#include <TMatrixD.h>
#include <TMatrixDSym.h>
#include "AliLog.h"
#include "AliTrackFitterKalman.h"
ClassImp(AliTrackFitterKalman)
const Double_t AliTrackFitterKalman::fgkMaxChi2=33.;
AliTrackFitterKalman::
AliTrackFitterKalman(AliTrackPointArray *array, Bool_t owner):
AliTrackFitter(array,owner),
fMaxChi2(fgkMaxChi2)
{
}
Bool_t AliTrackFitterKalman::Begin(Int_t first, Int_t last) {
fPoints->Sort();
AliTrackPoint fp,lp;
fPoints->GetPoint(fp,first); fPoints->GetPoint(lp,last);
return MakeSeed(&fp,&lp);
}
Bool_t AliTrackFitterKalman::
MakeSeed(const AliTrackPoint *p0, const AliTrackPoint *p1) {
Double_t x0=p0->GetX(), y0=p0->GetY(), z0=p0->GetZ();
Double_t dx=p1->GetX()-x0, dy=p1->GetY()-y0, dz=p1->GetZ()-z0;
if (dy==0.) {
AliError("Seeds perpendicular to Y axis are not allowed !");
return kFALSE;
}
Double_t vx=dx/dy;
Double_t vz=dz/dy;
Double_t par[5]={x0,y0,z0,vx,vz};
const Float_t *cv0=p0->GetCov();
const Float_t *cv1=p1->GetCov();
Double_t rdy2=(cv0[3]+cv1[3])/dy/dy;
Double_t svx2=(cv0[0]+cv1[0])/dy/dy + vx*vx*rdy2;
Double_t svz2=(cv0[5]+cv1[5])/dy/dy + vz*vz*rdy2;
Double_t cov[15]={
cv0[0],
cv0[1],cv0[3],
cv0[2],cv0[4],cv0[5],
0.,0.,0.,svx2,
0.,0.,0.,0.,svz2
};
SetSeed(par,cov);
return kTRUE;
}
Bool_t AliTrackFitterKalman::AddPoint(const AliTrackPoint *p)
{
if (!Propagate(p)) return kFALSE;
Double_t chi2=GetPredictedChi2(p);
if (chi2>fMaxChi2) return kFALSE;
if (!Update(p,chi2)) return kFALSE;
return kTRUE;
}
Double_t AliTrackFitterKalman::GetPredictedChi2(const AliTrackPoint *p) const {
Float_t txyz[3]={static_cast<Float_t>(GetParam()[0]),static_cast<Float_t>(GetParam()[1]),static_cast<Float_t>(GetParam()[2])};
TMatrixDSym &cv=*fCov;
Float_t tcov[6]={
static_cast<Float_t>(cv(0,0)),static_cast<Float_t>(cv(1,0)),static_cast<Float_t>(cv(2,0)),
static_cast<Float_t>(cv(1,1)),static_cast<Float_t>(cv(2,1)),
static_cast<Float_t>(cv(2,2))
};
AliTrackPoint tp(txyz,tcov,p->GetVolumeID());
Double_t chi2=p->GetResidual(tp,kTRUE);
return chi2;
}
Bool_t AliTrackFitterKalman::Propagate(const AliTrackPoint *p) {
TMatrixDSym &cv=*fCov;
Double_t s=p->GetY() - fParams[1];
Double_t sig2=s*s/12.;
Double_t vx=fParams[3], vz=fParams[4];
fParams[0] += s*vx;
fParams[1] += s;
fParams[2] += s*vz;
Double_t
c00 = cv(0,0) + 2*s*cv(3,0) + s*s*cv(3,3) + vx*vx*sig2,
c10 = cv(1,0) + s*cv(1,3) + vx*sig2, c11=cv(1,1) + sig2,
c20 = cv(2,0) + s*(cv(4,0) + cv(2,3)) + s*s*cv(4,3) + vx*vz*sig2,
c21 = cv(2,1) + s*cv(4,1) + vz*sig2,
c22 = cv(2,2) + 2*s*cv(4,2) + s*s*cv(4,4) + vz*vz*sig2,
c30 = cv(3,0) + s*cv(3,3), c31 = cv(3,1),
c32 = cv(3,2) + s*cv(3,4), c33 = cv(3,3),
c40 = cv(4,0) + s*cv(4,3), c41 = cv(4,1),
c42 = cv(4,2) + s*cv(4,4), c43 = cv(4,3), c44 = cv(4,4);
cv(0,0)=c00; cv(0,1)=c10; cv(0,2)=c20; cv(0,3)=c30; cv(0,4)=c40;
cv(1,0)=c10; cv(1,1)=c11; cv(1,2)=c21; cv(1,3)=c31; cv(1,4)=c41;
cv(2,0)=c20; cv(2,1)=c21; cv(2,2)=c22; cv(2,3)=c32; cv(2,4)=c42;
cv(3,0)=c30; cv(3,1)=c31; cv(3,2)=c32; cv(3,3)=c33; cv(3,4)=c43;
cv(4,0)=c40; cv(4,1)=c41; cv(4,2)=c42; cv(4,3)=c43; cv(4,4)=c44;
return kTRUE;
}
Bool_t AliTrackFitterKalman::Update(const AliTrackPoint *p, Double_t chi2) {
TMatrixDSym &c=*fCov;
const Float_t *cov=p->GetCov();
TMatrixDSym v(3);
v(0,0)=cov[0]+c(0,0); v(0,1)=cov[1]+c(0,1); v(0,2)=cov[2]+c(0,2);
v(1,0)=cov[1]+c(1,0); v(1,1)=cov[3]+c(1,1); v(1,2)=cov[4]+c(1,2);
v(2,0)=cov[2]+c(2,0); v(2,1)=cov[4]+c(2,1); v(2,2)=cov[5]+c(2,2);
if (TMath::Abs(v.Determinant()) < 1.e-33) return kFALSE;
v.Invert();
TMatrixD ch(5,3);
ch(0,0)=c(0,0); ch(0,1)=c(0,1); ch(0,2)=c(0,2);
ch(1,0)=c(1,0); ch(1,1)=c(1,1); ch(1,2)=c(1,2);
ch(2,0)=c(2,0); ch(2,1)=c(2,1); ch(2,2)=c(2,2);
ch(3,0)=c(3,0); ch(3,1)=c(3,1); ch(3,2)=c(3,2);
ch(4,0)=c(4,0); ch(4,1)=c(4,1); ch(4,2)=c(4,2);
TMatrixD k(ch,TMatrixD::kMult,v);
TMatrixD d(3,1);
d(0,0) = p->GetX() - fParams[0];
d(1,0) = p->GetY() - fParams[1];
d(2,0) = p->GetZ() - fParams[2];
TMatrixD x(k,TMatrixD::kMult,d);
fParams[0]+=x(0,0);
fParams[1]+=x(1,0);
fParams[2]+=x(2,0);
fParams[3]+=x(3,0);
fParams[4]+=x(4,0);
TMatrixD hc(3,5);
hc(0,0)=c(0,0);hc(0,1)=c(0,1);hc(0,2)=c(0,2);hc(0,3)=c(0,3);hc(0,4)=c(0,4);
hc(1,0)=c(1,0);hc(1,1)=c(1,1);hc(1,2)=c(1,2);hc(1,3)=c(1,3);hc(1,4)=c(1,4);
hc(2,0)=c(2,0);hc(2,1)=c(2,1);hc(2,2)=c(2,2);hc(2,3)=c(2,3);hc(2,4)=c(2,4);
TMatrixD s(k,TMatrixD::kMult,hc);
c(0,0)-=s(0,0);c(0,1)-=s(0,1);c(0,2)-=s(0,2);c(0,3)-=s(0,3);c(0,4)-=s(0,4);
c(1,0)-=s(1,0);c(1,1)-=s(1,1);c(1,2)-=s(1,2);c(1,3)-=s(1,3);c(1,4)-=s(1,4);
c(2,0)-=s(2,0);c(2,1)-=s(2,1);c(2,2)-=s(2,2);c(2,3)-=s(2,3);c(2,4)-=s(2,4);
c(3,0)-=s(3,0);c(3,1)-=s(3,1);c(3,2)-=s(3,2);c(3,3)-=s(3,3);c(3,4)-=s(3,4);
c(4,0)-=s(4,0);c(4,1)-=s(4,1);c(4,2)-=s(4,2);c(4,3)-=s(4,3);c(4,4)-=s(4,4);
fChi2 += chi2;
fNdf += 2;
return kTRUE;
}
Bool_t AliTrackFitterKalman::GetPCA(const AliTrackPoint &p, AliTrackPoint &i) const
{
TMatrixD t(3,1);
Double_t s=p.GetY() - fParams[1];
Double_t vx=fParams[3], vz=fParams[4];
t(0,0) = fParams[0] + s*vx;
t(1,0) = fParams[1] + s;
t(2,0) = fParams[2] + s*vz;
TMatrixDSym tC(3);
{
Double_t sig2=s*s/12.;
tC(0,0) = vx*vx*sig2;
tC(1,0) = vx*sig2;
tC(1,1) = sig2;
tC(2,0) = vx*vz*sig2;
tC(2,1) = vz*sig2;
tC(2,2) = vz*vz*sig2;
tC(0,1) = tC(1,0); tC(0,2) = tC(2,0);
tC(1,2) = tC(2,1);
}
TMatrixD m(3,1);
m(0,0)=p.GetX();
m(1,0)=p.GetY();
m(2,0)=p.GetZ();
TMatrixDSym mC(3);
{
const Float_t *cv=p.GetCov();
mC(0,0)=cv[0]; mC(0,1)=cv[1]; mC(0,2)=cv[2];
mC(1,0)=cv[1]; mC(1,1)=cv[3]; mC(1,2)=cv[4];
mC(2,0)=cv[2]; mC(2,1)=cv[4]; mC(2,2)=cv[5];
}
TMatrixDSym tmW(tC);
tmW+=mC;
if (TMath::Abs(tmW.Determinant()) < 1.e-33) return kFALSE;
tmW.Invert();
TMatrixD mW(tC,TMatrixD::kMult,tmW);
TMatrixD tW(mC,TMatrixD::kMult,tmW);
TMatrixD mi(mW,TMatrixD::kMult,m);
TMatrixD ti(tW,TMatrixD::kMult,t);
ti+=mi;
TMatrixD iC(tC,TMatrixD::kMult,tmW);
iC*=mC;
Double_t sig2=1.;
iC(0,0) += vx*vx*sig2;
iC(0,1) += vx*sig2;
iC(1,1) += sig2;
iC(0,2) += vx*vz*sig2;
iC(1,2) += vz*sig2;
iC(2,2) += vz*vz*sig2;
Float_t cov[6]={
static_cast<Float_t>(iC(0,0)), static_cast<Float_t>(iC(0,1)), static_cast<Float_t>(iC(0,2)),
static_cast<Float_t>(iC(1,1)), static_cast<Float_t>(iC(1,2)),
static_cast<Float_t>(iC(2,2))
};
i.SetXYZ(ti(0,0),ti(1,0),ti(2,0),cov);
UShort_t id=p.GetVolumeID();
i.SetVolumeID(id);
return kTRUE;
}
void
AliTrackFitterKalman::SetSeed(const Double_t par[5], const Double_t cov[15]) {
for (Int_t i=0; i<5; i++) fParams[i]=par[i];
fParams[5]=0.;
delete fCov;
fCov=new TMatrixDSym(5);
TMatrixDSym &cv=*fCov;
cv(0,0)=cov[0 ];
cv(1,0)=cov[1 ]; cv(1,1)=cov[2 ];
cv(2,0)=cov[3 ]; cv(2,1)=cov[4 ]; cv(2,2)=cov[5 ];
cv(3,0)=cov[6 ]; cv(3,1)=cov[7 ]; cv(3,2)=cov[8 ]; cv(3,3)=cov[9 ];
cv(4,0)=cov[10]; cv(4,1)=cov[11]; cv(4,2)=cov[12]; cv(4,3)=cov[13]; cv(4,4)=cov[14];
cv(0,1)=cv(1,0);
cv(0,2)=cv(2,0); cv(1,2)=cv(2,1);
cv(0,3)=cv(3,0); cv(1,3)=cv(3,1); cv(2,3)=cv(3,2);
cv(0,4)=cv(4,0); cv(1,4)=cv(4,1); cv(2,4)=cv(4,2); cv(3,4)=cv(4,3);
}
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