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 //
 // G4InterpolationDriver inline implementation
 //
 // Created: D.Sorokin, 2018
 // --------------------------------------------------------------------
 
 #include "G4Exception.hh"
 #include "G4FieldUtils.hh"
 #include "G4LineSection.hh"
 
 #include <CLHEP/Units/SystemOfUnits.h>
 
 #include <algorithm>
 
 template <class T, G4bool StepperCachesDchord>
 G4InterpolationDriver<T, StepperCachesDchord>::G4InterpolationDriver(
   G4double hminimum, T* pStepper, G4int numComponents, G4int statisticsVerbose)
   : G4RKIntegrationDriver<T>(pStepper), fMinimumStep(hminimum), fVerboseLevel(statisticsVerbose)
 {
   if (numComponents != Base::GetStepper()->GetNumberOfVariables()) {
     std::ostringstream message;
     message << "Driver's number of integrated components " << numComponents
             << " != Stepper's number of components " << pStepper->GetNumberOfVariables();
     G4Exception("G4InterpolationDriver", "GeomField0002", FatalException, message);
   }
 
   for (G4int i = 0; i < Base::GetMaxNoSteps(); ++i) {
     fSteppers.push_back(
       {std::unique_ptr<T>(
          new T(pStepper->GetSpecificEquation(),  // Interpolating stepper must have this!
            pStepper->GetNumberOfVariables())),
         DBL_MAX, -DBL_MAX, 0.0});
   }
 
   fLastStepper = fSteppers.end();
 }
 
 template <class T, G4bool StepperCachesDchord>
 G4InterpolationDriver<T, StepperCachesDchord>::~G4InterpolationDriver()
 {
 #ifdef G4VERBOSE
   if (fVerboseLevel > 0) {
     G4cout << "G4ChordFinder statistics report: \n"
            << "  No trials: " << fTotalNoTrials << "  No Calls: " << fNoCalls
            << "  Max-trial: " << fmaxTrials << G4endl;
   }
 #endif
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::OnStartTracking()
 {
   fChordStepEstimate = DBL_MAX;
   fhnext = DBL_MAX;
   fTotalStepsForTrack = 0;
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::OnComputeStep(const G4FieldTrack* /*track*/)
 {
   fKeepLastStepper = false;
   fFirstStep = true;
   fLastStepper = fSteppers.end();
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::SetVerboseLevel(G4int level)
 {
   fVerboseLevel = level;
 }
 
 template <class T, G4bool StepperCachesDchord>
 G4int G4InterpolationDriver<T, StepperCachesDchord>::GetVerboseLevel() const
 {
   return fVerboseLevel;
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::Interpolate(
   G4double curveLength, field_utils::State& y) const
 {
   if (fLastStepper == fSteppers.end()) {
     std::ostringstream message;
     message << "LOGICK ERROR: fLastStepper == end";
     G4Exception("G4InterpolationDriver::Interpolate()", "GeomField1001", FatalException, message);
     return;
   }
 
   ConstStepperIterator end = fLastStepper + 1;
 
   auto it = std::lower_bound(fSteppers.cbegin(), end, curveLength,
     [](const InterpStepper& stepper, G4double value) { return stepper.end < value; });
   if (it == end) {
     if (curveLength - fLastStepper->end > CLHEP::perMillion) {
       std::ostringstream message;
       message << "curveLength = " << curveLength << " > " << fLastStepper->end;
       G4Exception("G4InterpolationDriver::Interpolate()", "GeomField1001", JustWarning, message);
     }
 
     return fLastStepper->stepper->Interpolate(1, y);
   }
 
   if (curveLength < it->begin) {
     if (it->begin - curveLength > CLHEP::perMillion) {
       std::ostringstream message;
       message << "curveLength = " << curveLength << " < " << it->begin;
       G4Exception("G4InterpolationDriver::Interpolate()", "GeomField1001", JustWarning, message);
     }
 
     return it->stepper->Interpolate(0, y);
   }
 
   return InterpolateImpl(curveLength, it, y);
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::InterpolateImpl(
   G4double curveLength, ConstStepperIterator it, field_utils::State& y) const
 {
   const G4double tau = (curveLength - it->begin) * it->inverseLength;
   return it->stepper->Interpolate(field_utils::clamp(tau, 0., 1.), y);
 }
 
 template <class T, G4bool StepperCachesDchord>
 G4double G4InterpolationDriver<T, StepperCachesDchord>::DistChord(const field_utils::State& yBegin,
   G4double curveLengthBegin, const field_utils::State& yEnd, G4double curveLengthEnd) const
 {
   if (StepperCachesDchord) {
     // optimization check if it worth
     //
     if (curveLengthBegin == fLastStepper->begin && curveLengthEnd == fLastStepper->end) {
       return fLastStepper->stepper
         ->DistChord();  // QssStepper Returns 0.0  !???  Not implemented => WRONG
     }
   }
 
   const G4double curveLengthMid = 0.5 * (curveLengthBegin + curveLengthEnd);
   field_utils::State yMid;
 
   Interpolate(curveLengthMid, yMid);
 
   return G4LineSection::Distline(field_utils::makeVector(yMid, field_utils::Value3D::Position),
     field_utils::makeVector(yBegin, field_utils::Value3D::Position),
     field_utils::makeVector(yEnd, field_utils::Value3D::Position));
 }
 
 template <class T, G4bool StepperCachesDchord>
 G4double G4InterpolationDriver<T, StepperCachesDchord>::AdvanceChordLimited(
   G4FieldTrack& track, G4double hstep, G4double epsStep, G4double chordDistance)
 {
   ++fTotalStepsForTrack;
 
   const G4double curveLengthBegin = track.GetCurveLength();
   const G4double hend = std::min(hstep, fChordStepEstimate);
   G4double hdid = 0.0;
   auto it = fSteppers.begin();
   G4double dChordStep = 0.0;
 
   field_utils::State yBegin, y;
   track.DumpToArray(yBegin);
   track.DumpToArray(y);
 
   if (fFirstStep) {
     Base::GetEquationOfMotion()->RightHandSide(y, fdydx);
     fFirstStep = false;
   }
 
   if (fKeepLastStepper) {
     std::swap(*fSteppers.begin(), *fLastStepper);
     it = fSteppers.begin();  // new begin, update iterator
     fLastStepper = it;
     hdid = it->end - curveLengthBegin;
     if (hdid > hend) {
       hdid = hend;
       InterpolateImpl(curveLengthBegin + hdid, it, y);
     }
     else {
       field_utils::copy(y, it->stepper->GetYOut());
     }
 
     dChordStep = DistChord(yBegin, curveLengthBegin, y, curveLengthBegin + hdid);
 
     ++it;
   }
 
   // accurate advance & check chord distance
   G4double h = fhnext;
   for (; hdid < hend && dChordStep < chordDistance && it != fSteppers.end(); ++it) {
     h = std::min(h, hstep - hdid);
 
     // make one step
     hdid += OneGoodStep(it, y, fdydx, h, epsStep, curveLengthBegin + hdid, &track);
 
     // update last stepper
     fLastStepper = it;
 
     // estimate chord distance
     dChordStep =
       std::max(dChordStep, DistChord(yBegin, curveLengthBegin, y, curveLengthBegin + hdid));
   }
 
   // Now, either
   //   - full integration ( hdid >= hend )
   //   - estimated chord has exceeded limit 'chordDistance'
   //   - reached maximum number of steps (from number of steppers.)
 
   // update step estimation
   if (h > fMinimumStep) {
     fhnext = h;
   }
 
   // CheckState();
 
   // update chord step estimate
   //
   hdid =
     FindNextChord(yBegin, curveLengthBegin, y, curveLengthBegin + hdid, dChordStep, chordDistance);
 
   const G4double curveLengthEnd = curveLengthBegin + hdid;
   fKeepLastStepper = fLastStepper->end - curveLengthEnd > CLHEP::perMillion;
   track.LoadFromArray(y, fLastStepper->stepper->GetNumberOfVariables());
   track.SetCurveLength(curveLengthBegin + hdid);
 
   return hdid;
 }
 
 template <class T, G4bool StepperCachesDchord>
 G4double G4InterpolationDriver<T, StepperCachesDchord>::FindNextChord(
   const field_utils::State& yBegin, G4double curveLengthBegin, field_utils::State& yEnd,
   G4double curveLengthEnd, G4double dChord, G4double chordDistance)
 {
   G4double hstep = curveLengthEnd - curveLengthBegin;
   G4double curveLength = curveLengthEnd;
 
   G4int i = 1;
   for (; i < fMaxTrials && dChord > chordDistance && curveLength > fLastStepper->begin; ++i) {
     // crop step size
     hstep = CalcChordStep(hstep, dChord, chordDistance);
 
     // hstep should be in the last stepper
     hstep = std::max(hstep, fLastStepper->begin - curveLengthBegin);
     curveLength = curveLengthBegin + hstep;
 
     // use fLastStepper!
     InterpolateImpl(curveLength, fLastStepper, yEnd);
 
     // update chord distance
     dChord = DistChord(yBegin, curveLengthBegin, yEnd, curveLength);
   }
 
   // dChord may be zero
   //
   if (dChord > 0.0) {
     fChordStepEstimate = hstep * std::sqrt(chordDistance / dChord);
   }
 
   if (i == fMaxTrials) {
     G4Exception(
       "G4InterpolationDriver::FindNextChord()", "GeomField1001", JustWarning, "cannot converge");
   }
 
   AccumulateStatistics(i);
 
   return hstep;
 }
 
 // Is called to estimate the next step size, even for successful steps,
 // in order to predict an accurate 'chord-sensitive' first step
 // which is likely to assist in more performant 'stepping'.
 //
 template <class T, G4bool StepperCachesDchord>
 G4double G4InterpolationDriver<T, StepperCachesDchord>::CalcChordStep(
   G4double stepTrialOld, G4double dChordStep, G4double chordDistance)
 {
   const G4double chordStepEstimate = stepTrialOld * std::sqrt(chordDistance / dChordStep);
   G4double stepTrial = fFractionNextEstimate * chordStepEstimate;
 
   if (stepTrial <= 0.001 * stepTrialOld) {
     if (dChordStep > 1000.0 * chordDistance) {
       stepTrial = stepTrialOld * 0.03;
     }
     else {
       if (dChordStep > 100. * chordDistance) {
         stepTrial = stepTrialOld * 0.1;
       }
       else  // Try halving the length until dChordStep OK
       {
         stepTrial = stepTrialOld * 0.5;
       }
     }
   }
   else if (stepTrial > 1000.0 * stepTrialOld) {
     stepTrial = 1000.0 * stepTrialOld;
   }
 
   if (stepTrial == 0.0) {
     stepTrial = 0.000001;
   }
 
   // A more sophisticated chord-finder could figure out a better
   // stepTrial, from dChordStep and the required d_geometry
   //   e.g.
   //      Calculate R, r_helix (eg at orig point)
   //      if( stepTrial < 2 pi  R )
   //          stepTrial = R arc_cos( 1 - chordDistance / r_helix )
   //      else
   //          ??
 
   return stepTrial;
 }
 
 template <class T, G4bool StepperCachesDchord>
 G4bool G4InterpolationDriver<T, StepperCachesDchord>::AccurateAdvance(
   G4FieldTrack& track, G4double hstep, G4double /*eps*/, G4double /*hinitial*/
 )
 {
   if (hstep == 0.0) {
     std::ostringstream message;
     message << "Proposed step is zero; hstep = " << hstep << " !";
     G4Exception("G4InterpolationDriver::AccurateAdvance()", "GeomField1001", JustWarning, message);
     return true;
   }
 
   if (hstep < 0) {
     std::ostringstream message;
     message << "Invalid run condition." << G4endl << "Proposed step is negative; hstep = " << hstep
             << "." << G4endl << "Requested step cannot be negative! Aborting event.";
     G4Exception(
       "G4InterpolationDriver::AccurateAdvance()", "GeomField0003", EventMustBeAborted, message);
     return false;
   }
 
   const G4double curveLength = track.GetCurveLength();
   const G4double curveLengthEnd = curveLength + hstep;
 
   field_utils::State y;
   Interpolate(curveLengthEnd, y);
 
   track.LoadFromArray(y, Base::GetStepper()->GetNumberOfVariables());
   track.SetCurveLength(curveLengthEnd);
 
   return true;
 }
 
 // Driver for one Runge-Kutta Step with monitoring of local truncation error
 // to ensure accuracy and adjust stepsize. Input are dependent variable
 // array y[0,...,5] and its derivative dydx[0,...,5] at the
 // starting value of the independent variable x . Also input are stepsize
 // to be attempted htry, and the required accuracy eps. On output y and x
 // are replaced by their new values, hdid is the stepsize that was actually
 // accomplished, and hnext is the estimated next stepsize.
 // This is similar to the function rkqs from the book:
 // Numerical Recipes in C: The Art of Scientific Computing (NRC), Second
 // Edition, by William H. Press, Saul A. Teukolsky, William T.
 // Vetterling, and Brian P. Flannery (Cambridge University Press 1992),
 // 16.2 Adaptive StepSize Control for Runge-Kutta, p. 719
 //
 template <class T, G4bool StepperCachesDchord>
 G4double G4InterpolationDriver<T, StepperCachesDchord>::OneGoodStep(StepperIterator it,
   field_utils::State& y, field_utils::State& dydx, G4double& hstep, G4double epsStep,
   G4double curveLength, G4FieldTrack* /*track*/)
 
 {
   G4double error2 = DBL_MAX;
   field_utils::State yerr, ytemp, dydxtemp;
   G4double h = hstep;
 
   G4int i = 0;
   for (; i < fMaxTrials; ++i) {
     it->stepper->Stepper(y, dydx, h, ytemp, yerr, dydxtemp);
     error2 = field_utils::relativeError2(y, yerr, h, epsStep);
 
     if (error2 <= 1.0) {
       hstep = std::max(Base::GrowStepSize2(h, error2), fMinimumStep);
       break;
     }
 
     // don't control error for small steps
     if (h <= fMinimumStep) {
       hstep = fMinimumStep;
       break;
     }
 
     h = std::max(Base::ShrinkStepSize2(h, error2), fMinimumStep);
   }
 
   if (i == fMaxTrials) {
     G4Exception(
       "G4InterpolationDriver::OneGoodStep()", "GeomField1001", JustWarning, "cannot converge");
     hstep = std::max(Base::ShrinkStepSize2(h, error2), fMinimumStep);
   }
 
   // set interpolation inverval
   it->begin = curveLength;
   it->end = curveLength + h;
   it->inverseLength = 1. / h;
 
   // setup interpolation
   it->stepper->SetupInterpolation();
 
   field_utils::copy(dydx, dydxtemp);
   field_utils::copy(y, ytemp);
 
   return h;
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::PrintState() const
 {
   using namespace field_utils;
   State prevEnd, currBegin;
   auto prev = fSteppers.begin();
 
   G4cout << "====== curr state ========" << G4endl;
   for (auto i = fSteppers.begin(); i <= fLastStepper; ++i) {
     i->stepper->Interpolate(0, currBegin);
 
     G4cout << "cl_begin: " << i->begin << " "
            << "cl_end: " << i->end << " ";
 
     if (prev != i) {
       prev->stepper->Interpolate(1, prevEnd);
       auto prevPos = makeVector(prevEnd, Value3D::Position);
       auto currPos = makeVector(currBegin, Value3D::Position);
       G4cout << "diff_begin: " << (prevPos - currPos).mag();
     }
 
     G4cout << G4endl;
     prev = i;
   }
 
   const G4double clBegin = fSteppers.begin()->begin;
   const G4double clEnd = fLastStepper->end;
   const G4double hstep = (clEnd - clBegin) / 10.;
   State yBegin, yCurr;
   Interpolate(0, yBegin);
   for (G4double cl = clBegin; cl <= clEnd + 1e-12; cl += hstep) {
     Interpolate(cl, yCurr);
     auto d = DistChord(yBegin, clBegin, yCurr, cl);
     G4cout << "cl: " << cl << " chord_distance: " << d << G4endl;
   }
 
   G4cout << "==========================" << G4endl;
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::CheckState() const
 {
   G4int smallSteps = 0;
   for (auto i = fSteppers.begin(); i <= fLastStepper; ++i) {
     G4double stepLength = i->end - i->begin;
     if (stepLength < fMinimumStep) {
       ++smallSteps;
     }
   }
 
   if (smallSteps > 1) {
     std::ostringstream message;
     message << "====== curr state ========\n";
     for (auto i = fSteppers.begin(); i <= fLastStepper; ++i) {
       message << "cl_begin: " << i->begin << " "
               << "cl_end: " << i->end << "\n";
     }
 
     G4Exception("G4InterpolationDriver::CheckState()", "GeomField0003", FatalException, message);
   }
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::AccumulateStatistics(G4int noTrials)
 {
   fTotalNoTrials += noTrials;
   ++fNoCalls;
 
   if (noTrials > fmaxTrials) {
     fmaxTrials = noTrials;
   }
 }
 
 template <class T, G4bool StepperCachesDchord>
 void G4InterpolationDriver<T, StepperCachesDchord>::StreamInfo(std::ostream& os) const
 {
   os << "State of G4InterpolationDriver: " << std::endl;
   os << "--Base state (G4RKIntegrationDriver): " << std::endl;
   Base::StreamInfo(os);
   os << "  fMinimumStep   =      " << fMinimumStep << std::endl;
   // os << "  Max number of Steps = " << fMaxNoSteps << std::endl;
   // os << "  Safety factor       = " << safety  << std::endl;
   // os << "  Power - shrink      = " << pshrnk << std::endl;
   // os << "  Power - grow        = " << pgrow << std::endl;
   // os << "  threshold - shrink  = " << errorConstraintShrink << std::endl;
   // os << "  threshold - grow    = " << errorConstraintGrow   << std::endl;
 
   os << "  Max num of Trials   = " << fMaxTrials << std::endl;
   os << "  Fract Next Estimate = " << fFractionNextEstimate << std::endl;
   os << "  Smallest Curve Fract= " << fSmallestCurveFraction << std::endl;
 
   os << "  VerboseLevel        = " << fVerboseLevel << std::endl;
   os << "  KeepLastStepper     = " << fKeepLastStepper << std::endl;
 }

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