DReferenceTrajectory.cc

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// $Id$
//
//    File: DReferenceTrajectory.cc
// Created: Wed Jul 19 13:42:58 EDT 2006
// Creator: davidl (on Darwin swire-b241.jlab.org 8.7.0 powerpc)
//

#include <signal.h>
#include <memory>
#include <cmath>

#include <DVector3.h>
using namespace std;
#include <math.h>
#include <algorithm>

#include "DReferenceTrajectory.h"
#include "DTrackCandidate.h"
#include "DMagneticFieldStepper.h"
#include <TMatrix.h>
#include "HDGEOMETRY/DRootGeom.h"
#define ONE_THIRD 0.33333333333333333
#define TWO_THIRD 0.66666666666666667
#define EPS 1e-8
#define QuietNaN std::numeric_limits<double>::quiet_NaN()

struct StepStruct {DReferenceTrajectory::swim_step_t steps[256];};

//---------------------------------
// DReferenceTrajectory    (Constructor)
//---------------------------------
DReferenceTrajectory::DReferenceTrajectory(const DMagneticFieldMap *bfield
                                          , double q
                                          , swim_step_t *swim_steps
                                          , int max_swim_steps
                                          , double step_size)
{
   // Copy some values into data members
   this->q = q;
   this->step_size = step_size;
   this->bfield = bfield;
   this->Nswim_steps = 0;
   this->dist_to_rt_depth = 0;
   this->mass = 0.13957; // assume pion mass until otherwise specified
   this->mass_sq=this->mass*this->mass;
   this->hit_cdc_endplate = false;
   this->RootGeom=NULL;
   this->geom = NULL;
   this->ploss_direction = kForward;
   this->check_material_boundaries = true;
   this->zmin_track_boundary = -100.0;  // boundary at which to stop swimming
   this->zmax_track_boundary = 670.0;   // boundary at which to stop swimming
   this->Rsqmax_interior = 65.0*65.0; // Maximum radius (in cm) corresponding to inside of BCAL
   this->Rsqmax_exterior = 88.0*88.0; // Maximum radius (in cm) corresponding to outside of BCAL
   
   this->last_phi = 0.0;
   this->last_swim_step = NULL;
   this->last_dist_along_wire = 0.0;
   this->last_dz_dphi = 0.0;
   
   this->debug_level = 0;
   
   // Initialize some values from configuration parameters
   BOUNDARY_STEP_FRACTION = 0.80;
   MIN_STEP_SIZE = 0.1; // cm
   MAX_STEP_SIZE = 3.0;    // cm
   int MAX_SWIM_STEPS = 2500;
   
   gPARMS->SetDefaultParameter("TRK:BOUNDARY_STEP_FRACTION" , BOUNDARY_STEP_FRACTION, "Fraction of estimated distance to boundary to use as step size");
   gPARMS->SetDefaultParameter("TRK:MIN_STEP_SIZE" , MIN_STEP_SIZE, "Minimum step size in cm to take when swimming a track with adaptive step sizes");
   gPARMS->SetDefaultParameter("TRK:MAX_STEP_SIZE" , MAX_STEP_SIZE, "Maximum step size in cm to take when swimming a track with adaptive step sizes");
   gPARMS->SetDefaultParameter("TRK:MAX_SWIM_STEPS" , MAX_SWIM_STEPS, "Number of swim steps for DReferenceTrajectory to allocate memory for (when not using external buffer)");
   gPARMS->SetDefaultParameter("TRK:DEBUG_LEVEL" , this->debug_level);
   
   // It turns out that the greatest bottleneck in speed here comes from
   // allocating/deallocating the large block of memory required to hold
   // all of the trajectory info. The preferred way of calling this is 
   // with a pointer allocated once at program startup. This code block
   // though allows it to be allocated here if necessary.
   if(!swim_steps){
      own_swim_steps = true;
      this->max_swim_steps = MAX_SWIM_STEPS;
      this->swim_steps = new swim_step_t[this->max_swim_steps];
   }else{
      own_swim_steps = false;
      this->max_swim_steps = max_swim_steps;
      this->swim_steps = swim_steps;
   }
}

//---------------------------------
// DReferenceTrajectory    (Copy Constructor)
//---------------------------------
DReferenceTrajectory::DReferenceTrajectory(const DReferenceTrajectory& rt)
{
   /// The copy constructor will always allocate its own memory for the
   /// swim steps and set its internal flag to indicate that is owns them
   /// regardless of the owner of the source trajectory's.

   this->Nswim_steps = rt.Nswim_steps;
   this->q = rt.q;
   this->max_swim_steps = rt.max_swim_steps;
   this->own_swim_steps = true;
   this->step_size = rt.step_size;
   this->bfield = rt.bfield;
   this->last_phi = rt.last_phi;
   this->last_dist_along_wire = rt.last_dist_along_wire;
   this->last_dz_dphi = rt.last_dz_dphi;
   this->RootGeom = rt.RootGeom;
   this->geom = rt.geom;
   this->dist_to_rt_depth = 0;
   this->mass = rt.GetMass();
   this->mass_sq=this->mass*this->mass;
   this->ploss_direction = rt.ploss_direction;
   this->check_material_boundaries = rt.GetCheckMaterialBoundaries();
   this->BOUNDARY_STEP_FRACTION = rt.GetBoundaryStepFraction();
   this->MIN_STEP_SIZE = rt.GetMinStepSize();
   this->MAX_STEP_SIZE = rt.GetMaxStepSize();
   this->debug_level=rt.debug_level;
   this->zmin_track_boundary = -100.0;  // boundary at which to stop swimming
   this->zmax_track_boundary = 670.0;   // boundary at which to stop swimming
   this->Rsqmax_interior = 65.0*65.0; // Maximum radius (in cm) corresponding to inside of BCAL
   this->Rsqmax_exterior = 88.0*88.0; // Maximum radius (in cm) corresponding to outside of BCAL
   

   this->swim_steps = new swim_step_t[this->max_swim_steps];
   this->last_swim_step = NULL;
   for(int i=0; i<Nswim_steps; i++)
   {
      swim_steps[i] = rt.swim_steps[i];
      if(&(rt.swim_steps[i]) == rt.last_swim_step)
         this->last_swim_step = &(swim_steps[i]);
   }

}

//---------------------------------
// operator=               (Assignment operator)
//---------------------------------
DReferenceTrajectory& DReferenceTrajectory::operator=(const DReferenceTrajectory& rt)
{
   /// The assignment operator will always make sure the memory allocated
   /// for the swim_steps is owned by the object being copied into.
   /// If it already owns memory of sufficient size, then it will be
   /// reused. If it owns memory that is too small, it will be freed and
   /// a new block allocated. If it does not own its swim_steps coming
   /// in, then it will allocate memory so that it does own it on the
   /// way out.
   
   if(&rt == this)return *this; // protect against self copies

   // Free memory if block is too small
   if(own_swim_steps==true && max_swim_steps<rt.Nswim_steps){
      delete[] swim_steps;
      swim_steps=NULL;
   }
   
   // Forget memory block if we don't currently own it
   if(!own_swim_steps){
      swim_steps=NULL;
   }

   this->Nswim_steps = rt.Nswim_steps;
   this->q = rt.q;
   this->max_swim_steps = rt.max_swim_steps;
   this->own_swim_steps = true;
   this->step_size = rt.step_size;
   this->bfield = rt.bfield;
   this->last_phi = rt.last_phi;
   this->last_dist_along_wire = rt.last_dist_along_wire;
   this->last_dz_dphi = rt.last_dz_dphi;
   this->RootGeom = rt.RootGeom;
   this->geom = rt.geom;
   this->dist_to_rt_depth = rt.dist_to_rt_depth;
   this->mass = rt.GetMass();
   this->mass_sq=this->mass*this->mass;
   this->ploss_direction = rt.ploss_direction;
   this->check_material_boundaries = rt.GetCheckMaterialBoundaries();
   this->BOUNDARY_STEP_FRACTION = rt.GetBoundaryStepFraction();
   this->MIN_STEP_SIZE = rt.GetMinStepSize();
   this->MAX_STEP_SIZE = rt.GetMaxStepSize();

   // Allocate memory if needed
   if(swim_steps==NULL)this->swim_steps = new swim_step_t[this->max_swim_steps];

   // Copy swim steps
   this->last_swim_step = NULL;
   for(int i=0; i<Nswim_steps; i++)
   {
      swim_steps[i] = rt.swim_steps[i];
      if(&(rt.swim_steps[i]) == rt.last_swim_step)
         this->last_swim_step = &(swim_steps[i]);
   }

   
   return *this;
}

//---------------------------------
// ~DReferenceTrajectory    (Destructor)
//---------------------------------
DReferenceTrajectory::~DReferenceTrajectory()
{
   if(own_swim_steps){
      delete[] swim_steps;
   }
}

//---------------------------------
// CopyWithShift
//---------------------------------
void DReferenceTrajectory::CopyWithShift(const DReferenceTrajectory *rt, DVector3 shift)
{
   // First, do a straight copy
   *this = *rt;
   
   // Second, shift all positions
   for(int i=0; i<Nswim_steps; i++)swim_steps[i].origin += shift;
}


//---------------------------------
// Reset
//---------------------------------
void DReferenceTrajectory::Reset(void){
   //reset DReferenceTrajectory for re-use
   this->Nswim_steps = 0;
   this->ploss_direction = kForward;
   this->mass = 0.13957; // assume pion mass until otherwise specified
   this->mass_sq=this->mass*this->mass;
   this->hit_cdc_endplate = false;
   this->last_phi = 0.0;
   this->last_swim_step = NULL;
   this->last_dist_along_wire = 0.0;
   this->last_dz_dphi = 0.0;
   this->dist_to_rt_depth = 0;
   this->check_material_boundaries = true;
}

//---------------------------------
// FastSwim -- light-weight swim to a wire that does not treat multiple 
// scattering but does handle energy loss.
// No checks for distance to boundaries are done.
//---------------------------------
void DReferenceTrajectory::FastSwim(const DVector3 &pos, const DVector3 &mom,
                DVector3 &last_pos,DVector3 &last_mom,
                double q,double smax,
                const DCoordinateSystem *wire){
  const DVector3 wire_origin=wire->origin;
  const DVector3 wire_dir=wire->udir;
  FastSwim(pos,mom,last_pos,last_mom,q,wire_origin,wire_dir,smax);
}
void DReferenceTrajectory::FastSwim(const DVector3 &pos, const DVector3 &mom,
                DVector3 &last_pos,DVector3 &last_mom,
                double q,
                const DVector3 &origin,
                const DVector3 &dir,double smax){

  DVector3 mypos(pos);
  DVector3 mymom(mom);

  // Initialize the stepper
  DMagneticFieldStepper stepper(bfield, q, &pos, &mom);
  double s=0,doca=1000.,old_doca=1000.,dP_dx=0.;
  //  double mass=GetMass();
  while (s<smax){
    // Save old value of doca
    old_doca=doca;

    // Adjust step size to take smaller steps in regions of high momentum loss
    if(geom){  
      double KrhoZ_overA=0.0;
      double rhoZ_overA=0.0;
      double LogI=0.0;
      double X0=0.0;
      if (geom->FindMatALT1(mypos,mymom,KrhoZ_overA,rhoZ_overA,LogI,X0)
     ==NOERROR){ 
   // Calculate momentum loss due to ionization
   dP_dx = dPdx(mymom.Mag(), KrhoZ_overA, rhoZ_overA,LogI);
   double my_step_size = 0.0001/fabs(dP_dx);
      
   if(my_step_size>MAX_STEP_SIZE)my_step_size=MAX_STEP_SIZE; // maximum step size in cm
   if(my_step_size<MIN_STEP_SIZE)my_step_size=MIN_STEP_SIZE; // minimum step size in cm
   
   if (ploss_direction==kBackward) my_step_size*=-1.;
   stepper.SetStepSize(my_step_size);
      }
    }
    // Swim to next
    double ds=stepper.Step(NULL);
    s+=fabs(ds);
    stepper.GetPosMom(mypos,mymom);

    // Take into account energy loss
    double ptot=mymom.Mag();
    //    if (ploss_direction==kForward) ptot+=dP_dx*ds;
    //else ptot-=dP_dx*ds; 
    ptot+=dP_dx*ds;

    mymom.SetMag(ptot);
    stepper.SetStartingParams(q, &mypos, &mymom);
    
    // Break if we have passed the line to which we are trying to find the doca
    DVector3 linepos=origin;
    if (fabs(dir.z())>0.){
      linepos+=((mypos.z()-origin.z())/dir.z())*dir;
    }
    doca=(linepos-mypos).Mag();
    if (doca>old_doca) break;

    // Store the position and momentum for this step
    last_pos=mypos;
    last_mom=mymom;
  }  
}

// Faster version of swimmer that only deals with the region inside the bore of
// the magnet.  This is intended to be used with the hit selector, so is a 
// paired-down version of the usual trajectory.
void DReferenceTrajectory::FastSwimForHitSelection(const DVector3 &pos, const DVector3 &mom, double q){
  DMagneticFieldStepper stepper(bfield, q, &pos, &mom);
  if(step_size>0.0)stepper.SetStepSize(step_size);

  // Step until we leave the active tracking region
  swim_step_t *swim_step = this->swim_steps;
  Nswim_steps = 0;
  double itheta02 = 0.0;
  double itheta02s = 0.0;
  double itheta02s2 = 0.0;
  double X0sum=0.0;
  swim_step_t *last_step=NULL;

  for(double s=0; fabs(s)<1000.; Nswim_steps++, swim_step++){
       
    if(Nswim_steps>=this->max_swim_steps){
      if (debug_level>0){
   jerr<<__FILE__<<":"<<__LINE__<<" Too many steps in trajectory. Truncating..."<<endl;
      }
      break;
    }
    
    stepper.GetDirs(swim_step->sdir, swim_step->tdir, swim_step->udir);
    stepper.GetPosMom(swim_step->origin, swim_step->mom);
    stepper.GetBField(swim_step->B);
    swim_step->Ro = stepper.GetRo();
    swim_step->s = s;
    swim_step->t = 0.; // we do not need the time for our purpose...
    
    double Rsq=swim_step->origin.Perp2();
    double z=swim_step->origin.Z();
    if (z>345. || z<0. || Rsq>60.*60.){
      Nswim_steps++; break;
    }

    //magnitude of momentum and beta
    double p_sq=swim_step->mom.Mag2();
    double one_over_beta_sq=1.+mass_sq/p_sq;

    // Add material if geom is not NULL
    double dP = 0.0;
    double dP_dx=0.0;
    if(geom){
      double KrhoZ_overA=0.0;
      double rhoZ_overA=0.0;
      double LogI=0.0;
      double X0=0.0;
      jerror_t err = geom->FindMatALT1(swim_step->origin, swim_step->mom, KrhoZ_overA, rhoZ_overA,LogI, X0);
      if(err == NOERROR){
   if(X0>0.0){
     double p=sqrt(p_sq);
     double delta_s = s;
     if(last_step)delta_s -= last_step->s;
     double radlen = delta_s/X0;
     
     if(radlen>1.0E-5){ // PDG 2008 pg 271, second to last paragraph
               
       //  double theta0 = 0.0136*sqrt(one_over_beta_sq)/p*sqrt(radlen)*(1.0+0.038*log(radlen)); // From PDG 2008 eq 27.12
       //double theta02 = theta0*theta0;
       double factor=1.0+0.038*log(radlen);
       double theta02=1.8496e-4*factor*factor*radlen*one_over_beta_sq/p_sq;

       itheta02 += theta02;
       itheta02s += s*theta02;
       itheta02s2 += s*s*theta02;
       X0sum+=X0;
     }
     
     // Calculate momentum loss due to ionization
     dP_dx = dPdx(p, KrhoZ_overA, rhoZ_overA,LogI);
   }
      }
      last_step = swim_step;
    }
    swim_step->itheta02 = itheta02;
    swim_step->itheta02s = itheta02s;
    swim_step->itheta02s2 = itheta02s2;
    swim_step->invX0=Nswim_steps/X0sum;
    
    if(step_size<0.0){ // step_size<0 indicates auto-calculated step size
      // Adjust step size to take smaller steps in regions of high momentum loss
      double my_step_size = 0.0001/fabs(dP_dx);
      if(my_step_size>MAX_STEP_SIZE)my_step_size=MAX_STEP_SIZE; // maximum step size in cm
      if(my_step_size<MIN_STEP_SIZE)my_step_size=MIN_STEP_SIZE; // minimum step size in cm
      
      stepper.SetStepSize(my_step_size);
    }

    // Swim to next
    double ds=stepper.FastStep();
  
    // Calculate momentum loss due to the step we're about to take
    dP = ds*dP_dx;
  
    // Adjust momentum due to ionization losses
    if(dP!=0.0){
      DVector3 pos, mom;
      stepper.GetPosMom(pos, mom);
      double ptot = mom.Mag() - dP; // correct for energy loss
      if (ptot<0.005) {Nswim_steps++; break;}
      mom.SetMag(ptot);
      stepper.SetStartingParams(q, &pos, &mom);
    }
    s += ds; 
  }
}

// Faster version of the swimmer that uses an alternate stepper and does not
// check for material boundaries.
void DReferenceTrajectory::FastSwim(const DVector3 &pos, const DVector3 &mom, double q,double smax, double zmin,double zmax){
  
  /// (Re)Swim the trajectory starting from pos with momentum mom.
  /// This will use the charge and step size (if given) passed to
  /// the constructor when the object was created. It will also
  /// (re)use the swim_step buffer, replacing it's contents.
  
  // If the charged passed to us is greater that 10, it means use the charge
  // already stored in the class. Otherwise, use what was passed to us.
  if(fabs(q)>10)
    q = this->q;
  else
    this->q = q;
  
  DMagneticFieldStepper stepper(bfield, q, &pos, &mom);
  if(step_size>0.0)stepper.SetStepSize(step_size);

  // Step until we hit a boundary (don't track more than 20 meters)
  swim_step_t *swim_step = this->swim_steps;
  double t=0.;
  Nswim_steps = 0;
  double itheta02 = 0.0;
  double itheta02s = 0.0;
  double itheta02s2 = 0.0;
  double X0sum=0.0;
  swim_step_t *last_step=NULL;
  double old_radius_sq=1e6;

  // Variables used to tag the step at which the track passes into one one of
  // the outer detectors
  index_at_bcal=-1;
  index_at_tof=-1;
  index_at_fcal=-1;
  bool hit_bcal=false,hit_fcal=false,hit_tof=false;
   
  for(double s=0; fabs(s)<smax; Nswim_steps++, swim_step++){
       
    if(Nswim_steps>=this->max_swim_steps){
      if (debug_level>0){
   jerr<<__FILE__<<":"<<__LINE__<<" Too many steps in trajectory. Truncating..."<<endl;
      }
      break;
    }
    
    stepper.GetDirs(swim_step->sdir, swim_step->tdir, swim_step->udir);
    stepper.GetPosMom(swim_step->origin, swim_step->mom);
    stepper.GetBField(swim_step->B);
    swim_step->Ro = stepper.GetRo();
    swim_step->s = s;
    swim_step->t = t;

    //magnitude of momentum and beta
    double p_sq=swim_step->mom.Mag2();
    double one_over_beta_sq=1.+mass_sq/p_sq;

    // Add material if geom or RootGeom is not NULL
    // If both are non-NULL, then use RootGeom
    double dP = 0.0;
    double dP_dx=0.0;
    if(RootGeom || geom){
      double KrhoZ_overA=0.0;
      double rhoZ_overA=0.0;
      double LogI=0.0;
      double X0=0.0;
      jerror_t err;
      if(RootGeom){
   double rhoZ_overA,rhoZ_overA_logI;
   err = RootGeom->FindMatLL(swim_step->origin,
              rhoZ_overA, 
              rhoZ_overA_logI, 
              X0);
   KrhoZ_overA=0.1535e-3*rhoZ_overA;
   LogI=rhoZ_overA_logI/rhoZ_overA;
      }else{
   err = geom->FindMatALT1(swim_step->origin, swim_step->mom, KrhoZ_overA, rhoZ_overA,LogI, X0);
      }
      if(err == NOERROR){
   if(X0>0.0){
     double p=sqrt(p_sq);
     double delta_s = s;
     if(last_step)delta_s -= last_step->s;
     double radlen = delta_s/X0;
     
     if(radlen>1.0E-5){ // PDG 2008 pg 271, second to last paragraph
               
       //  double theta0 = 0.0136*sqrt(one_over_beta_sq)/p*sqrt(radlen)*(1.0+0.038*log(radlen)); // From PDG 2008 eq 27.12
       //double theta02 = theta0*theta0;
       double factor=1.0+0.038*log(radlen);
       double theta02=1.8496e-4*factor*factor*radlen*one_over_beta_sq/p_sq;

       itheta02 += theta02;
       itheta02s += s*theta02;
       itheta02s2 += s*s*theta02;
       X0sum+=X0;
     }
     
     // Calculate momentum loss due to ionization
     dP_dx = dPdx(p, KrhoZ_overA, rhoZ_overA,LogI);
   }
      }
      last_step = swim_step;
    }
    swim_step->itheta02 = itheta02;
    swim_step->itheta02s = itheta02s;
    swim_step->itheta02s2 = itheta02s2;
    swim_step->invX0=Nswim_steps/X0sum;
    
    
    if(step_size<0.0){ // step_size<0 indicates auto-calculated step size
      // Adjust step size to take smaller steps in regions of high momentum loss
      double my_step_size = 0.0001/fabs(dP_dx);
      if(my_step_size>MAX_STEP_SIZE)my_step_size=MAX_STEP_SIZE; // maximum step size in cm
      if(my_step_size<MIN_STEP_SIZE)my_step_size=MIN_STEP_SIZE; // minimum step size in cm
      
      stepper.SetStepSize(my_step_size);
    }

    // Swim to next
    double ds=stepper.FastStep();
  
    // Calculate momentum loss due to the step we're about to take
    dP = ds*dP_dx;
  
    // Adjust momentum due to ionization losses
    if(dP!=0.0){
      DVector3 pos, mom;
      stepper.GetPosMom(pos, mom);
      double ptot = mom.Mag() - dP; // correct for energy loss
      if (ptot<0.005) {Nswim_steps++; break;}
      mom.SetMag(ptot);
      stepper.SetStartingParams(q, &pos, &mom);
    }
      
    // update flight time
    t+=ds*sqrt(one_over_beta_sq)/SPEED_OF_LIGHT;
    s += ds;
  
    // Mark places along trajectory where we pass into one of the 
    // main detectors
    double Rsq=swim_step->origin.Perp2();
    double z=swim_step->origin.Z();
    if (hit_bcal==false && Rsq>Rsqmax_interior && z<407 &&z>0){
      index_at_bcal=Nswim_steps-1;
      hit_bcal=true;
    }
    if (hit_tof==false && z>606.){
      index_at_tof=Nswim_steps-1;
      hit_tof=true;
    }
    if (hit_fcal==false && z>625.){
      index_at_fcal=Nswim_steps-1;
      hit_fcal=true;     
    }
    
    
    // Exit the loop if we are already inside the volume of the BCAL
    // and the radius is decreasing
    if (Rsq<old_radius_sq && Rsq>Rsqmax_interior && z<407.0 && z>-100.0){
      Nswim_steps++; break;
    }
         
    // Exit loop if we leave the tracking volume
    if (z>zmax){Nswim_steps++; break;} 
    if(Rsq>Rsqmax_exterior && z<407.0){Nswim_steps++; break;} // ran into BCAL
    if (fabs(swim_step->origin.X())>160.0
   || fabs(swim_step->origin.Y())>160.0)
      {Nswim_steps++; break;} // left extent of TOF + 31cm Buffer
    if(z>670.0){Nswim_steps++; break;} // ran into FCAL
    if(z<zmin){Nswim_steps++; break;} // exit upstream
    
    old_radius_sq=Rsq;
  }
  
  // OK. At this point the positions of the trajectory in the lab
  // frame have been recorded along with the momentum of the
  // particle and the directions of reference trajectory
  // coordinate system at each point.
}

//---------------------------------
// Swim
//---------------------------------
void DReferenceTrajectory::Swim(const DVector3 &pos, const DVector3 &mom, double q, const TMatrixFSym *cov,double smax, const DCoordinateSystem *wire)
{
        /// (Re)Swim the trajectory starting from pos with momentum mom.
   /// This will use the charge and step size (if given) passed to
   /// the constructor when the object was created. It will also
   /// (re)use the sim_step buffer, replacing it's contents.

   // If the charged passed to us is greater that 10, it means use the charge
   // already stored in the class. Otherwise, use what was passed to us.
   if(fabs(q)>10)
      q = this->q;
   else
      this->q = q;

   DMagneticFieldStepper stepper(bfield, q, &pos, &mom);
   if(step_size>0.0)stepper.SetStepSize(step_size);

   // Step until we hit a boundary (don't track more than 20 meters)
   swim_step_t *swim_step = this->swim_steps;
   double t=0.;
   Nswim_steps = 0;
   double itheta02 = 0.0;
   double itheta02s = 0.0;
   double itheta02s2 = 0.0;
   double X0sum=0.0;
   swim_step_t *last_step=NULL;
   double old_radius_sq=1e6;
   
   TMatrixFSym mycov(7);
   if (cov!=NULL){
     mycov=*cov;
   }

   // Reset flag indicating whether we hit the CDC endplate
   // and get the parameters of the endplate so we can check
   // if we hit it while swimming.
   //hit_cdc_endplate = false;
   /*
#if 0 // The GetCDCEndplate call goes all the way back to the XML and slows down
      // overall tracking by a factor of 20. Therefore, we skip finding it
     // and just hard-code the values instead.  1/28/2011  DL
   double cdc_endplate_z=150+17;  // roughly, from memory
   double cdc_endplate_dz=5.0;      // roughly, from memory
   double cdc_endplate_rmin=10.0; // roughly, from memory
   double cdc_endplate_rmax=55.0; // roughly, from memory
   if(geom)geom->GetCDCEndplate(cdc_endplate_z, cdc_endplate_dz, cdc_endplate_rmin, cdc_endplate_rmax);
   double cdc_endplate_zmin = cdc_endplate_z - cdc_endplate_dz/2.0;
   double cdc_endplate_zmax = cdc_endplate_zmin + cdc_endplate_dz;
#else
   double cdc_endplate_rmin=10.0; // roughly, from memory
   double cdc_endplate_rmax=55.0; // roughly, from memory
   double cdc_endplate_zmin = 167.6;
   double cdc_endplate_zmax = 168.2;
#endif   
   */

#if 0
   // Get Bfield from stepper to initialize Bz_old
   DVector3 B;
   stepper.GetBField(B);
   double Bz_old = B.z();
#endif

   // Variables used to tag the step at which the track passes into one 
   // one of the outer detectors
   index_at_bcal=-1;
   index_at_tof=-1;
   index_at_fcal=-1;
   bool hit_bcal=false,hit_fcal=false,hit_tof=false;
   
   for(double s=0; fabs(s)<smax; Nswim_steps++, swim_step++){
   
      if(Nswim_steps>=this->max_swim_steps){
        if (debug_level>0){
         jerr<<__FILE__<<":"<<__LINE__<<" Too many steps in trajectory. Truncating..."<<endl;
        }
         break;
      }

      stepper.GetDirs(swim_step->sdir, swim_step->tdir, swim_step->udir);
      stepper.GetPosMom(swim_step->origin, swim_step->mom);
      swim_step->Ro = stepper.GetRo();
      swim_step->s = s;
      swim_step->t = t;
   
      //magnitude of momentum and beta
      double p_sq=swim_step->mom.Mag2();
      double one_over_beta_sq=1.+mass_sq/p_sq;

      // Add material if geom or RootGeom is not NULL
      // If both are non-NULL, then use RootGeom
      double dP = 0.0;
      double dP_dx=0.0;
      double s_to_boundary=1.0E6; // initialize to "infinity" in case we don't set this below
      if(RootGeom || geom){
         double KrhoZ_overA=0.0;
         double rhoZ_overA=0.0;
         double LogI=0.0;
         double X0=0.0;
         jerror_t err;
         if(RootGeom){
           double rhoZ_overA,rhoZ_overA_logI;
           err = RootGeom->FindMatLL(swim_step->origin,
                      rhoZ_overA, 
                      rhoZ_overA_logI, 
                      X0);
           KrhoZ_overA=0.1535e-3*rhoZ_overA;
           LogI=rhoZ_overA_logI/rhoZ_overA;
         }else{
            if(check_material_boundaries){
               err = geom->FindMatALT1(swim_step->origin, swim_step->mom, KrhoZ_overA, rhoZ_overA,LogI, X0, &s_to_boundary);
            }else{
               err = geom->FindMatALT1(swim_step->origin, swim_step->mom, KrhoZ_overA, rhoZ_overA,LogI, X0);
            }
            
            // Check if we hit the CDC endplate
            //double z = swim_step->origin.Z();
            //if(z>=cdc_endplate_zmin && z<=cdc_endplate_zmax){
            // double r = swim_step->origin.Perp();
            // if(r>=cdc_endplate_rmin && r<=cdc_endplate_rmax){
            // hit_cdc_endplate = true;
            //}
            //}
         }

         if(err == NOERROR){
           if(X0>0.0){
             double p=sqrt(p_sq);
             double delta_s = s;
             if(last_step)delta_s -= last_step->s;
             double radlen = delta_s/X0;
             
             if(radlen>1.0E-5){ // PDG 2008 pg 271, second to last paragraph
               
               //  double theta0 = 0.0136*sqrt(one_over_beta_sq)/p*sqrt(radlen)*(1.0+0.038*log(radlen)); // From PDG 2008 eq 27.12
               //double theta02 = theta0*theta0;
               double factor=1.0+0.038*log(radlen);
               double theta02=1.8496e-4*factor*factor*radlen*one_over_beta_sq/p_sq;
               
               itheta02 += theta02;
               itheta02s += s*theta02;
               itheta02s2 += s*s*theta02;
               X0sum+=X0;
              
               if (cov){
            
               }
             }

             // Calculate momentum loss due to ionization
             dP_dx = dPdx(p, KrhoZ_overA, rhoZ_overA,LogI);
           }
         }
         last_step = swim_step;
      }
      swim_step->itheta02 = itheta02;
      swim_step->itheta02s = itheta02s;
      swim_step->itheta02s2 = itheta02s2;
      swim_step->invX0=Nswim_steps/X0sum;

      // Adjust step size to take smaller steps in regions of high momentum loss or field gradient
      if(step_size<0.0){ // step_size<0 indicates auto-calculated step size
         // Take step so as to change momentum by 100keV
         //double my_step_size=p/fabs(dP_dx)*0.01;
         double my_step_size = 0.0001/fabs(dP_dx);

         // Now check the field gradient
#if 0
         stepper.GetBField(B);
         double Bz = B.z();
         if (fabs(Bz-Bz_old)>EPS){
           double my_step_size_B=0.01*my_step_size
             *fabs(Bz/(Bz_old-Bz));
           if (my_step_size_B<my_step_size) 
             my_step_size=my_step_size_B;
         }
         Bz_old=Bz; // Save old z-component of B-field
#endif
         // Use the estimated distance to the boundary to make sure we don't overstep
         // into a high density region and miss some material. Use half the estimated
         // distance since it's only an estimate. Note that even though this would lead
         // to infinitely small steps, there is a minimum step size imposed below to
         // ensure the step size is reasonable.
         /*
         double step_size_to_boundary = BOUNDARY_STEP_FRACTION*s_to_boundary;
         if(step_size_to_boundary < my_step_size)my_step_size = step_size_to_boundary;
         */

         if(my_step_size>MAX_STEP_SIZE)my_step_size=MAX_STEP_SIZE; // maximum step size in cm
         if(my_step_size<MIN_STEP_SIZE)my_step_size=MIN_STEP_SIZE; // minimum step size in cm

         stepper.SetStepSize(my_step_size);
      }

      // Swim to next
      double ds=stepper.Step(NULL,&swim_step->B);
      if (cov){
        PropagateCovariance(ds,q,mass_sq,mom,pos,swim_step->B,mycov);
        swim_step->cov_t_t=mycov(6,6);
        swim_step->cov_px_t=mycov(6,0);
        swim_step->cov_py_t=mycov(6,1);
        swim_step->cov_pz_t=mycov(6,2);
      }

      // Calculate momentum loss due to the step we're about to take
      dP = ds*dP_dx;

      // Adjust momentum due to ionization losses
      if(dP!=0.0){
         DVector3 pos, mom;
         stepper.GetPosMom(pos, mom);
         double ptot = mom.Mag() - dP; // correct for energy loss
         bool ranged_out = false;
         /*
         if (ptot<0.05){
           swim_step->origin.Print();
           cout<<"N: " << Nswim_steps <<" x " << pos.x() <<" y " <<pos.y() <<" z " << pos.z() <<" r " << pos.Perp()<< " s " << s  << " p " << ptot << endl;
         }
         */
         if(ptot<0.005)ranged_out=true;
         if(dP<0.0 && ploss_direction==kForward)ranged_out=true;
         if(dP>0.0 && ploss_direction==kBackward)ranged_out=true;
         //if(mom.Mag()==0.0)ranged_out=true;
         if(ranged_out){
            Nswim_steps++; // This will at least allow for very low momentum particles to have 1 swim step
            break;
         }
         mom.SetMag(ptot);
         stepper.SetStartingParams(q, &pos, &mom);
      }
      
      // update flight time
      t+=ds*sqrt(one_over_beta_sq)/SPEED_OF_LIGHT;
      s += ds;

      // Mark places along trajectory where we pass into one of the 
      // main detectors
      double Rsq=swim_step->origin.Perp2();
      double z=swim_step->origin.Z();
      if (hit_bcal==false && Rsq>Rsqmax_interior && z<407 &&z>0){
        index_at_bcal=Nswim_steps-1;
        hit_bcal=true;
      }
      if (hit_tof==false && z>618.){
        index_at_tof=Nswim_steps-1;
        hit_tof=true;
      }
      if (hit_fcal==false && z>625.){
        index_at_fcal=Nswim_steps-1;
        hit_fcal=true;
      }

      // Exit the loop if we are already inside the volume of the BCAL
      // and the radius is decreasing
      if (Rsq<old_radius_sq && Rsq>Rsqmax_interior && z<407.0 && z>-100.0){
        Nswim_steps++; break;
      }
   
      
      // Exit loop if we leave the tracking volume
      if(Rsq>Rsqmax_exterior && z<407.0){Nswim_steps++; break;} // ran into BCAL
      if (fabs(swim_step->origin.X())>160.0
          || fabs(swim_step->origin.Y())>160.0)
        {Nswim_steps++; break;} // left extent of TOF + 31cm Buffer
      if(z>zmax_track_boundary){Nswim_steps++; break;} // ran into FCAL
      if(z<zmin_track_boundary){Nswim_steps++; break;} // exit upstream
      if(wire && Nswim_steps>0){ // optionally check if we passed a wire we're supposed to be swimming to
         swim_step_t *closest_step = FindClosestSwimStep(wire);
         if(++closest_step!=swim_step){Nswim_steps++; break;}
      }

      old_radius_sq=Rsq;
   }

   // OK. At this point the positions of the trajectory in the lab
   // frame have been recorded along with the momentum of the
   // particle and the directions of reference trajectory
   // coordinate system at each point.
}

// Routine to find position on the trajectory where the track crosses a radial
// position R.  Also returns the path length to this position.
jerror_t DReferenceTrajectory::GetIntersectionWithRadius(double R,
                      DVector3 &mypos,
                      double *s,
                      double *t,
                      DVector3 *p_at_intersection) const{
  mypos.SetXYZ(QuietNaN,QuietNaN,QuietNaN);
  if(p_at_intersection)
    p_at_intersection->SetXYZ(QuietNaN,QuietNaN,QuietNaN);

  if(Nswim_steps<1){
    _DBG_<<"No swim steps! You must \"Swim\" the track before calling GetIntersectionWithRadius(...)"<<endl;
  }
  // Return early if the radius at the end of the reference trajectory is still less than R
  double outer_radius=swim_steps[Nswim_steps-1].origin.Perp();
  if (outer_radius<R){
    if (s) *s=0.;
    if (t) *t=0.;
    return VALUE_OUT_OF_RANGE;
  }
  // Return early if the radius at the beginning of the trajectory is outside
  // the radius to which we are trying to match
  double inner_radius=swim_steps[0].origin.Perp();
  if (inner_radius>R){
    if (s) *s=0.;
    if (t) *t=0.;
    return VALUE_OUT_OF_RANGE;
  }

  // Loop over swim steps and find the one that crosses the radius
  swim_step_t *swim_step = swim_steps;
  swim_step_t *step=NULL;
  swim_step_t *last_step=NULL;

  //  double inner_radius=swim_step->origin.Perp();
  for(int i=0; i<Nswim_steps; i++, swim_step++){
    if (swim_step->origin.Perp()>R){
      step=swim_step;
      break;
    }
    if (swim_step->origin.Z()>407.0) return VALUE_OUT_OF_RANGE;
    last_step=swim_step;
  }
  if (step==NULL||last_step==NULL) return VALUE_OUT_OF_RANGE;
  if (p_at_intersection!=NULL){
    *p_at_intersection=last_step->mom;
  }

  // At this point, the location where the track intersects the cyclinder 
  // is somewhere between last_step and step. For simplicity, we're going
  // to just find the intersection of the cylinder with the line that joins
  // the 2 positions. We do this by working in the X/Y plane only and
  // finding the value of "alpha" which is the fractional distance the
  // intersection point is between last_pos and mypos. We'll then apply
  // the alpha found in the 2D X/Y space to the 3D x/y/Z space to find
  // the actual intersection point.
  DVector2 x1(last_step->origin.X(), last_step->origin.Y());
  DVector2 x2(step->origin.X(), step->origin.Y());
  DVector2 dx = x2-x1;
  double A = dx.Mod2();
  double B = 2.0*(x1.X()*dx.X() + x1.Y()*dx.Y());
  double C = x1.Mod2() - R*R;

  double sqrt_D=sqrt(B*B-4.0*A*C);
  double one_over_denom=0.5/A;
  double alpha1 = (-B + sqrt_D)*one_over_denom;
  double alpha2 = (-B - sqrt_D)*one_over_denom;
  double alpha = alpha1;
  if(alpha1<0.0 || alpha1>1.0)alpha=alpha2;
  if(!isfinite(alpha))return VALUE_OUT_OF_RANGE;

  DVector3 delta = step->origin - last_step->origin;
  mypos = last_step->origin + alpha*delta;

  // The value of s actually represents the pathlength
  // to the outside point. Adjust it back to the
  // intersection point (approximately).
  if (s) *s = step->s-(1.0-alpha)*delta.Mag();

  // flight time
  if (t){   
    double p_sq=step->mom.Mag2();
    double one_over_beta=sqrt(1.+mass_sq/p_sq);
    *t = step->t-(1.0-alpha)*delta.Mag()*one_over_beta/SPEED_OF_LIGHT;
  }

  return NOERROR;
}

//---------------------------------
// GetIntersectionWithPlane
//---------------------------------
jerror_t DReferenceTrajectory::GetIntersectionWithPlane(const DVector3 &origin, const DVector3 &norm, DVector3 &pos, double *s,double *t,double *var_t,DetectorSystem_t detector) const{
  DVector3 dummy;
  return GetIntersectionWithPlane(origin,norm,pos,dummy,s,t,var_t,detector);
}
jerror_t DReferenceTrajectory::GetIntersectionWithPlane(const DVector3 &origin, const DVector3 &norm, DVector3 &pos, DVector3 &p_at_intersection, double *s,
                     double *t,double *var_t,DetectorSystem_t detector) const
{
   /// Get the intersection point of this trajectory with a plane.
   /// The plane is specified by <i>origin</i> and <i>norm</i>. The
   /// <i>origin</i> vector should give the coordinates of any point
   /// on the plane and <i>norm</i> should give a vector normal to
   /// the plane. The <i>norm</i> vector will be copied and normalized
   /// so it can be of any magnitude upon entry.
   ///
   /// The coordinates of the intersection point will copied into
   /// the supplied <i>pos</i> vector. If a non-NULL pointer for <i>s</i>
   /// is passed in, the pathlength of the trajectory from its begining
   /// to the intersection point is copied into location pointed to.
   
   // Set reasonable defaults
   pos.SetXYZ(0,0,0);
   if(s)*s=0.0;
   if(t)*t=0.0;
   p_at_intersection.SetXYZ(0,0,0);
   
   // Return early if the z-position of the plane with which we are 
   // intersecting is beyong the reference trajectory.
   if (origin.z()>swim_steps[Nswim_steps-1].origin.z()){
     return VALUE_OUT_OF_RANGE;
   }
   // Find the closest swim step to the position where the track crosses
   // the plane
   int first_i=0;
   switch(detector){
   case SYS_FCAL:
     if (index_at_fcal<0) return VALUE_OUT_OF_RANGE;
     first_i=index_at_fcal;
     break;
   case SYS_TOF:
     if (index_at_tof<0) return VALUE_OUT_OF_RANGE;
     first_i=index_at_tof;
     break;
   default: 
     break;
   }
   swim_step_t *step=FindPlaneCrossing(origin,norm,first_i,detector);
   if(!step){
      _DBG_<<"Could not find closest swim step!"<<endl;
      return RESOURCE_UNAVAILABLE;
   }

   // Here we follow a scheme described in more detail in the 
   // DistToRT(DVector3 hit) method below. The basic idea is to
   // express a point on the helix in terms of a single variable
   // and then solve for that variable by setting the distance 
   // to zero.
   //
   //   x = Ro*(cos(phi) - 1)
   //   y = Ro*sin(phi)
   //   z = phi*(dz/dphi)
   //
   // As is done below, we work in the RT coordinate system. Well,
   // sort of. The distance to the plane is given by:
   //
   //   d = ( x - c ).n
   //
   // where x is a point on the helix, c is the "origin" point
   // which lies somewhere in the plane and n is the "norm"
   // vector. Since we want a point in the plane, we set d=0
   // and solve for phi (with the components of x expressed in
   // terms of phi as given in the DistToRT method below).
   //
   // Thus, the equation we need to solve is:
   //
   // x.n - c.n = 0
   //
   // notice that "c" only gets dotted into "n" so that
   // dot product can occur in any coordinate system. Therefore,
   // we do that in the lab coordinate system to avoid the
   // overhead of transforming "c" to the RT system. The "n"
   // vector, however, still must be transformed.
   //
   // Expanding the trig functions to 2nd order in phi, performing
   // the x.n dot product, and gathering equal powers of phi
   // leads us to he following:
   //
   //  (-Ro*nx/2)*phi^2 + (Ro*ny+dz_dphi*nz)*phi - c.n = 0
   //
   // which is quadratic in phi. We solve for both roots, but use
   // the one with the smller absolute value (if both are finite).

   double &Ro = step->Ro;

   // OK, having said all of that, it turns out that the above 
   // mechanism will tend to fail in regions of low or no
   // field because the value of Ro is very large. Thus, we need to
   // use a straight line projection in such cases. We also
   // want to use a straight line projection if the helical intersection
   // fails for some other reason.
   //
   // The algorthim is then to only try the helical calculation
   // for small (<10m) values of Ro and then do the straight line
   // if R is larger than that OR the helical calculation fails.

   // Try helical calculation
   if(Ro<1000.0){
      double nx = norm.Dot(step->sdir);
      double ny = norm.Dot(step->tdir);
      double nz = norm.Dot(step->udir);
   
      double delta_z = step->mom.Dot(step->udir);
      double delta_phi = step->mom.Dot(step->tdir)/Ro;
      double dz_dphi = delta_z/delta_phi;
      
      double A = -Ro*nx/2.0;
      double B = Ro*ny + dz_dphi*nz;
      double C = norm.Dot(step->origin-origin);
      double sqroot=sqrt(B*B-4.0*A*C);
      double twoA=2.0*A;

      double phi_1 = (-B + sqroot)/(twoA);
      double phi_2 = (-B - sqroot)/(twoA);
      
      double phi = fabs(phi_1)<fabs(phi_2) ? phi_1:phi_2;
      if(!isfinite(phi_1))phi = phi_2;
      if(!isfinite(phi_2))phi = phi_1;
      if(isfinite(phi)){
      
         double my_s = -Ro/2.0 * phi*phi;
         double my_t = Ro * phi;
         double my_u = dz_dphi * phi;
         
         pos = step->origin + my_s*step->sdir + my_t*step->tdir + my_u*step->udir;
         p_at_intersection = step->mom;
         if(s){
            double delta_s = sqrt(my_t*my_t + my_u*my_u);
            *s = step->s + (phi>0 ? +delta_s:-delta_s);
         }    
         // flight time
         if (t){
           double delta_s = sqrt(my_t*my_t + my_u*my_u);
           double ds=(phi>0 ? +delta_s:-delta_s);
           double p_sq=step->mom.Mag2();
           double one_over_beta=sqrt(1.+mass_sq/p_sq);
           *t = step->t+ds*one_over_beta/SPEED_OF_LIGHT;
         }
         if (var_t){
           *var_t=step->cov_t_t;
         }
         
         // Success. Go ahead and return
         return NOERROR;
      }
   }
   
   // If we got here then we need to try a straight line calculation
   double p_sq=step->mom.Mag2();
   double dz_over_pz=(origin.z()-step->origin.z())/step->mom.z();
   double ds=sqrt(p_sq)*dz_over_pz;
   pos.SetXYZ(step->origin.x()+dz_over_pz*step->mom.x(),
         step->origin.y()+dz_over_pz*step->mom.y(),
         origin.z());
   p_at_intersection = step->mom;

   if(s){
      *s = step->s + ds;
   }
   // flight time
   if (t){
     double one_over_beta=sqrt(1.+mass_sq/p_sq);
     *t = step->t+ds*one_over_beta/SPEED_OF_LIGHT;
   }
   // Flight time variance
   if (var_t){
     *var_t=step->cov_t_t;
   }

   return NOERROR;
}

//---------------------------------
// InsertSteps
//---------------------------------
int DReferenceTrajectory::InsertSteps(const swim_step_t *start_step, double delta_s, double step_size)
{
   /// Insert additional steps into the reference trajectory starting
   /// at start_step and swimming for at least delta_s by step_size
   /// sized steps. Both delta_s and step_size are in centimeters.
   /// If the value of delta_s is negative then the particle's momentum
   /// and charge are reversed before swimming. This could be a problem
   /// if energy loss is implemented.
   
   if(!start_step)return -1;

   // We do this by creating another, temporary DReferenceTrajectory object
   // on the stack and swimming it.
   DVector3 pos = start_step->origin;
   DVector3 mom = start_step->mom;
   double my_q = q;
   int direction = +1;
   if(delta_s<0.0){
      mom *= -1.0;
      my_q = -q;
      direction = -1;
   }
   
   // Here I allocate the steps using an auto_ptr so I don't have to mess with
   // deleting them at all of the possible exits. The problem with auto_ptr
   // is it can't handle arrays so it has to be wrapped in a struct.
   auto_ptr<StepStruct> steps_aptr(new StepStruct);
   DReferenceTrajectory::swim_step_t *steps = steps_aptr->steps;
   DReferenceTrajectory rt(bfield , my_q , steps , 256);
   rt.SetStepSize(step_size);
   rt.Swim(pos, mom, my_q,NULL,fabs(delta_s));
   if(rt.Nswim_steps==0)return 1;

   // Check that there is enough space to add these points
   if((Nswim_steps+rt.Nswim_steps)>max_swim_steps){
      //_DBG_<<"Not enough swim steps available to add new ones! Max="<<max_swim_steps<<" had="<<Nswim_steps<<" new="<<rt.Nswim_steps<<endl;
      return 2;
   }
   
   // At this point, we may have swum forward or backwards so the points
   // will need to be added either before start_step or after it. We also
   // may want to replace an old step that overlaps our high density steps
   // since they are presumably more accurate. Find the indexes of the
   // existing steps that the new steps will be inserted between.
   double sdiff = rt.swim_steps[rt.Nswim_steps-1].s;
   double s1 = start_step->s;
   double s2 = start_step->s + (double)direction*sdiff;
   double smin = s1<s2 ? s1:s2;
   double smax = s1<s2 ? s2:s1;
   int istep_start = 0;
   int istep_end = 0;
   for(int i=0; i<Nswim_steps; i++){
      if(swim_steps[i].s <  smin)istep_start = i;
      if(swim_steps[i].s <= smax)istep_end = i+1;
   }
   
   // istep_start and istep_end now point to the steps we want to keep.
   // All steps between them (exclusive) will be overwritten. Note that 
   // the original start_step should be in the "overwrite" range since 
   // it is included already in the new trajectory.
   int steps_to_overwrite = istep_end - istep_start - 1;
   int steps_to_shift = rt.Nswim_steps - steps_to_overwrite;
   
   // Shift the steps down (or is it up?) starting with istep_end.
   for(int i=Nswim_steps-1; i>=istep_end; i--)swim_steps[i+steps_to_shift] = swim_steps[i];
   
   // Copy the new steps into this object
   double s_0 = start_step->s;
   double itheta02_0 = start_step->itheta02;
   double itheta02s_0 = start_step->itheta02s;
   double itheta02s2_0 = start_step->itheta02s2;
   for(int i=0; i<rt.Nswim_steps; i++){
      int index = direction>0 ? (istep_start+1+i):(istep_start+1+rt.Nswim_steps-1-i);
      swim_steps[index] = rt.swim_steps[i];
      swim_steps[index].s = s_0 + (double)direction*swim_steps[index].s;
      swim_steps[index].itheta02 = itheta02_0 + (double)direction*swim_steps[index].itheta02;
      swim_steps[index].itheta02s = itheta02s_0 + (double)direction*swim_steps[index].itheta02s;
      swim_steps[index].itheta02s2 = itheta02s2_0 + (double)direction*swim_steps[index].itheta02s2;
      if(direction<0.0){
         swim_steps[index].sdir *= -1.0;
         swim_steps[index].tdir *= -1.0;
      }
   }
   Nswim_steps += rt.Nswim_steps-steps_to_overwrite;

   // Note that the above procedure may leave us with "kinks" in the itheta0 
   // variables. It may be that we need to recalculate those for all of the 
   // new points and the ones after them by making one more pass. I'm hoping
   // it is a realitively small correction though so we can skip it here.
   return 0;
}

//---------------------------------
// DistToRTwithTime
//---------------------------------
double DReferenceTrajectory::DistToRTwithTime(DVector3 hit, double *s,double *t,
                     double *var_t,
                     DetectorSystem_t detector) const{
  double dist=DistToRT(hit,s,detector);
  if (s!=NULL && t!=NULL) 
  {
    if(last_swim_step==NULL)
    {
      *s = 1.0E6;
      *t = 1.0E6;
      if (var_t!=NULL){
   *var_t=1.0E6;
      }
    }
    else
    {
      double p_sq=last_swim_step->mom.Mag2();
      double one_over_beta=sqrt(1.+mass_sq/p_sq);
      *t=last_swim_step->t+(*s-last_swim_step->s)*one_over_beta/SPEED_OF_LIGHT;
      if (var_t!=NULL){
   *var_t=last_swim_step->cov_t_t;
      }
    }
  }
  return dist;
}

//---------------------------------
// DistToRT
//---------------------------------
double DReferenceTrajectory::DistToRT(DVector3 hit, double *s,
                  DetectorSystem_t detector) const
{
   last_swim_step=NULL;
   if(Nswim_steps<1)_DBG__;

   int start_index=0;
   switch(detector){
   case SYS_BCAL:
     if (index_at_bcal<0) return numeric_limits<double>::quiet_NaN();
     start_index=index_at_bcal;
     break; 
   case SYS_FCAL:
     if (index_at_fcal<0) return numeric_limits<double>::quiet_NaN();
     start_index=index_at_fcal;
     break;
   case SYS_TOF:
     if (index_at_tof<0) return numeric_limits<double>::quiet_NaN();
     start_index=index_at_tof;
     break;
   default:
     break;
   }

   // First, find closest step to point
   swim_step_t *swim_step = &swim_steps[start_index];
   swim_step_t *step=NULL;
   
   //double min_delta2 = 1.0E6;
   double old_delta2=10.e6,delta2=1.0e6;
   
   // Check if we should start at the end of the reference trajectory 
   // or the beginning...
   int last_index=Nswim_steps-1;
   double forward_delta2=(swim_step->origin - hit).Mag2();
   double backward_delta2=(swim_steps[last_index].origin-hit).Mag2();

   if (forward_delta2<backward_delta2){ // start at the beginning
     for(int i=start_index; i<Nswim_steps; i++, swim_step++){
       
       DVector3 pos_diff = swim_step->origin - hit;
       delta2 = pos_diff.Mag2();

       if (delta2>old_delta2){
         break;
       }
       
       //if(delta2 < min_delta2){
       //min_delta2 = delta2;
       
       step = swim_step;
       old_delta2=delta2;
       //}
     }
   }
   else{// start at the end
     for(int i=last_index; i>=start_index; i--){
       swim_step=&swim_steps[i];
       DVector3 pos_diff = swim_step->origin - hit;
       delta2 = pos_diff.Mag2();
       if (delta2>old_delta2) break;
       
       //if(delta2 < min_delta2){
       //min_delta2 = delta2;
       
       step = swim_step;
       old_delta2=delta2;
       //}
     }

   }

   if(step==NULL){
      // It seems to occasionally occur that we have 1 swim step
      // and it's values are invalid. Supress warning messages
      // for these as they are "known" (even if not fully understood!)
     if(s != NULL)
       *s = 1.0E6;
     if(Nswim_steps>1){
       _DBG_<<"\"hit\" passed to DistToRT(DVector3) out of range!"<<endl;
       _DBG_<<"hit x,y,z = "<<hit.x()<<", "<<hit.y()<<", "<<hit.z()<<"  Nswim_steps="<<Nswim_steps<<"  min_delta2="<<delta2<<endl;
     }
     return 1.0E6;
   }
   
   // store last step
   last_swim_step=step;

   
   // Next, define a point on the helical segment defined by the
   // swim step it the RT coordinate system. The directions of
   // the RT coordinate system are defined by step->xdir, step->ydir,
   // and step->zdir. The coordinates of a point on the helix
   // in this coordinate system are:
   //
   //   x = Ro*(cos(phi) - 1)
   //   y = Ro*sin(phi)
   //   z = phi*(dz/dphi)
   //
   // where phi is the phi angle of the point in this coordinate system.
   // phi=0 corresponds to the swim step point itself
   //
   // Transform the given coordinates to the RT coordinate system
   // and call these x0,y0,z0. Then, the distance of point to a
   // point on the helical segment is given by:
   //
   //   d^2 = (x0-x)^2 + (y0-y)^2 + (z0-z)^2
   //
   // where x,y,z are all functions of phi as given above.
   //
   // writing out d^2 in terms of phi, but using the small angle
   // approximation for the trig functions, an equation for the
   // distance in only phi is obtained. Taking the derivative 
   // and setting it equal to zero leaves a 3rd order polynomial
   // in phi whose root corresponds to the minimum distance.
   // Skipping some math, this equation has the form:
   //
   // d(d^2)/dphi = 0 = Ro^2*phi^3 + 2*alpha*phi + beta
   //
   // where:
   //       alpha = x0*Ro + Ro^2 + (dz/dphi)^2
   //
   //        beta = -2*y0*Ro - 2*z0*(dz/dphi)
   //
   // The above 3rd order poly is convenient in that it does not
   // contain a phi^2 term. This means we can skip the step
   // done in the general case where a change of variables is
   // made such that the 2nd order term disappears.
   //
   // In general, an equation of the form
   //
   //  w^3 + 3.0*b*w + 2*c = 0 
   //
   // has one real root:
   //
   //  w0 = q - p
   //
   // where:
   //    q^3 = d - c
   //    p^3 = d + c
   //    d^2 = b^3 + c^2      (don't confuse with d^2 above!)
   //
   // So for us ...
   //
   //    3b = 2*alpha/(Ro^2)
   //    2c = beta/(Ro^2)

   hit -= step->origin;
   double x0 = hit.Dot(step->sdir);
   double y0 = hit.Dot(step->tdir);
   double z0 = hit.Dot(step->udir);
   double &Ro = step->Ro;
   double Ro2 = Ro*Ro;
   double delta_z = step->mom.Dot(step->udir);
   double delta_phi = step->mom.Dot(step->tdir)/Ro;
   double dz_dphi = delta_z/delta_phi;
   
   //  double alpha = x0*Ro + Ro2 + pow(dz_dphi,2.0);
   double alpha=x0*Ro + Ro2 +dz_dphi*dz_dphi;
   //  double beta = -2.0*y0*Ro - 2.0*z0*dz_dphi;
   double beta = -2.0*(y0*Ro + z0*dz_dphi);
   //  double b = (2.0*alpha/Ro2)/3.0;
   double b= TWO_THIRD*alpha/Ro2;
   //  double c = (beta/Ro2)/2.0;
   double c = 0.5*(beta/Ro2);
   //  double d = sqrt(pow(b,3.0) + pow(c,2.0));
   double d2=b*b*b+c*c;
   double phi=0.,dist2=1e8;
   if (d2>=0){
     double d=sqrt(d2);
     //double q = pow(d-c, ONE_THIRD);
     //double p = pow(d+c, ONE_THIRD);
     double p=cbrt(d+c);
     double q=cbrt(d-c);
     phi = q - p;
     if (fabs(phi)<0.2){ // check small angle approximation
       double phisq=phi*phi;
     
       dist2 = 0.25*Ro2*phisq*phisq + alpha*phisq + beta*phi 
         + x0*x0 + y0*y0 + z0*z0;
     }
     else{
       return numeric_limits<double>::quiet_NaN();
     }
   }
   else{
     // Use DeMoivre's theorem to find the cube root of a complex
     // number.  In this case there are three real solutions.
     double d=sqrt(-d2);
     c*=-1.;
     double temp=sqrt(cbrt(c*c+d*d));
     double theta1=ONE_THIRD*atan2(d,c);
     double sum_over_2=temp*cos(theta1);
     double diff_over_2=-temp*sin(theta1);

     double phi0=2.*sum_over_2;
     double phi0sq=phi0*phi0;
     double phi1=-sum_over_2+sqrt(3)*diff_over_2;
     double phi1sq=phi1*phi1;
     double phi2=-sum_over_2-sqrt(3)*diff_over_2;
     double phi2sq=phi2*phi2;
     double d2_2 = 0.25*Ro2*phi2sq*phi2sq + alpha*phi2sq + beta*phi2 + x0*x0 + y0*y0 + z0*z0;
     double d2_1 = 0.25*Ro2*phi1sq*phi1sq + alpha*phi1sq + beta*phi1 + x0*x0 + y0*y0 + z0*z0; 
     double d2_0 = 0.25*Ro2*phi0sq*phi0sq + alpha*phi0sq + beta*phi0 + x0*x0 + y0*y0 + z0*z0;
 
     if (d2_0<d2_1 && d2_0<d2_2){
       phi=phi0;
       dist2=d2_0;
     }
     else if (d2_1<d2_0 && d2_1<d2_2){
       phi=phi1;
       dist2=d2_1;
     }
     else{
       phi=phi2;
       dist2=d2_2;
     }
     if (fabs(phi)<0.2){ // Check small angle approximation
       return numeric_limits<double>::quiet_NaN();
     }

   }
   
   // Calculate distance along track ("s")
   if(s!=NULL){
      double dz = dz_dphi*phi;
      double Rodphi = Ro*phi;
      double ds = sqrt(dz*dz + Rodphi*Rodphi);
      *s = step->s + (phi>0.0 ? ds:-ds);
   }

   this->last_phi = phi;
   this->last_swim_step = step;
   this->last_dz_dphi = dz_dphi;

   return sqrt(dist2);
}

//---------------------------------
// FindClosestSwimStep
//---------------------------------
DReferenceTrajectory::swim_step_t* DReferenceTrajectory::FindClosestSwimStep(const DCoordinateSystem *wire, int *istep_ptr) const
{
   /// Find the closest swim step to the given wire. The value of
   /// "L" should be the active wire length. The coordinate system
   /// defined by "wire" should have its origin at the center of
   /// the wire with the wire running in the direction of udir.
   
   if(istep_ptr)*istep_ptr=-1;
   
   if(Nswim_steps<1){
      _DBG_<<"No swim steps! You must \"Swim\" the track before calling FindClosestSwimStep(...)"<<endl;
   }

   // Make sure we have a wire first!
   if(!wire)return NULL;
   
   // Loop over swim steps and find the one closest to the wire
   swim_step_t *swim_step = swim_steps;
   swim_step_t *step=NULL;
   //double min_delta2 = 1.0E6;
   double old_delta2=1.0e6;
   double L_over_2 = wire->L/2.0; // half-length of wire in cm
   int istep=-1;

   double dx, dy, dz;
  
  // w is a vector to the origin of the wire
  // u is a unit vector along the wire
  
  double wx, wy, wz;
  double ux, uy, uz;
  
  wx = wire->origin.X();
  wy = wire->origin.Y();
  wz = wire->origin.Z();
  
  ux = wire->udir.X();
  uy = wire->udir.Y();
  uz = wire->udir.Z();
  
  int i;
  for(i=0; i<Nswim_steps; i++, swim_step++){
      // Find the point's position along the wire. If the point
      // is past the end of the wire, calculate the distance
      // from the end of the wire.
    //      DVector3 pos_diff = swim_step->origin - wire->origin;

    dx = swim_step->origin.X() - wx;
    dy = swim_step->origin.Y() - wy;
    dz = swim_step->origin.Z() - wz;
      
    //    double u = wire->udir.Dot(pos_diff);
    double u = ux * dx + uy * dy + uz * dz;

      // Find distance perpendicular to wire
    //      double delta2 = pos_diff.Mag2() - u*u;
    double delta2 = dx*dx + dy*dy + dz*dz - u*u;

      // If point is past end of wire, calculate distance
      // from wire's end by adding on distance along wire direction.
      if( fabs(u)>L_over_2){
      //       delta2 += pow(fabs(u)-L_over_2, 2.0);
        double u_minus_L_over_2=fabs(u)-L_over_2;
      delta2 += ( u_minus_L_over_2*u_minus_L_over_2 );
      // printf("step %d\n",i);
      }

      if(debug_level>3)_DBG_<<"delta2="<<delta2<<"  old_delta2="<<old_delta2<<endl;
      if (delta2>old_delta2) break;

      //if(delta2 < min_delta2){
      // min_delta2 = delta2;
      step = swim_step;
      istep=i;

      //}
      //printf("%d delta %f min %f\n",i,delta2,min_delta2);
      old_delta2=delta2;
   }

   if(istep_ptr)*istep_ptr=istep;
   
   if(debug_level>3)_DBG_<<"found closest step at i="<<i<<"  istep_ptr="<<istep_ptr<<endl;

   return step;   
}

//---------------------------------
// FindClosestSwimStep
//---------------------------------
DReferenceTrajectory::swim_step_t* DReferenceTrajectory::FindClosestSwimStep(const DVector3 &origin, DVector3 norm, int *istep_ptr) const
{
   /// Find the closest swim step to the plane specified by origin
   /// and norm. origin should indicate any point in the plane and
   /// norm a vector normal to the plane.
   if(istep_ptr)*istep_ptr=-1;
   
   if(Nswim_steps<1){
      _DBG_<<"No swim steps! You must \"Swim\" the track before calling FindClosestSwimStep(...)"<<endl;
   }

   // Make sure normal vector is unit lenght
   norm.SetMag(1.0);

   // Loop over swim steps and find the one closest to the plane
   swim_step_t *swim_step = swim_steps;
   swim_step_t *step=NULL;
   //double min_dist = 1.0E6;
   double old_dist=1.0e6;
   int istep=-1;

   for(int i=0; i<Nswim_steps; i++, swim_step++){
   
      // Distance to plane is dot product of normal vector with any
      // vector pointing from the current step to a point in the plane
      double dist = fabs(norm.Dot(swim_step->origin-origin));

      if (dist>old_dist) break;

      // Check if we're the closest step
      //if(dist < min_dist){
      //min_dist = dist;

      step = swim_step;
      istep=i;
         //}
      old_dist=dist;

      // We should probably have a break condition here so we don't
      // waste time looking all the way to the end of the track after
      // we've passed the plane.
   }

   if(istep_ptr)*istep_ptr=istep;

   return step;   
}


//---------------------------------
// FindPlaneCrossing
//---------------------------------
DReferenceTrajectory::swim_step_t* DReferenceTrajectory::FindPlaneCrossing(const DVector3 &origin, DVector3 norm,int first_i,DetectorSystem_t detector) const
{
  /// Find the closest swim step to the position where the track crosses
  /// the plane specified by origin
  /// and norm. origin should indicate any point in the plane and
  /// norm a vector normal to the plane.
   
   if(Nswim_steps<1){
      _DBG_<<"No swim steps! You must \"Swim\" the track before calling FindPlaneCrossing(...)"<<endl;
      raise(SIGSEGV);// force seg. fault
   }

   // Make sure normal vector is unit length
   norm.SetMag(1.0);

   // Loop over swim steps and find the one closest to the plane
   swim_step_t *swim_step = &swim_steps[first_i];
   swim_step_t *step=NULL;
   double old_dist=1.0e6;

   // Check if we should start from the beginning of the reference 
   // trajectory or the end
   int last_index=Nswim_steps-1;
   double forward_dist= norm.Dot(swim_step->origin-origin);
   if( forward_dist == 0.0 ) return swim_step;
   double backward_dist= norm.Dot(swim_steps[last_index].origin-origin);
   if( backward_dist ==0.0 ) return &swim_steps[last_index];
   if (detector==SYS_START || fabs(forward_dist)<fabs(backward_dist)){ // start at beginning
     for(int i=first_i; i<Nswim_steps; i++, swim_step++){
         
       // Distance to plane is dot product of normal vector with any
       // vector pointing from the current step to a point in the plane
       //double dist = fabs(norm.Dot(swim_step->origin-origin));
       double dist = norm.Dot(swim_step->origin-origin);
         
       // We've crossed the plane when the sign of dist changes
       if (dist*old_dist<0 && i>0) {
         if (fabs(dist)<fabs(old_dist)){
      step=swim_step;
         }
         break;
       }
       step = swim_step;
       old_dist=dist;
     }
   }
   else{ // start at end
     for(int i=last_index; i>=0; i--){
       swim_step=&swim_steps[i];
       double dist = norm.Dot(swim_step->origin-origin);
       // We've crossed the plane when the sign of dist changes
       if (dist*old_dist<0 && i<last_index) {
         if (fabs(dist)<fabs(old_dist)){
      step=swim_step;
         }
         break;
       }
       step = swim_step;
       old_dist=dist;
     }

   }

   return step;   
}




//---------------------------------
// DistToRT
//---------------------------------
double DReferenceTrajectory::DistToRT(const DCoordinateSystem *wire, double *s) const
{
   /// Find the closest distance to the given wire in cm. The value of
   /// "L" should be the active wire length (in cm). The coordinate system
   /// defined by "wire" should have its origin at the center of
   /// the wire with the wire running in the direction of udir.
   swim_step_t *step=FindClosestSwimStep(wire);

   return (step && step->s>0) ? DistToRT(wire, step, s):std::numeric_limits<double>::quiet_NaN();
}

//---------------------------------
// DistToRTBruteForce
//---------------------------------
double DReferenceTrajectory::DistToRTBruteForce(const DCoordinateSystem *wire, double *s) const
{
   /// Find the closest distance to the given wire in cm. The value of
   /// "L" should be the active wire length (in cm). The coordinate system
   /// defined by "wire" should have its origin at the center of
   /// the wire with the wire running in the direction of udir.
   swim_step_t *step=FindClosestSwimStep(wire);

   return step ? DistToRTBruteForce(wire, step, s):std::numeric_limits<double>::quiet_NaN();
}

//------------------
// DistToRT
//------------------
double DReferenceTrajectory::DistToRT(const DCoordinateSystem *wire, const swim_step_t *step, double *s) const
{
   /// Calculate the distance of the given wire(in the lab
   /// reference frame) to the Reference Trajectory which the
   /// given swim step belongs to. This uses the momentum directions
   /// and positions of the swim step
   /// to define a curve and calculate the distance of the hit
   /// from it. The swim step should be the closest one to the wire.
   /// IMPORTANT: This approximates the helix locally by a parabola.
   /// This means the swim step should be fairly close
   /// to the wire so that this approximation is valid. If the
   /// reference trajectory from which the swim step came is too
   /// sparse, the results will not be nearly as good.
   
   // Interestingly enough, this is one of the harder things to figure
   // out in the tracking code which is why the explanations may be
   // a bit long.

   // The general idea is to define the helix in a coordinate system
   // in which the wire runs along the z-axis. The distance to the
   // wire is then defined just in the X/Y plane of this coord. system.
   // The distance is expressed as a function of the phi angle in the
   // natural coordinate system of the helix. This way, phi=0 corresponds
   // to the swim step point itself and the DOCA point should be
   // at a small phi angle.
   //
   // The minimum distance between the helical segment and the wire
   // will be a function of sin(phi), cos(phi) and phi. Approximating
   // sin(phi) by phi and cos(phi) by (1-phi^2) leaves a 4th order
   // polynomial in phi. Taking the derivative leaves a 3rd order
   // polynomial whose root is the phi corresponding to the 
   // Distance Of Closest Approach(DOCA) point on the helix. Plugging
   // that value of phi back into the distance formula gives
   // us the minimum distance between the track and the wire.

   // First, we need to define the coordinate system in which the 
   // wire runs along the z-axis. This is actually done already
   // in the CDC package for each wire once, at program start.
   // The directions of the axes are defined in wire->sdir,
   // wire->tdir, and wire->udir.
   
   // Next, define a point on the helical segment defined by the
   // swim step it the RT coordinate system. The directions of
   // the RT coordinate system are defined by step->xdir, step->ydir,
   // and step->zdir. The coordinates of a point on the helix
   // in this coordinate system are:
   //
   //   x = Ro*(cos(phi) - 1)
   //   y = Ro*sin(phi)
   //   z = phi*(dz/dphi)
   //
   // where phi is the phi angle of the point in this coordinate system.
   
   // Now, a vector describing the helical point in the LAB coordinate
   // system is:
   //
   //  h = x*xdir + y*ydir + z*zdir + pos
   //
   // where h,xdir,ydir,zdir and pos are all 3-vectors.
   // xdir,ydir,zdir are unit vectors defining the directions
   // of the RT coord. system axes in the lab coord. system.
   // pos is a vector defining the position of the swim step
   // in the lab coord.system 
   
   // Now we just need to find the extent of "h" in the wire's
   // coordinate system (period . means dot product):
   //
   // s = (h-wpos).sdir
   // t = (h-wpos).tdir
   // u = (h-wpos).udir
   //
   // where wpos is the position of the center of the wire in
   // the lab coord. system and is given by wire->wpos.

   // At this point, the values of s,t, and u repesent a point
   // on the helix in the coord. system of the wire with the
   // wire in the "u" direction and positioned at the origin.
   // The distance(squared) from the wire to the point on the helix
   // is given by:
   //
   // d^2 = s^2 + t^2
   //
   // where s and t are both functions of phi.

   // So, we'll define the values of "s" and "t" above as:
   //
   //   s = A*x + B*y + C*z + D
   //   t = E*x + F*y + G*z + H
   //
   // where A,B,C,D,E,F,G, and H are constants defined below
   // and x,y,z are all functions of phi defined above.
   // (period . means dot product)
   //
   // A = sdir.xdir
   // B = sdir.ydir
   // C = sdir.zdir
   // D = sdir.(pos-wpos)
   //
   // E = tdir.xdir
   // F = tdir.ydir
   // G = tdir.zdir
   // H = tdir.(pos-wpos)
   const DVector3 &xdir = step->sdir;
   const DVector3 &ydir = step->tdir;
   const DVector3 &zdir = step->udir;
   const DVector3 &sdir = wire->sdir;
   const DVector3 &tdir = wire->tdir;
   const DVector3 &udir = wire->udir;
   DVector3 pos_diff = step->origin - wire->origin;
   
   double A = sdir.Dot(xdir);
   double B = sdir.Dot(ydir);
   double C = sdir.Dot(zdir);
   double D = sdir.Dot(pos_diff);

   double E = tdir.Dot(xdir);
   double F = tdir.Dot(ydir);
   double G = tdir.Dot(zdir);
   double H = tdir.Dot(pos_diff);

   // OK, here is the dirty part. Using the approximations given above
   // to write the x and y functions in terms of phi^2 and phi (instead
   // of cos and sin) we put them into the equations for s and t above.
   // Then, inserting those into the equation for d^2 above that, we
   // get a very long equation in terms of the constants A,...H and
   // phi up to 4th order. Combining coefficients for similar powers
   // of phi yields an equation of the form:
   //
   // d^2 = Q*phi^4 + R*phi^3 + S*phi^2 + T*phi + U
   //
   // The dirty part is that it takes the better part of a sheet of
   // paper to work out the relations for Q,...U in terms of
   // A,...H, and Ro, dz/dphi. You can work it out yourself on
   // paper to verify that the equations below are correct.
   double Ro = step->Ro;
   double Ro2 = Ro*Ro;
   double delta_z = step->mom.Dot(step->udir);
   double delta_phi = step->mom.Dot(step->tdir)/Ro;
   double dz_dphi = delta_z/delta_phi;
   double dz_dphi2=dz_dphi*dz_dphi;
   double Ro_dz_dphi=Ro*dz_dphi;

   // double Q = pow(A*Ro/2.0, 2.0) + pow(E*Ro/2.0, 2.0);
   double Q=0.25*Ro2*(A*A+E*E);
   // double R = -(2.0*A*B*Ro2 + 2.0*A*C*Ro_dz_dphi + 2.0*E*F*Ro2 + 2.0*E*G*Ro_dz_dphi)/2.0;
   double R = -((A*B+E*F)*Ro2 + (A*C+E*G)*Ro_dz_dphi);
   // double S = pow(B*Ro, 2.0) + pow(C*dz_dphi,2.0) + 2.0*B*C*Ro_dz_dphi - 2.0*A*D*Ro/2.0
   //+ pow(F*Ro, 2.0) + pow(G*dz_dphi,2.0) + 2.0*F*G*Ro_dz_dphi - 2.0*E*H*Ro/2.0;
   double S= (B*B+F*F)*Ro2+(C*C+G*G)*dz_dphi2+2.0*(B*C+F*G)*Ro_dz_dphi
     -(A*D+E*H)*Ro;
   // double T = 2.0*B*D*Ro + 2.0*C*D*dz_dphi + 2.0*F*H*Ro + 2.0*G*H*dz_dphi; 
   double T = 2.0*((B*D+F*H)*Ro + (C*D+G*H)*dz_dphi);
   double U = D*D + H*H;
   
   // Aaarghh! my fingers hurt just from typing all of that!
   //
   // OK, now we differentiate the above equation for d^2 to get:
   //
   // d(d^2)/dphi = 4*Q*phi^3 + 3*R*phi^2 + 2*S*phi + T
   //
   // NOTE: don't confuse "R" with "Ro" in the above equations!
   //
   // Now we have to solve the 3rd order polynomial for the phi value of
   // the point of closest approach on the RT. This is a well documented
   // procedure. Essentially, when you have an equation of the form:
   //
   //  x^3 + a2*x^2 + a1*x + a0 = 0;
   //
   // a change of variables is made such that w = x + a2/3 which leads
   // to a third order poly with no w^2 term:
   //
   //  w^3 + 3.0*b*w + 2*c = 0 
   //
   // where:
   //    b = a1/3 - (a2^2)/9
   //    c = a0/2 - a1*a2/6  + (a2^3)/27
   //
   // The one real root of this is:
   //
   //  w0 = q - p
   //
   // where:
   //    q^3 = d - c
   //    p^3 = d + c
   //    d^2 = b^3 + c^2      (don't confuse with d^2 above!)
   //
   // For us this means that:
   //    a2 = 3*R/(4*Q)
   //    a1 = 2*S/(4*Q)
   //    a0 =   T/(4*Q)
   //
   // A potential problem could occur if Q is at or very close to zero.
   // This situation occurs when both A and E are zero. This would mean
   // that both sdir and tdir are perpendicular to xdir which means
   // xdir is in the same direction as udir (got that?). Physically,
   // this corresponds to the situation when both the momentum and
   // the magnetic field are perpendicular to the wire (though not
   // necessarily perpendicular to each other). This situation can't
   // really occur in the CDC detector where the chambers are well
   // contained in a region where the field is essentially along z as
   // are the wires.
   //
   // Just to be safe, we check that Q is greater than
   // some minimum before solving for phi. If it is too small, we fall
   // back to solving the quadratic equation for phi.
   double phi =0.0;
   if(fabs(Q)>1.0E-6){
     /*
      double fourQ = 4.0*Q;
      double a2 = 3.0*R/fourQ;
      double a1 = 2.0*S/fourQ;
      double a0 =     T/fourQ;
     */
     double one_over_fourQ=0.25/Q;
     double a2=3.0*R*one_over_fourQ;
     double a1=2.0*S*one_over_fourQ;
     double a0=T*one_over_fourQ;
     double a2sq=a2*a2;
     /*
      double b = a1/3.0 - a2*a2/9.0;
      double c = a0/2.0 - a1*a2/6.0 + a2*a2*a2/27.0;
     */
     double b=ONE_THIRD*(a1-ONE_THIRD*a2sq);
     double c=0.5*(a0-ONE_THIRD*a1*a2)+a2*a2sq/27.0;
     double my_d2=b*b*b+c*c;
     if (my_d2>0){
       //double d = sqrt(pow(b, 3.0) + pow(c, 2.0)); // occasionally, this is zero. See below
       double d=sqrt(my_d2);
       //double q = pow(d - c, ONE_THIRD);
       //double p = pow(d + c, ONE_THIRD);
       double q=cbrt(d-c);
       double p=cbrt(d+c);
       
       double w0 = q - p;
       //phi = w0 - a2/3.0;
       phi = w0 - ONE_THIRD*a2;
     }
     else{
       // Use DeMoivre's theorem to find the cube root of a complex
       // number.  In this case there are three real solutions.
       double d=sqrt(-my_d2);
       c*=-1.;
       double temp=sqrt(cbrt(c*c+d*d));
       double theta1=ONE_THIRD*atan2(d,c);
       double sum_over_2=temp*cos(theta1);
       double diff_over_2=-temp*sin(theta1);

       double phi0=-a2/3+2.*sum_over_2;
       double phi1=-a2/3-sum_over_2+sqrt(3)*diff_over_2;
       double phi2=-a2/3-sum_over_2-sqrt(3)*diff_over_2;

       double d2_0 = U + phi0*(T + phi0*(S + phi0*(R + phi0*Q)));
       double d2_1 = U + phi1*(T + phi1*(S + phi1*(R + phi1*Q)));
       double d2_2 = U + phi2*(T + phi2*(S + phi2*(R + phi2*Q)));

       if (d2_0<d2_1 && d2_0<d2_2){
         phi=phi0;
       }
       else if (d2_1<d2_0 && d2_1<d2_2){
         phi=phi1;
       }
       else{
         phi=phi2;
       }
     }
   }
   
   if(fabs(Q)<=1.0E-6 || !isfinite(phi)){
      double a = 3.0*R;
      double b = 2.0*S;
      double c = 1.0*T;
      phi = (-b + sqrt(b*b - 4.0*a*c))/(2.0*a); 
   }
   
   // The accuracy of this method is limited by how close the step is to the
   // actual minimum. If the value of phi is large then the step size is
   // not too close and we should add another couple of steps in the right
   // place in order to get a more accurate value. Note that while this will
   // increase the time it takes this round, presumably the fitter will be
   // calling this often for each wire and having a high density of points
   // near the wires will just make subsequent calls go quicker. This also
   // allows larger initial step sizes with the high density regions getting
   // filled in as needed leading to overall faster tracking.
#if 0
   if(isfinite(phi) && fabs(phi)>2.0E-4){
      if(dist_to_rt_depth>=3){
         _DBG_<<"3 or more recursive calls to DistToRT(). Something is wrong! bailing ..."<<endl;
         //for(int k=0; k<Nswim_steps; k++){
         // DVector3 &v = swim_steps[k].origin;
         // _DBG_<<"  "<<k<<": "<<v.X()<<", "<<v.Y()<<", "<<v.Z()<<endl;
         //}
         //exit(-1);
         return std::numeric_limits<double>::quiet_NaN();
      }
      double scale_step = 1.0;
      double s_range = 1.0*scale_step;
      double step_size = 0.02*scale_step;
      int err = InsertSteps(step, phi>0.0 ? +s_range:-s_range, step_size);       // Add new steps near this step by swimming in the direction of phi
      if(!err){
         step=FindClosestSwimStep(wire);                          // Find the new closest step
         if(!step)return std::numeric_limits<double>::quiet_NaN();
         dist_to_rt_depth++;
         double doca = DistToRT(wire, step, s);                      // re-call ourself with the new step
         dist_to_rt_depth--;
         return doca;
      }else{
         if(err<0)return std::numeric_limits<double>::quiet_NaN();
         
         // If InsertSteps() returns an error > 0 then it indicates that it
         // was unable to add additional steps (perhaps because there
         // aren't enough spaces available). In that case, we just go ahead
         // and use the phi we have and make the best estimate possible.
      }
   }
#endif
   
   // It is possible at this point that the value of phi corresponds to
   // a point past the end of the wire. We should check for this here and
   // recalculate, if necessary, the DOCA at the end of the wire. First,
   // calculate h (the vector defined way up above) and dot it into the
   // wire's u-direction to get the position of the DOCA point along the
   // wire.
   double x = -0.5*Ro*phi*phi;
   double y = Ro*phi;
   double z = dz_dphi*phi;
   DVector3 h = pos_diff + x*xdir + y*ydir + z*zdir;
   double u = h.Dot(udir);
   if(fabs(u) > wire->L/2.0){
      // Looks like our DOCA point is past the end of the wire.
      // Find phi corresponding to the end of the wire.
      double L_over_2 = u>0.0 ? wire->L/2.0:-wire->L/2.0;
      double a = -0.5*Ro*udir.Dot(xdir);
      double b = Ro*udir.Dot(ydir) + dz_dphi*udir.Dot(zdir);
      double c = udir.Dot(pos_diff) - L_over_2;
      double twoa=2.0*a;
      double sqroot=sqrt(b*b-4.0*a*c);
      double phi1 = (-b + sqroot)/(twoa); 
      double phi2 = (-b - sqroot)/(twoa);
      phi = fabs(phi1)<fabs(phi2) ? phi1:phi2;
      u=L_over_2;
   }
   this->last_dist_along_wire = u;

   // Use phi to calculate DOCA
   double d2 = U + phi*(T + phi*(S + phi*(R + phi*Q)));
   double d = sqrt(d2);

   // Calculate distance along track ("s")
   double dz = dz_dphi*phi;
   double Rodphi = Ro*phi;
   double ds = sqrt(dz*dz + Rodphi*Rodphi);
   if(s)*s=step->s + (phi>0.0 ? ds:-ds);
   if(debug_level>3){
     _DBG_<<"distance to rt: "<< step->s + (phi>0.0 ? ds:-ds) <<" from step at "<<step->s<<" with ds="<<ds<<" d="<<d<<" dz="<<dz<<" Rodphi="<<Rodphi<<endl;
      _DBG_<<"phi="<<phi<<" U="<<U<<" u="<<u<<endl;
   }

   // Remember phi and step so additional info on the point can be obtained
   this->last_phi = phi;
   this->last_swim_step = step;
   this->last_dz_dphi = dz_dphi;

   return d; // WARNING: This could return nan!
}

//------------------
// DistToRTBruteForce
//------------------
double DReferenceTrajectory::DistToRTBruteForce(const DCoordinateSystem *wire, const swim_step_t *step, double *s) const
{
   /// Calculate the distance of the given wire(in the lab
   /// reference frame) to the Reference Trajectory which the
   /// given swim step belongs to. This uses the momentum directions
   /// and positions of the swim step
   /// to define a curve and calculate the distance of the hit
   /// from it. The swim step should be the closest one to the wire.
   /// IMPORTANT: This calculates the distance using a "brute force"
   /// method of taking tiny swim steps to find the minimum distance.
   /// It is vey SLOW and you should be using DistToRT(...) instead.
   /// This is only here to provide an independent check of DistToRT(...).
   
   const DVector3 &xdir = step->sdir;
   const DVector3 &ydir = step->tdir;
   const DVector3 &zdir = step->udir;
   const DVector3 &sdir = wire->sdir;
   const DVector3 &tdir = wire->tdir;
   DVector3 pos_diff = step->origin - wire->origin;
   
   double Ro = step->Ro;
   double delta_z = step->mom.Dot(step->udir);
   double delta_phi = step->mom.Dot(step->tdir)/Ro;
   double dz_dphi = delta_z/delta_phi;

   // Brute force
   double min_d2 = 1.0E6;
   double phi=M_PI;
   for(int i=-2000; i<2000; i++){
      double myphi=(double)i*0.000005;
      DVector3 d = Ro*(cos(myphi)-1.0)*xdir
                  + Ro*sin(myphi)*ydir
                  + dz_dphi*myphi*zdir
                  + pos_diff;

      double d2 = pow(d.Dot(sdir),2.0) + pow(d.Dot(tdir),2.0);
      if(d2<min_d2){
         min_d2 = d2;
         phi = myphi;
         this->last_phi = myphi;
      }
   }
   double d2 = min_d2;
   double d = sqrt(d2);
   this->last_phi = phi;
   this->last_swim_step = step;
   this->last_dz_dphi = dz_dphi;
   
   // Calculate distance along track ("s")
   double dz = dz_dphi*phi;
   double Rodphi = Ro*phi;
   double ds = sqrt(dz*dz + Rodphi*Rodphi);
   if(s)*s=step->s + (phi>0.0 ? ds:-ds);

   return d;
}

//------------------
// Straw_dx
//------------------
double DReferenceTrajectory::Straw_dx(const DCoordinateSystem *wire, double radius) const
{
   /// Find the distance traveled within the specified radius of the
   /// specified wire. This will give the "dx" component of a dE/dx
   /// measurement for cylindrical geometry as we have with straw tubes.
   ///
   /// At this point, the estimate is done using a simple linear 
   /// extrapolation from the DOCA point in the direction of the momentum
   /// to the 2 points at which it itersects the given radius. Segments
   /// which extend past the end of the wire will be clipped to the end
   /// of the wire before calculating the total dx.
   
   // First, find the DOCA point for this wire
   double s;
   double doca = DistToRT(wire, &s);
   if(!isfinite(doca))
      return 0.0;

   // If doca is outside of the given radius, then we're done
   if(doca>=radius)return 0.0;
   
   // Get the location and momentum direction of the DOCA point
   DVector3 pos, momdir;
   GetLastDOCAPoint(pos, momdir);
   if(momdir.Mag()!=0.0)momdir.SetMag(1.0);
   
   // Get wire direction
   const DVector3 &udir = wire->udir;
   
   // Calculate vectors used to form quadratic equation for "alpha"
   // the distance along the mometum direction from the DOCA point
   // to the intersection with a cylinder of the given radius.
   DVector3 A = udir.Cross(pos-wire->origin);
   DVector3 B = udir.Cross(momdir);
   
   // If the magnitude of B is zero at this point, it means the momentum
   // direction is parallel to the wire. In this case, this method will
   // not work. Return NaN.
   if(B.Mag()<1.0E-10)return std::numeric_limits<double>::quiet_NaN();
   
   double a = B.Mag();
   double b = A.Dot(B);
   double c = A.Mag() - radius;
   double d = sqrt(b*b - 4.0*a*c);
   
   // The 2 roots should correspond to the 2 intersection points.
   double alpha1 = (-b + d)/(2.0*a);
   double alpha2 = (-b - d)/(2.0*a);
   
   DVector3 int1 = pos + alpha1*momdir;
   DVector3 int2 = pos + alpha2*momdir;
   
   // Check if point1 is past the end of the wire
   double q = udir.Dot(int1 - wire->origin);
   if(fabs(q) > wire->L/2.0){
      double gamma = udir.Dot(wire->origin - pos) + (q>0.0 ? +1.0:-1.0)*wire->L/2.0;
      gamma /= momdir.Dot(udir);
      int1 = pos + gamma*momdir;
   }

   // Check if point2 is past the end of the wire
   q = udir.Dot(int2 - wire->origin);
   if(fabs(q) > wire->L/2.0){
      double gamma = udir.Dot(wire->origin - pos) + (q>0.0 ? +1.0:-1.0)*wire->L/2.0;
      gamma /= momdir.Dot(udir);
      int2 = pos + gamma*momdir;
   }
   
   // Calculate distance
   DVector3 delta = int1 - int2;
   
   return delta.Mag();
}

//------------------
// GetLastDOCAPoint
//------------------
void DReferenceTrajectory::GetLastDOCAPoint(DVector3 &pos, DVector3 &mom) const
{
   /// Use values saved by the last call to one of the DistToRT functions
   /// to calculate the 3-D DOCA position in lab coordinates and momentum
   /// in GeV/c.
   
   if(last_swim_step==NULL){
      if(Nswim_steps>0){
         last_swim_step = &swim_steps[0];
         last_phi = 0.0;
      }else{
         pos.SetXYZ(QuietNaN,QuietNaN,QuietNaN);
         mom.SetXYZ(QuietNaN,QuietNaN,QuietNaN);
         return;
      }
   }

   // If last_phi is not finite, set it to 0 as a last resort
   if(!isfinite(last_phi))last_phi = 0.0;
   
   const DVector3 &xdir = last_swim_step->sdir;
   const DVector3 &ydir = last_swim_step->tdir;
   const DVector3 &zdir = last_swim_step->udir;

   double x = -(last_swim_step->Ro/2.0)*last_phi*last_phi;
   double y = last_swim_step->Ro*last_phi;
   double z = last_dz_dphi*last_phi;

   pos = last_swim_step->origin + x*xdir + y*ydir + z*zdir;
   mom = last_swim_step->mom;

   mom.Rotate(-last_phi, zdir);
}

//------------------
// GetLastDOCAPoint
//------------------
DVector3 DReferenceTrajectory::GetLastDOCAPoint(void) const
{
   /// Use values saved by the last call to one of the DistToRT functions
   /// to calculate the 3-D DOCA position in lab coordinates. This is
   /// mainly intended for debugging.
   if(last_swim_step==NULL){
      if(Nswim_steps>0){
         last_swim_step = &swim_steps[0];
         last_phi = 0.0;
      }else{
         return DVector3(QuietNaN,QuietNaN,QuietNaN);
      }
   }
   const DVector3 &xdir = last_swim_step->sdir;
   const DVector3 &ydir = last_swim_step->tdir;
   const DVector3 &zdir = last_swim_step->udir;
   double Ro = last_swim_step->Ro;
   double delta_z = last_swim_step->mom.Dot(zdir);
   double delta_phi = last_swim_step->mom.Dot(ydir)/Ro;
   double dz_dphi = delta_z/delta_phi;

   double x = -(Ro/2.0)*last_phi*last_phi;
   double y = Ro*last_phi;
   double z = dz_dphi*last_phi;

   return last_swim_step->origin + x*xdir + y*ydir + z*zdir;
}

//------------------
// dPdx
//------------------
double DReferenceTrajectory::dPdx_from_A_Z_rho(double ptot, double A, double Z, double density) const
{
   double I = (Z*12.0 + 7.0)*1.0E-9; // From Leo 2nd ed. pg 25.
   if (Z>=13) I=(9.76*Z+58.8*pow(Z,-0.19))*1.0e-9;
   double rhoZ_overA=density*Z/A;
   double KrhoZ_overA = 0.1535e-3*rhoZ_overA;

   return dPdx(ptot, KrhoZ_overA,rhoZ_overA,log(I));
}

//------------------
// dPdx
//------------------
double DReferenceTrajectory::dPdx(double ptot, double KrhoZ_overA, 
              double rhoZ_overA,double LogI) const
{
   /// Calculate the momentum loss per unit distance traversed of the material with
   /// the given A, Z, and density. Value returned is in GeV/c per cm
   /// This follows the July 2008 PDG section 27.2 ppg 268-270.
   if(mass==0.0)return 0.0; // no ionization losses for neutrals
   
   double gammabeta = ptot/mass;
   double gammabeta2=gammabeta*gammabeta;
   double gamma = sqrt(gammabeta2+1.);
   double beta = gammabeta/gamma;
   double beta2=beta*beta;
   double me = 0.511E-3;
   double m_ratio=me/mass;
   double two_me_gammabeta2=2.*me*gammabeta2;

   double Tmax = two_me_gammabeta2/(1.0+2.0*gamma*m_ratio+m_ratio*m_ratio);
   //double K = 0.307075E-3; // GeV gm^-1 cm^2
   // Density effect
   double delta=0.;  
   double X=log10(gammabeta);
   double X0,X1;
   double Cbar=2.*(LogI-log(28.816e-9*sqrt(rhoZ_overA)))+1.;
   if (rhoZ_overA>0.01){ // not a gas
     if (LogI<-1.6118){ // I<100
       if (Cbar<=3.681) X0=0.2;
       else X0=0.326*Cbar-1.;
       X1=2.;
     }
     else{
       if (Cbar<=5.215) X0=0.2;
       else X0=0.326*Cbar-1.5;
       X1=3.;
     }
   }
   else { // gases
     X1=4.;
     if (Cbar<=9.5) X0=1.6;
     else if (Cbar>9.5 && Cbar<=10.) X0=1.7;
     else if (Cbar>10 && Cbar<=10.5) X0=1.8;    
     else if (Cbar>10.5 && Cbar<=11.) X0=1.9;
     else if (Cbar>11.0 && Cbar<=12.25) X0=2.;
     else if (Cbar>12.25 && Cbar<=13.804){
       X0=2.;
       X1=5.;
     }
     else {
       X0=0.326*Cbar-2.5;
       X1=5.;
     } 
   }
   if (X>=X0 && X<X1)
     delta=4.606*X-Cbar+(Cbar-4.606*X0)*pow((X1-X)/(X1-X0),3.);
   else if (X>=X1)
     delta= 4.606*X-Cbar;     

   double dEdx = KrhoZ_overA/beta2*(log(two_me_gammabeta2*Tmax) 
                -2.*LogI - 2.0*beta2 -delta);

   double dP_dx = dEdx/beta;

   //double g = 0.350/sqrt(-log(0.06));
   //dP_dx *= 1.0 + exp(-pow(ptot/g,2.0)); // empirical for really low momentum particles

   
   if(ploss_direction==kBackward)dP_dx = -dP_dx;

   return dP_dx;
}

//------------------
// Dump
//------------------
void DReferenceTrajectory::Dump(double zmin, double zmax)
{  
   swim_step_t *step = swim_steps;
   for(int i=0; i<Nswim_steps; i++, step++){
      vector<pair<string,string> > item;
      double x = step->origin.X();
      double y = step->origin.Y();
      double z = step->origin.Z();
      if(z<zmin || z>zmax)continue;

      double px = step->mom.X();
      double py = step->mom.Y();
      double pz = step->mom.Z();
      
      cout<<i<<": ";
      cout<<"(x,y,z)=("<<x<<","<<y<<","<<z<<") ";
      cout<<"(px,py,pz)=("<<px<<","<<py<<","<<pz<<") ";
      cout<<"(Ro,s,t)=("<<step->Ro<<","<<step->s<<","<<step->t<<") ";
      cout<<endl;
   }
   
}

// Propagate the covariance matrix for {px,py,pz,x,y,z,t} along the step ds
jerror_t DReferenceTrajectory::PropagateCovariance(double ds,double q,
                     double mass_sq,
                     const DVector3 &mom,
                     const DVector3 &pos,
                     const DVector3 &B,
                     TMatrixFSym &C) const{
  DMatrix J(7,7);

  double one_over_p_sq=1./mom.Mag2();
  double one_over_p=sqrt(one_over_p_sq);
  double px=mom.X();
  double py=mom.Y();
  double pz=mom.Z();
  double Bx=B.x(),By=B.y(),Bz=B.z();

  double ds_over_p=ds*one_over_p;
  double factor=0.003*q*ds_over_p;
  double temp=(Bz*py-Bx*pz)*one_over_p_sq;
  J(0,0)=1-factor*px*temp;
  J(0,1)=factor*(Bz-py*temp);
  J(0,2)=-factor*(By+pz*temp);

  temp=(Bx*pz-Bz*px)*one_over_p_sq;
  J(1,0)=-factor*(Bz+px*temp);
  J(1,1)=1-factor*py*temp;
  J(1,2)=factor*(Bx-pz*temp);

  temp=(By*px-Bx*py)*one_over_p_sq;
  J(2,0)=factor*(By-px*temp);
  J(2,1)=-factor*(Bx+py*temp);
  J(2,2)=1-factor*pz*temp;

  J(3,3)=1.;
  double ds_over_p3=one_over_p_sq*ds_over_p;
  J(3,0)=ds_over_p*(1-px*px*one_over_p_sq);
  J(3,1)=-px*py*ds_over_p3;
  J(3,2)=-px*pz*ds_over_p3;

  J(4,4)=1.;
  J(4,0)=J(3,1);
  J(4,1)=ds_over_p*(1-py*py*one_over_p_sq);
  J(4,2)=-py*pz*ds_over_p3;

  J(5,5)=1.;
  J(5,0)=J(3,2);
  J(5,1)=J(4,2);
  J(5,2)=ds_over_p*(1-pz*pz*one_over_p_sq);
  
  J(6,6)=1.;
  
  double fac2=(-ds/SPEED_OF_LIGHT)*mass_sq*one_over_p_sq*one_over_p_sq
    /sqrt(1.+mass_sq*one_over_p_sq);
  J(6,0)=fac2*px;
  J(6,1)=fac2*py;
  J(6,2)=fac2*pz;
 
  C=C.Similarity(J);

  return NOERROR;
}

// Find the position along a reference trajectory closest to a line.
// The error matrix for the line can also be input via a pointer.  The error
// matrix is expected to be 7x7 with the order {Px,Py,Pz,X,Y,Z,T}.
// Outputs the kinematic data object (including the covariance) at this 
// position, and the doca and the variance on the doca.
jerror_t DReferenceTrajectory::FindPOCAtoLine(const DVector3 &origin,
                     const DVector3 &dir,
                     const DMatrixDSym *covline, 
                     DKinematicData *track_kd,
                     DVector3 &commonpos, double &doca, double &var_doca) const{ 
  const swim_step_t *swim_step=this->swim_steps;

  shared_ptr<TMatrixFSym> cov = (track_kd!=NULL) ? dResourcePool_TMatrixFSym->Get_SharedResource() : nullptr;
  if(track_kd!=NULL)
  {
     cov->ResizeTo(7, 7);
     *cov = *(track_kd->errorMatrix());
  }
  doca=1000.;
  double tflight=0.;
  double mass_sq=this->mass_sq;
  double q=this->q;
  double step_size=1.0,s=-step_size;
  DVector3 oldpos,oldmom;
  DVector3 point=origin;

  // Find the magnitude of the direction vector
  double pscale=dir.Mag();
  // If the magnitude of the direction vector is zero, don't bother to propagate
  // along a line from the input origin...
  bool move_along_line=(pscale>0)?true:false;

  // Propagate along the reference trajectory, comparing to the line at each
  // step
  for (int i=0;i<this->Nswim_steps-1; i++, swim_step++){
    DVector3 pos=swim_step->origin;     
    DVector3 diff=pos-point;
    double new_doca=diff.Mag();
    if (new_doca>doca){
      if (i==1){  // backtrack to find the true doca
   tflight=0.;
   
   swim_step=this->swim_steps;
   if(track_kd!=NULL)
      *cov=*track_kd->errorMatrix();
   
   pos=swim_step->origin;
   DVector3 mom=swim_step->mom;
   DMagneticFieldStepper stepper(this->bfield, this->q, &pos, &mom);

   int inew=0;
   while (inew<100){
     DVector3 B;
     double ds=stepper.Step(&pos,&B,-0.5);
     // Compute the revised estimate for the doca
     diff=pos-point;
     new_doca=diff.Mag();
     
     if(new_doca > doca) break;  

     // Propagate the covariance matrix of the track along the trajectory
     if(track_kd!=NULL){
       this->PropagateCovariance(ds,q,mass_sq,mom,oldpos,B,*cov);
     }
     
     // Store the current positions, doca and adjust flight times
     oldpos=pos;
     doca=new_doca;
     
     double one_over_p_sq=1./mom.Mag2();
     tflight+=ds*sqrt(1.+mass_sq*one_over_p_sq)/SPEED_OF_LIGHT;
     
     // New momentum
     stepper.GetMomentum(mom);

     oldmom=/*(-1.)*/mom;
     inew++;

     // New point on line
     if (move_along_line){
       point-=(step_size/pscale)*dir;
       s-=step_size;
     }
   }
      }
      if(track_kd!=NULL)
      {
        track_kd->setErrorMatrix(cov);
        track_kd->setMomentum(oldmom);
        track_kd->setPosition(oldpos);
        track_kd->setTime(track_kd->time() + tflight);
      }
      
      // Compute the variance on the doca
      diff=oldpos-point;
      double dx=diff.x();
      double dy=diff.y();
      double dz=diff.z();
      
      if(track_kd==NULL)
        break;
      //calculate var_doca
      if (covline==NULL){
   var_doca=(dx*dx*((*cov)(kX,kX))+dy*dy*((*cov)(kY,kY))
        +dz*dz*((*cov)(kZ,kZ))+2.*dx*dy*((*cov)(kX,kY))
        +2.*dx*dz*((*cov)(kX,kZ))+2.*dy*dz*((*cov)(kY,kZ)))
     /(doca*doca);
      }
      else{
   DMatrixDSym cov2(*covline);
   if (move_along_line){
     double two_s=2.*s;
     double s_sq=s*s;
     cov2(kX,kX)+=two_s*cov2(kPx,kX)+s_sq*cov2(kPx,kPx); 
     cov2(kY,kY)+=two_s*cov2(kPy,kY)+s_sq*cov2(kPy,kPy);
     cov2(kZ,kZ)+=two_s*cov2(kPz,kZ)+s_sq*cov2(kPz,kPz);
   }
   var_doca=(dx*dx*((*cov)(kX,kX)+cov2(kX,kX))
        +dy*dy*((*cov)(kY,kY)+cov2(kY,kY))
        +dz*dz*((*cov)(kZ,kZ)+cov2(kZ,kZ))
        +2.*dx*dy*((*cov)(kX,kY)+cov2(kX,kY))
        +2.*dx*dz*((*cov)(kX,kZ)+cov2(kX,kZ))
        +2.*dy*dz*((*cov)(kY,kZ)+cov2(kY,kZ)))
     /(doca*doca);
      }
      break;
    }
    // New point on line
    if (move_along_line){
      point+=(step_size/pscale)*dir;
      s+=step_size;
    }

    // Propagate the covariance matrix of the track along the trajectory
    if(track_kd!=NULL)
      this->PropagateCovariance(this->swim_steps[i+1].s-swim_step->s,q,mass_sq,swim_step->mom,swim_step->origin,swim_step->B,*cov);

    // Store the current position and doca
    oldpos=pos;
    oldmom=swim_step->mom;
    tflight=swim_step->t;
    doca=new_doca;
  }

   // "Vertex" is mid-point of line connecting the positions of closest
   // approach of the two tracks
   commonpos = 0.5*(oldpos + point);

  return NOERROR;
}

// Find the position along a reference trajectory closest to a given point.
// The error matrix for the point can also be input via a pointer. The error
// matrix is expected to be 7x7, with the order {Px,Py,Pz,X,Y,Z,T}.
//  Outputs the kinematic data object (including the covariance) at this 
// position,and the doca and the variance on the doca.
jerror_t DReferenceTrajectory::FindPOCAtoPoint(const DVector3 &point,
                      const DMatrixDSym *covpoint, 
                      DKinematicData *track_kd,
                      double &doca, double &var_doca) const{ 
  if (track_kd==NULL) return RESOURCE_UNAVAILABLE;
  
  DVector3 dir, commonpos;
  return FindPOCAtoLine(point,dir,covpoint,track_kd,commonpos,doca,var_doca);
}

// Find the mid-point of the line connecting the points of closest approach of the
// trajectories of two tracks.  Return the positions, momenta, and error matrices 
// at these points for the two tracks.
jerror_t DReferenceTrajectory::IntersectTracks(const DReferenceTrajectory *rt2, DKinematicData *track1_kd, DKinematicData *track2_kd, DVector3 &pos, double &doca, double &var_doca, double &vertex_chi2, bool DoFitVertex) const {
  const swim_step_t *swim_step1=this->swim_steps;
  const swim_step_t *swim_step2=rt2->swim_steps;
  
  TMatrixFSym cov1(7), cov2(7);
  shared_ptr<TMatrixFSym> locCovarianceMatrix1 = (track1_kd != NULL) ? dResourcePool_TMatrixFSym->Get_SharedResource() : nullptr;
  shared_ptr<TMatrixFSym> locCovarianceMatrix2 = (track2_kd != NULL) ? dResourcePool_TMatrixFSym->Get_SharedResource() : nullptr;

  if((track1_kd != NULL) && (track2_kd != NULL)){
     locCovarianceMatrix1->ResizeTo(7, 7);
     locCovarianceMatrix2->ResizeTo(7, 7);
    cov1=*track1_kd->errorMatrix();
    cov2=*track2_kd->errorMatrix();
  }

  double q1=this->q;
  double q2=rt2->q;
  double mass_sq1=this->mass_sq;
  double mass_sq2=rt2->mass_sq;
  vertex_chi2=0.;
  
  // Initialize the doca and traverse both particles' trajectories
  doca=1000.;
  double tflight1=0.,tflight2=0.;
  for (int i=0;i<this->Nswim_steps-1&&i<rt2->Nswim_steps-1; i++, swim_step1++, swim_step2++){
    DVector3 pos1=swim_step1->origin;
    DVector3 pos2=swim_step2->origin;
    DVector3 diff=pos1-pos2;
    double new_doca=diff.Mag();
 
    if (new_doca>doca){
      int prev_i=i-1;         
      // positions and momenta of tracks at the center of the 
      // bracketed region
      pos1=this->swim_steps[prev_i].origin;
      DVector3 mom1=this->swim_steps[prev_i].mom;
      pos2=rt2->swim_steps[prev_i].origin;
      DVector3 mom2=rt2->swim_steps[prev_i].mom;

      // If we break out of the loop immediately, we have not bracketed the 
      // doca yet...
      if (i==1) {  // backtrack to find the true doca
   tflight1=tflight2=0.;
   if((track1_kd != NULL) && (track2_kd != NULL)){
     cov1=*track1_kd->errorMatrix();
     cov2=*track2_kd->errorMatrix();
   }
   // Initialize the steppers
   DMagneticFieldStepper stepper1(this->bfield, q1, &pos1, &mom1);
   DMagneticFieldStepper stepper2(this->bfield, q2, &pos2, &mom2);

   // Do the backtracking...
   int inew=0;
   DVector3 oldpos1=pos1;
   DVector3 oldpos2=pos2;
   while (inew<20){
     if (pos1.z()<0. || pos2.z()<0. || pos1.z()>400. || pos2.z()>400.
         || pos1.Perp()>65. || pos2.Perp()>65.){
       break;
     }
     DVector3 B1,B2;
     double ds1=stepper1.Step(&pos1,&B1,-0.5);
     double ds2=stepper2.Step(&pos2,&B2,-0.5);
     
     // Compute the revised estimate for the doca
     diff=pos1-pos2;
     new_doca=diff.Mag();

     if(new_doca > doca){
       pos1=oldpos1;
       pos2=oldpos2;
       break;
     }
     
     // Propagate the covariance matrices along the trajectories
     if((track1_kd != NULL) && (track2_kd != NULL)){
       this->PropagateCovariance(ds1,q1,mass_sq1,mom1,oldpos1,B1,cov1);
       rt2->PropagateCovariance(ds2,q2,mass_sq2,mom2,oldpos2,B2,cov2);
     }
              
     // Store the current positions, doca and adjust flight times
     oldpos1=pos1;
     oldpos2=pos2;
     doca=new_doca;
     
     double one_over_p1_sq=1./mom1.Mag2();
     tflight1+=ds1*sqrt(1.+mass_sq1*one_over_p1_sq)/SPEED_OF_LIGHT;
              
     double one_over_p2_sq=1./mom2.Mag2();
     tflight2+=ds2*sqrt(1.+mass_sq2*one_over_p2_sq)/SPEED_OF_LIGHT;
     
     // New momenta
     stepper1.GetMomentum(mom1);
     stepper2.GetMomentum(mom2);
   }
      }
           
      // Use Brent's algorithm to find a better approximation for 
      // the poca of the two tracks
      double ds=0.5;
      BrentsAlgorithm(pos1,mom1,pos2,mom2,ds,q2,doca);

      // "Vertex" is mid-point of line connecting the positions of closest
      // approach of the two tracks
      pos=0.5*(pos1+pos2);
          
      if((track1_kd != NULL) && (track2_kd != NULL)){
   if (DoFitVertex){
     // Use lagrange multiplier method to try to find a better common 
     // vertex between the two tracks  
     FitVertex(pos1,mom1,pos2,mom2,cov1,cov2,pos,vertex_chi2);
   }
   // Compute the variance on the doca
   diff=pos1-pos2;
   if (DoFitVertex) doca=diff.Mag(); // update if necessary
   double dx=diff.x();
   double dy=diff.y();
   double dz=diff.z();
   var_doca=(dx*dx*(cov1(kX,kX)+cov2(kX,kX))
        +dy*dy*(cov1(kY,kY)+cov2(kY,kY))
        +dz*dz*(cov1(kZ,kZ)+cov2(kZ,kZ))
        +2.*dx*dy*(cov1(kX,kY)+cov2(kX,kY))
        +2.*dx*dz*(cov1(kX,kZ)+cov2(kX,kZ))
        +2.*dy*dz*(cov1(kY,kZ)+cov2(kY,kZ)))
     /(doca*doca);

     
   // Adjust flight times
   double one_over_p1_sq=1./mom1.Mag2();
   tflight1+=ds*sqrt(1.+mass_sq1*one_over_p1_sq)/SPEED_OF_LIGHT;
              
   double one_over_p2_sq=1./mom2.Mag2();
   tflight2+=ds*sqrt(1.+mass_sq2*one_over_p2_sq)/SPEED_OF_LIGHT;

   *locCovarianceMatrix1 = cov1;
   track1_kd->setErrorMatrix(locCovarianceMatrix1);
   track1_kd->setMomentum(mom1);
   track1_kd->setPosition(pos1);
   track1_kd->setTime(track1_kd->time() + tflight1);

   *locCovarianceMatrix2 = cov2;
   track2_kd->setErrorMatrix(locCovarianceMatrix2);
   track2_kd->setMomentum(mom2);
   track2_kd->setPosition(pos2);
   track2_kd->setTime(track2_kd->time() + tflight2);
      }      
      break;
    }

    // Propagate the covariance matrices along the trajectories
    if((track1_kd != NULL) && (track2_kd != NULL)){
      this->PropagateCovariance(this->swim_steps[i+1].s-swim_step1->s,q1,mass_sq1,swim_step1->mom,swim_step1->origin,swim_step1->B,cov1);
      rt2->PropagateCovariance(rt2->swim_steps[i+1].s-swim_step2->s,q2,mass_sq2,swim_step2->mom,swim_step2->origin,swim_step2->B,cov2);
    }
    
    // Store the current positions and doca
    tflight1=swim_step1->t;
    tflight2=swim_step2->t;
    doca=new_doca;
  }
  
  return NOERROR;
}


// Routine for finding the minimum of a function bracketed between two values
// (see Numerical Recipes in C, pp. 404-405).
#define ITMAX 20
#define CGOLD 0.3819660
#define EPS2  1.e-4
#define ZEPS 1.0e-10
#define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
#define SIGN(a,b) ((b)>=0.0?fabs(a):-fabs(a))
jerror_t DReferenceTrajectory::BrentsAlgorithm(DVector3 &pos1,DVector3 &mom1,
                      DVector3 &pos2,DVector3 &mom2,
                      double ds,double q2,
                      double &doca) const{
  double d=0.,u=0.;
  double e=0.0; // will be distance moved on step before last 
  double ax=0.;
  double bx=-ds;
  double cx=-2.*ds;

  double a=(ax<cx?ax:cx);
  double b=(ax>cx?ax:cx);
  double x=bx,w=bx,v=bx;

  // initialization
  double fw=doca;
  double fv=fw;
  double fx=fw;
  double u_old=x;
  DMagneticFieldStepper stepper1(this->bfield, this->q, &pos1, &mom1);
  DMagneticFieldStepper stepper2(this->bfield, q2, &pos2, &mom2);

  // main loop
  for (unsigned int iter=1;iter<=ITMAX;iter++){
    double xm=0.5*(a+b);
    double tol1=EPS2*fabs(x)+ZEPS;
    double tol2=2.0*tol1;
    if (fabs(x-xm)<=(tol2-0.5*(b-a))){
      doca=(pos1-pos2).Mag();

      // New momenta
      stepper1.GetMomentum(mom1);
      stepper2.GetMomentum(mom2);

      return NOERROR;
    }
    // trial parabolic fit
    if (fabs(e)>tol1){
      double x_minus_w=x-w;
      double x_minus_v=x-v;
      double r=x_minus_w*(fx-fv);
      double q=x_minus_v*(fx-fw);
      double p=x_minus_v*q-x_minus_w*r;
      q=2.0*(q-r);
      if (q>0.0) p=-p;
      q=fabs(q);
      double etemp=e;
      e=d;
      if (fabs(p)>=fabs(0.5*q*etemp) || p<=q*(a-x) || p>=q*(b-x))
   // fall back on the Golden Section technique
   d=CGOLD*(e=(x>=xm?a-x:b-x));
      else{
   // parabolic step
   d=p/q;
   u=x+d;
   if (u-a<tol2 || b-u <tol2)
     d=SIGN(tol1,xm-x);
      }                 
    } else{
      d=CGOLD*(e=(x>=xm?a-x:b-x));
    }
    u=(fabs(d)>=tol1 ? x+d: x+SIGN(tol1,d));

    // Function evaluation
    double du=u_old-u;
    stepper1.Step(&pos1,NULL,du);
    stepper2.Step(&pos2,NULL,du);
    DVector3 diff=pos1-pos2;
    double fu=diff.Mag();
    u_old=u;

    if (fu<=fx){
      if (u>=x) a=x; else b=x;
      SHFT(v,w,x,u);
      SHFT(fv,fw,fx,fu);      
    }
    else {
      if (u<x) a=u; else b=u;
      if (fu<=fw || w==x){
   v=w;
   w=u;
   fv=fw;
   fw=fu;
      }
      else if (fu<=fv || v==x || v==w){
   v=u;
   fv=fu;
      }
    }
  }
  
  // We only get here if there is a convergence issue...
  doca=(pos1-pos2).Mag();
  stepper1.GetMomentum(mom1);
  stepper2.GetMomentum(mom2);

  return NOERROR;
}


// Use lagrange multiplier method to find better approximation for the vertex
// position given the track momenta and positions and the corresponding error
// matrices.  See Frodesen, et al., Probability and Statistics in Particle 
// Physics, pp 298-320.
// Assumes we can ignore the magnetic field.
void DReferenceTrajectory::FitVertex(const DVector3 &pos1,const DVector3 &mom1,
                 const DVector3 &pos2,const DVector3 &mom2,
                 const TMatrixFSym &cov1,
                 const TMatrixFSym &cov2,
                 DVector3 &pos,double &vertex_chi2,double q1,double q2) const{
  // Vectors of measured quantities (eta0) and these quantities after adjustment
  // based on constraints (eta)
  TMatrixD eta0(12,1),eta(12,1);
  // Vectors of unmeasured quantities (common vertex {x,y,z})
  TMatrixD xi(3,1),xi_old(3,1);
  TMatrixD f(4,1); // vector representing constraint equations
  TMatrixD F_eta(4,12);  // Matrix of derivatives of f with respect to eta
  TMatrixD F_xi(4,3);  // Matrix of derivatives of f with respect to xi

  // Initialize to the guess to the vertex position 
  xi(0,0)=pos.x();
  xi(1,0)=pos.y();
  xi(2,0)=pos.z();  

  // B-field
  double Bz=fabs(bfield->GetBz(xi(0,0),xi(1,0),xi(2,0)));
  bool got_field=false;
  double a1=0.,a2=0.;
  if (Bz>0.01){
    a1=0.003*Bz*q1;
    a2=0.003*Bz*q2;
    got_field=true;
  }

  // Initialize to the measured values
  eta0(kX,0)=pos1.x();
  eta0(kY,0)=pos1.y();
  eta0(kZ,0)=pos1.z();
  eta0(kPx,0)=mom1.x();
  eta0(kPy,0)=mom1.y();
  eta0(kPz,0)=mom1.z(); 
  eta0(kX+6,0)=pos2.x();
  eta0(kY+6,0)=pos2.y();
  eta0(kZ+6,0)=pos2.z();
  eta0(kPx+6,0)=mom2.x();
  eta0(kPy+6,0)=mom2.y();
  eta0(kPz+6,0)=mom2.z();

  // Fill error matrix V from covariance matrices from the two tracks
  TMatrixD V(12,12);
  for (int m=0;m<6;m++){
    for (int n=0;n<6;n++){
      V(m,n)=cov1(n,m);
      V(m+6,n+6)=cov2(n,m);     
    }
  }

  // Start with the actual measurement
  eta=eta0;
  
  // Define some matrices needed for some of the internal steps of the procedure
  TMatrixD LagMul(4,1);  //Lagrange multipliers
  TMatrixD r(4,1);  // r=f+F_eta*(eta0-eta)
  TMatrixD S(4,4); // S=F_eta*V*F_eta^T
      
  if (debug_level>1){
    cout << "Measured quantities:" <<endl;
    eta.Print(); 
    cout << "Covariance matrix for measured quantities:"<<endl;
    V.Print();
    cout << "Initial guess for common vertex position:"<<endl;
    xi.Print();
  }
  // Iterate to find the minimum chi^2 
  double chi2=1.e6,chi2_old=1e6;
  for (int iter=0;iter<4;iter++){
    chi2_old=chi2;
    
    double dx1=xi(0,0)-eta(kX,0);
    double dy1=xi(1,0)-eta(kY,0);
    double dz1=xi(2,0)-eta(kZ,0); 
    double dx2=xi(0,0)-eta(kX+6,0);
    double dy2=xi(1,0)-eta(kY+6,0);
    double dz2=xi(2,0)-eta(kZ+6,0);
    double px1=eta(kPx,0);
    double py1=eta(kPy,0);
    double pz1=eta(kPz,0);  
    double px2=eta(kPx+6,0);
    double py2=eta(kPy+6,0);
    double pz2=eta(kPz+6,0);
    
    // Constraint equations
    if (got_field==false){
      // No field...
      f(0,0)=pz1*dx1-px1*dz1;
      f(1,0)=pz1*dy1-py1*dz1; 
      f(2,0)=pz2*dx2-px2*dz2;
      f(3,0)=pz2*dy2-py2*dz2;
    }
    else{
      double twoks1=0.;
      if (fabs(pz1)>1e-8) twoks1=a1*dz1/pz1; 
      double one_minus_cos_2ks1=1.-cos(twoks1);
      double sin_2ks1=sin(twoks1);
      f(0,0)=a1*dx1-px1*sin_2ks1+py1*one_minus_cos_2ks1;
      f(1,0)=a1*dy1-py1*sin_2ks1-px1*one_minus_cos_2ks1;

      double twoks2=0.;
      if (fabs(pz2)>1e-8) twoks2=a2*dz2/pz2; 
      double one_minus_cos_2ks2=1.-cos(twoks2);
      double sin_2ks2=sin(twoks2);
      f(2,0)=a2*dx2-px2*sin_2ks2+py2*one_minus_cos_2ks2;
      f(3,0)=a2*dy2-py2*sin_2ks2-px2*one_minus_cos_2ks2;
      
    }
    
    if (iter>0){
      TMatrixD LagMul_T(TMatrixD::kTransposed,LagMul);
      chi2=(LagMul_T*S*LagMul)(0,0);
      LagMul_T*=2.;
      chi2+=(LagMul_T*f)(0,0);

      if (debug_level>0){
   cout << "iter " << iter << " : chi2=" << chi2 <<  endl;
   if (debug_level>1){
     cout << "Constraint equations:" << endl;
     f.Print();
     cout << "Unmeasured quantities:" << endl;
     xi.Print();
     cout << "Measured quantities:" << endl;
     eta.Print();
   }
      }
      
      //if (chi2>chi2_old) break;
    }
     
    if (got_field==false){
      // Compute the Jacobian matrix for eta
      F_eta(0,kX)=-pz1;
      F_eta(0,kZ)=+px1;
      F_eta(0,kPx)=-dz1;
      F_eta(0,kPz)=+dx1;  
      F_eta(1,kY)=-pz1;
      F_eta(1,kZ)=+py1;
      F_eta(1,kPy)=-dz1;
      F_eta(1,kPz)=+dy1; 
      F_eta(2,kX+6)=-pz2;
      F_eta(2,kZ+6)=+px2;
      F_eta(2,kPx+6)=-dz2;
      F_eta(2,kPz+6)=+dx2;  
      F_eta(3,kY+6)=-pz2;
      F_eta(3,kZ+6)=+py2;
      F_eta(3,kPy+6)=-dz2;
      F_eta(3,kPz+6)=+dy2;
    
      // Compute the Jacobian matrix for xi
      F_xi(0,0)=pz1;
      F_xi(0,2)=-px1;
      F_xi(1,1)=pz1;
      F_xi(1,2)=-py1; 
      F_xi(2,0)=pz2;
      F_xi(2,2)=-px2;
      F_xi(3,1)=pz2;
      F_xi(3,2)=-py2;
    }
    else{ 
      // Compute the Jacobian matrix for eta
      double twoks1=0.;
      if (fabs(pz1)>1e-8) twoks1=a1*dz1/pz1; 
      double cos_2ks1=cos(twoks1);
      double one_minus_cos_2ks1=1.-cos_2ks1;
      double sin_2ks1=sin(twoks1);
      F_eta(0,kX)=-a1;
      F_eta(0,kZ)=(-a1/pz1)*(py1*sin_2ks1-px1*cos_2ks1);
      F_eta(0,kPx)=-sin_2ks1;
      F_eta(0,kPy)=one_minus_cos_2ks1;
      F_eta(0,kPz)=(a1*dz1/(pz1*pz1))*(px1*cos_2ks1-py1*sin_2ks1);
      F_eta(1,kY)=-a1;
      F_eta(1,kZ)=(a1/pz1)*(py1*cos_2ks1+px1*sin_2ks1);
      F_eta(1,kPy)=-sin_2ks1;
      F_eta(1,kPx)=-one_minus_cos_2ks1; 
      F_eta(1,kPz)=(a1*dz1/(pz1*pz1))*(px1*cos_2ks1-py1*sin_2ks1); 
      double twoks2=0.;
      if (fabs(pz2)>1e-8) twoks2=a2*dz2/pz2; 
      double cos_2ks2=cos(twoks2);
      double one_minus_cos_2ks2=1.-cos_2ks2;
      double sin_2ks2=sin(twoks2);
      F_eta(2,kX+6)=-a2;
      F_eta(2,kZ+6)=(-a2/pz2)*(py2*sin_2ks2-px2*cos_2ks2);
      F_eta(2,kPx+6)=-sin_2ks2;
      F_eta(2,kPy+6)=one_minus_cos_2ks2;
      F_eta(2,kPz+6)=(a2*dz2/(pz2*pz2))*(px2*cos_2ks2-py2*sin_2ks2);
      F_eta(3,kY+6)=-a2;
      F_eta(3,kZ+6)=(a2/pz2)*(py2*cos_2ks2+px2*sin_2ks2);
      F_eta(3,kPy+6)=-sin_2ks2;
      F_eta(3,kPx+6)=-one_minus_cos_2ks2; 
      F_eta(3,kPz+6)=(a2*dz2/(pz2*pz2))*(px2*cos_2ks2-py2*sin_2ks2);

      // Compute the Jacobian matrix for xi
      F_xi(0,0)=-F_eta(0,kX);
      F_xi(0,2)=-F_eta(0,kZ);
      F_xi(1,1)=-F_eta(1,kY);
      F_xi(1,2)=-F_eta(1,kZ);
      F_xi(2,0)=-F_eta(2,kX+6);
      F_xi(2,2)=-F_eta(2,kZ+6);
      F_xi(3,1)=-F_eta(3,kY+6);
      F_xi(3,2)=-F_eta(3,kZ+6);

    }
    
    if (debug_level>1){ 
      cout << "Jacobian matrices for eta and xi" <<endl;
      F_eta.Print();      
      F_xi.Print();      
    }
        
    TMatrixD F_eta_T(TMatrixD::kTransposed,F_eta);
    TMatrixD F_xi_T(TMatrixD::kTransposed,F_xi);
    
    // Adjust xi, then the Lagrange multipliers, then eta for this iteration
    xi_old=xi;
    S=F_eta*V*F_eta_T;
    TMatrixD Sinv(TMatrixD::kInverted,S);
    r=f+F_eta*(eta0-eta);
    TMatrixD Mtemp(TMatrixD::kInverted,F_xi_T*Sinv*F_xi);
    xi=xi_old-Mtemp*F_xi_T*Sinv*r;
    LagMul=Sinv*(r+F_xi*(xi-xi_old));
    eta=eta0-V*F_eta_T*LagMul;
  }
  pos.SetXYZ(xi_old(0,0),xi_old(1,0),xi_old(2,0));
  vertex_chi2=chi2_old;
}