GhostTrackVertexFinder.cc

Go to the documentation of this file.

#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 : public std::unary_function<
                    RefCountedVertexTrack, bool> {
        VtxTrackIs(const TransientTrack &track) : track(track) {}
        bool operator()(const RefCountedVertexTrack &vtxTrack) const
        { return vtxTrack->linearizedTrack()->track() == track; }

        const TransientTrack &track;
    };

    static inline Vector3 conv(const GlobalVector &vec)
    {
        Vector3 result;
        result[0] = vec.x();
        result[1] = vec.y();
        result[2] = vec.z();
        return result;
    }

    static inline double sqr(double arg) { return arg * arg; }
}

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(0) {}

    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_new());
}

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);

    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_new(), chi2,
                           linState[0]->predictedStateParameters()[1],
                           linState[0]->predictedStateParameters()[2]) ||
        !covarianceUpdate(cov, conv(pca2 - point), err2.matrix_new(), 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_new() +
                   scale2 * vtx2.error().matrix_new();

    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_new() +
                     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::auto_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(...) {
            // 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;
}