RK4PreciseStep Class Reference

#include <RK4PreciseStep.h>

Public Member Functions
double	distance (const CartesianState &a, const CartesianState &b) const
CartesianState	operator() (const CartesianState &start, const RKCartesianDerivative &deriv, double step, double eps) const
std::pair< CartesianState, double >	stepWithAccuracy (const CartesianState &start, const RKCartesianDerivative &deriv, double step) const

Private Member Functions
bool	verbose () const

Detailed Description

Definition at line 10 of file RK4PreciseStep.h.

Member Function Documentation

double RK4PreciseStep::distance	(	const CartesianState &	a,
		const CartesianState &	b
	)		const

Definition at line 60 of file RK4PreciseStep.cc.

References Basic3DVector< T >::mag(), mag(), CartesianState::momentum(), and CartesianState::position().

Referenced by stepWithAccuracy().

                                                                                      {
  return (a.position() - b.position()).mag() + (a.momentum() - b.momentum()).mag() / b.momentum().mag();
}

CartesianState RK4PreciseStep::operator()	(	const CartesianState &	start,
		const RKCartesianDerivative &	deriv,
		double	step,
		double	eps
	)		const

Definition at line 6 of file RK4PreciseStep.cc.

References gather_cfg::cout, mps_splice::currentStart, SiStripPI::max, SiStripPI::min, Basic3DVector< T >::perp(), CartesianState::position(), funct::pow(), command_line::start, stepWithAccuracy(), verbose(), and Basic3DVector< T >::z().

                                                            {
  const double Safety = 0.9;
  double remainigStep = step;
  double stepSize = step;
  CartesianState currentStart = start;
  int nsteps = 0;
  std::pair<CartesianState, double> tryStep;

  do {
    tryStep = stepWithAccuracy(currentStart, deriv, stepSize);
    nsteps++;
    if (tryStep.second < eps) {
      if (remainigStep - stepSize < eps / 2) {
        if (verbose())
          std::cout << "Accuracy reached, and full step taken in " << nsteps << " steps" << std::endl;
        return tryStep.first;  // we are there
      } else {
        remainigStep -= stepSize;
        // increase step size
        double factor = std::min(Safety * pow(fabs(eps / tryStep.second), 0.2), 4.);
        stepSize = std::min(stepSize * factor, remainigStep);
        currentStart = tryStep.first;
        if (verbose())
          std::cout << "Accuracy reached, but " << remainigStep << " remain after " << nsteps
                    << " steps. Step size increased by " << factor << " to " << stepSize << std::endl;
      }
    } else {
      // decrease step size
      double factor = std::max(Safety * pow(fabs(eps / tryStep.second), 0.25), 0.1);
      stepSize *= factor;
      if (verbose())
        std::cout << "Accuracy not yet reached: delta = " << tryStep.second << ", step reduced by " << factor << " to "
                  << stepSize << ", (R,z)= " << currentStart.position().perp() << ", " << currentStart.position().z()
                  << std::endl;
    }
  } while (remainigStep > eps / 2);

  return tryStep.first;
}

std::pair< CartesianState, double > RK4PreciseStep::stepWithAccuracy	(	const CartesianState &	start,
		const RKCartesianDerivative &	deriv,
		double	step
	)		const

Definition at line 49 of file RK4PreciseStep.cc.

References change_name::diff, distance(), and SiPixelPI::one.

Referenced by operator()().

                                                                                      {
  RK4OneStep solver;
  CartesianState one(solver(start, deriv, step));
  CartesianState firstHalf(solver(start, deriv, step / 2));
  CartesianState secondHalf(solver(firstHalf, deriv, step / 2));
  double diff = distance(one, secondHalf);
  return std::pair<CartesianState, double>(secondHalf, diff);
}

bool RK4PreciseStep::verbose ( ) const

private

Definition at line 64 of file RK4PreciseStep.cc.

Referenced by operator()().

{ return true; }