GhostTrackVertexFinder.cc

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#include <algorithm>
#include <iterator>
#include <vector>
#include <map>
#include <set>
 
#include <Math/SVector.h>
#include <Math/SMatrix.h>
#include <Math/MatrixFunctions.h>
 
#include "DataFormats/GeometryVector/interface/GlobalPoint.h"
#include "DataFormats/GeometryVector/interface/GlobalVector.h"
#include "DataFormats/GeometryCommonDetAlgo/interface/GlobalError.h"
 
#include "DataFormats/BeamSpot/interface/BeamSpot.h"
 
#include "TrackingTools/TrajectoryParametrization/interface/GlobalTrajectoryParameters.h"
#include "TrackingTools/TrajectoryState/interface/TrajectoryStateOnSurface.h"
#include "TrackingTools/TrajectoryState/interface/FreeTrajectoryState.h"
#include "TrackingTools/GeomPropagators/interface/AnalyticalImpactPointExtrapolator.h"
#include "TrackingTools/TransientTrack/interface/TransientTrack.h"
#include "TrackingTools/TransientTrack/interface/TransientTrackFromFTSFactory.h"
 
#include "RecoVertex/VertexPrimitives/interface/TransientVertex.h"
#include "RecoVertex/VertexPrimitives/interface/VertexFitter.h"
#include "RecoVertex/VertexPrimitives/interface/VertexState.h"
#include "RecoVertex/VertexPrimitives/interface/CachingVertex.h"
#include "RecoVertex/VertexPrimitives/interface/LinearizedTrackState.h"
#include "RecoVertex/VertexPrimitives/interface/ConvertError.h"
#include "RecoVertex/VertexPrimitives/interface/ConvertToFromReco.h"
#include "RecoVertex/VertexTools/interface/LinearizedTrackStateFactory.h"
#include "RecoVertex/VertexTools/interface/VertexTrackFactory.h"
#include "RecoVertex/VertexTools/interface/VertexDistance3D.h"
#include "RecoVertex/VertexTools/interface/GeometricAnnealing.h"
#include "RecoVertex/KalmanVertexFit/interface/KalmanVertexFitter.h"
#include "RecoVertex/AdaptiveVertexFit/interface/AdaptiveVertexFitter.h"
 
#include "RecoVertex/GhostTrackFitter/interface/GhostTrack.h"
#include "RecoVertex/GhostTrackFitter/interface/GhostTrackState.h"
#include "RecoVertex/GhostTrackFitter/interface/GhostTrackFitter.h"
#include "RecoVertex/GhostTrackFitter/interface/GhostTrackPrediction.h"
#include "RecoVertex/GhostTrackFitter/interface/SequentialGhostTrackFitter.h"
#include "RecoVertex/GhostTrackFitter/interface/KalmanGhostTrackUpdater.h"
 
#include "RecoVertex/GhostTrackFitter/interface/GhostTrackVertexFinder.h"
 
// #define DEBUG
 
#ifdef DEBUG
#include "RecoBTag/SecondaryVertex/interface/TrackKinematics.h"
#endif
 
using namespace reco;
 
namespace {
  using namespace ROOT::Math;
 
  typedef SVector<double, 3> Vector3;
 
  typedef SMatrix<double, 3, 3, MatRepSym<double, 3> > Matrix3S;
  typedef SMatrix<double, 2, 2, MatRepSym<double, 2> > Matrix2S;
  typedef SMatrix<double, 2, 3> Matrix23;
 
  typedef ReferenceCountingPointer<VertexTrack<5> > RefCountedVertexTrack;
  typedef ReferenceCountingPointer<LinearizedTrackState<5> > RefCountedLinearizedTrackState;
 
  struct VtxTrackIs {
    VtxTrackIs(const TransientTrack &track) : track(track) {}
    bool operator()(const RefCountedVertexTrack &vtxTrack) const {
      return vtxTrack->linearizedTrack()->track() == track;
    }
 
    const TransientTrack &track;
  };
 
  inline Vector3 conv(const GlobalVector &vec) {
    Vector3 result;
    result[0] = vec.x();
    result[1] = vec.y();
    result[2] = vec.z();
    return result;
  }
 
  inline double sqr(double arg) { return arg * arg; }
}  // namespace
 
struct GhostTrackVertexFinder::FinderInfo {
  FinderInfo(const CachingVertex<5> &primaryVertex,
             const GhostTrack &ghostTrack,
             const BeamSpot &beamSpot,
             bool hasBeamSpot,
             bool hasPrimaries)
      : primaryVertex(primaryVertex),
        pred(ghostTrack.prediction()),
        prior(ghostTrack.prior()),
        states(ghostTrack.states()),
        beamSpot(beamSpot),
        hasBeamSpot(hasBeamSpot),
        hasPrimaries(hasPrimaries),
        field(nullptr) {}
 
  const CachingVertex<5> &primaryVertex;
  GhostTrackPrediction pred;
  GhostTrackPrediction prior;
  std::vector<GhostTrackState> states;
  VertexState beamSpot;
  bool hasBeamSpot;
  bool hasPrimaries;
  const MagneticField *field;
  TransientTrack ghostTrack;
};
 
static TransientTrack transientGhostTrack(const GhostTrackPrediction &pred, const MagneticField *field) {
  return TransientTrackFromFTSFactory().build(pred.fts(field));
}
 
static double vtxErrorLong(const GlobalError &error, const GlobalVector &dir) {
  return ROOT::Math::Similarity(conv(dir), error.matrix());
}
 
static GlobalPoint vtxMean(const GlobalPoint &p1, const GlobalError &e1, const GlobalPoint &p2, const GlobalError &e2) {
  GlobalVector diff = p2 - p1;
 
  double err1 = vtxErrorLong(e1, diff);
  double err2 = vtxErrorLong(e2, diff);
 
  double weight = err1 / (err1 + err2);
 
  return p1 + weight * diff;
}
 
static VertexState stateMean(const VertexState &v1, const VertexState &v2) {
  return VertexState(vtxMean(v1.position(), v1.error(), v2.position(), v2.error()), v1.error() + v2.error());
}
 
static bool covarianceUpdate(
    Matrix3S &cov, const Vector3 &residual, const Matrix3S &error, double &chi2, double theta, double phi) {
  using namespace ROOT::Math;
 
  Matrix23 jacobian;
  jacobian(0, 0) = std::cos(phi) * std::cos(theta);
  jacobian(0, 1) = std::sin(phi) * std::cos(theta);
  jacobian(0, 2) = -std::sin(theta);
  jacobian(1, 0) = -std::sin(phi);
  jacobian(1, 1) = std::cos(phi);
 
  Matrix2S measErr = Similarity(jacobian, error);
  Matrix2S combErr = Similarity(jacobian, cov) + measErr;
  if (!measErr.Invert() || !combErr.Invert())
    return false;
 
  cov -= SimilarityT(jacobian * cov, combErr);
  chi2 += Similarity(jacobian * residual, measErr);
 
  return true;
}
 
static CachingVertex<5> vertexAtState(const TransientTrack &ghostTrack,
                                      const GhostTrackPrediction &pred,
                                      const GhostTrackState &state) {
  LinearizedTrackStateFactory linTrackFactory;
  VertexTrackFactory<5> vertexTrackFactory;
 
  if (!state.isValid())
    return CachingVertex<5>();
 
  GlobalPoint pca1 = pred.position(state.lambda());
  GlobalError err1 = pred.positionError(state.lambda());
 
  GlobalPoint pca2 = state.globalPosition();
  GlobalError err2 = state.cartesianError();
 
  GlobalPoint point = vtxMean(pca1, err1, pca2, err2);
 
  const TransientTrack &recTrack = state.track();
 
  RefCountedLinearizedTrackState linState[2] = {linTrackFactory.linearizedTrackState(point, ghostTrack),
                                                linTrackFactory.linearizedTrackState(point, recTrack)};
  if (!linState[0]->isValid() || !linState[1]->isValid())
    return CachingVertex<5>();
 
  Matrix3S cov = SMatrixIdentity();
  cov *= 10000;
  double chi2 = 0.;
  if (!covarianceUpdate(cov,
                        conv(pca1 - point),
                        err1.matrix(),
                        chi2,
                        linState[0]->predictedStateParameters()[1],
                        linState[0]->predictedStateParameters()[2]) ||
      !covarianceUpdate(cov,
                        conv(pca2 - point),
                        err2.matrix(),
                        chi2,
                        linState[1]->predictedStateParameters()[1],
                        linState[1]->predictedStateParameters()[2]))
    return CachingVertex<5>();
 
  GlobalError error(cov);
  VertexState vtxState(point, error);
 
  std::vector<RefCountedVertexTrack> linTracks(2);
  linTracks[0] = vertexTrackFactory.vertexTrack(linState[0], vtxState);
  linTracks[1] = vertexTrackFactory.vertexTrack(linState[1], vtxState);
 
  return CachingVertex<5>(point, error, linTracks, chi2);
}
 
static RefCountedVertexTrack relinearizeTrack(const RefCountedVertexTrack &track,
                                              const VertexState &state,
                                              const VertexTrackFactory<5> factory) {
  RefCountedLinearizedTrackState linTrack = track->linearizedTrack();
  linTrack = linTrack->stateWithNewLinearizationPoint(state.position());
  return factory.vertexTrack(linTrack, state);
}
 
static std::vector<RefCountedVertexTrack> relinearizeTracks(const std::vector<RefCountedVertexTrack> &tracks,
                                                            const VertexState &state) {
  VertexTrackFactory<5> vertexTrackFactory;
 
  std::vector<RefCountedVertexTrack> finalTracks;
  finalTracks.reserve(tracks.size());
 
  for (std::vector<RefCountedVertexTrack>::const_iterator iter = tracks.begin(); iter != tracks.end(); ++iter)
    finalTracks.push_back(relinearizeTrack(*iter, state, vertexTrackFactory));
 
  return finalTracks;
}
 
double GhostTrackVertexFinder::vertexCompat(
    const CachingVertex<5> &vtx1, const CachingVertex<5> &vtx2, const FinderInfo &info, double scale1, double scale2) {
  Vector3 diff = conv(vtx2.position() - vtx1.position());
  Matrix3S cov = scale1 * vtx1.error().matrix() + scale2 * vtx2.error().matrix();
 
  return sqr(ROOT::Math::Dot(diff, diff)) / ROOT::Math::Similarity(cov, diff);
}
 
static double trackVertexCompat(const CachingVertex<5> &vtx, const RefCountedVertexTrack &vertexTrack) {
  using namespace ROOT::Math;
 
  TransientTrack track = vertexTrack->linearizedTrack()->track();
  GlobalPoint point = vtx.position();
  AnalyticalImpactPointExtrapolator extrap(track.field());
  TrajectoryStateOnSurface tsos = extrap.extrapolate(track.impactPointState(), point);
 
  if (!tsos.isValid())
    return 1.0e6;
 
  GlobalPoint point1 = vtx.position();
  GlobalPoint point2 = tsos.globalPosition();
  Vector3 dir = conv(point2 - point1);
  Matrix3S error = vtx.error().matrix() + tsos.cartesianError().matrix().Sub<Matrix3S>(0, 0);
  if (!error.Invert())
    return 1.0e6;
 
  return ROOT::Math::Similarity(error, dir);
}
 
GhostTrackVertexFinder::GhostTrackVertexFinder()
    : maxFitChi2_(10.0), mergeThreshold_(3.0), primcut_(2.0), seccut_(5.0), fitType_(kAlwaysWithGhostTrack) {}
 
GhostTrackVertexFinder::GhostTrackVertexFinder(
    double maxFitChi2, double mergeThreshold, double primcut, double seccut, FitType fitType)
    : maxFitChi2_(maxFitChi2), mergeThreshold_(mergeThreshold), primcut_(primcut), seccut_(seccut), fitType_(fitType) {}
 
GhostTrackVertexFinder::~GhostTrackVertexFinder() {}
 
GhostTrackFitter &GhostTrackVertexFinder::ghostTrackFitter() const {
  if (!ghostTrackFitter_.get())
    ghostTrackFitter_.reset(new GhostTrackFitter);
 
  return *ghostTrackFitter_;
}
 
VertexFitter<5> &GhostTrackVertexFinder::vertexFitter(bool primary) const {
  std::unique_ptr<VertexFitter<5> > *ptr = primary ? &primVertexFitter_ : &secVertexFitter_;
  if (!ptr->get())
    ptr->reset(new AdaptiveVertexFitter(GeometricAnnealing(primary ? primcut_ : seccut_)));
 
  return **ptr;
}
 
#ifdef DEBUG
static void debugTrack(const TransientTrack &track, const TransientVertex *vtx = 0) {
  const FreeTrajectoryState &fts = track.initialFreeState();
  GlobalVector mom = fts.momentum();
  std::cout << "\tpt = " << mom.perp() << ", eta = " << mom.eta() << ", phi = " << mom.phi()
            << ", charge = " << fts.charge();
  if (vtx && vtx->hasTrackWeight())
    std::cout << ", w = " << vtx->trackWeight(track) << std::endl;
  else
    std::cout << std::endl;
}
 
static void debugTracks(const std::vector<TransientTrack> &tracks, const TransientVertex *vtx = 0) {
  TrackKinematics kin;
  for (std::vector<TransientTrack>::const_iterator iter = tracks.begin(); iter != tracks.end(); ++iter) {
    debugTrack(*iter, vtx);
    try {
      TrackBaseRef track = iter->trackBaseRef();
      kin.add(*track);
    } catch (exception const &e) {
      // ignore, yeah this is debugging, so shut up ^^
    }
  }
 
  std::cout << "mass = " << kin.vectorSum().M() << std::endl;
}
 
static void debugTracks(const std::vector<RefCountedVertexTrack> &tracks) {
  std::vector<TransientTrack> tracks_;
  for (std::vector<RefCountedVertexTrack>::const_iterator iter = tracks.begin(); iter != tracks.end(); ++iter) {
    std::cout << "+ " << (*iter)->linearizedTrack()->linearizationPoint() << std::endl;
    tracks_.push_back((*iter)->linearizedTrack()->track());
  }
  debugTracks(tracks_);
}
 
static void debugVertex(const TransientVertex &vtx, const GhostTrackPrediction &pred) {
  double origin = 0.;
  std::cout << vtx.position() << "-> " << vtx.totalChiSquared() << " with " << vtx.degreesOfFreedom() << std::endl;
 
  double err = std::sqrt(vtxErrorLong(vtx.positionError(), pred.direction()) / pred.rho2());
  std::cout << "* " << (pred.lambda(vtx.position()) * pred.rho() - origin) << " +-" << err << " => "
            << ((pred.lambda(vtx.position()) * pred.rho() - origin) / err) << std::endl;
 
  std::vector<TransientTrack> tracks = vtx.originalTracks();
  debugTracks(tracks, &vtx);
}
#endif
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const GlobalVector &direction,
                                                              double coneRadius,
                                                              const std::vector<TransientTrack> &tracks) const {
  return vertices(RecoVertex::convertPos(primaryVertex.position()),
                  RecoVertex::convertError(primaryVertex.error()),
                  direction,
                  coneRadius,
                  tracks);
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const GlobalVector &direction,
                                                              double coneRadius,
                                                              const reco::BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &tracks) const {
  return vertices(RecoVertex::convertPos(primaryVertex.position()),
                  RecoVertex::convertError(primaryVertex.error()),
                  direction,
                  coneRadius,
                  beamSpot,
                  tracks);
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const GlobalVector &direction,
                                                              double coneRadius,
                                                              const reco::BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &primaries,
                                                              const std::vector<TransientTrack> &tracks) const {
  return vertices(RecoVertex::convertPos(primaryVertex.position()),
                  RecoVertex::convertError(primaryVertex.error()),
                  direction,
                  coneRadius,
                  beamSpot,
                  primaries,
                  tracks);
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GlobalPoint &primaryPosition,
                                                              const GlobalError &primaryError,
                                                              const GlobalVector &direction,
                                                              double coneRadius,
                                                              const std::vector<TransientTrack> &tracks) const {
  GhostTrack ghostTrack = ghostTrackFitter().fit(primaryPosition, primaryError, direction, coneRadius, tracks);
 
  CachingVertex<5> primary(primaryPosition, primaryError, std::vector<RefCountedVertexTrack>(), 0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack, primary);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GlobalPoint &primaryPosition,
                                                              const GlobalError &primaryError,
                                                              const GlobalVector &direction,
                                                              double coneRadius,
                                                              const BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &tracks) const {
  GhostTrack ghostTrack = ghostTrackFitter().fit(primaryPosition, primaryError, direction, coneRadius, tracks);
 
  CachingVertex<5> primary(primaryPosition, primaryError, std::vector<RefCountedVertexTrack>(), 0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack, primary, beamSpot, true);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GlobalPoint &primaryPosition,
                                                              const GlobalError &primaryError,
                                                              const GlobalVector &direction,
                                                              double coneRadius,
                                                              const BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &primaries,
                                                              const std::vector<TransientTrack> &tracks) const {
  GhostTrack ghostTrack = ghostTrackFitter().fit(primaryPosition, primaryError, direction, coneRadius, tracks);
 
  std::vector<RefCountedVertexTrack> primaryVertexTracks;
  if (!primaries.empty()) {
    LinearizedTrackStateFactory linTrackFactory;
    VertexTrackFactory<5> vertexTrackFactory;
 
    VertexState state(primaryPosition, primaryError);
 
    for (std::vector<TransientTrack>::const_iterator iter = primaries.begin(); iter != primaries.end(); ++iter) {
      RefCountedLinearizedTrackState linState = linTrackFactory.linearizedTrackState(primaryPosition, *iter);
 
      primaryVertexTracks.push_back(vertexTrackFactory.vertexTrack(linState, state));
    }
  }
 
  CachingVertex<5> primary(primaryPosition, primaryError, primaryVertexTracks, 0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack, primary, beamSpot, true, true);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GlobalPoint &primaryPosition,
                                                              const GlobalError &primaryError,
                                                              const GhostTrack &ghostTrack) const {
  CachingVertex<5> primary(primaryPosition, primaryError, std::vector<RefCountedVertexTrack>(), 0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack, primary);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GlobalPoint &primaryPosition,
                                                              const GlobalError &primaryError,
                                                              const BeamSpot &beamSpot,
                                                              const GhostTrack &ghostTrack) const {
  CachingVertex<5> primary(primaryPosition, primaryError, std::vector<RefCountedVertexTrack>(), 0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack, primary, beamSpot, true);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GlobalPoint &primaryPosition,
                                                              const GlobalError &primaryError,
                                                              const BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &primaries,
                                                              const GhostTrack &ghostTrack) const {
  std::vector<RefCountedVertexTrack> primaryVertexTracks;
  if (!primaries.empty()) {
    LinearizedTrackStateFactory linTrackFactory;
    VertexTrackFactory<5> vertexTrackFactory;
 
    VertexState state(primaryPosition, primaryError);
 
    for (std::vector<TransientTrack>::const_iterator iter = primaries.begin(); iter != primaries.end(); ++iter) {
      RefCountedLinearizedTrackState linState = linTrackFactory.linearizedTrackState(primaryPosition, *iter);
 
      primaryVertexTracks.push_back(vertexTrackFactory.vertexTrack(linState, state));
    }
  }
 
  CachingVertex<5> primary(primaryPosition, primaryError, primaryVertexTracks, 0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack, primary, beamSpot, true, true);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const GhostTrack &ghostTrack) const {
  return vertices(
      RecoVertex::convertPos(primaryVertex.position()), RecoVertex::convertError(primaryVertex.error()), ghostTrack);
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const BeamSpot &beamSpot,
                                                              const GhostTrack &ghostTrack) const {
  return vertices(RecoVertex::convertPos(primaryVertex.position()),
                  RecoVertex::convertError(primaryVertex.error()),
                  beamSpot,
                  ghostTrack);
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &primaries,
                                                              const GhostTrack &ghostTrack) const {
  return vertices(RecoVertex::convertPos(primaryVertex.position()),
                  RecoVertex::convertError(primaryVertex.error()),
                  beamSpot,
                  primaries,
                  ghostTrack);
}
 
static GhostTrackPrediction dummyPrediction(const Vertex &primaryVertex, const Track &ghostTrack) {
  return GhostTrackPrediction(RecoVertex::convertPos(primaryVertex.position()),
                              RecoVertex::convertError(primaryVertex.error()),
                              GlobalVector(ghostTrack.px(), ghostTrack.py(), ghostTrack.pz()),
                              0.05);
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const Track &ghostTrack,
                                                              const std::vector<TransientTrack> &tracks,
                                                              const std::vector<float> &weights) const {
  GhostTrack ghostTrack_(ghostTrack,
                         tracks,
                         weights,
                         dummyPrediction(primaryVertex, ghostTrack),
                         RecoVertex::convertPos(primaryVertex.position()),
                         true);
 
  CachingVertex<5> primary(RecoVertex::convertPos(primaryVertex.position()),
                           RecoVertex::convertError(primaryVertex.error()),
                           std::vector<RefCountedVertexTrack>(),
                           0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack_, primary);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack_.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const Track &ghostTrack,
                                                              const BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &tracks,
                                                              const std::vector<float> &weights) const {
  GhostTrack ghostTrack_(ghostTrack,
                         tracks,
                         weights,
                         dummyPrediction(primaryVertex, ghostTrack),
                         RecoVertex::convertPos(primaryVertex.position()),
                         true);
 
  CachingVertex<5> primary(RecoVertex::convertPos(primaryVertex.position()),
                           RecoVertex::convertError(primaryVertex.error()),
                           std::vector<RefCountedVertexTrack>(),
                           0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack_, primary, beamSpot, true);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack_.prediction());
#endif
 
  return result;
}
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const Vertex &primaryVertex,
                                                              const Track &ghostTrack,
                                                              const BeamSpot &beamSpot,
                                                              const std::vector<TransientTrack> &primaries,
                                                              const std::vector<TransientTrack> &tracks,
                                                              const std::vector<float> &weights) const {
  GhostTrack ghostTrack_(ghostTrack,
                         tracks,
                         weights,
                         dummyPrediction(primaryVertex, ghostTrack),
                         RecoVertex::convertPos(primaryVertex.position()),
                         true);
 
  std::vector<RefCountedVertexTrack> primaryVertexTracks;
  if (!primaries.empty()) {
    LinearizedTrackStateFactory linTrackFactory;
    VertexTrackFactory<5> vertexTrackFactory;
 
    VertexState state(RecoVertex::convertPos(primaryVertex.position()),
                      RecoVertex::convertError(primaryVertex.error()));
 
    for (std::vector<TransientTrack>::const_iterator iter = primaries.begin(); iter != primaries.end(); ++iter) {
      RefCountedLinearizedTrackState linState = linTrackFactory.linearizedTrackState(state.position(), *iter);
 
      primaryVertexTracks.push_back(vertexTrackFactory.vertexTrack(linState, state));
    }
  }
 
  CachingVertex<5> primary(RecoVertex::convertPos(primaryVertex.position()),
                           RecoVertex::convertError(primaryVertex.error()),
                           primaryVertexTracks,
                           0.);
 
  std::vector<TransientVertex> result = vertices(ghostTrack_, primary, beamSpot, true, true);
 
#ifdef DEBUG
  for (std::vector<TransientVertex>::const_iterator iter = result.begin(); iter != result.end(); ++iter)
    debugVertex(*iter, ghostTrack_.prediction());
#endif
 
  return result;
}
 
static double fitChi2(const CachingVertex<5> &vtx) { return vtx.totalChiSquared() / vtx.degreesOfFreedom(); }
 
std::vector<CachingVertex<5> > GhostTrackVertexFinder::initialVertices(const FinderInfo &info) const {
  std::vector<CachingVertex<5> > vertices;
  for (std::vector<GhostTrackState>::const_iterator iter = info.states.begin(); iter != info.states.end(); ++iter) {
    if (!iter->isValid())
      continue;
 
    GhostTrackState state(*iter);
    state.linearize(info.pred);
 
    if (!state.isValid())
      continue;
 
    CachingVertex<5> vtx = vertexAtState(info.ghostTrack, info.pred, state);
 
    if (vtx.isValid())  // && fitChi2(vtx) < maxFitChi2_)
      vertices.push_back(vtx);
  }
 
  return vertices;
}
 
static void mergeTrackHelper(const std::vector<RefCountedVertexTrack> &tracks,
                             std::vector<RefCountedVertexTrack> &newTracks,
                             const VertexState &state,
                             const VtxTrackIs &ghostTrackFinder,
                             RefCountedVertexTrack &ghostTrack,
                             const VertexTrackFactory<5> &factory) {
  for (std::vector<RefCountedVertexTrack>::const_iterator iter = tracks.begin(); iter != tracks.end(); ++iter) {
    bool gt = ghostTrackFinder(*iter);
    if (gt && ghostTrack)
      continue;
 
    RefCountedVertexTrack track = relinearizeTrack(*iter, state, factory);
 
    if (gt)
      ghostTrack = *iter;
    else
      newTracks.push_back(*iter);
  }
}
 
CachingVertex<5> GhostTrackVertexFinder::mergeVertices(const CachingVertex<5> &vertex1,
                                                       const CachingVertex<5> &vertex2,
                                                       const FinderInfo &info,
                                                       bool isPrimary) const {
  VertexTrackFactory<5> vertexTrackFactory;
 
  VertexState state = stateMean(vertex1.vertexState(), vertex2.vertexState());
  std::vector<RefCountedVertexTrack> linTracks;
  VtxTrackIs isGhostTrack(info.ghostTrack);
  RefCountedVertexTrack vtxGhostTrack;
 
  mergeTrackHelper(vertex1.tracks(), linTracks, state, isGhostTrack, vtxGhostTrack, vertexTrackFactory);
  mergeTrackHelper(vertex2.tracks(), linTracks, state, isGhostTrack, vtxGhostTrack, vertexTrackFactory);
 
  if (vtxGhostTrack && (fitType_ == kAlwaysWithGhostTrack || linTracks.size() < 2))
    linTracks.push_back(vertexTrackFactory.vertexTrack(vtxGhostTrack->linearizedTrack(), vtxGhostTrack->vertexState()));
 
  try {
    CachingVertex<5> vtx;
    if (info.hasBeamSpot && isPrimary)
      vtx = vertexFitter(true).vertex(linTracks, info.beamSpot.position(), info.beamSpot.error());
    else
      vtx = vertexFitter(isPrimary).vertex(linTracks);
    if (vtx.isValid())
      return vtx;
  } catch (const VertexException &e) {
    // fit failed
  }
 
  return CachingVertex<5>();
}
 
bool GhostTrackVertexFinder::recursiveMerge(std::vector<CachingVertex<5> > &vertices, const FinderInfo &info) const {
  typedef std::pair<unsigned int, unsigned int> Indices;
 
  std::multimap<float, Indices> compatMap;
  unsigned int n = vertices.size();
  for (unsigned int i = 0; i < n; i++) {
    const CachingVertex<5> &v1 = vertices[i];
    for (unsigned int j = i + 1; j < n; j++) {
      const CachingVertex<5> &v2 = vertices[j];
 
      float compat = vertexCompat(v1, v2, info, i == 0 ? primcut_ : seccut_, seccut_);
 
      if (compat > mergeThreshold_)
        continue;
 
      compatMap.insert(std::make_pair(compat, Indices(i, j)));
    }
  }
 
  bool changesMade = false;
  bool repeat = true;
  while (repeat) {
    repeat = false;
    for (std::multimap<float, Indices>::const_iterator iter = compatMap.begin(); iter != compatMap.end(); ++iter) {
      unsigned int v1 = iter->second.first;
      unsigned int v2 = iter->second.second;
 
      CachingVertex<5> newVtx = mergeVertices(vertices[v1], vertices[v2], info, v1 == 0);
      if (!newVtx.isValid() || (v1 != 0 && fitChi2(newVtx) > maxFitChi2_))
        continue;
 
      std::swap(vertices[v1], newVtx);
      vertices.erase(vertices.begin() + v2);
      n--;
 
      std::multimap<float, Indices> newCompatMap;
      for (++iter; iter != compatMap.end(); ++iter) {
        if (iter->second.first == v1 || iter->second.first == v2 || iter->second.second == v1 ||
            iter->second.second == v2)
          continue;
 
        Indices indices = iter->second;
        indices.first -= indices.first > v2;
        indices.second -= indices.second > v2;
 
        newCompatMap.insert(std::make_pair(iter->first, indices));
      }
      std::swap(compatMap, newCompatMap);
 
      for (unsigned int i = 0; i < n; i++) {
        if (i == v1)
          continue;
 
        const CachingVertex<5> &other = vertices[i];
        float compat =
            vertexCompat(vertices[v1], other, info, v1 == 0 ? primcut_ : seccut_, i == 0 ? primcut_ : seccut_);
 
        if (compat > mergeThreshold_)
          continue;
 
        compatMap.insert(std::make_pair(compat, Indices(std::min(i, v1), std::max(i, v1))));
      }
 
      changesMade = true;
      repeat = true;
      break;
    }
  }
 
  return changesMade;
}
 
bool GhostTrackVertexFinder::reassignTracks(std::vector<CachingVertex<5> > &vertices_, const FinderInfo &info) const {
  std::vector<std::pair<RefCountedVertexTrack, std::vector<RefCountedVertexTrack> > > trackBundles(vertices_.size());
 
  VtxTrackIs isGhostTrack(info.ghostTrack);
 
  bool assignmentChanged = false;
  for (std::vector<CachingVertex<5> >::const_iterator iter = vertices_.begin(); iter != vertices_.end(); ++iter) {
    std::vector<RefCountedVertexTrack> vtxTracks = iter->tracks();
 
    if (vtxTracks.empty()) {
      LinearizedTrackStateFactory linTrackFactory;
      VertexTrackFactory<5> vertexTrackFactory;
 
      RefCountedLinearizedTrackState linState = linTrackFactory.linearizedTrackState(iter->position(), info.ghostTrack);
 
      trackBundles[iter - vertices_.begin()].first = vertexTrackFactory.vertexTrack(linState, iter->vertexState());
    }
 
    for (std::vector<RefCountedVertexTrack>::const_iterator track = vtxTracks.begin(); track != vtxTracks.end();
         ++track) {
      if (isGhostTrack(*track)) {
        trackBundles[iter - vertices_.begin()].first = *track;
        continue;
      }
 
      if ((*track)->weight() < 1e-3) {
        trackBundles[iter - vertices_.begin()].second.push_back(*track);
        continue;
      }
 
      unsigned int idx = iter - vertices_.begin();
      double best = 1.0e9;
      for (std::vector<CachingVertex<5> >::const_iterator vtx = vertices_.begin(); vtx != vertices_.end(); ++vtx) {
        if (info.pred.lambda(vtx->position()) < info.pred.lambda(vertices_[0].position()))
          continue;
 
        double compat = sqr(trackVertexCompat(*vtx, *track));
 
        compat /= (vtx == vertices_.begin()) ? primcut_ : seccut_;
 
        if (compat < best) {
          best = compat;
          idx = vtx - vertices_.begin();
        }
      }
 
      if ((int)idx != iter - vertices_.begin())
        assignmentChanged = true;
 
      trackBundles[idx].second.push_back(*track);
    }
  }
 
  if (!assignmentChanged)
    return false;
 
  VertexTrackFactory<5> vertexTrackFactory;
  std::vector<CachingVertex<5> > vertices;
  vertices.reserve(vertices_.size());
 
  for (std::vector<CachingVertex<5> >::const_iterator iter = vertices_.begin(); iter != vertices_.end(); ++iter) {
    const std::vector<RefCountedVertexTrack> &tracks = trackBundles[iter - vertices_.begin()].second;
    if (tracks.empty())
      continue;
 
    CachingVertex<5> vtx;
 
    if (tracks.size() == 1) {
      const TransientTrack &track = tracks[0]->linearizedTrack()->track();
 
      int idx = -1;
      for (std::vector<GhostTrackState>::const_iterator iter = info.states.begin(); iter != info.states.end(); ++iter) {
        if (iter->isTrack() && iter->track() == track) {
          idx = iter - info.states.begin();
          break;
        }
      }
      if (idx < 0)
        continue;
 
      vtx = vertexAtState(info.ghostTrack, info.pred, info.states[idx]);
      if (!vtx.isValid())
        continue;
    } else {
      std::vector<RefCountedVertexTrack> linTracks = relinearizeTracks(tracks, iter->vertexState());
 
      if (fitType_ == kAlwaysWithGhostTrack)
        linTracks.push_back(
            relinearizeTrack(trackBundles[iter - vertices_.begin()].first, iter->vertexState(), vertexTrackFactory));
 
      bool primary = iter == vertices_.begin();
      try {
        if (primary && info.hasBeamSpot)
          vtx = vertexFitter(true).vertex(linTracks, info.beamSpot.position(), info.beamSpot.error());
        else
          vtx = vertexFitter(primary).vertex(linTracks);
      } catch (const VertexException &e) {
        // fit failed;
      }
      if (!vtx.isValid())
        return false;
    }
 
    vertices.push_back(vtx);
  };
 
  std::swap(vertices_, vertices);
  return true;
}
 
void GhostTrackVertexFinder::refitGhostTrack(std::vector<CachingVertex<5> > &vertices, FinderInfo &info) const {
  VtxTrackIs isGhostTrack(info.ghostTrack);
 
  std::vector<GhostTrackState> states;
  std::vector<unsigned int> oldStates;
  oldStates.reserve(info.states.size());
 
  for (std::vector<CachingVertex<5> >::const_iterator iter = vertices.begin(); iter != vertices.end(); ++iter) {
    std::vector<RefCountedVertexTrack> vtxTracks = iter->tracks();
 
    oldStates.clear();
    for (std::vector<RefCountedVertexTrack>::const_iterator track = vtxTracks.begin(); track != vtxTracks.end();
         ++track) {
      if (isGhostTrack(*track) || (*track)->weight() < 1e-3)
        continue;
 
      const TransientTrack &tt = (*track)->linearizedTrack()->track();
 
      int idx = -1;
      for (std::vector<GhostTrackState>::const_iterator iter = info.states.begin(); iter != info.states.end(); ++iter) {
        if (iter->isTrack() && iter->track() == tt) {
          idx = iter - info.states.begin();
          break;
        }
      }
 
      if (idx >= 0)
        oldStates.push_back(idx);
    }
 
    if (oldStates.size() == 1)
      states.push_back(info.states[oldStates[0]]);
    else
      states.push_back(GhostTrackState(iter->vertexState()));
  }
 
  KalmanGhostTrackUpdater updater;
  SequentialGhostTrackFitter fitter;
  double ndof, chi2;
  info.pred = fitter.fit(updater, info.prior, states, ndof, chi2);
  TransientTrack ghostTrack = transientGhostTrack(info.pred, info.field);
 
  std::swap(info.states, states);
  states.clear();
 
  std::vector<CachingVertex<5> > newVertices;
  for (std::vector<CachingVertex<5> >::const_iterator iter = vertices.begin(); iter != vertices.end(); ++iter) {
    std::vector<RefCountedVertexTrack> vtxTracks = iter->tracks();
 
    int idx = -1;
    bool redo = false;
    for (std::vector<RefCountedVertexTrack>::iterator track = vtxTracks.begin(); track != vtxTracks.end(); ++track) {
      if (isGhostTrack(*track)) {
        LinearizedTrackStateFactory linTrackFactory;
        VertexTrackFactory<5> vertexTrackFactory;
 
        *track = vertexTrackFactory.vertexTrack(linTrackFactory.linearizedTrackState(iter->position(), ghostTrack),
                                                iter->vertexState());
        redo = true;
        continue;
      }
 
      const TransientTrack &tt = (*track)->linearizedTrack()->track();
 
      if (idx >= 0) {
        idx = -1;
        break;
      }
 
      for (std::vector<GhostTrackState>::const_iterator it = info.states.begin(); it != info.states.end(); ++it) {
        if (!it->isTrack())
          continue;
 
        if (it->track() == tt) {
          idx = it - info.states.begin();
          break;
        }
      }
    }
 
    if (idx >= 0) {
      CachingVertex<5> vtx = vertexAtState(ghostTrack, info.pred, info.states[idx]);
      if (vtx.isValid())
        newVertices.push_back(vtx);
    } else if (redo) {
      bool primary = iter == vertices.begin();
      CachingVertex<5> vtx;
      if (primary && info.hasBeamSpot)
        vtx = vertexFitter(true).vertex(vtxTracks, info.beamSpot.position(), info.beamSpot.error());
      else
        vtx = vertexFitter(primary).vertex(vtxTracks);
      if (vtx.isValid())
        newVertices.push_back(vtx);
    } else
      newVertices.push_back(*iter);
  }
 
  std::swap(newVertices, vertices);
  info.ghostTrack = ghostTrack;
}
 
// implementation
 
std::vector<TransientVertex> GhostTrackVertexFinder::vertices(const GhostTrack &ghostTrack,
                                                              const CachingVertex<5> &primary,
                                                              const BeamSpot &beamSpot,
                                                              bool hasBeamSpot,
                                                              bool hasPrimaries) const {
  FinderInfo info(primary, ghostTrack, beamSpot, hasBeamSpot, hasPrimaries);
 
  std::vector<TransientVertex> result;
  if (info.states.empty())
    return result;
 
  info.field = info.states[0].track().field();
  info.ghostTrack = transientGhostTrack(info.pred, info.field);
 
  std::vector<CachingVertex<5> > vertices = initialVertices(info);
  if (primary.isValid()) {
    vertices.push_back(primary);
    if (vertices.size() > 1)
      std::swap(vertices.front(), vertices.back());
  }
 
  unsigned int reassigned = 0;
  while (reassigned < 3) {
    if (vertices.size() < 2)
      break;
 
#ifdef DEBUG
    for (std::vector<CachingVertex<5> >::const_iterator iter = vertices.begin(); iter != vertices.end(); ++iter)
 
      debugVertex(*iter, ghostTrack.prediction());
 
    std::cout << "----- recursive merging: ---------" << std::endl;
#endif
 
    bool changed = recursiveMerge(vertices, info);
    if ((!changed && !reassigned) || vertices.size() < 2)
      break;
    if (changed)
      reassigned = 0;
 
    if (fitType_ == kRefitGhostTrackWithVertices) {
      refitGhostTrack(vertices, info);
      changed = true;
    }
 
    try {
#ifdef DEBUG
      for (std::vector<CachingVertex<5> >::const_iterator iter = vertices.begin(); iter != vertices.end(); ++iter)
        debugVertex(*iter, ghostTrack.prediction());
      std::cout << "----- reassignment: ---------" << std::endl;
#endif
      if (reassignTracks(vertices, info)) {
        reassigned++;
        changed = true;
      } else
        reassigned = 0;
    } catch (const VertexException &e) {
      // just keep vertices as they are
    }
 
    if (!changed)
      break;
  }
 
  for (std::vector<CachingVertex<5> >::const_iterator iter = vertices.begin(); iter != vertices.end(); ++iter) {
    std::vector<RefCountedVertexTrack> tracks = iter->tracks();
    std::vector<RefCountedVertexTrack> newTracks;
    newTracks.reserve(tracks.size());
 
    std::remove_copy_if(tracks.begin(), tracks.end(), std::back_inserter(newTracks), VtxTrackIs(info.ghostTrack));
 
    if (newTracks.empty())
      continue;
 
    CachingVertex<5> vtx(iter->vertexState(), newTracks, iter->totalChiSquared());
    result.push_back(vtx);
  }
 
  return result;
}