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FairGeaneUtil.cxx
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FairGeaneUtil.cxx
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// ------------------------------------------------------------------
// Version of June 10th
// modified to work properly in q/p variables instead of 1/p
// ------------------------------------------------------------------
#include <iostream>
#include "FairGeaneUtil.h"
#include "TGeoTorus.h"
#include "TMath.h"
using namespace std;
FairGeaneUtil::FairGeaneUtil() : TObject() { }
FairGeaneUtil::~FairGeaneUtil() { }
void FairGeaneUtil::FromPtToSC(Double_t PC[3], Double_t RC[15],
// output
Double_t* PD, Double_t* RD, Int_t& IERR)
{
// -------------------------------------------------------------
//
// TRANSFORM ERROR MATRIX
//
// FROM SC VARIABLES (q/Pt,LAMBDA,PHI,YT,ZT)
// FROM SC VARIABLES (q/P,LAMBDA,PHI,YT,ZT)
//
// INPUT
// CH Charge of the paticle
// PC[3] (q/Pt, Lambda, Phi, Yt, Zt)
// RC[15] error matrix in upper triangular form
//
// OUTPUT
// PD[3] (q/P, Lambda, Phi, Yt, Zt)
// RD[15] error matrix in upper triangular form
// IERR =1 when track is perp to X-axis of Master
//
// Author EMC Collaboration
// Translated in C/Rot by A. Rotondi (June 2007)
//
// -------------------------------------------------------------------
Double_t A[5][5], S[15], COSL, SINL;
Double_t Vec[25];
IERR = 0;
memset(RD,0,sizeof(*RD));
COSL = cos(PC[1]);
if(TMath::Abs(COSL) < 1.e-7) {
IERR =1;
return;
}
SINL = sin(PC[1]);
PD[0] = PC[0]*COSL;
PD[1] = PC[1];
PD[2] = PC[2];
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
// copy input in an internal vector S
for(Int_t I=0; I<15; I++) { S[I]=RC[I]; }
A[0][0] = COSL;
A[1][1] = 1.0;
A[2][2] = 1.0;
A[3][3] = 1.0;
A[4][4] = 1.0;
A[0][1] = -PC[0]*SINL;
// transformation
FromMatToVec(A,Vec);
SymmProd(Vec,S,S);
// copy the result in S in the output vector
for(Int_t I=0; I<15; I++) { RD[I]=S[I]; }
}
void FairGeaneUtil::FromPtToSD(Double_t PD[3], Double_t RD[15], Double_t H[3], Int_t CH,
Double_t SPU, Double_t DJ[2], Double_t DK[2],
// output
Int_t& IERR, Double_t* PC, Double_t* RC)
{
//
// **************************************************************************
//
// *** TRANSFORMS ERROR MATRIX
// FROM VARIABLES (q/Pt,V',W',V,W)
// FROM VARIABLES (q/P, V',W',V,W)
//
// input
// PD[3] (q/P, Lambda, Phi, Yt, Zt)
// RD[15] error matrix in upper triangular form
// H[3] magnetic field
// CH CHARGE OF PARTICLE
// CHARGE AND MAGNETIC FIELD ARE NEEDED
// FOR CORRELATION TERMS (V',YT),(V',ZT),(W',YT),(W',ZT)
// THESE CORRELATION TERMS APPEAR BECAUSE RC IS ASSUMED
// TO BE THE ERROR MATRIX FOR FIXED S (PATH LENGTH)
// AND RD FOR FIXED U
// SPU SIGN OF U-COMPONENT OF PARTICLE MOMENTUM
// spu = sign[p·(DJ x DK)]
// DJ[2] UNIT VECTOR IN V-DIRECTION
// DK[2] UNIT VECTOR IN W-DIRECTION OF DETECTOR SYSTEM
//
// output
// PC[3] (q/Pt, Lambda, Phi, Yt, Zt)
// RC[15] error matrix in upper triangular form
// IERR =1 when track is perp to X-axis of Master
//
// Author EMC Collaboration
// Translated in C/Rot by A. Rotondi (June 2007)
//
// -------------------------------------------------------------------
//
Double_t A[5][5], S[15], TN[3], COSL, SINL, COSL1;
Double_t PM, HM, UN[3], VN[3], DI[3], TVW[3];
Double_t UJ, UK, VJ, VK, HA, HAM, Q, SINZ, COSZ;
Double_t CFACT8 = 2.997925e-04;
Double_t Vec[25];
// ------------------------------------------------------------------
IERR=0;
TVW[0]=1./TMath::Sqrt(1.+PD[1]*PD[1]+PD[2]*PD[2]);
if(SPU < 0.) { TVW[0]=-TVW[0]; }
TVW[1]=PD[1]*TVW[0];
TVW[2]=PD[2]*TVW[0];
DI[0]=DJ[1]*DK[2]-DJ[2]*DK[1];
DI[1]=DJ[2]*DK[0]-DJ[0]*DK[2];
DI[2]=DJ[0]*DK[1]-DJ[1]*DK[0];
for(Int_t I=0; I<3; I++) {
TN[I]=TVW[0]*DI[I]+TVW[1]*DJ[I]+TVW[2]*DK[I];
}
COSL=TMath::Sqrt(TMath::Abs(1.-TN[2]*TN[2]));
if(COSL < 1.e-30) { COSL = 1.e-30; }
COSL1=1./COSL;
SINL = TN[2];
PC[0]=PD[0]*COSL;
PC[1]=PD[1];
PC[2]=PD[2];
PM=PC[0];
if(TMath::Abs (TN[0]) < 1.E-30) { TN[0] = 1.e-30; }
UN[0]=-TN[1]*COSL1;
UN[1]=TN[0]*COSL1;
UN[2]=0.;
VN[0]=-TN[2]*UN[1];
VN[1]=TN[2]*UN[0];
VN[2]=COSL;
UJ=UN[0]*DJ[0]+UN[1]*DJ[1]+UN[2]*DJ[2];
UK=UN[0]*DK[0]+UN[1]*DK[1]+UN[2]*DK[2];
VJ=VN[0]*DJ[0]+VN[1]*DJ[1]+VN[2]*DJ[2];
VK=VN[0]*DK[0]+VN[1]*DK[1]+VN[2]*DK[2];
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
// copy input in an internal vector S
for(Int_t I=0; I<15; I++) { S[I]=RD[I]; }
if(CH != 0.) {
HA=TMath::Sqrt(H[0]*H[0]+H[1]*H[1]+H[2]*H[2]);
HAM=HA*PM;
if(HAM != 0.) {
HM=CH/HA;
Q=-HAM*CFACT8;
SINZ=-(H[0]*UN[0]+H[1]*UN[1]+H[2]*UN[2])*HM;
COSZ= (H[0]*VN[0]+H[1]*VN[1]+H[2]*VN[2])*HM;
A[0][3] = Q*TVW[1]*SINZ*(SINL*PD[0]);
A[0][4] = Q*TVW[2]*SINZ*(SINL*PD[0]);
}
}
A[0][0] = COSL;
A[1][1] = 1.;
A[2][2] = 1.;
A[3][3] = 1.;
A[4][4] = 1.;
A[0][1] = -TVW[0]*VJ*(SINL*PD[0]);
A[0][2] = -TVW[0]*VK*(SINL*PD[0]);
// transformation
FromMatToVec(A,Vec);
SymmProd(Vec,S,S);
// copy the result in S in the output vector
for(Int_t I=0; I<15; I++) { RC[I]=S[I]; }
}
void FairGeaneUtil::FromSCToPt(Double_t PC[3], Double_t RC[15],
// output
Double_t* PD, Double_t* RD, Int_t& IERR)
{
// -------------------------------------------------------------
//
// TRANSFORM ERROR MATRIX
//
// FROM SC VARIABLES (q/P,LAMBDA,PHI,YT,ZT)
// FROM SC VARIABLES (q/Pt,LAMBDA,PHI,YT,ZT)
//
// INPUT
// PC[3] (q/P, Lambda, Phi, Yt, Zt)
// RC[15] error matrix in upper triangular form
//
// OUTPUT
// PD[3] (q/Pt, Lambda, Phi, Yt, Zt)
// RD[15] error matrix in upper triangular form
// IERR =1 when track is perp to X-axis of Master
//
// Author EMC Collaboration
// Translated in C/Rot by A. Rotondi (June 2007)
//
// -------------------------------------------------------------------
Double_t A[5][5], S[15], COSL, COSL1;
Double_t TANL;
Double_t Vec[25];
IERR = 0;
memset(RD,0,sizeof(*RD));
COSL = cos(PC[1]);
if(TMath::Abs(COSL) < 1.e-7) {
IERR = 1;
return;
}
COSL1 = 1./COSL;
TANL = tan(PC[1]);
PD[0] = PC[0]*COSL1;
PD[1] = PC[1];
PD[2] = PC[2];
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
// copy input in an internal vector S
for(Int_t I=0; I<15; I++) { S[I]=RC[I]; }
A[0][0] = COSL1;
A[1][1] = 1.0;
A[2][2] = 1.0;
A[3][3] = 1.0;
A[4][4] = 1.0;
A[0][1] = PD[0]*TANL;
// transformation
FromMatToVec(A,Vec);
SymmProd(Vec,S,S);
// copy the result in S in the output vector
for(Int_t I=0; I<15; I++) { RD[I]=S[I]; }
}
void FairGeaneUtil::FromSCToSD(Double_t PC[3], Double_t RC[15], Double_t H[3], Int_t CH,
Double_t DJ[3], Double_t DK[3],
// output
Int_t& IERR, Double_t& SPU,
Double_t* PD, Double_t* RD)
{
// ----------------------------------------------------------------------
// Transform Error Matrix
// FROM SC (transverse system) VARIABLES (q/P,LAMBDA,PHI,YT,ZT)
// TO SD (detector system) VARIABLES (q/P,V',W',V,W)
// Authors: A. Haas and W. Wittek
// Translated in CRoot by A. Rotondi and A. Fontana June 2007
// INPUT
// PC(3) q/P,LAMBDA,PHI
// H(3) MAGNETIC FIELD
// RC(15) ERROR MATRIX IN SC VARIABLES (TRIANGLE)
// CH CHARGE OF PARTICLE
// CHARGE AND MAGNETIC FIELD ARE NEEDED
// FOR CORRELATION TERMS (V',YT),(V',ZT),(W',YT),(W',ZT)
// THESE CORRELATION TERMS APPEAR BECAUSE RC IS ASSUMED
// TO BE THE ERROR MATRIX FOR FIXED S (PATH LENGTH)
// AND RD FOR FIXED U
// DJ(3) UNIT VECTOR IN V-DIRECTION
// DK(3) UNIT VECTOR IN W-DIRECTION OF DETECTOR SYSTEM
// OUTPUT
// RD(15) ERROR MATRIX IN q/P,V',W',V,W (TRIANGLE)
// PD(3) q/P,V',W'
// IERR = 1 PARTICLE MOVES PERPENDICULAR TO U-AXIS
// ( V',W' ARE NOT DEFINED )
// SPU SIGN OF U-COMPONENT OF PARTICLE MOMENTUM
// spu = sign[p·(DJ x DK)]
//
// ------------------------------------------------------------------------
Double_t A[5][5], S[15], TN[3], COSL, COSP;
Double_t UN[3], VN[3], DI[3], TVW[3];
Double_t Vec[25];
Double_t CFACT8= 2.997925e-04;
Double_t T1R, T2R, T3R, SINP, SINZ, COSZ, HA, HM, HAM;
Double_t Q, UI, VI, UJ, UK, VJ, VK;
IERR=0;
memset(RD,0,sizeof(*RD));
memset(PD,0,sizeof(*PD));
COSL=TMath::Cos(PC[1]);
SINP=TMath::Sin(PC[2]);
COSP=TMath::Cos(PC[2]);
TN[0]=COSL*COSP;
TN[1]=COSL*SINP;
TN[2]=TMath::Sin(PC[1]);
// DI = DJ x DK
DI[0]=DJ[1]*DK[2]-DJ[2]*DK[1];
DI[1]=DJ[2]*DK[0]-DJ[0]*DK[2];
DI[2]=DJ[0]*DK[1]-DJ[1]*DK[0];
TVW[0]=TN[0]*DI[0]+TN[1]*DI[1]+TN[2]*DI[2];
SPU=1.;
if(TVW[0] < 0.) { SPU=-1.; }
TVW[1]=TN[0]*DJ[0]+TN[1]*DJ[1]+TN[2]*DJ[2];
TVW[2]=TN[0]*DK[0]+TN[1]*DK[1]+TN[2]*DK[2];
// track lies in the detector plane: stop calculations
if(TMath::Abs(TVW[0]) < 1.e-7) {
IERR = 1;
return;
}
T1R=1./TVW[0];
PD[0] = PC[0];
PD[1] = TVW[1]*T1R;
PD[2] = TVW[2]*T1R;
UN[0] = -SINP;
UN[1] = COSP;
UN[2] = 0.;
VN[0] =-TN[2]*UN[1];
VN[1] = TN[2]*UN[0];
VN[2] = COSL;
UJ=UN[0]*DJ[0]+UN[1]*DJ[1]+UN[2]*DJ[2];
UK=UN[0]*DK[0]+UN[1]*DK[1]+UN[2]*DK[2];
VJ=VN[0]*DJ[0]+VN[1]*DJ[1]+VN[2]*DJ[2];
VK=VN[0]*DK[0]+VN[1]*DK[1]+VN[2]*DK[2];
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
// copy input in an internal vector S
for(Int_t I=0; I<15; I++) { S[I]=RC[I]; }
if(CH != 0.) {
//charged particles
HA=TMath::Sqrt(H[0]*H[0]+H[1]*H[1]+H[2]*H[2]);
HAM=HA*PC[0];
if(HAM != 0.) {
// ... in a magnetic field
HM=CH/HA;
Q=-HAM*CFACT8;
SINZ=-(H[0]*UN[0]+H[1]*UN[1]+H[2]*UN[2])*HM;
COSZ= (H[0]*VN[0]+H[1]*VN[1]+H[2]*VN[2])*HM;
T3R=Q*pow(T1R,3);
UI=UN[0]*DI[0]+UN[1]*DI[1]+UN[2]*DI[2];
VI=VN[0]*DI[0]+VN[1]*DI[1]+VN[2]*DI[2];
A[1][3] = -UI*(VK*COSZ-UK*SINZ)*T3R;
A[1][4] = -VI*(VK*COSZ-UK*SINZ)*T3R;
A[2][3] = UI*(VJ*COSZ-UJ*SINZ)*T3R;
A[2][4] = VI*(VJ*COSZ-UJ*SINZ)*T3R;
}
}
T2R=T1R*T1R;
// Transformation matrix from SC to SD
A[0][0] = 1.;
A[1][1] = -UK*T2R;
A[1][2] = VK*COSL*T2R;
A[2][1] = UJ*T2R;
A[2][2] = -VJ*COSL*T2R;
A[3][3] = VK*T1R;
A[3][4] = -UK*T1R;
A[4][3] = -VJ*T1R;
A[4][4] = UJ*T1R;
// transformation
FromMatToVec(A,Vec);
SymmProd(Vec,S,S);
// copy the result in S in the output vector
for(Int_t I=0; I<15; I++) { RD[I]=S[I]; }
}
void FairGeaneUtil::FromSD1ToSD2(Double_t PD1[2], Double_t RD1[15],Double_t H[2],
Int_t CH, Double_t SP1,
Double_t DJ1[2], Double_t DK1[2],
Double_t DJ2[2], Double_t DK2[2],
// output
Int_t& IERR, Double_t& SP2,
Double_t* PD2, Double_t* RD2)
{
// -------------------------------------------------------------------------
//
// TRANSFORMS ERROR MATRIX
// FROM VARIABLES (q/P,V1',W1',V1,W1)
// TO VARIABLES (q/P,V2',W2',V2,W2)
//
// Authors: A. Haas and W. Wittek
// Translated in C/Root by A. Fontana and A. Rotondi (June 2007)
//
//
// INPUT
// PD1[2] q/P,V1',W1'
// H[2] MAGNETIC FIELD
// RD1(15) ERROR MATRIX IN 1/P,V1',W1',V1,W1 (Triangular)
// CH CHARGE OF PARTICLE
// CHARGE AND MAGNETIC FIELD ARE NEEDED
// FOR CORRELATION TERMS (V2',V1),(V2',W1),(W2',V1),(W2',W1)
// THESE CORRELATION TERMS APPEAR BECAUSE RD1 IS ASSUMED
// TO BE THE ERROR MATRIX FOR FIXED U1
// AND RD2 FOR FIXED U2
// SP1 SIGN OF U1-COMPONENT OF PARTICLE MOMENTUM INPUT
// DJ1[2] UNIT VECTOR IN V1-DIRECTION
// DK1[2] UNIT VECTOR IN W1-DIRECTION OF SYSTEM 1
// DJ2[2] UNIT VECTOR IN V2-DIRECTION
// DK2[2] UNIT VECTOR IN W2-DIRECTION OF SYSTEM 2
//
//
// OUTPUT
// PD2[3] q/P,V2',W2'
// RD2[15] ERROR MATRIX IN 1/P,V2',W2',V2,W2 (Triangular)
// SP2 SIGN OF U2-COMPONENT OF PARTICLE MOMENTUM OUTPUT
// IERR = 0 TRANSFORMATION OK
// = 1 MOMENTUM PERPENDICULAR TO U2-DIRECTION
// (V2',W2' NOT DEFINed)
// = 2 MOMENTUM PERPENDICULAR TO X-AXIS
//
// ----------------------------------------------------------------------
Double_t A[5][5], S[15], TN[3], COSL, COSL1;
Double_t SINZ, COSZ, UN[3], VN[3];
Double_t Vec[25];
Double_t PM, TR, TS, TT, HA, HM, HAM, Q;
Double_t UJ1, UK1, UJ2, UK2, VJ1, VJ2, VK1, VK2;
Double_t SJ1I2, SK1I2, SK2U, SK2V, SJ2U, SJ2V;
Double_t DI1[3], DI2[3], TVW1[3], TVW2[3];
Double_t CFACT8= 2.997925e-04;
IERR=0;
memset(PD2,0,sizeof(*PD2));
memset(RD2,0,sizeof(*RD2));
PM=PD1[0];
TVW1[0]=1./sqrt(1.+PD1[1]*PD1[1]+PD1[2]*PD1[2]);
if(SP1 < 0.) { TVW1[0]=-TVW1[0]; }
TVW1[1]=PD1[1]*TVW1[0];
TVW1[2]=PD1[2]*TVW1[0];
DI1[0]=DJ1[1]*DK1[2]-DJ1[2]*DK1[1];
DI1[1]=DJ1[2]*DK1[0]-DJ1[0]*DK1[2];
DI1[2]=DJ1[0]*DK1[1]-DJ1[1]*DK1[0];
for(Int_t I=0; I<3; I++) {
TN[I]=TVW1[0]*DI1[I]+TVW1[1]*DJ1[I]+TVW1[2]*DK1[I];
}
DI2[0]=DJ2[1]*DK2[2]-DJ2[2]*DK2[1];
DI2[1]=DJ2[2]*DK2[0]-DJ2[0]*DK2[2];
DI2[2]=DJ2[0]*DK2[1]-DJ2[1]*DK2[0];
TVW2[0]=TN[0]*DI2[0]+TN[1]*DI2[1]+TN[2]*DI2[2];
TVW2[1]=TN[0]*DJ2[0]+TN[1]*DJ2[1]+TN[2]*DJ2[2];
TVW2[2]=TN[0]*DK2[0]+TN[1]*DK2[1]+TN[2]*DK2[2];
if(TMath::Abs(TVW2[0]) < 1.e-7) {
// track lies in the v-w plane: stop calculations
IERR = 1;
return;
}
TR=1./TVW2[0];
SP2=1;
if(TVW2[0] < 0.) { SP2=-1; }
PD2[0]=PD1[0];
PD2[1]=TVW2[1]*TR;
PD2[2]=TVW2[2]*TR;
COSL=sqrt(TMath::Abs(1.-TN[2]*TN[2]));
if(TMath::Abs(COSL) < 1.e-7) {
// track perp to X-axis of Master: stop calculations
IERR=2;
return;
}
COSL1=1./COSL;
UN[0]=-TN[1]*COSL1;
UN[1]=TN[0]*COSL1;
UN[2]=0.;
VN[0]=-TN[2]*UN[1];
VN[1]=TN[2]*UN[0];
VN[2]=COSL;
UJ1=UN[0]*DJ1[0]+UN[1]*DJ1[1]+UN[2]*DJ1[2];
UK1=UN[0]*DK1[0]+UN[1]*DK1[1]+UN[2]*DK1[2];
VJ1=VN[0]*DJ1[0]+VN[1]*DJ1[1]+VN[2]*DJ1[2];
VK1=VN[0]*DK1[0]+VN[1]*DK1[1]+VN[2]*DK1[2];
UJ2=UN[0]*DJ2[0]+UN[1]*DJ2[1]+UN[2]*DJ2[2];
UK2=UN[0]*DK2[0]+UN[1]*DK2[1]+UN[2]*DK2[2];
VJ2=VN[0]*DJ2[0]+VN[1]*DJ2[1]+VN[2]*DJ2[2];
VK2=VN[0]*DK2[0]+VN[1]*DK2[1]+VN[2]*DK2[2];
// reset working vectors and matrices
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
for(Int_t J=0; J<15; J++) { S[J]=RD1[J]; }
if(CH != 0.) {
// a charged particle
HA=sqrt(H[0]*H[0]+H[1]*H[1]+H[2]*H[2]);
HAM=HA*PM;
if(HAM != 0.) {
// ...in a magnetic field
HM=CH/HA;
Q=-HAM*CFACT8;
TT=-Q*pow(TR,3);
SJ1I2=DJ1[0]*DI2[0]+DJ1[1]*DI2[1]+DJ1[2]*DI2[2];
SK1I2=DK1[0]*DI2[0]+DK1[1]*DI2[1]+DK1[2]*DI2[2];
SK2U=DK2[0]*UN[0]+DK2[1]*UN[1]+DK2[2]*UN[2];
SK2V=DK2[0]*VN[0]+DK2[1]*VN[1]+DK2[2]*VN[2];
SJ2U=DJ2[0]*UN[0]+DJ2[1]*UN[1]+DJ2[2]*UN[2];
SJ2V=DJ2[0]*VN[0]+DJ2[1]*VN[1]+DJ2[2]*VN[2];
SINZ=-(H[0]*UN[0]+H[1]*UN[1]+H[2]*UN[2])*HM;
COSZ= (H[0]*VN[0]+H[1]*VN[1]+H[2]*VN[2])*HM;
A[1][3] = -TT*SJ1I2*(SK2U*SINZ-SK2V*COSZ);
A[1][4] = -TT*SK1I2*(SK2U*SINZ-SK2V*COSZ);
A[2][3] = TT*SJ1I2*(SJ2U*SINZ-SJ2V*COSZ);
A[2][4] = TT*SK1I2*(SJ2U*SINZ-SJ2V*COSZ);
}
}
A[0][0] = 1.;
A[3][3] = TR*(UJ1*VK2-VJ1*UK2);
A[3][4] = TR*(UK1*VK2-VK1*UK2);
A[4][3] = TR*(VJ1*UJ2-UJ1*VJ2);
A[4][4] = TR*(VK1*UJ2-UK1*VJ2);
TS=TR*TVW1[0];
A[1][1] = A[3][3]*TS;
A[1][2] = A[3][4]*TS;
A[2][1] = A[4][3]*TS;
A[2][2] = A[4][4]*TS;
// transformation A*SA
FromMatToVec(A,Vec);
SymmProd(Vec,S,S);
// final error (covariance) matrix in upper-triangular form
// std::cout<<"SD1toSD2: "<<PD2[0]<<","<<PD2[1]<<","<<PD2[2]<<","<<std::endl;
for(Int_t J=0; J<15; J++) {
RD2[J]=S[J];
// std::cout<<S[J]<<" ";
}
}
void FairGeaneUtil::FromSDToPt(Double_t PD[3], Double_t RD[15], Double_t H[3],
Int_t CH, Double_t SPU, Double_t DJ[3], Double_t DK[3],
// output
Int_t& IERR, Double_t* PC, Double_t* RC)
{
//
// -------------------------------------------------------------
//
// TRANSFORM ERROR MATRIX
// FROM VARIABLES (q/P,V',W',V,W)
// FROM VARIABLES (q/Pt,V',W',V,W)
//
// input
// PD[3] (q/P, Lambda, Phi, Yt, Zt)
// RD[15] error matrix in upper triangular form
// H[3] magnetic field
// CH CHARGE OF PARTICLE
// CHARGE AND MAGNETIC FIELD ARE NEEDED
// FOR CORRELATION TERMS (V',YT),(V',ZT),(W',YT),(W',ZT)
// THESE CORRELATION TERMS APPEAR BECAUSE RC IS ASSUMED
// TO BE THE ERROR MATRIX FOR FIXED S (PATH LENGTH)
// AND RD FOR FIXED U
// SPU SIGN OF U-COMPONENT OF PARTICLE MOMENTUM
// spu = sign[p·(DJ x DK)]
// DJ(3) UNIT VECTOR IN V-DIRECTION
// DK(3) UNIT VECTOR IN W-DIRECTION OF DETECTOR SYSTEM
//
// output
// PC[3] (q/Pt, Lambda, Phi, Yt, Zt)
// RC[15] error matrix in upper triangular form
// IERR =1 when track is perp to X-axis of Master
//
// Author EMC Collaboration
// Translated in C/Rot by A. Rotondi (June 2007)
//
// -------------------------------------------------------------------
//
//
//
Double_t A[5][5], S[15], TN[3], TANL, COSL, COSL1;
Double_t PM, HM, UN[3], VN[3], DI[3], TVW[3];
Double_t CFACT8 = 2.997925e-04;
Double_t UJ, UK, VJ, VK, HA, HAM, Q, SINZ, COSZ;
Double_t Vec[25];
// ------------------------------------------------------------------
IERR=0;
PM=PD[0];
TVW[0]=1./TMath::Sqrt(1.+PD[1]*PD[1]+PD[2]*PD[2]);
if(SPU<0.) { TVW[0]=-TVW[0]; }
TVW[1]=PD[1]*TVW[0];
TVW[2]=PD[2]*TVW[0];
DI[0]=DJ[1]*DK[2]-DJ[2]*DK[1];
DI[1]=DJ[2]*DK[0]-DJ[0]*DK[2];
DI[2]=DJ[0]*DK[1]-DJ[1]*DK[0];
for(Int_t I=0; I<3; I++) {
TN[I]=TVW[0]*DI[I]+TVW[1]*DJ[I]+TVW[2]*DK[I];
}
COSL=TMath::Sqrt(TMath::Abs(1.-TN[2]*TN[2]));
if(COSL < 1.e-30) { COSL = 1.e-30; }
COSL1=1./COSL;
TANL = TN[2]*COSL1;
PC[0]=PD[0]*COSL1;
PC[1]=PD[1];
PC[2]=PD[2];
if(TMath::Abs (TN[0])< 1.e-30) { TN[0] = 1.e-30; }
UN[0]=-TN[1]*COSL1;
UN[1]=TN[0]*COSL1;
UN[2]=0.;
VN[0]=-TN[2]*UN[1];
VN[1]=TN[2]*UN[0];
VN[2]=COSL;
UJ=UN[0]*DJ[0]+UN[1]*DJ[1]+UN[2]*DJ[2];
UK=UN[0]*DK[0]+UN[1]*DK[1]+UN[2]*DK[2];
VJ=VN[0]*DJ[0]+VN[1]*DJ[1]+VN[2]*DJ[2];
VK=VN[0]*DK[0]+VN[1]*DK[1]+VN[2]*DK[2];
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
// copy input in an internal vector S
for(Int_t I=0; I<15; I++) { S[I]=RD[I]; }
if(CH != 0.) {
HA=TMath::Sqrt(H[0]*H[0]+H[1]*H[1]+H[2]*H[2]);
HAM=HA*PM;
if(HAM != 0.) {
HM=CH/HA;
Q=-HAM*CFACT8;
SINZ=-(H[0]*UN[0]+H[1]*UN[1]+H[2]*UN[2])*HM;
COSZ= (H[0]*VN[0]+H[1]*VN[1]+H[2]*VN[2])*HM;
A[0][3] = -Q*TVW[1]*SINZ*(TANL*PC[0]);
A[0][4] = -Q*TVW[2]*SINZ*(TANL*PC[0]);
}
}
A[0][0] = COSL1;
A[1][1] = 1.;
A[2][2] = 1.;
A[3][3] = 1.;
A[4][4] = 1.;
A[0][1] = TVW[0]*VJ*(TANL*PC[0]);
A[0][2] = TVW[0]*VK*(TANL*PC[0]);
// transformation
FromMatToVec(A,Vec);
SymmProd(Vec,S,S);
// copy the result in S in the output vector
for(Int_t I=0; I<15; I++) { RC[I]=S[I]; }
}
void FairGeaneUtil::FromSDToSC(Double_t PD[3], Double_t RD[15], Double_t H[3], Int_t CH,
Double_t SPU, Double_t DJ[3], Double_t DK[3],
// output
Int_t& IERR, Double_t* PC, Double_t* RC)
{
// ----------------------------------------------------------------------
//
// Tranform error matrix
// FROM SD (detector plane) VARIABLES (q/P,V',W',V,W)
// TO SC (transverse system) VARIABLES (q/P,LAMBDA,PHI,YT,ZT)
//
// Authors: A. Haas and W. Wittek
// Translated in C/Root by A. Rotondi and A. Fontana (June 2007)
//
//
// INPUT
// PD(3) q/P,V',W'
// H(3) MAGNETIC FIELD
// RD(15) ERROR MATRIX IN 1/P,V',W',V,W (Triangular)
// CH CHARGE OF PARTICLE
// CHARGE AND MAGNETIC FIELD ARE NEEDED
// FOR CORRELATION TERMS (LAMBDA,V),(LAMBDA,W),(PHI,V),(PHI,W)
// THESE CORRELATION TERMS APPEAR BECAUSE RC IS ASSUMED
// TO BE THE ERROR MATRIX FOR FIXED S (PATH LENGTH)
// AND RD FOR FIXED U
// SPU SIGN OF U-COMPONENT OF PARTICLE MOMENTUM
// spu = sign[p·(DJ x DK)]
// DJ(3) UNIT VECTOR IN V-DIRECTION
// DK(3) UNIT VECTOR IN W-DIRECTION OF DETECTOR SYSTEM
//
// OUTPUT
// PC(3) q/P,LAMBDA,PHI
// RC(15) ERROR MATRIX IN SC VARIABLES
// IERR NOT USED
//
// ---------------------------------------------------------------------
Double_t A[5][5], S[15], TN[3];
Double_t SINZ, COSZ, COSL, COSL1;
Double_t UN[3], VN[3], DI[3], TVW[3];
Double_t Vec[25];
Double_t CFACT8= 2.997925e-04;
Double_t HA, HM, HAM, Q, UJ, UK, VJ, VK;
Double_t PM;
IERR=0;
memset(RC,0,sizeof(*RC));
memset(PC,0,sizeof(*PC));
PM=PD[0];
TVW[0]=1./TMath::Sqrt(1.+PD[1]*PD[1]+PD[2]*PD[2]);
if(SPU < 0.) { TVW[0]=-TVW[0]; }
TVW[1]=PD[1]*TVW[0];
TVW[2]=PD[2]*TVW[0];
DI[0]=DJ[1]*DK[2]-DJ[2]*DK[1];
DI[1]=DJ[2]*DK[0]-DJ[0]*DK[2];
DI[2]=DJ[0]*DK[1]-DJ[1]*DK[0];
for(Int_t I=0; I<3; I++) {
TN[I]=TVW[0]*DI[I]+TVW[1]*DJ[I]+TVW[2]*DK[I];
}
PC[0] = PD[0];
PC[1] = TMath::ASin(TN[2]);
if(TMath::Abs(TN[0]) < 1.e-30) { TN[0] = 1.e-30; }
PC[2] = TMath::ATan2(TN[1],TN[0]);
COSL=TMath::Sqrt(TMath::Abs(1.-TN[2]*TN[2]));
if(COSL < 1.e-30) { COSL = 1.e-30; }
COSL1 = 1./COSL;
UN[0] = -TN[1]*COSL1;
UN[1] = TN[0]*COSL1;
UN[2] = 0.;
VN[0] = -TN[2]*UN[1];
VN[1] = TN[2]*UN[0];
VN[2] = COSL;
UJ = UN[0]*DJ[0]+UN[1]*DJ[1]+UN[2]*DJ[2];
UK = UN[0]*DK[0]+UN[1]*DK[1]+UN[2]*DK[2];
VJ = VN[0]*DJ[0]+VN[1]*DJ[1]+VN[2]*DJ[2];
VK = VN[0]*DK[0]+VN[1]*DK[1]+VN[2]*DK[2];
// prepare matrices and vectors
for(Int_t I=0; I<5; I++) {
for(Int_t K=0; K<5; K++) {
A[I][K]=0.;
}
}
for(Int_t J=0; J<15; J++) { S[J]=RD[J]; }
if(CH != 0.) {
// charged particle
HA=TMath::Sqrt(H[0]*H[0]+H[1]*H[1]+H[2]*H[2]);
HAM=HA*PM;
if(HAM != 0.) {
// .... in a magnetic field
HM=CH/HA;
Q=-HAM*CFACT8;
SINZ=-(H[0]*UN[0]+H[1]*UN[1]+H[2]*UN[2])*HM;
COSZ= (H[0]*VN[0]+H[1]*VN[1]+H[2]*VN[2])*HM;
A[1][3] = -Q*TVW[1]*SINZ;
A[1][4] = -Q*TVW[2]*SINZ;
A[2][3] = -Q*TVW[1]*COSZ*COSL1;
A[2][4] = -Q*TVW[2]*COSZ*COSL1;
}
}
A[0][0] = 1.;
A[1][1] = TVW[0]*VJ;
A[1][2] = TVW[0]*VK;
A[2][1] = TVW[0]*UJ*COSL1;
A[2][2] = TVW[0]*UK*COSL1;
A[3][3] = UJ;
A[3][4] = UK;
A[4][3] = VJ;
A[4][4] = VK;
// transformation matrix
FromMatToVec(A, Vec);
SymmProd(Vec,S,S);
// copy the result in S in the output vector
for(Int_t I=0; I<15; I++) { RC[I]=S[I]; }
}
void FairGeaneUtil::FromVec15ToMat25(Double_t V[15], fiveMat& A)
{
//
// ------------------------------------------------------
// Passage from a 15-dim vector to a symmetric 5x5 matrix
// following the upper triangular convention
//
// Author A. Rotondi June 2007
//
// ------------------------------------------------------
A[0][0] = V[0];
A[0][1] = V[1];
A[0][2] = V[2];
A[0][3] = V[3];
A[0][4] = V[4];
A[1][1] = V[5];
A[1][2] = V[6];
A[1][3] = V[7];
A[1][4] = V[8];
A[2][2] = V[9];
A[2][3] = V[10];
A[2][4] = V[11];
A[3][3] = V[12];
A[3][4] = V[13];
A[4][4] = V[14];
for(Int_t I=0; I<5; I++) {
for(Int_t k=I; k<5; k++) {
A[k][I] = A[I][k];
}
}
}
void FairGeaneUtil::FromVecToMat(fiveMat& A, Double_t V[25])
{
//
// ------------------------------------------------------
// Passage from 25-dim vector to a symmetric 5x5 matrix
// (FoRTRAN column convention)
//
// Author A. Rotondi June 2007
//
// ------------------------------------------------------
A[0][0] = V[0];
A[1][0] = V[1];
A[2][0] = V[2];
A[3][0] = V[3];
A[4][0] = V[4];
A[0][1] = V[5];;
A[1][1] = V[6];;
A[2][1] = V[7];;
A[3][1] = V[8];;
A[4][1] = V[9];;
A[0][2] = V[10] ;
A[1][2] = V[11] ;
A[2][2] = V[12] ;
A[3][2] = V[13] ;
A[4][2] = V[14] ;
A[0][3] = V[15] ;
A[1][3] = V[16] ;
A[2][3] = V[17] ;
A[3][3] = V[18] ;
A[4][3] = V[19] ;
A[0][4] = V[20] ;
A[1][4] = V[21] ;
A[2][4] = V[22] ;
A[3][4] = V[23] ;
A[4][4] = V[24] ;
}
void FairGeaneUtil::FromMarsToSC(Double_t PD[3], Double_t RD[6][6], Double_t H[3], Int_t CH,
// output
Double_t* PC, Double_t* RC)
{
// ----------------------------------------------------------------------
//
// Tranform error matrix
// FROM MASTER VARIABLES (px, py,pz, x, y, z)
// TO SC (transverse system) VARIABLES (q/p, lambda, phi, yt, zt)
// momentum along x axis (GEANE convention)
//
// Method: the matrix in MARS is transformed in a detctor SD system
// with the detector plane coincident with the SC transverse plane.
// Then, the SD to SC routine is used.
// In this way the track length s is not modified by the transformation.
//
// Authors: A. Rotondi and A. Fontana (June 2007)
// rewritten by A. Rotondi and Lia Lavezzi (may 2008)
//
// INPUT
// PD(3) px, py, pz
// RD(6,6) ERROR MATRIX from MASTER Reference System
// covariances of (px, py, pz, x, y, z)
//
// CH CHARGE OF PARTICLE
// H(3) MAGNETIC FIELD components