QuasianalyticLineReconstruction.cxx

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/*
  Copyright (C) 2002-2024 CERN for the benefit of the ATLAS collaboration
*/
 
#include "MdtCalibFitters/QuasianalyticLineReconstruction.h"
 
#include <TString.h>  // for Form
 
#include <cmath>
#include <fstream>
#include <iostream>
 
#include "AthenaKernel/getMessageSvc.h"
#include "CLHEP/GenericFunctions/CumulativeChiSquare.hh"
#include "CLHEP/Units/PhysicalConstants.h"
#include "CLHEP/Units/SystemOfUnits.h"
#include "GaudiKernel/MsgStream.h"
#include "time.h"
 
using namespace MuonCalib;
 
void QuasianalyticLineReconstruction::init() {
    init(0.5 * CLHEP::mm);  // default road width = 0.5 CLHEP::mm
    return;
}
void QuasianalyticLineReconstruction::init(const double  r_road_width) {
    //::::::::::::::::::
    //:: SET TIME-OUT ::
    //::::::::::::::::::
 
    m_time_out = 10.0;
 
    //::::::::::::::::::::::::::::
    //:: SET THE MAXIMUM RADIUS ::
    //::::::::::::::::::::::::::::
 
    m_r_max = 14.6;
 
    //::::::::::::::::::::::::
    //:: SET THE ROAD WIDTH ::
    //::::::::::::::::::::::::
 
    m_road_width = r_road_width;
 
    return;
}
MTStraightLine QuasianalyticLineReconstruction::tangent(const Amg::Vector3D& r_w1, const double  r_r1, const double  r_sigma12,
                                                        const Amg::Vector3D& r_w2, const double  r_r2, const double  r_sigma22,
                                                        const int& r_case) const {
    //:::::::::::::::
    //:: VARIABLES ::
    //:::::::::::::::
 
    double sinalpha;                                         // auxiliary sinus of an angle
    double cosalpha;                                         // auxiliary sinus of an angle
    Amg::Vector3D e2prime(0., 0., 0.), e3prime(0., 0., 0.);  // auxiliary direction vectors
    MTStraightLine tang;                                     // tangent to drift circles of a hit pair
    Amg::Vector3D p1(0., 0., 0.), p2(0., 0., 0.);            // hit points defining a tangent
    Amg::Vector3D null_vec(0.0, 0.0, 0.0);                   // auxiliary 0 vector
    double mx1=0, bx1=0, mx2=0, bx2=0;                       // auxiliary track parameters
 
    //::::::::::::::::::::::::::::::::::::::::::::
    //:: CHECK WHETHER THE SELECTED CASE EXISTS ::
    //::::::::::::::::::::::::::::::::::::::::::::
 
    if (r_case < 1 || r_case > 4) {
        throw std::runtime_error(
            Form("File: %s, Line: %d\nQuasianalyticLineReconstruction::tangent() - Illegal case %i, must be 1,2,3, or 4.", __FILE__,
                 __LINE__, r_case));
    }
 
    //:::::::::::::::::::::::::::::::::::::
    //:: CALCULATE THE REQUESTED TANGENT ::
    //:::::::::::::::::::::::::::::::::::::
 
    // local coordinate axis vectors //
    e3prime = (r_w2 - r_w1).unit();
    e2prime = Amg::Vector3D(0.0, e3prime.z(), -e3prime.y());
 
    // case 1 and 2 //
    if (r_case == 1 || r_case == 2) {
        sinalpha = std::abs(r_r2 - r_r1) / (r_w2 - r_w1).mag();
        cosalpha = std::sqrt(1.0 - sinalpha * sinalpha);
 
        // case 1 //
        if (r_case == 1) {
            p1 = r_w1 + ((1 && r_r2 >= r_r1) - (1 && r_r2 < r_r1)) * r_r1 * (cosalpha * e2prime - sinalpha * e3prime);
            p2 = r_w2 + ((1 && r_r2 >= r_r1) - (1 && r_r2 < r_r1)) * r_r2 * (cosalpha * e2prime - sinalpha * e3prime);
        }
 
        // case 2 //
        if (r_case == 2) {
            p1 = r_w1 - ((1 && r_r2 >= r_r1) - (1 && r_r2 < r_r1)) * r_r1 * (cosalpha * e2prime + sinalpha * e3prime);
            p2 = r_w2 - ((1 && r_r2 >= r_r1) - (1 && r_r2 < r_r1)) * r_r2 * (cosalpha * e2prime + sinalpha * e3prime);
        }
    }
 
    // case 3 and 4 //
    if (r_case == 3 || r_case == 4) {
        sinalpha = (r_r1 + r_r2) / (r_w2 - r_w1).mag();
        cosalpha = std::sqrt(1.0 - sinalpha * sinalpha);
 
        // case 3 //
        if (r_case == 3) {
            p1 = r_w1 + r_r1 * (cosalpha * e2prime + sinalpha * e3prime);
            p2 = r_w2 - r_r2 * (cosalpha * e2prime + sinalpha * e3prime);
        }
 
        // case 4 //
        if (r_case == 4) {
            p1 = r_w1 - r_r1 * (cosalpha * e2prime - sinalpha * e3prime);
            p2 = r_w2 + r_r2 * (cosalpha * e2prime - sinalpha * e3prime);
        }
    }
 
    // calculation of the tangent and estimation of its errors //
    if ((p2 - p1).z() != 0.0) {
        tang = MTStraightLine(p1, p2 - p1, null_vec, null_vec);
    } else {
        Amg::Vector3D direction(p2 - p1);
        direction[2] = 1.0e-99;
        tang = MTStraightLine(p1, direction, null_vec, null_vec);
    }
    mx1 = tang.a_x1();
    bx1 = tang.b_x1();
    mx2 = tang.a_x2();
    bx2 = tang.b_x2();
    tang = MTStraightLine(mx1, bx1, mx2, bx2, 1.0, 1.0, std::sqrt(r_sigma12 + r_sigma22) / std::abs(p2.z() - p1.z()),
                          std::sqrt(r_sigma12 + p1.z() * p1.z() * (r_sigma12 + r_sigma22) / std::pow(p2.z() - p1.z(), 2)));
    // errors in mx1 and bx1 are arbitrary since they are
    // not used at a later stage.
 
    return tang;
}
MTStraightLine QuasianalyticLineReconstruction::track_candidate(const IndexSet& r_index_set, const int& r_k_cand, const int& r_l_cand,
                                                                const int& r_cand_case, const std::vector<Amg::Vector3D>& r_w,
                                                                const std::vector<double>& r_r, const std::vector<double>& r_sigma2,
                                                                double& r_chi2) const {
    //:::::::::::::::
    //:: VARIABLES ::
    //:::::::::::::::
 
    int nb_hits(r_index_set.size());                               // number of hits used in the track
                                                                   // reconstruction
    int nb_tangents(0);                                            // number of tangents used in the track
                                                                   // reconstruction
    std::vector<double> mx1, bx1, mx2, bx2;                        // slopes and intercepts of the
                                                                   // tangents building the track
    std::vector<double> mx1_err, bx1_err, mx2_err, bx2_err;        // their errors
    MTStraightLine aux_track;                                      // auxiliary straight line
    MTStraightLine tang;                                           // tangent to drift circles of a hit pair
    Amg::Vector3D d1(0.0, 0.0, 0.0), d2(0.0, 0.0, 0.0);            // auxiliary distance vectors
    Amg::Vector3D e2prime(0.0, 0.0, 0.0), e3prime(0.0, 0.0, 0.0);  // auxiliary basis vectors
    Amg::Vector3D a(0.0, 0.0, 0.0), u(0.0, 0.0, 0.0);              // position and direction vector of the candidate
                                                                   // tangent
    double sinalpha;                                               // auxiliary sinus of an angle
    double cosalpha;                                               // auxiliary sinus of an angle
    Amg::Vector3D p1(0.0, 0.0, 0.0), p2(0.0, 0.0, 0.0);            // hit points defining a tangent
    Amg::Vector3D null_vec(0.0, 0.0, 0.0);                         // auxiliary 0 vector
    double sum[4];                                                 // auxiliary summation variables
 
    //:::::::::::::::::::::
    //:: GET THE TANGENT ::
    //:::::::::::::::::::::
 
    // calculate the tangent //
    aux_track = tangent(r_w[r_k_cand], r_r[r_k_cand], r_sigma2[r_k_cand], r_w[r_l_cand], r_r[r_l_cand], r_sigma2[r_l_cand], r_cand_case);
    a = aux_track.positionVector();
    u = (aux_track.directionVector()).unit();
 
    // store the parameters of this tangent //
    mx1.push_back(aux_track.a_x1());
    mx1_err.push_back(aux_track.a_x1_error());
    bx1.push_back(aux_track.b_x1());
    bx1_err.push_back(aux_track.b_x1_error());
    mx2.push_back(aux_track.a_x2());
    mx2_err.push_back(aux_track.a_x2_error());
    bx2.push_back(aux_track.b_x2());
    bx2_err.push_back(aux_track.b_x2_error());
 
    //:::::::::::::::::::::::::::::::::::::::::::::::::::::
    //:: LOOP OVER THE OTHER HITS AND CALCULATE TANGENTS ::                                                            //
    //:::::::::::::::::::::::::::::::::::::::::::::::::::::
 
    for (int kk = 0; kk < nb_hits - 1; kk++) {
        for (int ll = kk + 1; ll < nb_hits; ll++) {
            int k(r_index_set[kk]);
            int l(r_index_set[ll]);
 
            if (k == r_k_cand && l == r_l_cand) { continue; }
 
            // local coordinate axis vectors //
            e3prime = (r_w[l] - r_w[k]).unit();
            e2prime = Amg::Vector3D(0.0, e3prime.z(), -e3prime.y());
 
            // distance vectors //
            d1 = (r_w[k] - a).dot(u) * u - (r_w[k] - a);
            d1[0] = (0.0);
            d2 = (r_w[l] - a).dot(u) * u - (r_w[l] - a);
            d2[0] = (0.0);
 
            // one must distinguish 2 cases //
 
            // case 1: candidate tangent passes both wires on the same side //
            if (d1.dot(d2) >= 0) {
                sinalpha = std::abs(r_r[l] - r_r[k]) / (r_w[l] - r_w[k]).mag();
                cosalpha = std::sqrt(1.0 - sinalpha * sinalpha);
 
                if (d1.dot(e2prime) >= 0) {
                    if (r_r[k] <= r_r[l]) {
                        p1 = r_w[k] + r_r[k] * (cosalpha * e2prime - sinalpha * e3prime);
                    } else {
                        p1 = r_w[k] + r_r[k] * (cosalpha * e2prime + sinalpha * e3prime);
                    }
                } else {
                    if (r_r[k] >= r_r[l]) {
                        p1 = r_w[k] - r_r[k] * (cosalpha * e2prime - sinalpha * e3prime);
                    } else {
                        p1 = r_w[k] - r_r[k] * (cosalpha * e2prime + sinalpha * e3prime);
                    }
                }
 
                if (d2.dot(e2prime) >= 0) {
                    if (r_r[k] <= r_r[l]) {
                        p2 = r_w[l] + r_r[l] * (cosalpha * e2prime - sinalpha * e3prime);
                    } else {
                        p2 = r_w[l] + r_r[l] * (cosalpha * e2prime + sinalpha * e3prime);
                    }
                } else {
                    if (r_r[k] >= r_r[l]) {
                        p2 = r_w[l] - r_r[l] * (cosalpha * e2prime - sinalpha * e3prime);
                    } else {
                        p2 = r_w[l] - r_r[l] * (cosalpha * e2prime + sinalpha * e3prime);
                    }
                }
            }
 
            // case 2: candidate tangent passes both wires on opposite sides //
            if (d1.dot(d2) < 0) {
                sinalpha = (r_r[l] + r_r[k]) / (r_w[l] - r_w[k]).mag();
                cosalpha = std::sqrt(1.0 - sinalpha * sinalpha);
 
                // case 2(a) //
                if (d1.dot(e2prime) >= 0 && d2.dot(e2prime) <= 0) {
                    p1 = r_w[k] + r_r[k] * (cosalpha * e2prime + sinalpha * e3prime);
                    p2 = r_w[l] - r_r[l] * (cosalpha * e2prime + sinalpha * e3prime);
                }
 
                // case 2(b) //
                if (d1.dot(e2prime) < 0 && d2.dot(e2prime) >= 0) {
                    p1 = r_w[k] - r_r[k] * (cosalpha * e2prime - sinalpha * e3prime);
                    p2 = r_w[l] + r_r[l] * (cosalpha * e2prime - sinalpha * e3prime);
                }
            }
 
            // get the slope and intercept of the new tangents and error estimates //
            if ((p2 - p1).z() != 0.0) {
                tang = MTStraightLine(p1, p2 - p1, null_vec, null_vec);
            } else {
                Amg::Vector3D direction(p2 - p1);
                direction[2] = (1.0e-99);
                tang = MTStraightLine(p1, direction, null_vec, null_vec);
            }
            mx1.push_back(tang.a_x1());
            bx1.push_back(tang.b_x1());
            mx2.push_back(tang.a_x2());
            bx2.push_back(tang.b_x2());
 
            mx1_err.push_back(1.0);
            bx1_err.push_back(1.0);
 
            mx2_err.push_back((r_sigma2[k] + r_sigma2[l]) / std::pow(p2.z() - p1.z(), 2));
            bx2_err.push_back(r_sigma2[k] + p1.z() * p1.z() * (r_sigma2[k] + r_sigma2[l]) / std::pow(p2.z() - p1.z(), 2));
            // errors in x1 and x2 are arbitrary since they are not
            // used at a later stage.
 
            // increase the number of tangents //
            nb_tangents = nb_tangents + 1;
        }
    }
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    //:: CALCULATE A WEIGHTED AVERAGE OVER THE TANGENTS AND THE chi^2 FOR ::
    //:: THE RECONSTRUCTED TRAJECTORY                                     ::
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
 
    sum[0] = 0.0;
    sum[1] = 0.0;
    sum[2] = 0.0;
    sum[3] = 0.0;
    for (int k = 0; k < nb_tangents; k++) {
        if (mx2_err[k] > 0) {
            sum[0] = sum[0] + mx2[k] / mx2_err[k];
            sum[1] = sum[1] + 1.0 / mx2_err[k];
        } else {
            sum[0] = sum[0] + mx2[k];
            sum[1] = sum[1] + 1.0;
        }
        if (bx2_err[k] > 0) {
            sum[2] = sum[2] + bx2[k] / bx2_err[k];
            sum[3] = sum[3] + 1.0 / bx2_err[k];
        } else {
            sum[2] = sum[2] + bx2[k];
            sum[3] = sum[3] + 1.0;
        }
    }
 
    aux_track = MTStraightLine(0.0, 0.0, sum[0] / sum[1], sum[2] / sum[3], 0.0, 1.0, std::sqrt(1.0 / sum[1]), std::sqrt(1.0 / sum[3]));
 
    r_chi2 = 0.0;
    for (int k = 0; k < nb_hits; k++) {
        r_chi2 = r_chi2 + std::pow(aux_track.distFromLine(r_w[r_index_set[k]]) - r_r[r_index_set[k]], 2) / r_sigma2[k];
    }
 
    return aux_track;
}
 
double QuasianalyticLineReconstruction::roadWidth() const { return m_road_width; }
void QuasianalyticLineReconstruction::setRoadWidth(const double  r_road_width) { m_road_width = std::abs(r_road_width); }
void QuasianalyticLineReconstruction::setTimeOut(const double  time_out) { m_time_out = time_out; }
void QuasianalyticLineReconstruction::setMaxRadius(const double  maxR) {
    if (maxR < 7 || maxR > 15)
        throw std::runtime_error(Form(
            "File: %s, Line: %d\nQuasianalyticLineReconstruction::setMaxRadius() - given radius %.3f not supported, neither MDT nor sMDT",
            __FILE__, __LINE__, maxR));
    m_r_max = maxR;
}
bool QuasianalyticLineReconstruction::fit(MuonCalibSegment& r_segment) const {
    // select all hits //
    HitSelection selection(r_segment.mdtHitsOnTrack(), 0);
 
    // call the other fit function //
    return fit(r_segment, selection);
}
bool QuasianalyticLineReconstruction::fit(MuonCalibSegment& r_segment, HitSelection r_selection) const {
    MTStraightLine final_track;
    return fit(r_segment, r_selection, final_track);
}
bool QuasianalyticLineReconstruction::fit(MuonCalibSegment& r_segment, HitSelection r_selection, MTStraightLine& final_track) const {
    // VARIABLES //
 
    time_t start, end;  // start and end time (needed for time-out)
    time(&start);
    double diff;                       // difference of start and end time (needed for time-out)
    unsigned int nb_selected_hits(0);  // number of selected hits
    MdtHitVec selected_hits;           // vector of pointers to the
                                       // selected hits
    std::vector<unsigned> selected_hits_index(r_selection.size());
    // vector containing the indices
    // of the selected hits (needed
    // a requested refit)
    std::vector<Amg::Vector3D> w;                        // wire coordinates
    std::vector<double> r;                               // drift CLHEP::radii of the selected hits
    std::vector<double> sigma2;                          // sigma(r)^2 (spatial resolution in r)
    unsigned int counter1{0}, counter2{0}, counter3{0};  // auxiliary counters
    unsigned int max_cand_hits{0};                       // the maximum number of hits on a track candidate
                                                         // found so far
    int max_cand_HOTs{0};                                // the maximum number of hit tubes on a track
                                                         // candidate found so far
    int nb_candidates;                                   // number of candidate tracks
    std::vector<int> k_cand, l_cand;                     // candidate track index
    std::vector<int> cand_case;                          // tangent case for the candidate
    std::vector<int> nb_HOTs;                            // number of hits on a candidate
    int candidate{0};                                    // index of the candidate which becomes the track
    IndexSet aux_set;                                    // auxiliary index set
    std::vector<IndexSet> index_set;                     // index set for the storage of the hits
                                                         // forming a track
    std::vector<double> intercept;                       // intercepts of track candidates
    MTStraightLine tangents[4];                          // the four tangents to the drift circles of a
                                                         // hit pair
    MTStraightLine aux_track;                            // auxiliary track
    double aux_chi2;                                     // auxiliary chi^2 variable
    Amg::Vector3D null(0.0, 0.0, 0.0);
    Amg::Vector3D xhat(1.0, 0.0, 0.0);
    MTStraightLine initial_track(r_segment.position(), r_segment.direction(), null, null);
    // initial track stored in the segment
    Amg::Vector3D aux_pos, aux_dir;  // auxiliary position and direction vectors
 
    // GET THE NUMBER OF SELECTED HITS //
    if (r_segment.mdtHitsOnTrack() != r_selection.size()) {
        MsgStream log(Athena::getMessageSvc(), "QuasianalyticLineReconstruction");
        log << MSG::WARNING
            << "Class QuasianalyticLineReconstruction, method fit: Vector with selected hits unequal to the number of hits on the segment! "
               "The user selection will be ignored!"
            << endmsg;
        r_selection.clear();
        r_selection.assign(r_segment.hitsOnTrack(), 0);
    } else {
        for (unsigned int k : r_selection) {
            if (k == 0) { nb_selected_hits = nb_selected_hits + 1; }
        }
    }
 
    // FIX POTENTIAL SECOND-COORDINATE PROBLEM OF THE INITIAL TRACK SEGMENT //
 
    if (r_segment.direction().z() == 0.0) {
        Amg::Vector3D dir(r_segment.direction().x(), r_segment.direction().y(), 1.0);
        initial_track = MTStraightLine(r_segment.position(), dir, null, null);
    }
 
    // RETURN, IF THERE ARE LESS THAN 3 HITS, I.E. THE TRACK IS NOT UNIQUELY //
    // DEFINED BY THE HITS.                                                  //
 
    if (nb_selected_hits < 3) {
        MsgStream log(Athena::getMessageSvc(), "QuasianalyticLineReconstruction");
        log << MSG::WARNING << "Class QuasianalyticLineReconstruction, method fit: Too few hits for the track reconstructions!" << endmsg;
        return false;
    }
 
    // COPY THE WIRE COORDINATES TO A LOCAL VECTOR //
 
    // vector assignments //
    selected_hits.clear();        // = vector<const MdtCalibHitBase*>(nb_selected_hits);
    w.clear();                    // = vector<Amg::Vector3D>(nb_selected_hits);
    r.clear();                    // = vector<double>(nb_selected_hits);
    sigma2.clear();               // = vector<double>(nb_selected_hits);
    selected_hits_index.clear();  //
                                  // vector filling //
    counter2 = 0;
    for (unsigned int k = 0; k < r_segment.mdtHitsOnTrack(); k++) {
        // skip the hit, if it has not been selected //
        const MuonCalibSegment::MdtHitPtr hit = (r_segment.mdtHOT())[k];
        if (r_selection[k] == 1 || hit->sigmaDriftRadius() > 100.0) { continue; }
 
        // copy the hit information into local vectors //
        selected_hits.push_back(hit);
        selected_hits_index.push_back(k);
        w.push_back(Amg::Vector3D(0.0, (hit->localPosition()).y(), (hit->localPosition()).z()));
        r.push_back(std::abs(hit->driftRadius()));
        sigma2.push_back(hit->sigma2DriftRadius());
        // if the spatial resolution has not been set, set it to 0.1 CLHEP::mm //
        if (sigma2[counter2] == 0) { sigma2[counter2] = std::pow(0.1 * CLHEP::mm, 2); }
 
        counter2 = counter2 + 1;
    }
    nb_selected_hits = selected_hits.size();
    if (nb_selected_hits < 3) return false;
    // TRACK RECONSTRUCTION //
 
    // reset counters //
    max_cand_hits = 0;
    max_cand_HOTs = 0;
    nb_candidates = 0;
    // 1st step: loop over all hit pairs and determine a track candidate //
    for (unsigned int k = 0; k < nb_selected_hits; k++) {
        for (unsigned int l = k + 1; l < nb_selected_hits; l++) {
            // time-out //
            time(&end);
            diff = difftime(end, start);
            if (diff > m_time_out) {
                MsgStream log(Athena::getMessageSvc(), "QuasianalyticLineReconstruction");
                log << MSG::WARNING << "Class QuasianalyticLineReconstruction, method fit: time-out for track finding after " << m_time_out
                    << " seconds!" << endmsg;
                return false;
            }
 
            // 2nd step: determine all four tangents to the drift circles of the hit pair //
            for (unsigned int r_case = 1; r_case < 5; r_case++) {
                tangents[r_case - 1] = tangent(w[l], r[l], sigma2[l], w[k], r[k], sigma2[k], r_case);
            }
 
            // 3rd step: determine additional track points within the road width around //
            //           the four tangents                                              //
            for (unsigned int r_case = 1; r_case < 5; r_case++) {
                bool same(false);
                counter1 = 0;
                counter3 = 0;
                std::vector<int> indices;  // indices of the hits forming a
                                           // track
                for (unsigned int n = 0; n < nb_selected_hits; n++) {
                    MTStraightLine aux_line(w[n], xhat, null, null);
                    if (std::abs(std::abs(tangents[r_case - 1].signDistFrom(aux_line)) - r[n]) < m_r_max) { counter3++; }
                    if (std::abs(std::abs(tangents[r_case - 1].signDistFrom(aux_line)) - r[n]) <= m_road_width) {
                        counter1 = counter1 + 1;
                        indices.push_back(n);
                    }
                }
                if (counter1 > 2) {
                    aux_set = IndexSet(counter1, indices);
                    aux_set.sort();
                    for (int ca = 0; ca < nb_candidates; ca++) {
                        if (aux_set == index_set[ca] && std::abs(intercept[ca] - tangents[r_case - 1].b_x2()) < m_road_width) {
                            same = true;
                            break;
                        }
                    }
                    if (same) { continue; }
                    nb_candidates = nb_candidates + 1;
                    k_cand.push_back(k);
                    l_cand.push_back(l);
                    cand_case.push_back(r_case);
                    index_set.push_back(aux_set);
                    intercept.push_back(tangents[r_case - 1].b_x2());
                    nb_HOTs.push_back(counter3);
                    if (counter1 > max_cand_hits) { max_cand_hits = counter1; }
                }
            }
        }
    }
 
    // 4th step: reconstruct a straight-line trajectory for all candidates with   //
    //           the maximum number of hits, keep the one with the smallest chi^2 //
 
    // m_nb_track_hits = max_cand_hits;
    double chi2 = -1;
    if (max_cand_hits < 3) { return false; }
 
    candidate = 0;
    for (int ca = 0; ca < nb_candidates; ca++) {
        if (index_set[ca].size() < max_cand_hits) { continue; }
 
        aux_track = track_candidate(index_set[ca], k_cand[ca], l_cand[ca], cand_case[ca], w, r, sigma2, aux_chi2);
        if (nb_HOTs[ca] >= max_cand_HOTs) {
            max_cand_HOTs = nb_HOTs[ca];
            if (chi2 == -1.0 || chi2 > aux_chi2) {
                chi2 = aux_chi2;
                final_track = aux_track;
                candidate = ca;
            }
        }
    }
 
    MdtHitVec final_track_hits(max_cand_hits);
    for (unsigned int k = 0; k < max_cand_hits; k++) { final_track_hits[k] = selected_hits[index_set[candidate][k]]; }
 
    // make the segment in rphi as the initial segment //
    aux_pos = Amg::Vector3D(initial_track.b_x1(), final_track.b_x2(), 0);
    aux_dir = Amg::Vector3D(initial_track.a_x1(), final_track.a_x2(), 1.0);
    final_track = MTStraightLine(aux_pos, aux_dir, null, null);
 
    // 5th step: update the segment//
    if (std::isnan(chi2)) { chi2 = 1.0e6; }
    r_segment.set(chi2 / (max_cand_hits - 2), final_track.positionVector(), final_track.directionVector());
 
    std::vector<unsigned int> refit_hit_selection(r_selection.size(), 1);
    for (unsigned int k = 0; k < max_cand_hits; k++) { refit_hit_selection[selected_hits_index[index_set[candidate][k]]] = 0; }
    if (!m_refit && m_refine_segment) { r_segment.refineMdtSelection(refit_hit_selection); }
 
    // chi^2 refit, if requested //
    if (m_refit) {
        if (m_nfitter.fit(r_segment, refit_hit_selection)) {
            Amg::Vector3D dir(r_segment.direction());
            if (dir.z() == 0.0) { dir[2] = (1.0e-99); }
            MTStraightLine aux_line(r_segment.position(), dir, Amg::Vector3D(0.0, 0.0, 0.0), Amg::Vector3D(0.0, 0.0, 0.0));
            double a_err(final_track.a_x2_error());
            double b_err(final_track.b_x2_error());
            final_track = MTStraightLine(0.0, 0.0, aux_line.a_x2(), aux_line.b_x2(), 0.0, 0.0, a_err, b_err);
            aux_pos = Amg::Vector3D(initial_track.b_x1(), final_track.b_x2(), 0);
            aux_dir = Amg::Vector3D(initial_track.a_x1(), final_track.a_x2(), 1.0);
            final_track = MTStraightLine(aux_pos, aux_dir, null, null);
            // recompute chi^2 because of different convention in DCSLFitter //
            chi2 = 0.0;
            for (unsigned int k = 0; k < max_cand_hits; k++) {
                MTStraightLine wire(Amg::Vector3D(0.0, final_track_hits[k]->localPosition().y(), final_track_hits[k]->localPosition().z()),
                                    xhat, null, null);
                double d(std::abs(final_track.signDistFrom(wire)));
                double r(std::abs(final_track_hits[k]->driftRadius()));
                chi2 += std::pow(d - r, 2) / final_track_hits[k]->sigma2DriftRadius();
            }
            if (std::isnan(chi2)) { chi2 = 1.0e6; }
 
            r_segment.set(chi2 / (max_cand_hits - 2), final_track.positionVector(), final_track.directionVector());
            if (m_refine_segment) { r_segment.refineMdtSelection(refit_hit_selection); }
            return true;
        }
        return false;
    }
 
    // finish the update (necessary, if no refit has been performed) //
    for (MdtHitPtr& mdt_hit : r_segment.mdtHOT()) {
        MdtCalibHitBase& hit = *mdt_hit;
 
        Amg::Vector3D pos(0.0, (hit.localPosition()).y(), (hit.localPosition()).z());
        // wire position
        MTStraightLine aux_line(pos, xhat, null, null);
        double dist(final_track.signDistFrom(aux_line));  // track distance
        double dist_err(std::hypot(pos.z() * final_track.a_x2_error(), final_track.b_x2_error()));
        // approximate error of the track distance
        hit.setDistanceToTrack(dist, dist_err);
    }
    final_track.setUsedHits(final_track_hits);
    final_track.setChi2(chi2);
 
    return true;
}