| /* |
| [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 2011-2013 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/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 , |
| bool control_interpolation = false ) |
| : m_error_checker( eps_abs , eps_rel , factor_x, factor_dxdt ) , |
| 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+1 ) , |
| 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) ; 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 ) |
| { |
| 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) ) |
| 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 ) |
| { |
| const size_t max_count = 1000; |
| |
| if( m_first ) |
| { |
| typename odeint::unwrap_reference< System >::type &sys = system; |
| sys( get_current_state() , get_current_deriv() , m_t ); |
| } |
| |
| controlled_step_result res = fail; |
| m_t_last = m_t; |
| size_t count = 0; |
| 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; |
| if( count++ == max_count ) |
| throw std::overflow_error( "bulirsch_stoer : too much iterations!"); |
| } |
| 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=1.0/(m_interval_sequence[k-1]); |
| value_type facmin = pow BOOST_PREVENT_MACRO_SUBSTITUTION( STEPFAC3 , expo ); |
| value_type fac; |
| if (error == 0.0) |
| fac=1.0/facmin; |
| else |
| { |
| fac = STEPFAC2 / pow BOOST_PREVENT_MACRO_SUBSTITUTION( error / STEPFAC1 , expo ); |
| fac = max BOOST_PREVENT_MACRO_SUBSTITUTION( facmin/STEPFAC4 , min BOOST_PREVENT_MACRO_SUBSTITUTION( 1.0/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+1 ; ++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; |
| |
| 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; |
| |
| const 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 |
