RungeKuttaIntersector.cxx

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/*
  Copyright (C) 2002-2023 CERN for the benefit of the ATLAS collaboration
*/
 
// Runge-Kutta method for tracking a particle through a magnetic field
// (c) ATLAS Detector software
 
#include <cmath>
#include <iomanip>
#include "TrkDetDescrUtils/Intersection.h"
#include "TrkExRungeKuttaIntersector/RungeKuttaIntersector.h"
#include "TrkParameters/TrackParameters.h"
#include "TrkSurfaces/CylinderSurface.h"
#include "TrkSurfaces/DiscSurface.h"
#include "TrkSurfaces/PerigeeSurface.h"
#include "TrkSurfaces/PlaneSurface.h"
#include "TrkSurfaces/StraightLineSurface.h"
#include "TrkSurfaces/Surface.h"
 
namespace{
 
bool
isTrapped(const double distance,
          double& previousDistance,
          unsigned long long& stepsUntilTrapped)
{
  // catch loopers
  if (distance > previousDistance) {
    return true;
  }
 
  if (stepsUntilTrapped <= 0) {
    return true;
  }
 
  --stepsUntilTrapped;
 
  // store previous value to check steps are converging (with 10% safety factor)
  previousDistance = 1.1 * distance;
 
  return false;
}
 
}//end anonymous namespace
namespace Trk
{
 
RungeKuttaIntersector::RungeKuttaIntersector (const std::string&    type,
                          const std::string&    name, 
                          const IInterface*     parent)
    :   base_class      (type, name, parent),
    m_productionMode    (true),
    m_caloR0        (1900.*Gaudi::Units::mm),   // r min for calo high field gradient region
    m_caloR1        (2500.*Gaudi::Units::mm),   // r max for calo high field gradient region
    m_caloR2        (3500.*Gaudi::Units::mm),   // r min for calo medium field gradient region
    m_caloR3        (3700.*Gaudi::Units::mm),   // r min for calo outer flux return region
    m_caloR4        (3800.*Gaudi::Units::mm),   // r max for calo medium field gradient region
    m_caloZ0        (2350.*Gaudi::Units::mm),   // z min for calo medium field gradient region
    m_caloZ1        (2600.*Gaudi::Units::mm),   // z min for calo high field gradient region
    m_caloZ2        (3600.*Gaudi::Units::mm),   // z max for calo high field gradient region
    m_caloZ3        (6000.*Gaudi::Units::mm),   // z min for calo outer flux return region
    m_inDetR0       (400.*Gaudi::Units::mm),    // end of central barrel near constant field region
    m_inDetR1       (350.*Gaudi::Units::mm),    // inner radius of middle/outer transition region
    m_inDetR2       (800.*Gaudi::Units::mm),    // outer radius of low field gradient field region
    m_inDetZ0       (350.*Gaudi::Units::mm),    // end of central barrel near constant field region
    m_inDetZ1       (420.*Gaudi::Units::mm),    // start of well behaved transition region
    m_inDetZ2       (700.*Gaudi::Units::mm),    // start of endcap region
    m_momentumThreshold (1./20.*Gaudi::Units::MeV), // protection against loopers
    m_momentumWarnThreshold (1./450.*Gaudi::Units::MeV),    // warning threshold for intersection failure
    m_muonR0        (4300.*Gaudi::Units::mm),   // inner radius of barrel toroid region
    m_muonZ0        (6600.*Gaudi::Units::mm),   // start of endcap toroid region
    m_shortStepMax      (3.0*Gaudi::Units::mm),
    m_shortStepMin      (10.*Gaudi::Units::nanometer),
    m_solenoidR     (1300.*Gaudi::Units::mm),   // r max after coil (will take small steps near coil)
    m_solenoidZ     (3500.*Gaudi::Units::mm),   // z end of InDet region
    m_stepMax0      (8.0*Gaudi::Units::mm),
    m_stepMax1      (40.0*Gaudi::Units::mm),
    m_stepMax2      (80.0*Gaudi::Units::mm),
    m_stepMax3      (160.0*Gaudi::Units::mm),
    m_stepMax4      (320.0*Gaudi::Units::mm),
    m_stepsUntilTrapped (2000),
    m_third         (1./3.),
    m_toroidR0      (1850.0*Gaudi::Units::mm),  // endcap toroid central field - inner radius
    m_toroidR1      (3500.0*Gaudi::Units::mm),  // endcap toroid central field - outer radius
    m_toroidR2      (6000.0*Gaudi::Units::mm),  // after inner barrel or outer endcap coil
    m_toroidR3      (6500.0*Gaudi::Units::mm),  // toroid region -  radius above which long steps OK
    m_toroidZ0      (7000.0*Gaudi::Units::mm),  // endcap - near iron structure
    m_toroidZ1      (8000.0*Gaudi::Units::mm),  // endcap - high field gradient
    m_toroidZ2      (8700.0*Gaudi::Units::mm),  // barrel - before coil end loop
    m_toroidZ3      (9100.0*Gaudi::Units::mm),  // barrel - nearing coil end loop
    m_toroidZ4      (9500.0*Gaudi::Units::mm),  // endcap toroid full field and barrel coil regions
    m_toroidZ5      (9800.0*Gaudi::Units::mm),  // endcap toroid central field - inner z
    m_toroidZ6      (11400.0*Gaudi::Units::mm), // endcap toroid central field - outer z
    m_toroidZ7      (12900.0*Gaudi::Units::mm), // toroid exit fringe fields
    m_toroidZ8      (14000.0*Gaudi::Units::mm), // essentially out of any toroid fields
    m_countExtrapolations   (0),
    m_countShortStep    (0),
    m_countStep     (0),
    m_countStepReduction    (0)
{
    declareProperty("ProductionMode",       m_productionMode);
}
 
StatusCode
RungeKuttaIntersector::initialize(){
    // print name and package version
    ATH_MSG_DEBUG( "RungeKuttaIntersector::initialize()" );
 
    // initialize base class
    if (StatusCode::SUCCESS != AlgTool::initialize()) return StatusCode::FAILURE;
 
    // retrieve MagneticFieldTool and StraightLineIntersector
    ATH_CHECK( m_fieldCacheCondObjInputKey.initialize() );
 
    // productionMode gives steplengths tuned for use in production (adequate precision),
    // otherwise take very small steps for maximum precision but with a heavy execution penalty
    if (! m_productionMode){
      m_shortStepMax        = 500.*Gaudi::Units::nanometer;
      m_stepMax0        = 1.8*Gaudi::Units::mm;
      m_stepMax1        = 1.8*Gaudi::Units::mm;
      m_stepMax2        = 1.8*Gaudi::Units::mm;
      m_stepMax3        = 1.8*Gaudi::Units::mm;
      m_stepMax4        = 1.8*Gaudi::Units::mm;
      m_stepsUntilTrapped   = 20000;
    }
    
    return StatusCode::SUCCESS;
}
 
StatusCode
RungeKuttaIntersector::finalize()
{
    if (m_countExtrapolations)
    {
    msg(MSG::INFO)  << "finalized after " << m_countExtrapolations << " extrapolations,";
    double norm = 1./static_cast<double>(m_countExtrapolations);
    msg(MSG::INFO)   << std::setiosflags(std::ios::fixed)
             << " taking an average" << std::setw(7) << std::setprecision(1)
             << norm*static_cast<double>(m_countStep)
             << " full steps," << std::setw(5) << std::setprecision(2)
             << norm*static_cast<double>(m_countStepReduction)
             << " step reductions and" << std::setw(5) << std::setprecision(2)
             << norm*static_cast<double>(m_countShortStep)
             << " short final steps";
    msg(MSG::INFO)   << endmsg;
    }
 
    return StatusCode::SUCCESS;
}
 
std::optional<Trk::TrackSurfaceIntersection>
RungeKuttaIntersector::intersectSurface(const Surface&      surface,
                    const TrackSurfaceIntersection& trackIntersection,
                    const double        qOverP) const
{
    // trap low momentum
    if (std::abs(qOverP) > m_momentumThreshold)
    {
      ATH_MSG_DEBUG(" trapped as below momentum threshold" );
      return std::nullopt;
    }
 
    const auto surfaceType = surface.type();
    if (surfaceType == Trk::SurfaceType::Plane) {
      return intersectPlaneSurface(static_cast<const PlaneSurface&>(surface),
                                   trackIntersection, qOverP);
    }
    if (surfaceType == Trk::SurfaceType::Line) {
      return approachStraightLineSurface(
          static_cast<const StraightLineSurface&>(surface), trackIntersection,
          qOverP);
    }
    if (surfaceType == Trk::SurfaceType::Cylinder) {
      return intersectCylinderSurface(
          static_cast<const CylinderSurface&>(surface), trackIntersection,
          qOverP);
    }
    if (surfaceType == Trk::SurfaceType::Disc) {
      return intersectDiscSurface(static_cast<const DiscSurface&>(surface),
                                  trackIntersection, qOverP);
    }
    if (surfaceType == Trk::SurfaceType::Perigee) {
      return approachPerigeeSurface(static_cast<const PerigeeSurface&>(surface),
                                    trackIntersection, qOverP);
    }
 
    ATH_MSG_WARNING( " unrecognized Surface" );
    return std::nullopt;
}
                                    
std::optional<Trk::TrackSurfaceIntersection>
RungeKuttaIntersector::approachPerigeeSurface(const PerigeeSurface&     surface,
                          const TrackSurfaceIntersection&   trackIntersection,
                          const double          qOverP) const
{
    ++m_countExtrapolations;
    TrackSurfaceIntersection isect = trackIntersection;
    const Amg::Vector3D& pos = isect.position();
    const double rStart = pos.perp();
    const double zStart = pos.z();
    MagField::AtlasFieldCache fieldCache;
    initializeFieldCache(fieldCache);
    Amg::Vector3D fieldValue = field(pos, fieldCache);
 
    // straight line distance along track to closest approach to line
    const Amg::Vector3D& lineDirection  = (surface.transform().rotation()).col(2);
    double stepLength = 0;
    double distance = distanceToLine (isect, surface.center(),lineDirection, stepLength);
    unsigned long long stepsUntilTrapped =  m_stepsUntilTrapped;
    double previousDistance         = 1.1*distance;
 
    // integration loop (step)
    while (distance > m_shortStepMax)
    {
        if (isTrapped(distance, previousDistance, stepsUntilTrapped)) {
            // trapped
            if (msgLvl(MSG::DEBUG)) debugFailure (std::move(isect), surface, qOverP,
                                                  rStart, zStart, true);
            return std::nullopt;
        }
        assignStepLength(isect, stepLength);
        step(isect, fieldValue, stepLength, qOverP, fieldCache);
        distance = distanceToLine (isect, surface.center(),lineDirection, stepLength);
    }
 
    // if intersection OK: make short final step to surface - assuming constant field
    if (distance > m_shortStepMin)  shortStep(isect, fieldValue, stepLength, qOverP);
    return newIntersection(std::move(isect), surface, qOverP,
                           rStart, zStart);
}
    
std::optional<Trk::TrackSurfaceIntersection>
RungeKuttaIntersector::approachStraightLineSurface(const StraightLineSurface&       surface,
                           const TrackSurfaceIntersection&  trackIntersection,
                           const double                 qOverP) const
{
    ++m_countExtrapolations;
    TrackSurfaceIntersection isect = trackIntersection;
    const Amg::Vector3D& pos = isect.position();
    const double rStart = pos.perp();
    const double zStart = pos.z();
    MagField::AtlasFieldCache fieldCache;
    initializeFieldCache(fieldCache);
    Amg::Vector3D fieldValue = field(pos, fieldCache);
 
    // straight line distance along track to closest approach to line
    const Amg::Vector3D& lineDirection  = (surface.transform().rotation()).col(2);
    double stepLength = 0;
    double distance = distanceToLine (isect, surface.center(),lineDirection, stepLength);
    unsigned long long stepsUntilTrapped =  m_stepsUntilTrapped;
    double previousDistance         = 1.1*distance;
 
    // integration loop (step)
    while (distance > m_shortStepMax)
    {
        if (isTrapped(distance, previousDistance, stepsUntilTrapped)) {
            // trapped
            if (msgLvl(MSG::DEBUG)) debugFailure (std::move(isect), surface, qOverP,
                                                  rStart, zStart, true);
            return std::nullopt;
        }
        assignStepLength(isect, stepLength);
        step(isect, fieldValue, stepLength, qOverP,fieldCache);
        distance = distanceToLine (isect, surface.center(),lineDirection, stepLength);
    }
 
    // if intersection OK: make short final step assuming constant field
    if (distance > m_shortStepMin)  shortStep(isect, fieldValue, stepLength, qOverP);
    return newIntersection(std::move(isect), surface, qOverP,
                           rStart, zStart);
}
            
std::optional<Trk::TrackSurfaceIntersection>
RungeKuttaIntersector::intersectCylinderSurface (const CylinderSurface&         surface,
                         const TrackSurfaceIntersection&    trackIntersection,
                         const double               qOverP) const
{
    ++m_countExtrapolations;
    TrackSurfaceIntersection isect = trackIntersection;
    const Amg::Vector3D& pos = isect.position();
    const double rStart = pos.perp();
    const double zStart = pos.z();
    MagField::AtlasFieldCache fieldCache;
    initializeFieldCache(fieldCache);
    Amg::Vector3D fieldValue = field(pos, fieldCache);
 
    // calculate straight line distance along track to intersect with cylinder radius
    double cylinderRadius   = (surface.globalReferencePoint() - surface.center()).perp();
    Amg::Vector3D offset    = surface.center() - isect.position();
    double rCurrent     = offset.perp();
    double stepLength = 0;
    double distance = distanceToCylinder (isect, cylinderRadius,rCurrent,offset, stepLength);
    unsigned long long stepsUntilTrapped =  m_stepsUntilTrapped;
    double previousDistance     = 1.1*distance;
    bool trapped = false;
 
    // integration loop (step)
    while (distance > m_shortStepMax)
    {
        if (isTrapped(distance, previousDistance, stepsUntilTrapped)) {
            trapped = true;
            break;
        }
        assignStepLength(isect, stepLength);
        double rPrevious= rCurrent;
        step(isect, fieldValue, stepLength, qOverP,fieldCache);
        offset      = surface.center() - isect.position();
        rCurrent    = offset.perp();
        double deltaR1  = rCurrent - rPrevious;
        double deltaR2  = cylinderRadius - rCurrent;    
        double scale    = 1.;
        if (deltaR1 != 0.) scale = deltaR2 / deltaR1;
        if (scale < 1.)
        {
          stepLength *= scale;
          if (scale < -1.) {
            trapped = true;
            break;
          }
        }
        distance    = std::abs(stepLength);
    }
 
    // if intersection OK: make short final step assuming constant field
    if (! trapped
        && std::abs(cylinderRadius - rCurrent) < m_shortStepMax)
    {
        distance = distanceToCylinder (isect, cylinderRadius,rCurrent,offset, stepLength);
        // protect against divergence (looping)
        if (distance < m_shortStepMax)
        {
          if (distance > m_shortStepMin) shortStep(isect, fieldValue, stepLength, qOverP);
          return newIntersection(std::move(isect), surface, qOverP,
                                 rStart, zStart);
        }
    }
 
    // trapped
    if (msgLvl(MSG::DEBUG)) debugFailure (std::move(isect), surface, qOverP,
                                          rStart, zStart, true);
    return std::nullopt;
}
 
std::optional<Trk::TrackSurfaceIntersection>
RungeKuttaIntersector::intersectDiscSurface (const DiscSurface&         surface,
                         const TrackSurfaceIntersection&    trackIntersection,
                         const double           qOverP) const
{
    ++m_countExtrapolations;
    TrackSurfaceIntersection isect = trackIntersection;
    const Amg::Vector3D& pos = isect.position();
    const double rStart = pos.perp();
    const double zStart = pos.z();
    MagField::AtlasFieldCache fieldCache;
    initializeFieldCache(fieldCache);
    Amg::Vector3D fieldValue = field(pos, fieldCache);
 
    // straight line distance along track to intersect with disc
    double stepLength = 0;
    double distance = distanceToDisc (isect, surface.center().z(), stepLength);
    unsigned long long stepsUntilTrapped =  m_stepsUntilTrapped;
    double previousDistance     = 1.1*distance;
    
    // integration loop
    while (std::abs(stepLength) > m_shortStepMax)
    {
        if (isTrapped(distance, previousDistance, stepsUntilTrapped)) {
            // trapped
            if (msgLvl(MSG::DEBUG)) debugFailure (std::move(isect), surface, qOverP,
                                                  rStart, zStart, true);
            return std::nullopt;
        }
        assignStepLength(isect, stepLength);
        step(isect, fieldValue, stepLength, qOverP,fieldCache);
        distance = distanceToDisc (isect, surface.center().z(), stepLength);
    }
 
    // if intersection OK: make short final step assuming constant field
    if (std::abs(stepLength) > m_shortStepMin)  shortStep(isect, fieldValue, stepLength, qOverP);
    return newIntersection(std::move(isect), surface, qOverP,
                           rStart, zStart);
}
 
std::optional<Trk::TrackSurfaceIntersection>
RungeKuttaIntersector::intersectPlaneSurface(const PlaneSurface&        surface,
                         const TrackSurfaceIntersection&    trackIntersection,
                         const double           qOverP) const
{
    ++m_countExtrapolations;
    TrackSurfaceIntersection isect = trackIntersection;
    const Amg::Vector3D& pos = isect.position();
    const double rStart = pos.perp();
    const double zStart = pos.z();
    MagField::AtlasFieldCache fieldCache;
    initializeFieldCache(fieldCache);
    Amg::Vector3D fieldValue = field(pos, fieldCache);
 
    // straight line distance along track to intersect with plane
    double stepLength = 0;
    double distance = distanceToPlane (isect, surface.center(),surface.normal(), stepLength);
    unsigned long long stepsUntilTrapped =  m_stepsUntilTrapped;
    double previousDistance = 1.1*distance;
    
    // integration loop (step)
    while (distance > m_shortStepMax)
    {
        if (isTrapped(distance, previousDistance, stepsUntilTrapped)) {
            // trapped
            if (msgLvl(MSG::DEBUG)) debugFailure (std::move(isect), surface, qOverP,
                                                  rStart, zStart, true);
            return std::nullopt;
        }
        assignStepLength(isect, stepLength);
        step(isect, fieldValue, stepLength, qOverP, fieldCache);
        distance = distanceToPlane (isect, surface.center(),surface.normal(), stepLength);
    }
 
    // if intersection OK: make short final step assuming constant field
    if (distance > m_shortStepMin)  shortStep(isect, fieldValue, stepLength, qOverP);
    return newIntersection(std::move(isect), surface, qOverP,
                           rStart, zStart);
}
 
 
//<<<<<< PRIVATE FUNCTION DEFINITIONS                                   >>>>>>
 
void
RungeKuttaIntersector::assignStepLength (const TrackSurfaceIntersection& isect,
                                         double& stepLength) const
{
    const Amg::Vector3D& pos = isect.position();
    const double sinTheta = isect.direction().perp();
 
    // step length assigned according to abs value of current rz position
    // use default (large) value for most regions of InDet and Calo
    // TODO: consider bounded steps acc region => solves in/outwards problem
    const double zCurrent = std::abs(pos.z());
    const double rCurrent = pos.perp();
    double stepMax = m_stepMax3;
    // m_stepFlag       = 0;
 
    // first treat InDet and Solenoid regions
    // TODO: so far validated out to R = 1.0m
    if (rCurrent < m_solenoidR && zCurrent < m_solenoidZ) {
        if (rCurrent < m_inDetR2) {
            // inner barrel, forward tracks and endcap regions generally happy
            // with long steps double number of steps for middle barrel and much
            // of the transition region
            if (zCurrent < m_inDetZ0 && rCurrent < m_inDetR0) {
            // inner barrel
            // stepMax = m_stepMax3;
            } else if (zCurrent > m_inDetZ2 || sinTheta < 0.35) {
            // endcap and far forward
            // stepMax = m_stepMax3;
            }
 
            // double number of steps for most of the remainder
            else if (zCurrent > m_inDetZ1 && sinTheta < 0.60) {
            // barrel:endcap transition
            stepMax = m_stepMax2;
            } else if (rCurrent > m_inDetR0) {
            // middle barrel
            stepMax = m_stepMax2;
            }
 
            // the remaining transition region requires much shorter steps
            else {
            if (rCurrent > m_inDetR1) {
              // middle/outer transition region
              stepMax = m_stepMax1;
            } else {
              // inner transition (anomalous behaviour causing low pt track
              // rotation)
              stepMax = m_stepMax0;
            }
            }
        }
        // take care when moving to region with shorter steps
 
        // field less uniform (approaching coil structure)
        else if (rCurrent < 1000.)  // 1000
        {
            if (zCurrent > 700.) {
            // stepMax = m_stepMax3;
            // exception at higher radii (influence of coil structure)
            if (rCurrent > 850.)
              stepMax = m_stepMax2;
            }
            // // double number of steps for most of the remainder
            else if (zCurrent > 420. && sinTheta < 0.60) {
            // barrel:endcap transition
            stepMax = m_stepMax2;
            } else {
            // decrease step length with increasing radius
            if (rCurrent > 900.) {
              // coil structure
              stepMax = m_stepMax0;
            } else {
              // middle
              stepMax = m_stepMax1;
            }
            }
        } else {
            // field less uniform in vicinity of solenoid coils
            stepMax = m_stepMax1;
            if (zCurrent < 3000.)
            stepMax = m_stepMax0;
        }
    }
 
    // secondly treat MuonSpectrometer regions
    // start with central barrel
    else if (rCurrent > m_muonR0 && zCurrent < m_toroidZ4)  // Z3
    {
        // ++m_count0;
        // optimize - only refresh phi occasionally
        double period = M_PI / 4.;
        double phi = pos.phi() + 0.5 * period;
        if (phi < 0.)
            phi += 2. * M_PI;
        int n = static_cast<int>(phi / period);
        phi -= static_cast<double>(n) * period;
        if (phi > 0.5 * period)
            phi = period - phi;
 
        // sol 1: 12.1 full steps, 0.34 reduc, 0 short
        // sol 2: 12.0 full steps, 0.34 reduc, 0 short
        // sol 3: 11.9 full steps, 0.34 reduc, 0 short  (tidy-up)
        double radius = rCurrent;
        if (stepLength < 0.)
            radius -= m_stepMax2;
        if (zCurrent > m_toroidZ3 && phi < 0.04) {
            // fringe and coil regions
            stepMax = m_stepMax1;  
                                   // m_stepFlag    = 22;
                                   // ++m_count5;
        } else if (radius < 5300.) {
            // fringe and coil regions
            stepMax = m_stepMax1;  
                                   // m_stepFlag    = 21;
                                   // ++m_count1;
        }
        // note: long sector (phi>0.175) has max 1/3 outer steps as finishes at
        // lower r try: phi-extended long sector with stepMax3 for all  r > 5500
        else if (phi > 0.04 ||
                 (radius > 5500. &&
                  (radius < 9000. ||
                   (phi > 0.028 && radius < 9350.))))  // (extended) long sector
        {
            // central 'aircore' between coils
            stepMax = m_stepMax3;  
                                   // m_stepFlag    = 27;
                                   // ++m_count2;
        } else if (radius > 5500. && radius < 9350.) {
            // outer coil fringe region
            stepMax = m_stepMax2;  
                                   // m_stepFlag    = 28;
                                   // ++m_count3;
        } else {
            // outer coil region
            stepMax = m_stepMax1;  
                                   // m_stepFlag    = 29;
                                   // ++m_count4;
        }
    } else if (rCurrent > m_muonR0 || zCurrent > m_muonZ0) {
        if (zCurrent > m_toroidZ4) {
            if (zCurrent > m_toroidZ8) {
            // essentially out of any toroid fields
            stepMax = m_stepMax4;
            } else if (zCurrent > m_toroidZ7) {
            // toroid exit fringe fields
            stepMax = m_stepMax3;
            } else if (rCurrent > m_toroidR0 && rCurrent < m_toroidR1 &&
                       zCurrent > m_toroidZ5 && zCurrent < m_toroidZ6) {
            // endcap toroid central field
            stepMax = m_stepMax3;
            } else {
            // endcap toroid high field gradient and barrel coil regions
            stepMax = m_stepMax1;
            }
        } else if (rCurrent > m_toroidR3) {
            // main region of barrel toroid :
            // generally take long steps but with care near coil end loop
            if (zCurrent < m_toroidZ2) {
            stepMax = m_stepMax4;
            // if (rCurrent > 9000.) stepMax = m_stepMax3;
            // if (rCurrent > 9400.) stepMax = m_stepMax2;
            } else if (zCurrent < m_toroidZ3) {
            stepMax = m_stepMax3;
            } else {
            stepMax = m_stepMax1;
            }
        } else if (rCurrent > m_toroidR2) {
            // toroid field after inner barrel or outer endcap coil
            stepMax = m_stepMax3;
        } else if (zCurrent < m_toroidZ0 || zCurrent > m_toroidZ1 ||
                   rCurrent > m_muonR0) {
            // small steps in toroid high field regions and near iron structures
            stepMax = m_stepMax1;
        } else {
            // endcap toroid entrance fringe fields
            stepMax = m_stepMax3;
        }
    }
 
    // finally assign Calo regions
    else {
        if ((rCurrent < m_solenoidR) ||
            (rCurrent > m_caloR0 && rCurrent < m_caloR1) ||
            rCurrent > m_caloR3 ||
            (zCurrent > m_caloZ1 && zCurrent < m_caloZ2) ||
            zCurrent > m_caloZ3) {
            stepMax = m_stepMax1;
        } else if ((rCurrent > m_caloR2 && rCurrent < m_caloR4) ||
                   zCurrent > m_caloZ0) {
            stepMax = m_stepMax2;
        }
    }
 
    // finally reset stepLength as necessary
    if (std::abs(stepLength) < stepMax)
        return;
    if (stepLength > 0.) {
        stepLength = stepMax;
    } else {
        stepLength = -stepMax;
    }
}
 
void
RungeKuttaIntersector::debugFailure (TrackSurfaceIntersection&& isect,
                                     const Surface& surface,
                                     const double qOverP,
                                     const double rStart,
                                     const double zStart,
                                     const bool trapped) const
{
    // forget low momentum (prone to looping...)
    if (std::abs(qOverP) > m_momentumWarnThreshold) return;
 
    double pt   = 1.E+8;
    const double sinTheta = isect.direction().perp();
    if (qOverP != 0.) pt = sinTheta/(qOverP*Gaudi::Units::GeV);
 
    const double rCurrent = isect.position().perp();
    
    MsgStream log(msgSvc(), name());
    if (rCurrent > rStart)
    {
      log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right)
        << " fail to intersect surface when extrapolating outwards from R,Z"
        << std::setw(8) << std::setprecision(1) << rStart << ","
        << std::setw(7) << std::setprecision(0) << zStart << " mm, with pt"
        << std::setw(7) << std::setprecision(2) << pt << " GeV, direction eta"
        << std::setw(5) << std::setprecision(2) << isect.direction().eta();
    }
    else
    {
      log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right)
        << " fail to intersect surface when extrapolating inwards from R,Z"
        << std::setw(8) << std::setprecision(1) << rStart << ","
        << std::setw(7) << std::setprecision(0) << zStart << " mm, with pt"
        << std::setw(7) << std::setprecision(2) << pt << " GeV, direction eta"
        << std::setw(5) << std::setprecision(2) << isect.direction().eta();
    }
    // if (trapped) log << MSG::DEBUG << " looping in mag field ";
    log << MSG::DEBUG << endmsg;
    
    if (dynamic_cast<const PlaneSurface*>(&surface))
    {
        double stepLength = 0;
        (void)distanceToPlane (isect, surface.center(),surface.normal(), stepLength);
        log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right) << "   PlaneSurface"
        << " at R,Z" << std::setw(8) << std::setprecision(1) << surface.center().perp() << ","
        << std::setw(7) << std::setprecision(0) << surface.center().z()
        << "  at line distance " << std::setw(9) << std::setprecision(1) << stepLength;
        // if (trapped) log << MSG::DEBUG << " looping in mag field ";
        log << MSG::DEBUG << endmsg;
    }
    else if (dynamic_cast<const CylinderSurface*>(&surface))
    {
      double cylinderRadius = (surface.globalReferencePoint() - surface.center()).perp();
      Amg::Vector3D offset  = surface.center() - isect.position();
      double rCurrent       = offset.perp();
        double stepLength = 0;
        double distance = distanceToCylinder (isect, cylinderRadius,rCurrent,offset, stepLength);
        if (distance < m_shortStepMin)
        {
          log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right)
            << "  closest approach to CylinderSurface at radius "
            << std::setw(9) << std::setprecision(4) << rCurrent
            << " mm.  Cylinder radius " << std::setw(9) << std::setprecision(4) << cylinderRadius << " mm"
            << endmsg;
        }
        else
        {
          log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right) << "  CylinderSurface"
            << "  radius " << std::setw(6) << std::setprecision(1) << cylinderRadius
            << "  rCurrent " << std::setw(6) << std::setprecision(1) << rCurrent
            << "  distance " << std::setw(6) << std::setprecision(1) << stepLength;
          if (trapped) log << MSG::DEBUG << " looping in mag field ";
          log << MSG::DEBUG << endmsg;
        }
    }
    else if (dynamic_cast<const DiscSurface*>(&surface))
    {
        double stepLength = 0;
        (void)distanceToDisc (isect, surface.center().z(), stepLength);
        log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right) << "   DiscSurface"
        << " at R,Z" << std::setw(8) << std::setprecision(1) << surface.center().perp() << ","
        << std::setw(7) << std::setprecision(0) << surface.center().z()
        << "  at line distance " << std::setw(9) << std::setprecision(1) << stepLength;
        if (trapped) log << MSG::DEBUG << " looping in mag field ";
        log << MSG::DEBUG << endmsg;
    }
    else if (dynamic_cast<const PerigeeSurface*>(&surface))
    {
      log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right) << "   PerigeeSurface  "
        << endmsg;
    }
    else if (dynamic_cast<const StraightLineSurface*>(&surface))
    {
      log << MSG::DEBUG << std::setiosflags(std::ios::fixed|std::ios::right) << "   StraightLineSurface  "
        << endmsg;
    }
    log << MSG::DEBUG << endmsg;
}
 
void
RungeKuttaIntersector::shortStep (TrackSurfaceIntersection& isect,
                                  const Amg::Vector3D& fieldValue,
                                  const double stepLength,
                                  const double qOverP) const
{
    Amg::Vector3D& pos = isect.position();
    Amg::Vector3D& dir = isect.direction();
    const double cOverP = Gaudi::Units::c_light*qOverP;
 
    // as step except for const field assumption
    double    stepOverP     =  0.5*stepLength*cOverP;
    Amg::Vector3D product0  =  stepOverP*dir.cross(fieldValue);
    // intermediate point (half way through step)
    Amg::Vector3D direction1    =  dir + product0;
    Amg::Vector3D product1  =  stepOverP*direction1.cross(fieldValue);
    Amg::Vector3D direction2    =  dir + product1;
    Amg::Vector3D product2  =  stepOverP*direction2.cross(fieldValue);
    // step end point
    pos             += stepLength*(dir + m_third*(product0+product1+product2));
    Amg::Vector3D direction3    =  dir + 2.*product2;
    Amg::Vector3D product3  =  stepOverP*direction3.cross(fieldValue);
    dir             += m_third*(product0+product3 + 2.*(product1+product2));
    isect.pathlength()      += stepLength;
    ++m_countShortStep;
}
 
void
RungeKuttaIntersector::step (TrackSurfaceIntersection& isect,
                             Amg::Vector3D& fieldValue,
                             double& stepLength,
                             const double qOverP,
                             MagField::AtlasFieldCache &fieldCache) const
{
    Amg::Vector3D& pos = isect.position();
    Amg::Vector3D& dir = isect.direction();
    const double cOverP = Gaudi::Units::c_light*qOverP;
 
    double    stepOverP     =  0.5*stepLength*cOverP;
    Amg::Vector3D product0  =  stepOverP*dir.cross(fieldValue);
 
    // intermediate field look-up point (half way through step)
    Amg::Vector3D position1 =  pos + 0.5*stepLength*(dir + 0.5*product0);
    Amg::Vector3D fieldValue1   =  field(position1, fieldCache);
    Amg::Vector3D direction1    =  dir + product0;
    Amg::Vector3D product1  =  stepOverP*direction1.cross(fieldValue1);
    Amg::Vector3D direction2    =  dir + product1;
    Amg::Vector3D product2  =  stepOverP*direction2.cross(fieldValue1);
 
    // field look-up at step end point
    Amg::Vector3D offsetAtEnd   =  stepLength*(dir + m_third*(product0+product1+product2));
    Amg::Vector3D fieldAtEnd    =  field(pos+offsetAtEnd, fieldCache);
 
    // redo with reduced stepLength if non-uniform field derivative detected
    if ((fieldValue1 - 0.5 * (fieldValue + fieldAtEnd)).mag() > 0.00001 &&
        std::abs(stepLength) > m_stepMax0) {
      if (stepLength > 0.) {
          stepLength = m_stepMax0;
      } else {
          stepLength = -m_stepMax0;
      }
      ++m_countStepReduction;
      stepOverP = 0.5 * stepLength * cOverP;
      product0 = stepOverP * dir.cross(fieldValue);
      // intermediate point (half way through step)
      Amg::Vector3D position1p =
          pos + 0.5 * stepLength * (dir + 0.5 * product0);
      Amg::Vector3D fieldValue1p = field(position1p, fieldCache);
      Amg::Vector3D direction1p = dir + product0;
      product1 = stepOverP * direction1p.cross(fieldValue1p);
      Amg::Vector3D direction2p = dir + product1;
      product2 = stepOverP * direction2p.cross(fieldValue1p);
      // step end point
      offsetAtEnd =
          stepLength * (dir + m_third * (product0 + product1 + product2));
      fieldAtEnd = field(pos + offsetAtEnd, fieldCache);
    }
 
    Amg::Vector3D direction3 = dir + 2. * product2;
    Amg::Vector3D product3 = stepOverP * direction3.cross(fieldAtEnd);
    dir += m_third * (product0 + product3 + 2. * (product1 + product2));
    fieldValue = fieldAtEnd;
    pos += offsetAtEnd;
    isect.pathlength() += stepLength;
    ++m_countStep;
}
 
} // end of namespace