G4BulirschStoer Class Reference

#include <G4BulirschStoer.hh>

Public Types
enum class	step_result { success , fail }

Public Member Functions
	G4BulirschStoer (G4EquationOfMotion *equation, G4int nvar, G4double eps_rel, G4double max_dt=DBL_MAX)
G4EquationOfMotion *	GetEquationOfMotion ()
G4int	GetNumberOfVariables () const
void	reset ()
void	set_max_dt (G4double max_dt)
void	set_max_relative_error (G4double eps_rel)
void	SetEquationOfMotion (G4EquationOfMotion *equation)
step_result	try_step (const G4double in[], const G4double dxdt[], G4double &t, G4double out[], G4double &dt)

Private Member Functions
G4double	calc_h_opt (G4double h, G4double error, size_t k) const
void	extrapolate (size_t k, G4double xest[])
G4bool	in_convergence_window (G4int k) const
G4bool	set_k_opt (size_t k, G4double &dt)
G4bool	should_reject (G4double error, G4int k) const

Private Attributes
G4int	fnvar
G4double	h_opt [m_k_max+1]
G4double	m_coeff [m_k_max+1][m_k_max]
G4int	m_cost [m_k_max+1]
G4int	m_current_k_opt
G4double	m_dt_last
G4double	m_eps_rel
G4double	m_err [G4FieldTrack::ncompSVEC]
G4bool	m_first
G4int	m_interval_sequence [m_k_max+1]
G4bool	m_last_step_rejected
G4double	m_max_dt
G4ModifiedMidpoint	m_midpoint
G4double	m_table [m_k_max][G4FieldTrack::ncompSVEC]
G4double	work [m_k_max+1]

Static Private Attributes
static const G4int	m_k_max = 8

Detailed Description

Definition at line 43 of file G4BulirschStoer.hh.

Member Enumeration Documentation

step_result

enum class G4BulirschStoer::step_result

strong

Enumerator
success
fail

Definition at line 47 of file G4BulirschStoer.hh.

    {
      success,
      fail
    };

Constructor & Destructor Documentation

G4BulirschStoer()

G4BulirschStoer::G4BulirschStoer	(	G4EquationOfMotion *	equation,
		G4int	nvar,
		G4double	eps_rel,
		G4double	max_dt = DBL_MAX
	)

Definition at line 47 of file G4BulirschStoer.cc.

  : fnvar(nvar), m_eps_rel(eps_rel), m_midpoint(equation,nvar),
    m_last_step_rejected(false), m_first(true), m_dt_last(0.0), m_max_dt(max_dt)
{
  /* initialize sequence of stage numbers and work */
 
  for(G4int i = 0; i < m_k_max + 1; ++i)
  {
    m_interval_sequence[i] = 2 * (i + 1);
    if (i == 0)
    {
      m_cost[i] = m_interval_sequence[i];
    }
    else
    {
      m_cost[i] = m_cost[i-1] + m_interval_sequence[i];
    }
    for(G4int k = 0; k < i; ++k)
    {
      const G4double r = static_cast<G4double>(m_interval_sequence[i])
                       / static_cast<G4double>(m_interval_sequence[k]);
      m_coeff[i][k] = 1.0 / (r * r - 1.0); // coefficients for extrapolation
    }
 
    // crude estimate of optimal order
    m_current_k_opt = 4;
 
    // no calculation because log10 might not exist for value_type!
 
    //const G4double logfact = -log10(std::max(eps_rel, 1.0e-12)) * 0.6 + 0.5;
    //m_current_k_opt = std::max(1.,
    //                  std::min(static_cast<G4double>(m_k_max-1), logfact));
  }
}

References m_coeff, m_cost, m_current_k_opt, m_interval_sequence, and m_k_max.

Member Function Documentation

calc_h_opt()

G4double G4BulirschStoer::calc_h_opt ( G4double  h, G4double  error, size_t  k  ) const

private

Definition at line 259 of file G4BulirschStoer.cc.

{
  /* calculates the optimal step size for a given error and stage number */
 
  const G4double expo =  1.0 / (2 * k + 1);
  const G4double facmin = std::pow(STEPFAC3, expo);
  G4double fac;
 
  G4double facminInv= 1.0 / facmin;
  if (error == 0.0)
  {
    fac = facminInv;
  }
  else
  {
    fac = STEPFAC2 * std::pow(error * inv_STEPFAC1 , -expo);
    fac = std::max(facmin * inv_STEPFAC4, std::min( facminInv, fac));
  }
 
  return h * fac;
}

References error, fac, anonymous_namespace{G4BulirschStoer.cc}::inv_STEPFAC1, anonymous_namespace{G4BulirschStoer.cc}::inv_STEPFAC4, G4INCL::Math::max(), G4INCL::Math::min(), anonymous_namespace{G4BulirschStoer.cc}::STEPFAC2, and anonymous_namespace{G4BulirschStoer.cc}::STEPFAC3.

Referenced by try_step().

extrapolate()

void G4BulirschStoer::extrapolate ( size_t  k, G4double  xest[]  )

private

Definition at line 239 of file G4BulirschStoer.cc.

{
  /* polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
   * uses the obtained intermediate results to extrapolate to dt->0 */
 
  for(G4int j = k - 1 ; j > 0; --j)
  {
    for (G4int i = 0; i < fnvar; ++i)
    {
      m_table[j-1][i] = m_table[j][i] * (1. + m_coeff[k][j])
                      - m_table[j-1][i] * m_coeff[k][j];
    }
  }
  for (G4int i = 0; i < fnvar; ++i)
  {
    xest[i] = m_table[0][i] * (1. + m_coeff[k][0]) - xest[i] * m_coeff[k][0];
  }
}

References fnvar, m_coeff, and m_table.

Referenced by try_step().

GetEquationOfMotion()

G4EquationOfMotion * G4BulirschStoer::GetEquationOfMotion ( )

inline

GetNumberOfVariables()

G4int G4BulirschStoer::GetNumberOfVariables ( ) const

inline

in_convergence_window()

G4bool G4BulirschStoer::in_convergence_window ( G4int  k ) const

private

Definition at line 312 of file G4BulirschStoer.cc.

{
  if( (k == m_current_k_opt - 1) && !m_last_step_rejected )
  {
    return true; // decrease stepsize only if last step was not rejected
  }
  return (k == m_current_k_opt) || (k == m_current_k_opt + 1);
}

References m_current_k_opt, and m_last_step_rejected.

reset()

void G4BulirschStoer::reset

(

)

Definition at line 233 of file G4BulirschStoer.cc.

{
  m_first = true;
  m_last_step_rejected = false;
}

References m_first, and m_last_step_rejected.

Referenced by try_step().

set_k_opt()

G4bool G4BulirschStoer::set_k_opt ( size_t  k, G4double &  dt  )

private

Definition at line 282 of file G4BulirschStoer.cc.

{
  /* calculates the optimal stage number */
 
  if(k == 1)
  {
    m_current_k_opt = 2;
    return true;
  }
  if( (work[k-1] < KFAC1 * work[k]) || (k == m_k_max) )   // order decrease
  {
    m_current_k_opt = k - 1;
    dt = h_opt[ m_current_k_opt ];
    return true;
  }
  else if( (work[k] < KFAC2 * work[k-1])
          || m_last_step_rejected || (k == m_k_max-1) )
  {  // same order - also do this if last step got rejected
    m_current_k_opt = k;
    dt = h_opt[m_current_k_opt];
    return true;
  }
  else {   // order increase - only if last step was not rejected
    m_current_k_opt = k + 1;
    dt = h_opt[m_current_k_opt - 1] * m_cost[m_current_k_opt]
       / m_cost[m_current_k_opt - 1];
    return true;
  }
}

References h_opt, anonymous_namespace{G4BulirschStoer.cc}::KFAC1, anonymous_namespace{G4BulirschStoer.cc}::KFAC2, m_cost, m_current_k_opt, m_k_max, m_last_step_rejected, and work.

set_max_dt()

void G4BulirschStoer::set_max_dt ( G4double  max_dt )

inline

set_max_relative_error()

void G4BulirschStoer::set_max_relative_error ( G4double  eps_rel )

inline

SetEquationOfMotion()

void G4BulirschStoer::SetEquationOfMotion ( G4EquationOfMotion *  equation )

inline

should_reject()

G4bool G4BulirschStoer::should_reject ( G4double  error, G4int  k  ) const

private

Definition at line 322 of file G4BulirschStoer.cc.

{
  if(k == m_current_k_opt - 1)
  {
    const G4double d = G4double(m_interval_sequence[m_current_k_opt]
                              * m_interval_sequence[m_current_k_opt+1]);
    const G4double e = G4double(m_interval_sequence[0]);
    const G4double e2 = e*e; 
    // step will fail, criterion 17.3.17 in NR
    return error * e2 * e2 > d * d;  //  was return error > dOld * dOld; (where dOld= d/e; )
  }
  else if(k == m_current_k_opt)
  {
    const G4double d = G4double(m_interval_sequence[m_current_k_opt]);
    const G4double e = G4double(m_interval_sequence[0]);
    return error * e * e > d * d; //  was return error > dOld * dOld; (where dOld= d/e; )
  }
  else
  {
    return error > 1.0;
  }
}

References e2, error, m_current_k_opt, and m_interval_sequence.

Referenced by try_step().

try_step()

G4BulirschStoer::step_result G4BulirschStoer::try_step	(	const G4double	in[],
		const G4double	dxdt[],
		G4double &	t,
		G4double	out[],
		G4double &	dt
	)

Definition at line 84 of file G4BulirschStoer.cc.

{
  if(m_max_dt < dt)
  {
    // given step size is bigger then max_dt set limit and return fail
    //
    dt = m_max_dt;
    return step_result::fail;
  }
 
  if (dt != m_dt_last)
  {
    reset(); // step size changed from outside -> reset
  }
 
  G4bool reject = true;
 
  G4double new_h = dt;
 
  /* m_current_k_opt is the estimated current optimal stage number */
 
  for(G4int k = 0; k <= m_current_k_opt+1; ++k)
  {
    // the stage counts are stored in m_interval_sequence
    //
    m_midpoint.SetSteps(m_interval_sequence[k]);
    if(k == 0)
    {
      m_midpoint.DoStep(in, dxdt, out, dt);
      /* the first step, nothing more to do */
    }
    else
    {
      m_midpoint.DoStep(in, dxdt, m_table[k-1], dt);
      extrapolate(k, out);
      // get error estimate
      for (G4int i = 0; i < fnvar; ++i)
      {
        m_err[i] = out[i] - m_table[0][i];
      }
      const G4double error =
            field_utils::relativeError(out, m_err, dt, m_eps_rel);
      h_opt[k] = calc_h_opt(dt, error, k);
      work[k] = static_cast<G4double>(m_cost[k]) / h_opt[k];
 
      if( (k == m_current_k_opt-1) || m_first)  // convergence before k_opt ?
      {
        if(error < 1.0)
        {
          // convergence
          reject = false;
          if( (work[k] < KFAC2 * work[k-1]) || (m_current_k_opt <= 2) )
          {
            // leave order as is (except we were in first round)
            m_current_k_opt = std::min(m_k_max - 1 , std::max(2 , k + 1));
            new_h = h_opt[k];
            new_h *= static_cast<G4double>(m_cost[k + 1])
                   / static_cast<G4double>(m_cost[k]);
          }
          else
          {
            m_current_k_opt = std::min(m_k_max - 1, std::max(2, k));
            new_h = h_opt[k];
          }
          break;
        }
        else if(should_reject(error , k) && !m_first)
        {
          reject = true;
          new_h = h_opt[k];
          break;
        }
      }
      if(k == m_current_k_opt)  // convergence at k_opt ?
      {
        if(error < 1.0)
        {
          // convergence
          reject = false;
          if(work[k-1] < KFAC2 * work[k])
          {
            m_current_k_opt = std::max( 2 , m_current_k_opt-1 );
            new_h = h_opt[m_current_k_opt];
          }
          else if( (work[k] < KFAC2 * work[k-1]) && !m_last_step_rejected )
          {
            m_current_k_opt = std::min(m_k_max - 1, m_current_k_opt + 1);
            new_h = h_opt[k];
            new_h *= static_cast<G4double>(m_cost[m_current_k_opt])
                   / static_cast<G4double>(m_cost[k]);
          }
          else
          {
            new_h = h_opt[m_current_k_opt];
          }
          break;
        }
        else if(should_reject(error, k))
        {
          reject = true;
          new_h = h_opt[m_current_k_opt];
          break;
        }
      }
      if(k == m_current_k_opt + 1)  // convergence at k_opt+1 ?
      {
        if(error < 1.0)  // convergence
        {
          reject = false;
          if(work[k-2] < KFAC2 * work[k-1])
          {
            m_current_k_opt = std::max(2, m_current_k_opt - 1);
          }
          if((work[k] < KFAC2 * work[m_current_k_opt]) && !m_last_step_rejected)
          {
            m_current_k_opt = std::min(m_k_max - 1 , k);
          }
          new_h = h_opt[m_current_k_opt];
        }
        else
        {
          reject = true;
          new_h = h_opt[m_current_k_opt];
        }
        break;
      }
    }
  }
 
  if(!reject)
  {
    t += dt;
  }
 
  if(!m_last_step_rejected || new_h < dt)
  {
    // limit step size
    new_h = std::min(m_max_dt, new_h);
    m_dt_last = new_h;
    dt = new_h;
  }
 
  m_last_step_rejected = reject;
  m_first = false;
 
  return reject ? step_result::fail : step_result::success;
}

References calc_h_opt(), G4ModifiedMidpoint::DoStep(), error, extrapolate(), fail, fnvar, h_opt, anonymous_namespace{G4BulirschStoer.cc}::KFAC2, m_cost, m_current_k_opt, m_dt_last, m_eps_rel, m_err, m_first, m_interval_sequence, m_k_max, m_last_step_rejected, m_max_dt, m_midpoint, m_table, G4INCL::Math::max(), G4INCL::Math::min(), field_utils::relativeError(), reset(), G4ModifiedMidpoint::SetSteps(), should_reject(), success, and work.

Field Documentation

fnvar

G4int G4BulirschStoer::fnvar

private

Definition at line 85 of file G4BulirschStoer.hh.

Referenced by extrapolate(), and try_step().

h_opt

G4double G4BulirschStoer::h_opt[m_k_max+1]

private

Definition at line 121 of file G4BulirschStoer.hh.

Referenced by set_k_opt(), and try_step().

m_coeff

G4double G4BulirschStoer::m_coeff[m_k_max+1][m_k_max]

private

Definition at line 112 of file G4BulirschStoer.hh.

Referenced by extrapolate(), and G4BulirschStoer().

m_cost

G4int G4BulirschStoer::m_cost[m_k_max+1]

private

Definition at line 115 of file G4BulirschStoer.hh.

Referenced by G4BulirschStoer(), set_k_opt(), and try_step().

m_current_k_opt

G4int G4BulirschStoer::m_current_k_opt

private

Definition at line 102 of file G4BulirschStoer.hh.

Referenced by G4BulirschStoer(), in_convergence_window(), set_k_opt(), should_reject(), and try_step().

m_dt_last

G4double G4BulirschStoer::m_dt_last

private

Definition at line 96 of file G4BulirschStoer.hh.

Referenced by try_step().

m_eps_rel

G4double G4BulirschStoer::m_eps_rel

private

Definition at line 88 of file G4BulirschStoer.hh.

Referenced by try_step().

m_err

G4double G4BulirschStoer::m_err[G4FieldTrack::ncompSVEC]

private

Definition at line 105 of file G4BulirschStoer.hh.

Referenced by try_step().

m_first

G4bool G4BulirschStoer::m_first

private

Definition at line 94 of file G4BulirschStoer.hh.

Referenced by reset(), and try_step().

m_interval_sequence

G4int G4BulirschStoer::m_interval_sequence[m_k_max+1]

private

Definition at line 109 of file G4BulirschStoer.hh.

Referenced by G4BulirschStoer(), should_reject(), and try_step().

m_k_max

const G4int G4BulirschStoer::m_k_max = 8

staticprivate

Definition at line 75 of file G4BulirschStoer.hh.

Referenced by G4BulirschStoer(), set_k_opt(), and try_step().

m_last_step_rejected

G4bool G4BulirschStoer::m_last_step_rejected

private

Definition at line 93 of file G4BulirschStoer.hh.

Referenced by in_convergence_window(), reset(), set_k_opt(), and try_step().

m_max_dt

G4double G4BulirschStoer::m_max_dt

private

Definition at line 100 of file G4BulirschStoer.hh.

Referenced by try_step().

m_midpoint

G4ModifiedMidpoint G4BulirschStoer::m_midpoint

private

Definition at line 91 of file G4BulirschStoer.hh.

Referenced by try_step().

m_table

G4double G4BulirschStoer::m_table[m_k_max][G4FieldTrack::ncompSVEC]

private

Definition at line 118 of file G4BulirschStoer.hh.

Referenced by extrapolate(), and try_step().

work

G4double G4BulirschStoer::work[m_k_max+1]

private

Definition at line 124 of file G4BulirschStoer.hh.

Referenced by set_k_opt(), and try_step().

---

The documentation for this class was generated from the following files:

• source/geometry/magneticfield/include/G4BulirschStoer.hh
• source/geometry/magneticfield/src/G4BulirschStoer.cc