* provided "as is" without express or implied warranty. *
**************************************************************************/
+/* $Id$ */
+
//-------------------------------------------------------------------------
// Implementation of the AliKalmanTrack class
-//
+// that is the base for AliTPCtrack, AliITStrackV2 and AliTRDtrack
// Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch
//-------------------------------------------------------------------------
-
+#include "AliTracker.h"
#include "AliKalmanTrack.h"
+#include "TGeoManager.h"
ClassImp(AliKalmanTrack)
-Double_t AliKalmanTrack::fConvConst;
+//_______________________________________________________________________
+AliKalmanTrack::AliKalmanTrack():
+ fLab(-3141593),
+ fFakeRatio(0),
+ fChi2(0),
+ fMass(AliPID::ParticleMass(AliPID::kPion)),
+ fN(0),
+ fLocalConvConst(0),
+ fStartTimeIntegral(kFALSE),
+ fIntegratedLength(0)
+{
+ //
+ // Default constructor
+ //
+ if (AliTracker::GetFieldMap()==0) {
+ AliFatal("The magnetic field has not been set!");
+ }
+
+ for(Int_t i=0; i<AliPID::kSPECIES; i++) fIntegratedTime[i] = 0;
+}
+
+//_______________________________________________________________________
+AliKalmanTrack::AliKalmanTrack(const AliKalmanTrack &t):
+ TObject(t),
+ fLab(t.fLab),
+ fFakeRatio(t.fFakeRatio),
+ fChi2(t.fChi2),
+ fMass(t.fMass),
+ fN(t.fN),
+ fLocalConvConst(t.fLocalConvConst),
+ fStartTimeIntegral(t.fStartTimeIntegral),
+ fIntegratedLength(t.fIntegratedLength)
+{
+ //
+ // Copy constructor
+ //
+ if (AliTracker::GetFieldMap()==0) {
+ AliFatal("The magnetic field has not been set!");
+ }
+
+ for (Int_t i=0; i<AliPID::kSPECIES; i++)
+ fIntegratedTime[i] = t.fIntegratedTime[i];
+}
+
+//_______________________________________________________________________
+void AliKalmanTrack::StartTimeIntegral()
+{
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+ // Start time integration
+ // To be called at Vertex by ITS tracker
+ //
+
+ //if (fStartTimeIntegral)
+ // AliWarning("Reseting Recorded Time.");
+
+ fStartTimeIntegral = kTRUE;
+ for(Int_t i=0; i<AliPID::kSPECIES; i++) fIntegratedTime[i] = 0;
+ fIntegratedLength = 0;
+}
+
+//_______________________________________________________________________
+void AliKalmanTrack:: AddTimeStep(Double_t length)
+{
+ //
+ // Add step to integrated time
+ // this method should be called by a sublasses at the end
+ // of the PropagateTo function or by a tracker
+ // each time step is made.
+ //
+ // If integration not started function does nothing
+ //
+ // Formula
+ // dt = dl * sqrt(p^2 + m^2) / p
+ // p = pT * (1 + tg^2 (lambda) )
+ //
+ // pt = 1/external parameter [4]
+ // tg lambda = external parameter [3]
+ //
+ //
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+
+ static const Double_t kcc = 2.99792458e-2;
+
+ if (!fStartTimeIntegral) return;
+
+ fIntegratedLength += length;
+
+ Double_t xr, param[5];
+ Double_t pt, tgl;
+
+ GetExternalParameters(xr, param);
+ pt = 1/param[4] ;
+ tgl = param[3];
+
+ Double_t p = TMath::Abs(pt * TMath::Sqrt(1+tgl*tgl));
+
+ if (length > 100) return;
+
+ for (Int_t i=0; i<AliPID::kSPECIES; i++) {
+
+ Double_t mass = AliPID::ParticleMass(i);
+ Double_t correction = TMath::Sqrt( pt*pt * (1 + tgl*tgl) + mass * mass ) / p;
+ Double_t time = length * correction / kcc;
+
+ fIntegratedTime[i] += time;
+ }
+}
+
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetIntegratedTime(Int_t pdg) const
+{
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+ // Return integrated time hypothesis for a given particle
+ // type assumption.
+ //
+ // Input parameter:
+ // pdg - Pdg code of a particle type
+ //
+
+
+ if (!fStartTimeIntegral) {
+ AliWarning("Time integration not started");
+ return 0.;
+ }
+
+ for (Int_t i=0; i<AliPID::kSPECIES; i++)
+ if (AliPID::ParticleCode(i) == TMath::Abs(pdg)) return fIntegratedTime[i];
+
+ AliWarning(Form("Particle type [%d] not found", pdg));
+ return 0;
+}
+
+void AliKalmanTrack::GetIntegratedTimes(Double_t *times) const {
+ for (Int_t i=0; i<AliPID::kSPECIES; i++) times[i]=fIntegratedTime[i];
+}
+
+void AliKalmanTrack::SetIntegratedTimes(const Double_t *times) {
+ for (Int_t i=0; i<AliPID::kSPECIES; i++) fIntegratedTime[i]=times[i];
+}
+
+void AliKalmanTrack::External2Helix(Double_t helix[6]) const {
+ //--------------------------------------------------------------------
+ // External track parameters -> helix parameters
+ //--------------------------------------------------------------------
+ Double_t alpha,x,cs,sn;
+ GetExternalParameters(x,helix); alpha=GetAlpha();
+
+ cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
+ helix[5]=x*cs - helix[0]*sn; // x0
+ helix[0]=x*sn + helix[0]*cs; // y0
+//helix[1]= // z0
+ helix[2]=TMath::ASin(helix[2]) + alpha; // phi0
+//helix[3]= // tgl
+ helix[4]=helix[4]/GetLocalConvConst(); // C
+}
+
+static void Evaluate(const Double_t *h, Double_t t,
+ Double_t r[3], //radius vector
+ Double_t g[3], //first defivatives
+ Double_t gg[3]) //second derivatives
+{
+ //--------------------------------------------------------------------
+ // Calculate position of a point on a track and some derivatives
+ //--------------------------------------------------------------------
+ Double_t phase=h[4]*t+h[2];
+ Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
+
+ r[0] = h[5] + (sn - h[6])/h[4];
+ r[1] = h[0] - (cs - h[7])/h[4];
+ r[2] = h[1] + h[3]*t;
+
+ g[0] = cs; g[1]=sn; g[2]=h[3];
+
+ gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
+}
+
+Double_t AliKalmanTrack::
+GetDCA(const AliKalmanTrack *p, Double_t &xthis, Double_t &xp) const {
+ //------------------------------------------------------------
+ // Returns the (weighed !) distance of closest approach between
+ // this track and the track passed as the argument.
+ // Other returned values:
+ // xthis, xt - coordinates of tracks' reference planes at the DCA
+ //-----------------------------------------------------------
+ Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
+ Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
+ Double_t dx2=dy2;
+
+ //dx2=dy2=dz2=1.;
+
+ Double_t p1[8]; External2Helix(p1);
+ p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
+ Double_t p2[8]; p->External2Helix(p2);
+ p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
+
+
+ Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
+ Evaluate(p1,t1,r1,g1,gg1);
+ Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
+ Evaluate(p2,t2,r2,g2,gg2);
+
+ Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
+ Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
+
+ Int_t max=27;
+ while (max--) {
+ Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
+ Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
+ Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
+ (g1[1]*g1[1] - dy*gg1[1])/dy2 +
+ (g1[2]*g1[2] - dz*gg1[2])/dz2;
+ Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
+ (g2[1]*g2[1] + dy*gg2[1])/dy2 +
+ (g2[2]*g2[2] + dz*gg2[2])/dz2;
+ Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
+
+ Double_t det=h11*h22-h12*h12;
+
+ Double_t dt1,dt2;
+ if (TMath::Abs(det)<1.e-33) {
+ //(quasi)singular Hessian
+ dt1=-gt1; dt2=-gt2;
+ } else {
+ dt1=-(gt1*h22 - gt2*h12)/det;
+ dt2=-(h11*gt2 - h12*gt1)/det;
+ }
+
+ if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
+
+ //check delta(phase1) ?
+ //check delta(phase2) ?
+
+ if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
+ if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
+ if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
+ AliWarning(" stopped at not a stationary point !");
+ Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
+ if (lmb < 0.)
+ AliWarning(" stopped at not a minimum !");
+ break;
+ }
+
+ Double_t dd=dm;
+ for (Int_t div=1 ; ; div*=2) {
+ Evaluate(p1,t1+dt1,r1,g1,gg1);
+ Evaluate(p2,t2+dt2,r2,g2,gg2);
+ dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
+ dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
+ if (dd<dm) break;
+ dt1*=0.5; dt2*=0.5;
+ if (div>512) {
+ AliWarning(" overshoot !"); break;
+ }
+ }
+ dm=dd;
+
+ t1+=dt1;
+ t2+=dt2;
+
+ }
+
+ if (max<=0) AliWarning(" too many iterations !");
+
+ Double_t cs=TMath::Cos(GetAlpha());
+ Double_t sn=TMath::Sin(GetAlpha());
+ xthis=r1[0]*cs + r1[1]*sn;
+
+ cs=TMath::Cos(p->GetAlpha());
+ sn=TMath::Sin(p->GetAlpha());
+ xp=r2[0]*cs + r2[1]*sn;
+
+ return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
+}
+
+Double_t
+AliKalmanTrack::PropagateToDCA(AliKalmanTrack *p, Double_t d, Double_t x0) {
+ //--------------------------------------------------------------
+ // Propagates this track and the argument track to the position of the
+ // distance of closest approach.
+ // Returns the (weighed !) distance of closest approach.
+ //--------------------------------------------------------------
+ Double_t xthis,xp;
+ Double_t dca=GetDCA(p,xthis,xp);
+
+ if (!PropagateTo(xthis,d,x0)) {
+ //AliWarning(" propagation failed !");
+ return 1e+33;
+ }
+
+ if (!p->PropagateTo(xp,d,x0)) {
+ //AliWarning(" propagation failed !";
+ return 1e+33;
+ }
+
+ return dca;
+}
+
+
+
+
+
+Double_t AliKalmanTrack::MeanMaterialBudget(Double_t *start, Double_t *end, Double_t *mparam)
+{
+ //
+ // calculate mean material budget and material properties beween point start and end
+ // mparam - returns parameters used for dEdx and multiple scatering
+ //
+ // mparam[0] - density mean
+ // mparam[1] - rad length
+ // mparam[2] - A mean
+ // mparam[3] - Z mean
+ // mparam[4] - length
+ // mparam[5] - Z/A mean
+ // mparam[6] - number of boundary crosses
+ //
+ mparam[0]=0; mparam[1]=1; mparam[2] =0; mparam[3] =0, mparam[4]=0, mparam[5]=0; mparam[6]=0;
+ //
+ Double_t bparam[6], lparam[6]; // bparam - total param - lparam - local parameters
+ for (Int_t i=0;i<6;i++) bparam[i]=0; //
+
+ if (!gGeoManager) {
+ printf("ERROR: no TGeo\n");
+ return 0.;
+ }
+ //
+ Double_t length;
+ Double_t dir[3];
+ length = TMath::Sqrt((end[0]-start[0])*(end[0]-start[0])+
+ (end[1]-start[1])*(end[1]-start[1])+
+ (end[2]-start[2])*(end[2]-start[2]));
+ mparam[4]=length;
+ if (length<TGeoShape::Tolerance()) return 0.0;
+ Double_t invlen = 1./length;
+ dir[0] = (end[0]-start[0])*invlen;
+ dir[1] = (end[1]-start[1])*invlen;
+ dir[2] = (end[2]-start[2])*invlen;
+ // Initialize start point and direction
+ TGeoNode *currentnode = 0;
+ TGeoNode *startnode = gGeoManager->InitTrack(start, dir);
+ // printf("%s length=%f\n",gGeoManager->GetPath(),length);
+ if (!startnode) {
+ printf("ERROR: start point out of geometry\n");
+ return 0.0;
+ }
+ TGeoMaterial *material = startnode->GetVolume()->GetMedium()->GetMaterial();
+ lparam[0] = material->GetDensity();
+ lparam[1] = material->GetRadLen();
+ lparam[2] = material->GetA();
+ lparam[3] = material->GetZ();
+ lparam[4] = length;
+ lparam[5] = lparam[3]/lparam[2];
+ if (material->IsMixture()) {
+ lparam[1]*=lparam[0]; // different normalization in the modeler for mixture
+ TGeoMixture * mixture = (TGeoMixture*)material;
+ lparam[5] =0;
+ Double_t sum =0;
+ for (Int_t iel=0;iel<mixture->GetNelements();iel++){
+ sum += mixture->GetWmixt()[iel];
+ lparam[5]+= mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
+ }
+ lparam[5]/=sum;
+ }
+ gGeoManager->FindNextBoundary(length);
+ Double_t snext = gGeoManager->GetStep();
+ Double_t step = 0.0;
+ // If no boundary within proposed length, return current density
+ if (snext>=length) {
+ for (Int_t ip=0;ip<5;ip++) mparam[ip] = lparam[ip];
+ return lparam[0];
+ }
+ // Try to cross the boundary and see what is next
+ while (length>TGeoShape::Tolerance()) {
+ mparam[6]+=1.;
+ currentnode = gGeoManager->Step();
+ step += snext+1.E-6;
+ bparam[1] += snext*lparam[1];
+ bparam[2] += snext*lparam[2];
+ bparam[3] += snext*lparam[3];
+ bparam[5] += snext*lparam[5];
+ bparam[0] += snext*lparam[0];
+
+ if (snext>=length) break;
+ if (!currentnode) break;
+ // printf("%s snext=%f density=%f bparam[0]=%f\n", gGeoManager->GetPath(),snext,density,bparam[0]);
+ if (!gGeoManager->IsEntering()) {
+ gGeoManager->SetStep(1.E-3);
+ currentnode = gGeoManager->Step();
+ if (!gGeoManager->IsEntering() || !currentnode) {
+ // printf("ERROR: cannot cross boundary\n");
+ mparam[0] = bparam[0]/step;
+ mparam[1] = bparam[1]/step;
+ mparam[2] = bparam[2]/step;
+ mparam[3] = bparam[3]/step;
+ mparam[5] = bparam[5]/step;
+ mparam[4] = step;
+ mparam[0] = 0.; // if crash of navigation take mean density 0
+ mparam[1] = 1000000; // and infinite rad length
+ return bparam[0]/step;
+ }
+ step += 1.E-3;
+ snext += 1.E-3;
+ bparam[0] += lparam[0]*1.E-3;
+ bparam[1] += lparam[1]*1.E-3;
+ bparam[2] += lparam[2]*1.E-3;
+ bparam[3] += lparam[3]*1.E-3;
+ bparam[5] += lparam[5]*1.E-3;
+ }
+ length -= snext;
+ material = currentnode->GetVolume()->GetMedium()->GetMaterial();
+ lparam[0] = material->GetDensity();
+ lparam[1] = material->GetRadLen();
+ lparam[2] = material->GetA();
+ lparam[3] = material->GetZ();
+ lparam[5] = lparam[3]/lparam[2];
+ if (material->IsMixture()) {
+ lparam[1]*=lparam[0];
+ TGeoMixture * mixture = (TGeoMixture*)material;
+ lparam[5]=0;
+ Double_t sum =0;
+ for (Int_t iel=0;iel<mixture->GetNelements();iel++){
+ sum+= mixture->GetWmixt()[iel];
+ lparam[5]+= mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
+ }
+ lparam[5]/=sum;
+ }
+ gGeoManager->FindNextBoundary(length);
+ snext = gGeoManager->GetStep();
+ }
+ mparam[0] = bparam[0]/step;
+ mparam[1] = bparam[1]/step;
+ mparam[2] = bparam[2]/step;
+ mparam[3] = bparam[3]/step;
+ mparam[5] = bparam[5]/step;
+ return bparam[0]/step;
+
+}
+
+Double_t AliKalmanTrack::GetConvConst() {
+ return 1000/0.299792458/AliTracker::GetBz();
+}
+
+void AliKalmanTrack::SaveLocalConvConst() {
+ //---------------------------------------------------------------------
+ // Saves local conversion constant "curvature (1/cm) -> pt (GeV/c)"
+ //---------------------------------------------------------------------
+ if (AliTracker::UniformField()) {
+ fLocalConvConst=1000/0.299792458/AliTracker::GetBz();
+ } else {
+ Float_t r[3]; GetXYZ(r);
+ fLocalConvConst=1000/0.299792458/AliTracker::GetBz(r);
+ }
+}
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