath::Cos( bs ); double sB, cB; if ( TMath::Abs( bs ) > 1.e-10 ) { sB = s / Bz; cB = ( 1 - c ) / Bz; } else { sB = ( 1. - bs * bs / 6. ) * DS; cB = .5 * sB * bs; } double px = T0[3]; double py = T0[4]; double pz = T0[5]; double d[6] = { fParam[0] - T0[0], fParam[1] - T0[1], fParam[2] - T0[2], fParam[3] - T0[3], fParam[4] - T0[4], fParam[5] - T0[5] }; T0[0] = T0[0] + sB * px + cB * py; T0[1] = T0[1] - cB * px + sB * py; T0[2] = T0[2] + DS * pz ; T0[3] = c * px + s * py; T0[4] = -s * px + c * py; T0[5] = T0[5]; double mJ[6][6] = { {1, 0, 0, sB, cB, 0, }, {0, 1, 0, -cB, sB, 0, }, {0, 0, 1, 0, 0, DS, }, {0, 0, 0, c, s, 0, }, {0, 0, 0, -s, c, 0, }, {0, 0, 0, 0, 0, 1, } }; for ( int i = 0; i < 6; i++ ) { fParam[i] = T0[i]; for ( int j = 0; j < 6; j++ ) fParam[i] += mJ[i][j] * d[j]; } double mA[6][6]; for ( int k = 0, i = 0; i < 6; i++ ) for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = fCov[k]; double mJC[6][6]; for ( int i = 0; i < 6; i++ ) for ( int j = 0; j < 6; j++ ) { mJC[i][j] = 0; for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j]; } for ( int k = 0, i = 0; i < 6; i++ ) for ( int j = 0; j <= i; j++, k++ ) { fCov[k] = 0; for ( int l = 0; l < 6; l++ ) fCov[k] += mJC[i][l] * mJ[j][l]; } } //* Fit utilities void AliHLT3DTrackParam::InitializeCovarianceMatrix() { //* Initialization of covariance matrix for ( int i = 0; i < 21; i++ ) fCov[i] = 0; fSignQ = 0; fCov[0] = fCov[ 2] = fCov[ 5] = 100.; fCov[9] = fCov[14] = fCov[20] = 10000.; fChi2 = 0; fNDF = -5; } void AliHLT3DTrackParam::GetGlueMatrix( const double xyz[3], double G[6], const double *T0 ) const { //* ! if ( !T0 ) T0 = fParam; double dx = xyz[0] - T0[0], dy = xyz[1] - T0[1], dz = xyz[2] - T0[2]; double px2 = T0[3] * T0[3], py2 = T0[4] * T0[4], pz2 = T0[5] * T0[5]; double s2 = ( dx * dx + dy * dy + dz * dz ); double p2 = px2 + py2 + pz2; if ( p2 > 1.e-4 ) s2 /= p2; double x = T0[3] * s2; double xx = px2 * s2, xy = x * T0[4], xz = x * T0[5], yy = py2 * s2, yz = T0[4] * T0[5] * s2; G[ 0] = xx; G[ 1] = xy; G[ 2] = yy; G[ 3] = xz; G[ 4] = yz; G[ 5] = pz2 * s2; } void AliHLT3DTrackParam::Filter( const double m[3], const double V[6], const double G[6] ) { //* ! double c00 = fCov[ 0], c10 = fCov[ 1], c11 = fCov[ 2], c20 = fCov[ 3], c21 = fCov[ 4], c22 = fCov[ 5], c30 = fCov[ 6], c31 = fCov[ 7], c32 = fCov[ 8], c40 = fCov[10], c41 = fCov[11], c42 = fCov[12], c50 = fCov[15], c51 = fCov[16], c52 = fCov[17]; double z0 = m[0] - fParam[0], z1 = m[1] - fParam[1], z2 = m[2] - fParam[2]; double mS[6] = { c00 + V[0] + G[0], c10 + V[1] + G[1], c11 + V[2] + G[2], c20 + V[3] + G[3], c21 + V[4] + G[4], c22 + V[5] + G[5] }; double mSi[6]; mSi[0] = mS[4] * mS[4] - mS[2] * mS[5]; mSi[1] = mS[1] * mS[5] - mS[3] * mS[4]; mSi[3] = mS[2] * mS[3] - mS[1] * mS[4]; double det = 1. / ( mS[0] * mSi[0] + mS[1] * mSi[1] + mS[3] * mSi[3] ); mSi[0] *= det; mSi[1] *= det; mSi[3] *= det; mSi[2] = ( mS[3] * mS[3] - mS[0] * mS[5] ) * det; mSi[4] = ( mS[0] * mS[4] - mS[1] * mS[3] ) * det; mSi[5] = ( mS[1] * mS[1] - mS[0] * mS[2] ) * det; fNDF += 2; fChi2 += ( +( mSi[0] * z0 + mSi[1] * z1 + mSi[3] * z2 ) * z0 + ( mSi[1] * z0 + mSi[2] * z1 + mSi[4] * z2 ) * z1 + ( mSi[3] * z0 + mSi[4] * z1 + mSi[5] * z2 ) * z2 ); double k0, k1, k2 ; // k = CHtS k0 = c00 * mSi[0] + c10 * mSi[1] + c20 * mSi[3]; k1 = c00 * mSi[1] + c10 * mSi[2] + c20 * mSi[4]; k2 = c00 * mSi[3] + c10 * mSi[4] + c20 * mSi[5]; fParam[ 0] += k0 * z0 + k1 * z1 + k2 * z2 ; fCov [ 0] -= k0 * c00 + k1 * c10 + k2 * c20; k0 = c10 * mSi[0] + c11 * mSi[1] + c21 * mSi[3]; k1 = c10 * mSi[1] + c11 * mSi[2] + c21 * mSi[4]; k2 = c10 * mSi[3] + c11 * mSi[4] + c21 * mSi[5]; fParam[ 1] += k0 * z0 + k1 * z1 + k2 * z2 ; fCov [ 1] -= k0 * c00 + k1 * c10 + k2 * c20; fCov [ 2] -= k0 * c10 + k1 * c11 + k2 * c21; k0 = c20 * mSi[0] + c21 * mSi[1] + c22 * mSi[3]; k1 = c20 * mSi[1] + c21 * mSi[2] + c22 * mSi[4]; k2 = c20 * mSi[3] + c21 * mSi[4] + c22 * mSi[5]; fParam[ 2] += k0 * z0 + k1 * z1 + k2 * z2 ; fCov [ 3] -= k0 * c00 + k1 * c10 + k2 * c20; fCov [ 4] -= k0 * c10 + k1 * c11 + k2 * c21; fCov [ 5] -= k0 * c20 + k1 * c21 + k2 * c22; k0 = c30 * mSi[0] + c31 * mSi[1] + c32 * mSi[3]; k1 = c30 * mSi[1] + c31 * mSi[2] + c32 * mSi[4]; k2 = c30 * mSi[3] + c31 * mSi[4] + c32 * mSi[5]; fParam[ 3] += k0 * z0 + k1 * z1 + k2 * z2 ; fCov [ 6] -= k0 * c00 + k1 * c10 + k2 * c20; fCov [ 7] -= k0 * c10 + k1 * c11 + k2 * c21; fCov [ 8] -= k0 * c20 + k1 * c21 + k2 * c22; fCov [ 9] -= k0 * c30 + k1 * c31 + k2 * c32; k0 = c40 * mSi[0] + c41 * mSi[1] + c42 * mSi[3]; k1 = c40 * mSi[1] + c41 * mSi[2] + c42 * mSi[4]; k2 = c40 * mSi[3] + c41 * mSi[4] + c42 * mSi[5]; fParam[ 4] += k0 * z0 + k1 * z1 + k2 * z2 ; fCov [10] -= k0 * c00 + k1 * c10 + k2 * c20; fCov [11] -= k0 * c10 + k1 * c11 + k2 * c21; fCov [12] -= k0 * c20 + k1 * c21 + k2 * c22; fCov [13] -= k0 * c30 + k1 * c31 + k2 * c32; fCov [14] -= k0 * c40 + k1 * c41 + k2 * c42; k0 = c50 * mSi[0] + c51 * mSi[1] + c52 * mSi[3]; k1 = c50 * mSi[1] + c51 * mSi[2] + c52 * mSi[4]; k2 = c50 * mSi[3] + c51 * mSi[4] + c52 * mSi[5]; fParam[ 5] += k0 * z0 + k1 * z1 + k2 * z2 ; fCov [15] -= k0 * c00 + k1 * c10 + k2 * c20; fCov [16] -= k0 * c10 + k1 * c11 + k2 * c21; fCov [17] -= k0 * c20 + k1 * c21 + k2 * c22; fCov [18] -= k0 * c30 + k1 * c31 + k2 * c32; fCov [19] -= k0 * c40 + k1 * c41 + k2 * c42; fCov [20] -= k0 * c50 + k1 * c51 + k2 * c52; // fit charge double px = fParam[3]; double py = fParam[4]; double pz = fParam[5]; double p = TMath::Sqrt( px * px + py * py + pz * pz ); double pi = 1. / p; double qp = fSignQ * pi; double qp3 = qp * pi * pi; double c60 = qp3 * ( c30 + c40 + c50 ), c61 = qp3 * ( c31 + c41 + c51 ), c62 = qp3 * ( c32 + c42 + c52 ); k0 = c60 * mSi[0] + c61 * mSi[1] + c62 * mSi[3]; k1 = c60 * mSi[1] + c61 * mSi[2] + c62 * mSi[4]; k2 = c60 * mSi[3] + c61 * mSi[4] + c62 * mSi[5]; qp += k0 * z0 + k1 * z1 + k2 * z2 ; if ( qp > 0 ) fSignQ = 1; else if ( qp < 0 ) fSignQ = -1; else fSignQ = 0; } //* Other utilities void AliHLT3DTrackParam::SetDirection( double Direction[3] ) { //* Change track direction if ( fParam[3]*Direction[0] + fParam[4]*Direction[1] + fParam[5]*Direction[2] >= 0 ) return; fParam[3] = -fParam[3]; fParam[4] = -fParam[4]; fParam[5] = -fParam[5]; fSignQ = -fSignQ; fCov[ 6] = -fCov[ 6]; fCov[ 7] = -fCov[ 7]; fCov[ 8] = -fCov[ 8]; fCov[10] = -fCov[10]; fCov[11] = -fCov[11]; fCov[12] = -fCov[12]; fCov[15] = -fCov[15]; fCov[16] = -fCov[16]; fCov[17] = -fCov[17]; } void AliHLT3DTrackParam::RotateCoordinateSystem( double alpha ) { //* ! double cA = TMath::Cos( alpha ); double sA = TMath::Sin( alpha ); double x = fParam[0], y = fParam[1], px = fParam[3], py = fParam[4]; fParam[0] = x * cA + y * sA; fParam[1] = -x * sA + y * cA; fParam[2] = fParam[2]; fParam[3] = px * cA + py * sA; fParam[4] = -px * sA + py * cA; fParam[5] = fParam[5]; double mJ[6][6] = { { cA, sA, 0, 0, 0, 0 }, { -sA, cA, 0, 0, 0, 0 }, { 0, 0, 1, 0, 0, 0 }, { 0, 0, 0, cA, sA, 0 }, { 0, 0, 0, -sA, cA, 0 }, { 0, 0, 0, 0, 0, 1 } }; double mA[6][6]; for ( int k = 0, i = 0; i < 6; i++ ) for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = fCov[k]; double mJC[6][6]; for ( int i = 0; i < 6; i++ ) for ( int j = 0; j < 6; j++ ) { mJC[i][j] = 0; for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j]; } for ( int k = 0, i = 0; i < 6; i++ ) for ( int j = 0; j <= i; j++, k++ ) { fCov[k] = 0; for ( int l = 0; l < 6; l++ ) fCov[k] += mJC[i][l] * mJ[j][l]; } } void AliHLT3DTrackParam::Get5Parameters( double alpha, double T[6], double C[15] ) const { //* ! AliHLT3DTrackParam t = *this; t.RotateCoordinateSystem( alpha ); double x = t.fParam[0], y = t.fParam[1], z = t.fParam[2], px = t.fParam[3], py = t.fParam[4], pz = t.fParam[5], q = t.fSignQ; double p2 = px * px + py * py + pz * pz; if ( p2 < 1.e-8 ) p2 = 1; double n2 = 1. / p2; double n = sqrt( n2 ); T[5] = x; T[0] = y; T[1] = z; T[2] = py / px; T[3] = pz / px; T[4] = q * n; double mJ[5][6] = { { -T[2], 1, 0, 0, 0, 0 }, { -T[3], 0, 1, 0, 0, 0 }, { 0, 0, 0, -T[2] / px, 1. / px, 0 }, { 0, 0, 0, -T[3] / px, 0, 1. / px }, { 0, 0, 0, -T[4]*n2*px, -T[4]*n2*py, -T[4]*n2*pz} }; double mA[6][6]; for ( int k = 0, i = 0; i < 6; i++ ) for ( int j = 0; j <= i; j++, k++ ) mA[i][j] = mA[j][i] = t.fCov[k]; double mJC[5][6]; for ( int i = 0; i < 5; i++ ) for ( int j = 0; j < 6; j++ ) { mJC[i][j] = 0; for ( int k = 0; k < 6; k++ ) mJC[i][j] += mJ[i][k] * mA[k][j]; } for ( int k = 0, i = 0; i < 5; i++ ) for ( int j = 0; j <= i; j++, k++ ) { C[k] = 0; for ( int l = 0; l < 6; l++ ) C[k] += mJC[i][l] * mJ[j][l]; } }