StraightPatRec.cxx

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/*
  Copyright (C) 2002-2022 CERN for the benefit of the ATLAS collaboration
*/
 
#include "MdtCalibFitters/StraightPatRec.h"
 
#include <TString.h>  // for Form
 
#include <fstream>
#include <iostream>
 
#include "AthenaKernel/getMessageSvc.h"
#include "CLHEP/GenericFunctions/CumulativeChiSquare.hh"
#include "CLHEP/Units/PhysicalConstants.h"
#include "CLHEP/Units/SystemOfUnits.h"
#include "EventPrimitives/EventPrimitives.h"
#include "GaudiKernel/MsgStream.h"
#include "GeoPrimitives/GeoPrimitivesHelpers.h"
#include "MuonCalibMath/Combination.h"
#include "time.h"
 
using namespace MuonCalib;
 
void StraightPatRec::init() {
    init(0.5 * CLHEP::mm);  // default road width = 0.5 CLHEP::mm
    return;
}
 
void StraightPatRec::init(const double r_road_width) {
    //:::::::::::::::
    //:: VARIABLES ::
    //:::::::::::::::
 
    Amg::Vector3D null_vec(0.0, 0.0, 0.0);  // auxiliary 0 vector
 
    //::::::::::::::::::
    //:: SET TIME-OUT ::
    //::::::::::::::::::
 
    m_time_out = 10.0;
 
    //::::::::::::::::::::::::::::
    //:: SET THE MAXIMUM RADIUS ::
    //::::::::::::::::::::::::::::
 
    m_r_max = 15.0;
 
    //::::::::::::::::::::::::
    //:: SET THE ROAD WIDTH ::
    //::::::::::::::::::::::::
 
    m_road_width = r_road_width;
 
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
    //:: INITIALIZE PRIVATE VARIABLES WHICH ARE ACCESSIBLE BY METHODS ::
    //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
 
    // m_nb_track_hits = 0;
    // m_chi2 = 0.0;
    // m_track = MTStraightLine(null_vec, null_vec, null_vec, null_vec);
 
    m_fix_selection = false;
 
    return;
}
 
MTStraightLine StraightPatRec::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, e3prime;                      // auxiliary direction vectors
    MTStraightLine tang;                                 // tangent to drift circles of a hit pair
    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 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\nStraightPatRec::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();
    bx2 = 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 StraightPatRec::fitCandidate(MuonCalibSegment &r_segment, const std::vector<unsigned int> &r_selection,
                                            const MTStraightLine &cand_line) const {
    // VARIABLES //
    Amg::Vector3D null(0.0, 0.0, 0.0);
    Amg::Vector3D xhat(1.0, 0.0, 0.0);
 
    unsigned int num_selected_hits(0);
    for (unsigned int k : r_selection) {
        if (!k) { num_selected_hits++; }
    }
    if (num_selected_hits < 3) return cand_line;
 
    Amg::Vector3D init_dir(r_segment.direction());
    Amg::Vector3D init_pos(r_segment.position());
    // SET THE CORRECT SIGNED TRACK DISTANCES //
 
    r_segment.set(r_segment.chi2(), cand_line.positionVector(), cand_line.directionVector());
 
    for (unsigned int k = 0; k < r_segment.mdtHitsOnTrack(); k++) {
        MTStraightLine aux_line(r_segment.mdtHOT()[k]->localPosition(), xhat, null, null);
        r_segment.mdtHOT()[k]->setDistanceToTrack(cand_line.signDistFrom(aux_line), r_segment.mdtHOT()[k]->sigmaDriftRadius());
    }

    // Analitical fit of linearized measurements (transformation to reference frame is used) //
    unsigned int NLC = 2;  // number of fit parameters
 
    // Normalization on z-direction
    Amg::Vector3D dir_norm(r_segment.direction().x() / r_segment.direction().z(), r_segment.direction().y() / r_segment.direction().z(),
                           1.0);
 
    Amg::Vector3D refTransl(r_segment.position());
    refTransl[0] = 0;
    Amg::Vector3D refDir(dir_norm);
    refDir[0] = 0;
    refDir = refDir.unit();
 
    // Rotation Matrix for Toewr_to_track transformation
 
    double rotAngle = Amg::angle(Amg::Vector3D::UnitZ(), refDir) * (refDir.y()) / std::abs(refDir.y());
    Amg::AngleAxis3D RotMatr(rotAngle, Amg::Vector3D::UnitX());       // Matrix for Track reference transformation
    Amg::AngleAxis3D RotMatr_inv(-rotAngle, Amg::Vector3D::UnitX());  // inverse
 
    Amg::VectorX alpha = Amg::VectorX(NLC);
    alpha.setZero();
    Amg::VectorX betha = Amg::VectorX(NLC);
    betha.setZero();
    Amg::MatrixX Gamma = Amg::MatrixX(NLC, NLC);
    Gamma.setZero();
    // vector to store hit positions
    std::vector<Amg::Vector3D> hit_position_track;
 
    for (unsigned int l = 0; l < r_segment.mdtHitsOnTrack(); l++) {
        // Transformation to track reference frame
        Amg::Vector3D WirPosLocal = r_segment.mdtHOT()[l]->localPosition();
        Amg::Vector3D WirPosTrack = WirPosLocal - refTransl;
        WirPosTrack = RotMatr * WirPosTrack;
        double signedDrifRadius =
            std::abs(r_segment.mdtHOT()[l]->driftRadius()) *
            (r_segment.mdtHOT()[l]->signedDistanceToTrack() / std::abs(r_segment.mdtHOT()[l]->signedDistanceToTrack()));
        Amg::Vector3D HitPosTrack = WirPosTrack;
        HitPosTrack[0] = HitPosTrack.y() + signedDrifRadius;
        HitPosTrack[1] = r_segment.mdtHOT()[l]->sigma2DriftRadius();  // trick to store hit resolution
 
        hit_position_track.push_back(HitPosTrack);
 
        Amg::VectorX delta = Amg::VectorX(NLC);
        delta.setZero();
        delta[0] = 1.0;
        delta[1] = HitPosTrack.z();
 
        if (!r_selection[l]) {
            double weight = 1.0 / (r_segment.mdtHOT()[l]->sigma2DriftRadius());
            Gamma += weight * delta * delta.transpose();
            betha += weight * HitPosTrack.y() * delta;
        }
    }
 
    // solution of linear system of equations
    Gamma = Gamma.inverse();
    alpha = Gamma * betha;
 
    double refit_chi2(0.0);
    for (unsigned int j = 0; j < hit_position_track.size(); j++) {
        double res = (alpha[0] + alpha[1] * hit_position_track[j].z() - hit_position_track[j].y());
        if (!r_selection[j]) refit_chi2 += res * res / hit_position_track[j].x();
    }
 
    // Backward transformation
    Amg::Vector3D seg_dir(0.0, alpha[1], 1.0);
    seg_dir = RotMatr_inv * seg_dir;
    seg_dir[1] = seg_dir.y() / seg_dir.z();
    seg_dir[0] = init_dir.x() / init_dir.z();
    seg_dir[2] = 1.0;
 
    Amg::Vector3D seg_pos(0.0, alpha[0], 0.0);
    seg_pos = RotMatr_inv * seg_pos;
    seg_pos = seg_pos + refTransl;
 
    seg_pos[1] = seg_pos.y() + seg_dir.y() * (init_pos.z() - seg_pos.z());
    seg_pos[0] = init_pos.x();
    seg_pos[2] = init_pos.z();
 
    // Rewriting segment
    r_segment.set(refit_chi2 / (num_selected_hits - 2), seg_pos, seg_dir);
 
    MTStraightLine aux_line(seg_pos, seg_dir, Amg::Vector3D(0.0, 0.0, 0.0), Amg::Vector3D(0.0, 0.0, 0.0));
 
    for (unsigned int k = 0; k < r_segment.mdtHitsOnTrack(); k++) {
        MTStraightLine aux_t(r_segment.mdtHOT()[k]->localPosition(), xhat, null, null);
        r_segment.mdtHOT()[k]->setDistanceToTrack(aux_line.signDistFrom(aux_t), r_segment.mdtHOT()[k]->sigmaDriftRadius());
    }
 
    aux_line.setNumberOfTrackHits(num_selected_hits);
    aux_line.setChi2(refit_chi2);
    return aux_line;
}
 
double StraightPatRec::roadWidth() const { return m_road_width; }
 
void StraightPatRec::setRoadWidth(const double r_road_width) {
    m_road_width = std::abs(r_road_width);
    return;
}
void StraightPatRec::setTimeOut(const double time_out) {
    m_time_out = time_out;
    return;
}
 
void StraightPatRec::setFixSelection(bool fix_sel) { m_fix_selection = fix_sel; }
bool StraightPatRec::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 StraightPatRec::fit(MuonCalibSegment &r_segment, HitSelection r_selection) const { return fitCallByReference(r_segment, r_selection); }
bool StraightPatRec::fit(MuonCalibSegment &r_segment, HitSelection r_selection, MTStraightLine &line_track) const {
    return fitCallByReference(r_segment, r_selection, line_track);
}
bool StraightPatRec::fitCallByReference(MuonCalibSegment &r_segment, HitSelection &r_selection) const {
    MTStraightLine fitted_track{};
    return fitCallByReference(r_segment, r_selection, fitted_track);
}
bool StraightPatRec::fitCallByReference(MuonCalibSegment &r_segment, HitSelection &r_selection, MTStraightLine &fitted_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)
    Combination combination;
 
    std::vector<unsigned int> hit_index;  // hit indices for given selection
    unsigned int try_nb_hits;             // try this given number of hits for the
                                          // segment reconstruction
 
    MuonCalibSegment::MdtHitVec selected_hits;
    std::vector<unsigned int> selected_hits_index;
 
    Amg::Vector3D w_min, w_max;     // wire with the minimum local z coordinate,
                                    // wire with the maximum local z coordinate
    double r_min, r_max{};          // corresponding drift CLHEP::radii
    double sigma2_min, sigma2_max;  // corresponding spatial resolution
 
    unsigned int counter1;  // auxiliary counter
 
    unsigned int nb_candidates(0);  // number of straight-track candidates
 
    MTStraightLine tangents[4];  // the four tangents to the drift circles of a
                                 // hit pair
    MTStraightLine aux_track;    // auxiliary track
    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

    // RESET //
 
    if (r_segment.mdtHitsOnTrack() != r_selection.size()) {
        MsgStream log(Athena::getMessageSvc(), "StraightPatRec");
        log << MSG::WARNING
            << "fitCallByReference() - 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);
    }
 
    // Filling selected_hits vector
    for (unsigned int k = 0; k < r_segment.mdtHitsOnTrack(); k++) {
        if (!r_selection[k]) {
            selected_hits.push_back(r_segment.mdtHOT()[k]);
            selected_hits_index.push_back(k);
        }
    }

    // RETURN, IF THERE ARE LESS THAN 3 HITS, I.E. THE TRACK IS NOT UNIQUELY //
    // DEFINED BY THE HITS.                                                  //
 
    if (selected_hits.size() < 3) { return false; }

    // 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);
    }

    // TRACK RECONSTRUCTION //
    // try to find a segment with as many hits as selected initially //
 
    HitSelection final_selection(r_selection);
 
    try_nb_hits = selected_hits.size();
    //=============================================================================
    while (nb_candidates == 0) {
        //-----------------------------------------------------------------------------
        // Return in case of large amount of fake hits
        if (try_nb_hits < 5 && (selected_hits.size() - try_nb_hits) > 2) return false;
        // reset //
        double best_chi2ndf = -1.0;
        MTStraightLine best_aux_line(initial_track);
 
        // loop over all combinations //
        combination.setNewParameters(selected_hits.size(), try_nb_hits);
 
        //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
        for (unsigned int cb = 0; cb < combination.numberOfCombinations(); cb++) {
            //.............................................................................
 
            // time-out //
            time(&end);
            diff = difftime(end, start);
            if (diff > m_time_out) { return false; }
 
            // get the present hit combination //
            if (cb == 0) {
                combination.currentCombination(hit_index);
            } else {
                combination.nextCombination(hit_index);
            }
 
            // Current selection of hits
            HitSelection tmp_selection(r_selection);
            tmp_selection.assign(tmp_selection.size(), 1);
            for (unsigned int k = 0; k < try_nb_hits; k++) { tmp_selection[selected_hits_index[hit_index[k] - 1]] = 0; }
 
            // investigate the current combination //
            // find the wires with minimum and maximum local z //
            w_min = selected_hits[hit_index[0] - 1]->localPosition();
            w_max = selected_hits[hit_index[0] - 1]->localPosition();
            r_min = selected_hits[hit_index[0] - 1]->driftRadius();
            r_max = selected_hits[hit_index[0] - 1]->driftRadius();
            sigma2_min = selected_hits[hit_index[0] - 1]->sigma2DriftRadius();
            sigma2_max = selected_hits[hit_index[0] - 1]->sigma2DriftRadius();
            for (unsigned int k = 1; k < try_nb_hits; k++) {
                if (selected_hits[hit_index[k] - 1]->localPosition().z() < w_min.z()) {
                    w_min = selected_hits[hit_index[k] - 1]->localPosition();
                    r_min = selected_hits[hit_index[k] - 1]->driftRadius();
                    sigma2_min = selected_hits[hit_index[k] - 1]->sigma2DriftRadius();
                }
                if (selected_hits[hit_index[k] - 1]->localPosition().z() > w_max.z()) {
                    w_max = selected_hits[hit_index[k] - 1]->localPosition();
                    r_max = selected_hits[hit_index[k] - 1]->driftRadius();
                    sigma2_max = selected_hits[hit_index[k] - 1]->sigma2DriftRadius();
                }
            }
 
            // set the spatial resolution to 0.1 CLHEP::mm if it is 0 //
            if (sigma2_min == 0) { sigma2_min = 0.1; }
            if (sigma2_max == 0) { sigma2_max = 0.1; }
 
            // get the four segment candidates tangential to the outermost hits //
            for (unsigned int r_case = 1; r_case < 5; r_case++) {
                tangents[r_case - 1] = tangent(w_min, r_min, sigma2_min, w_max, r_max, sigma2_max, r_case);
            }
 
            // determine additional track points within the road width around //
            // the four tangents and determine a segment                      //
            for (unsigned int r_case = 1; r_case < 5; r_case++) {
                counter1 = 0;
                for (unsigned int n = 0; n < try_nb_hits; n++) {
                    MTStraightLine aux_line(selected_hits[hit_index[n] - 1]->localPosition(), xhat, null, null);
                    if (std::abs(std::abs(tangents[r_case - 1].signDistFrom(aux_line)) - selected_hits[hit_index[n] - 1]->driftRadius()) <=
                        m_road_width) {
                        counter1 = counter1 + 1;
                    }
                }
 
                // Used to fix initial configuration of hits
                if (m_fix_selection) counter1 = try_nb_hits;
                // perform a straight line fit for the candidate //
                if (counter1 == try_nb_hits) {
                    nb_candidates++;
                    aux_track = fitCandidate(r_segment, tmp_selection, tangents[r_case - 1]);
 
                    if ((best_chi2ndf == -1) || (best_chi2ndf > r_segment.chi2())) {
                        best_chi2ndf = r_segment.chi2();
                        best_aux_line = aux_track;
                        final_selection.assign(final_selection.size(), 1);
                        for (unsigned int j = 0; j < try_nb_hits; j++) { final_selection[selected_hits_index[hit_index[j] - 1]] = 0; }
                    }
                }
            }
            //.............................................................................
        }
        //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

        // MAKE THE FINAL STRAIGHT SEGMENT, IF POSSIBLE //
 
        MuonCalibSegment::MdtHitVec used_hits;
        if (nb_candidates > 0) {
            // store track hits, rewrite hit selection //
            for (unsigned int k = 0; k < r_selection.size(); k++) {
                r_selection[k] = final_selection[k];
                if (!final_selection[k]) { used_hits.push_back(r_segment.mdtHOT()[k]); }
            }
 
            // Final refit //
            fitted_track = fitCandidate(r_segment, final_selection, best_aux_line);
            fitted_track.setUsedHits(used_hits);
 
            if (m_refine_segment) { r_segment.refineMdtSelection(r_selection); }
 
        } else {
            try_nb_hits = try_nb_hits - 1;
            if (try_nb_hits < 3) { return false; }
        }
 
        //-----------------------------------------------------------------------------
    }
    //=============================================================================
 
    return fitted_track.chi2() > 0;
}