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Initial Commit
2018-02-08 21:28:33 -05:00
/*
[auto_generated]
boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp
[begin_description]
Implementaiton of the Burlish-Stoer method with dense output
[end_description]
Copyright 2011-2015 Mario Mulansky
Copyright 2011-2013 Karsten Ahnert
Copyright 2012 Christoph Koke
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or
copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#ifndef BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_DENSE_OUT_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_DENSE_OUT_HPP_INCLUDED
#include <iostream>
#include <algorithm>
#include <boost/config.hpp> // for min/max guidelines
#include <boost/numeric/odeint/util/bind.hpp>
#include <boost/math/special_functions/binomial.hpp>
#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
#include <boost/numeric/odeint/algebra/range_algebra.hpp>
#include <boost/numeric/odeint/algebra/default_operations.hpp>
#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
#include <boost/numeric/odeint/util/state_wrapper.hpp>
#include <boost/numeric/odeint/util/is_resizeable.hpp>
#include <boost/numeric/odeint/util/resizer.hpp>
#include <boost/numeric/odeint/util/unit_helper.hpp>
#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
#include <boost/type_traits.hpp>
namespace boost {
namespace numeric {
namespace odeint {
template<
class State ,
class Value = double ,
class Deriv = State ,
class Time = Value ,
class Algebra = typename algebra_dispatcher< State >::algebra_type ,
class Operations = typename operations_dispatcher< State >::operations_type ,
class Resizer = initially_resizer
>
class bulirsch_stoer_dense_out {
public:
typedef State state_type;
typedef Value value_type;
typedef Deriv deriv_type;
typedef Time time_type;
typedef Algebra algebra_type;
typedef Operations operations_type;
typedef Resizer resizer_type;
typedef dense_output_stepper_tag stepper_category;
#ifndef DOXYGEN_SKIP
typedef state_wrapper< state_type > wrapped_state_type;
typedef state_wrapper< deriv_type > wrapped_deriv_type;
typedef bulirsch_stoer_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > controlled_error_bs_type;
typedef typename inverse_time< time_type >::type inv_time_type;
typedef std::vector< value_type > value_vector;
typedef std::vector< time_type > time_vector;
typedef std::vector< inv_time_type > inv_time_vector; //should be 1/time_type for boost.units
typedef std::vector< value_vector > value_matrix;
typedef std::vector< size_t > int_vector;
typedef std::vector< wrapped_state_type > state_vector_type;
typedef std::vector< wrapped_deriv_type > deriv_vector_type;
typedef std::vector< deriv_vector_type > deriv_table_type;
#endif //DOXYGEN_SKIP
const static size_t m_k_max = 8;
bulirsch_stoer_dense_out(
value_type eps_abs = 1E-6 , value_type eps_rel = 1E-6 ,
value_type factor_x = 1.0 , value_type factor_dxdt = 1.0 ,
time_type max_dt = static_cast<time_type>(0) ,
bool control_interpolation = false )
: m_error_checker( eps_abs , eps_rel , factor_x, factor_dxdt ) ,
m_max_dt(max_dt) ,
m_control_interpolation( control_interpolation) ,
m_last_step_rejected( false ) , m_first( true ) ,
m_current_state_x1( true ) ,
m_error( m_k_max ) ,
m_interval_sequence( m_k_max+1 ) ,
m_coeff( m_k_max+1 ) ,
m_cost( m_k_max+1 ) ,
m_table( m_k_max ) ,
m_mp_states( m_k_max+1 ) ,
m_derivs( m_k_max+1 ) ,
m_diffs( 2*m_k_max+2 ) ,
STEPFAC1( 0.65 ) , STEPFAC2( 0.94 ) , STEPFAC3( 0.02 ) , STEPFAC4( 4.0 ) , KFAC1( 0.8 ) , KFAC2( 0.9 )
{
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
for( unsigned short i = 0; i < m_k_max+1; i++ )
{
/* only this specific sequence allows for dense output */
m_interval_sequence[i] = 2 + 4*i; // 2 6 10 14 ...
m_derivs[i].resize( m_interval_sequence[i] );
if( i == 0 )
m_cost[i] = m_interval_sequence[i];
else
m_cost[i] = m_cost[i-1] + m_interval_sequence[i];
m_coeff[i].resize(i);
for( size_t k = 0 ; k < i ; ++k )
{
const value_type r = static_cast< value_type >( m_interval_sequence[i] ) / static_cast< value_type >( m_interval_sequence[k] );
m_coeff[i][k] = 1.0 / ( r*r - static_cast< value_type >( 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 value_type logfact( -log10( max BOOST_PREVENT_MACRO_SUBSTITUTION( eps_rel , static_cast< value_type >( 1.0E-12 ) ) ) * 0.6 + 0.5 );
m_current_k_opt = max BOOST_PREVENT_MACRO_SUBSTITUTION( 1 , min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>( m_k_max-1 ) , static_cast<int>( logfact ) ));
*/
}
int num = 1;
for( int i = 2*(m_k_max)+1 ; i >=0 ; i-- )
{
m_diffs[i].resize( num );
num += (i+1)%2;
}
}
template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut >
controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , DerivOut &dxdt_new , time_type &dt )
{
if( m_max_dt != static_cast<time_type>(0) && detail::less_with_sign(m_max_dt, dt, dt) )
{
// given step size is bigger then max_dt
// set limit and return fail
dt = m_max_dt;
return fail;
}
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
using std::pow;
static const value_type val1( 1.0 );
bool reject( true );
time_vector h_opt( m_k_max+1 );
inv_time_vector work( m_k_max+1 );
m_k_final = 0;
time_type new_h = dt;
//std::cout << "t=" << t <<", dt=" << dt << ", k_opt=" << m_current_k_opt << ", first: " << m_first << std::endl;
for( size_t k = 0 ; k <= m_current_k_opt+1 ; k++ )
{
m_midpoint.set_steps( m_interval_sequence[k] );
if( k == 0 )
{
m_midpoint.do_step( system , in , dxdt , t , out , dt , m_mp_states[k].m_v , m_derivs[k]);
}
else
{
m_midpoint.do_step( system , in , dxdt , t , m_table[k-1].m_v , dt , m_mp_states[k].m_v , m_derivs[k] );
extrapolate( k , m_table , m_coeff , out );
// get error estimate
m_algebra.for_each3( m_err.m_v , out , m_table[0].m_v ,
typename operations_type::template scale_sum2< value_type , value_type >( val1 , -val1 ) );
const value_type error = m_error_checker.error( m_algebra , in , dxdt , m_err.m_v , dt );
h_opt[k] = calc_h_opt( dt , error , k );
work[k] = static_cast<value_type>( m_cost[k] ) / h_opt[k];
m_k_final = 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 = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(k)+1 ) );
new_h = h_opt[k] * static_cast<value_type>( m_cost[k+1] ) / static_cast<value_type>( m_cost[k] );
} else {
m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(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 = max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(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 = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , static_cast<int>(m_current_k_opt)+1 );
new_h = h_opt[k]*static_cast<value_type>( m_cost[m_current_k_opt] ) / static_cast<value_type>( 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 = max BOOST_PREVENT_MACRO_SUBSTITUTION( 2 , static_cast<int>(m_current_k_opt)-1 );
if( (work[k] < KFAC2*work[m_current_k_opt]) && !m_last_step_rejected )
m_current_k_opt = min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<int>(m_k_max)-1 , static_cast<int>(k) );
new_h = h_opt[m_current_k_opt];
} else
{
reject = true;
new_h = h_opt[m_current_k_opt];
}
break;
}
}
}
if( !reject )
{
//calculate dxdt for next step and dense output
typename odeint::unwrap_reference< System >::type &sys = system;
sys( out , dxdt_new , t+dt );
//prepare dense output
value_type error = prepare_dense_output( m_k_final , in , dxdt , out , dxdt_new , dt );
if( error > static_cast<value_type>(10) ) // we are not as accurate for interpolation as for the steps
{
reject = true;
new_h = dt * pow BOOST_PREVENT_MACRO_SUBSTITUTION( error , static_cast<value_type>(-1)/(2*m_k_final+2) );
} else {
t += dt;
}
}
//set next stepsize
if( !m_last_step_rejected || (new_h < dt) )
{
// limit step size
if( m_max_dt != static_cast<time_type>(0) )
{
new_h = detail::min_abs(m_max_dt, new_h);
}
dt = new_h;
}
m_last_step_rejected = reject;
if( reject )
return fail;
else
return success;
}
template< class StateType >
void initialize( const StateType &x0 , const time_type &t0 , const time_type &dt0 )
{
m_resizer.adjust_size( x0 , detail::bind( &controlled_error_bs_type::template resize_impl< StateType > , detail::ref( *this ) , detail::_1 ) );
boost::numeric::odeint::copy( x0 , get_current_state() );
m_t = t0;
m_dt = dt0;
reset();
}
/* =======================================================
* the actual step method that should be called from outside (maybe make try_step private?)
*/
template< class System >
std::pair< time_type , time_type > do_step( System system )
{
if( m_first )
{
typename odeint::unwrap_reference< System >::type &sys = system;
sys( get_current_state() , get_current_deriv() , m_t );
}
failed_step_checker fail_checker; // to throw a runtime_error if step size adjustment fails
controlled_step_result res = fail;
m_t_last = m_t;
while( res == fail )
{
res = try_step( system , get_current_state() , get_current_deriv() , m_t , get_old_state() , get_old_deriv() , m_dt );
m_first = false;
fail_checker(); // check for overflow of failed steps
}
toggle_current_state();
return std::make_pair( m_t_last , m_t );
}
/* performs the interpolation from a calculated step */
template< class StateOut >
void calc_state( time_type t , StateOut &x ) const
{
do_interpolation( t , x );
}
const state_type& current_state( void ) const
{
return get_current_state();
}
time_type current_time( void ) const
{
return m_t;
}
const state_type& previous_state( void ) const
{
return get_old_state();
}
time_type previous_time( void ) const
{
return m_t_last;
}
time_type current_time_step( void ) const
{
return m_dt;
}
/** \brief Resets the internal state of the stepper. */
void reset()
{
m_first = true;
m_last_step_rejected = false;
}
template< class StateIn >
void adjust_size( const StateIn &x )
{
resize_impl( x );
m_midpoint.adjust_size( x );
}
private:
template< class StateInOut , class StateVector >
void extrapolate( size_t k , StateVector &table , const value_matrix &coeff , StateInOut &xest , size_t order_start_index = 0 )
//polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
{
static const value_type val1( 1.0 );
for( int j=k-1 ; j>0 ; --j )
{
m_algebra.for_each3( table[j-1].m_v , table[j].m_v , table[j-1].m_v ,
typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][j + order_start_index] ,
-coeff[k + order_start_index][j + order_start_index] ) );
}
m_algebra.for_each3( xest , table[0].m_v , xest ,
typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][0 + order_start_index] ,
-coeff[k + order_start_index][0 + order_start_index]) );
}
template< class StateVector >
void extrapolate_dense_out( size_t k , StateVector &table , const value_matrix &coeff , size_t order_start_index = 0 )
//polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
{
// result is written into table[0]
static const value_type val1( 1.0 );
for( int j=k ; j>1 ; --j )
{
m_algebra.for_each3( table[j-1].m_v , table[j].m_v , table[j-1].m_v ,
typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][j + order_start_index - 1] ,
-coeff[k + order_start_index][j + order_start_index - 1] ) );
}
m_algebra.for_each3( table[0].m_v , table[1].m_v , table[0].m_v ,
typename operations_type::template scale_sum2< value_type , value_type >( val1 + coeff[k + order_start_index][order_start_index] ,
-coeff[k + order_start_index][order_start_index]) );
}
time_type calc_h_opt( time_type h , value_type error , size_t k ) const
{
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
using std::pow;
value_type expo = static_cast<value_type>(1)/(m_interval_sequence[k-1]);
value_type facmin = pow BOOST_PREVENT_MACRO_SUBSTITUTION( STEPFAC3 , expo );
value_type fac;
if (error == 0.0)
fac = static_cast<value_type>(1)/facmin;
else
{
fac = STEPFAC2 / pow BOOST_PREVENT_MACRO_SUBSTITUTION( error / STEPFAC1 , expo );
fac = max BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>( facmin/STEPFAC4 ) , min BOOST_PREVENT_MACRO_SUBSTITUTION( static_cast<value_type>(static_cast<value_type>(1)/facmin) , fac ) );
}
return h*fac;
}
bool in_convergence_window( size_t k ) const
{
if( (k == m_current_k_opt-1) && !m_last_step_rejected )
return true; // decrease order only if last step was not rejected
return ( (k == m_current_k_opt) || (k == m_current_k_opt+1) );
}
bool should_reject( value_type error , size_t k ) const
{
if( k == m_current_k_opt-1 )
{
const value_type d = m_interval_sequence[m_current_k_opt] * m_interval_sequence[m_current_k_opt+1] /
(m_interval_sequence[0]*m_interval_sequence[0]);
//step will fail, criterion 17.3.17 in NR
return ( error > d*d );
}
else if( k == m_current_k_opt )
{
const value_type d = m_interval_sequence[m_current_k_opt+1] / m_interval_sequence[0];
return ( error > d*d );
} else
return error > 1.0;
}
template< class StateIn1 , class DerivIn1 , class StateIn2 , class DerivIn2 >
value_type prepare_dense_output( int k , const StateIn1 &x_start , const DerivIn1 &dxdt_start ,
const StateIn2 & /* x_end */ , const DerivIn2 & /*dxdt_end */ , time_type dt )
/* k is the order to which the result was approximated */
{
/* compute the coefficients of the interpolation polynomial
* we parametrize the interval t .. t+dt by theta = -1 .. 1
* we use 2k+3 values at the interval center theta=0 to obtain the interpolation coefficients
* the values are x(t+dt/2) and the derivatives dx/dt , ... d^(2k+2) x / dt^(2k+2) at the midpoints
* the derivatives are approximated via finite differences
* all values are obtained from interpolation of the results from the increasing orders of the midpoint calls
*/
// calculate finite difference approximations to derivatives at the midpoint
for( int j = 0 ; j<=k ; j++ )
{
/* not working with boost units... */
const value_type d = m_interval_sequence[j] / ( static_cast<value_type>(2) * dt );
value_type f = 1.0; //factor 1/2 here because our interpolation interval has length 2 !!!
for( int kappa = 0 ; kappa <= 2*j+1 ; ++kappa )
{
calculate_finite_difference( j , kappa , f , dxdt_start );
f *= d;
}
if( j > 0 )
extrapolate_dense_out( j , m_mp_states , m_coeff );
}
time_type d = dt/2;
// extrapolate finite differences
for( int kappa = 0 ; kappa<=2*k+1 ; kappa++ )
{
for( int j=1 ; j<=(k-kappa/2) ; ++j )
extrapolate_dense_out( j , m_diffs[kappa] , m_coeff , kappa/2 );
// extrapolation results are now stored in m_diffs[kappa][0]
// divide kappa-th derivative by kappa because we need these terms for dense output interpolation
m_algebra.for_each1( m_diffs[kappa][0].m_v , typename operations_type::template scale< time_type >( static_cast<time_type>(d) ) );
d *= dt/(2*(kappa+2));
}
// dense output coefficients a_0 is stored in m_mp_states[0], a_i for i = 1...2k are stored in m_diffs[i-1][0]
// the error is just the highest order coefficient of the interpolation polynomial
// this is because we use only the midpoint theta=0 as support for the interpolation (remember that theta = -1 .. 1)
value_type error = 0.0;
if( m_control_interpolation )
{
boost::numeric::odeint::copy( m_diffs[2*k+1][0].m_v , m_err.m_v );
error = m_error_checker.error( m_algebra , x_start , dxdt_start , m_err.m_v , dt );
}
return error;
}
template< class DerivIn >
void calculate_finite_difference( size_t j , size_t kappa , value_type fac , const DerivIn &dxdt )
{
const int m = m_interval_sequence[j]/2-1;
if( kappa == 0) // no calculation required for 0th derivative of f
{
m_algebra.for_each2( m_diffs[0][j].m_v , m_derivs[j][m].m_v ,
typename operations_type::template scale_sum1< value_type >( fac ) );
}
else
{
// calculate the index of m_diffs for this kappa-j-combination
const int j_diffs = j - kappa/2;
m_algebra.for_each2( m_diffs[kappa][j_diffs].m_v , m_derivs[j][m+kappa].m_v ,
typename operations_type::template scale_sum1< value_type >( fac ) );
value_type sign = -1.0;
int c = 1;
//computes the j-th order finite difference for the kappa-th derivative of f at t+dt/2 using function evaluations stored in m_derivs
for( int i = m+static_cast<int>(kappa)-2 ; i >= m-static_cast<int>(kappa) ; i -= 2 )
{
if( i >= 0 )
{
m_algebra.for_each3( m_diffs[kappa][j_diffs].m_v , m_diffs[kappa][j_diffs].m_v , m_derivs[j][i].m_v ,
typename operations_type::template scale_sum2< value_type , value_type >( 1.0 ,
sign * fac * boost::math::binomial_coefficient< value_type >( kappa , c ) ) );
}
else
{
m_algebra.for_each3( m_diffs[kappa][j_diffs].m_v , m_diffs[kappa][j_diffs].m_v , dxdt ,
typename operations_type::template scale_sum2< value_type , value_type >( 1.0 , sign * fac ) );
}
sign *= -1;
++c;
}
}
}
template< class StateOut >
void do_interpolation( time_type t , StateOut &out ) const
{
// interpolation polynomial is defined for theta = -1 ... 1
// m_k_final is the number of order-iterations done for the last step - it governs the order of the interpolation polynomial
const value_type theta = 2 * get_unit_value( (t - m_t_last) / (m_t - m_t_last) ) - 1;
// we use only values at interval center, that is theta=0, for interpolation
// our interpolation polynomial is thus of order 2k+2, hence we have 2k+3 terms
boost::numeric::odeint::copy( m_mp_states[0].m_v , out );
// add remaining terms: x += a_1 theta + a2 theta^2 + ... + a_{2k} theta^{2k}
value_type theta_pow( theta );
for( size_t i=0 ; i<=2*m_k_final+1 ; ++i )
{
m_algebra.for_each3( out , out , m_diffs[i][0].m_v ,
typename operations_type::template scale_sum2< value_type >( static_cast<value_type>(1) , theta_pow ) );
theta_pow *= theta;
}
}
/* Resizer methods */
template< class StateIn >
bool resize_impl( const StateIn &x )
{
bool resized( false );
resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
resized |= adjust_size_by_resizeability( m_x2 , x , typename is_resizeable<state_type>::type() );
resized |= adjust_size_by_resizeability( m_dxdt1 , x , typename is_resizeable<state_type>::type() );
resized |= adjust_size_by_resizeability( m_dxdt2 , x , typename is_resizeable<state_type>::type() );
resized |= adjust_size_by_resizeability( m_err , x , typename is_resizeable<state_type>::type() );
for( size_t i = 0 ; i < m_k_max ; ++i )
resized |= adjust_size_by_resizeability( m_table[i] , x , typename is_resizeable<state_type>::type() );
for( size_t i = 0 ; i < m_k_max+1 ; ++i )
resized |= adjust_size_by_resizeability( m_mp_states[i] , x , typename is_resizeable<state_type>::type() );
for( size_t i = 0 ; i < m_k_max+1 ; ++i )
for( size_t j = 0 ; j < m_derivs[i].size() ; ++j )
resized |= adjust_size_by_resizeability( m_derivs[i][j] , x , typename is_resizeable<deriv_type>::type() );
for( size_t i = 0 ; i < 2*m_k_max+2 ; ++i )
for( size_t j = 0 ; j < m_diffs[i].size() ; ++j )
resized |= adjust_size_by_resizeability( m_diffs[i][j] , x , typename is_resizeable<deriv_type>::type() );
return resized;
}
state_type& get_current_state( void )
{
return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
}
const state_type& get_current_state( void ) const
{
return m_current_state_x1 ? m_x1.m_v : m_x2.m_v ;
}
state_type& get_old_state( void )
{
return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
}
const state_type& get_old_state( void ) const
{
return m_current_state_x1 ? m_x2.m_v : m_x1.m_v ;
}
deriv_type& get_current_deriv( void )
{
return m_current_state_x1 ? m_dxdt1.m_v : m_dxdt2.m_v ;
}
const deriv_type& get_current_deriv( void ) const
{
return m_current_state_x1 ? m_dxdt1.m_v : m_dxdt2.m_v ;
}
deriv_type& get_old_deriv( void )
{
return m_current_state_x1 ? m_dxdt2.m_v : m_dxdt1.m_v ;
}
const deriv_type& get_old_deriv( void ) const
{
return m_current_state_x1 ? m_dxdt2.m_v : m_dxdt1.m_v ;
}
void toggle_current_state( void )
{
m_current_state_x1 = ! m_current_state_x1;
}
default_error_checker< value_type, algebra_type , operations_type > m_error_checker;
modified_midpoint_dense_out< state_type , value_type , deriv_type , time_type , algebra_type , operations_type , resizer_type > m_midpoint;
time_type m_max_dt;
bool m_control_interpolation;
bool m_last_step_rejected;
bool m_first;
time_type m_t;
time_type m_dt;
time_type m_dt_last;
time_type m_t_last;
size_t m_current_k_opt;
size_t m_k_final;
algebra_type m_algebra;
resizer_type m_resizer;
wrapped_state_type m_x1 , m_x2;
wrapped_deriv_type m_dxdt1 , m_dxdt2;
wrapped_state_type m_err;
bool m_current_state_x1;
value_vector m_error; // errors of repeated midpoint steps and extrapolations
int_vector m_interval_sequence; // stores the successive interval counts
value_matrix m_coeff;
int_vector m_cost; // costs for interval count
state_vector_type m_table; // sequence of states for extrapolation
//for dense output:
state_vector_type m_mp_states; // sequence of approximations of x at distance center
deriv_table_type m_derivs; // table of function values
deriv_table_type m_diffs; // table of function values
//wrapped_state_type m_a1 , m_a2 , m_a3 , m_a4;
value_type STEPFAC1 , STEPFAC2 , STEPFAC3 , STEPFAC4 , KFAC1 , KFAC2;
};
/********** DOXYGEN **********/
/**
* \class bulirsch_stoer_dense_out
* \brief The Bulirsch-Stoer algorithm.
*
* The Bulirsch-Stoer is a controlled stepper that adjusts both step size
* and order of the method. The algorithm uses the modified midpoint and
* a polynomial extrapolation compute the solution. This class also provides
* dense output facility.
*
* \tparam State The state type.
* \tparam Value The value type.
* \tparam Deriv The type representing the time derivative of the state.
* \tparam Time The time representing the independent variable - the time.
* \tparam Algebra The algebra type.
* \tparam Operations The operations type.
* \tparam Resizer The resizer policy type.
*/
/**
* \fn bulirsch_stoer_dense_out::bulirsch_stoer_dense_out( value_type eps_abs , value_type eps_rel , value_type factor_x , value_type factor_dxdt , bool control_interpolation )
* \brief Constructs the bulirsch_stoer class, including initialization of
* the error bounds.
*
* \param eps_abs Absolute tolerance level.
* \param eps_rel Relative tolerance level.
* \param factor_x Factor for the weight of the state.
* \param factor_dxdt Factor for the weight of the derivative.
* \param control_interpolation Set true to additionally control the error of
* the interpolation.
*/
/**
* \fn bulirsch_stoer_dense_out::try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , DerivOut &dxdt_new , time_type &dt )
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed. Also, the internal order of the stepper is adjusted if required.
*
* \param system The system function to solve, hence the r.h.s. of the ODE.
* It must fulfill the Simple System concept.
* \param in The state of the ODE which should be solved.
* \param dxdt The derivative of state.
* \param t The value of the time. Updated if the step is successful.
* \param out Used to store the result of the step.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
/**
* \fn bulirsch_stoer_dense_out::initialize( const StateType &x0 , const time_type &t0 , const time_type &dt0 )
* \brief Initializes the dense output stepper.
*
* \param x0 The initial state.
* \param t0 The initial time.
* \param dt0 The initial time step.
*/
/**
* \fn bulirsch_stoer_dense_out::do_step( System system )
* \brief Does one time step. This is the main method that should be used to
* integrate an ODE with this stepper.
* \note initialize has to be called before using this method to set the
* initial conditions x,t and the stepsize.
* \param system The system function to solve, hence the r.h.s. of the
* ordinary differential equation. It must fulfill the Simple System concept.
* \return Pair with start and end time of the integration step.
*/
/**
* \fn bulirsch_stoer_dense_out::calc_state( time_type t , StateOut &x ) const
* \brief Calculates the solution at an intermediate point within the last step
* \param t The time at which the solution should be calculated, has to be
* in the current time interval.
* \param x The output variable where the result is written into.
*/
/**
* \fn bulirsch_stoer_dense_out::current_state( void ) const
* \brief Returns the current state of the solution.
* \return The current state of the solution x(t).
*/
/**
* \fn bulirsch_stoer_dense_out::current_time( void ) const
* \brief Returns the current time of the solution.
* \return The current time of the solution t.
*/
/**
* \fn bulirsch_stoer_dense_out::previous_state( void ) const
* \brief Returns the last state of the solution.
* \return The last state of the solution x(t-dt).
*/
/**
* \fn bulirsch_stoer_dense_out::previous_time( void ) const
* \brief Returns the last time of the solution.
* \return The last time of the solution t-dt.
*/
/**
* \fn bulirsch_stoer_dense_out::current_time_step( void ) const
* \brief Returns the current step size.
* \return The current step size.
*/
/**
* \fn bulirsch_stoer_dense_out::adjust_size( const StateIn &x )
* \brief Adjust the size of all temporaries in the stepper manually.
* \param x A state from which the size of the temporaries to be resized is deduced.
*/
}
}
}
#endif // BOOST_NUMERIC_ODEINT_STEPPER_BULIRSCH_STOER_HPP_INCLUDED
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