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boost/numeric/odeint/stepper/extrapolation_stepper.hpp

/*
  [auto_generated]
  boost/numeric/odeint/stepper/extrapolation_stepper.hpp

  [begin_description]
  extrapolation stepper
  [end_description]

  Copyright 2009-2015 Mario Mulansky

  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_EXTRAPOLATION_STEPPER_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_STEPPER_EXTRAPOLATION_STEPPER_HPP_INCLUDED

#include <iostream>

#include <algorithm>

#include <boost/config.hpp> // for min/max guidelines
#include <boost/static_assert.hpp>

#include <boost/numeric/odeint/util/bind.hpp>
#include <boost/numeric/odeint/util/unwrap_reference.hpp>

#include <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.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/util/detail/less_with_sign.hpp>

namespace boost
{
namespace numeric
{
namespace odeint
{

template < unsigned short Order, 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 >
#ifndef DOXYGEN_SKIP
class extrapolation_stepper
    : public explicit_error_stepper_base<
          extrapolation_stepper< Order, State, Value, Deriv, Time, Algebra,
                                 Operations, Resizer >,
          Order, Order, Order - 2, State, Value, Deriv, Time, Algebra,
          Operations, Resizer >
#else
class extrapolation_stepper : public explicit_error_stepper_base
#endif
{

  private:
    // check for Order being odd
    BOOST_STATIC_ASSERT_MSG(
        ( ( Order % 2 ) == 0 ) && ( Order > 2 ),
        "extrapolation_stepper requires even Order larger than 2" );

  public:
#ifndef DOXYGEN_SKIP
    typedef explicit_error_stepper_base<
        extrapolation_stepper< Order, State, Value, Deriv, Time, Algebra,
                               Operations, Resizer >,
        Order, Order, Order - 2, State, Value, Deriv, Time, Algebra, Operations,
        Resizer > stepper_base_type;
#else
    typedef explicit_error_stepper_base< extrapolation_stepper< ... >, ... >
    stepper_base_type;
#endif

    typedef typename stepper_base_type::state_type state_type;
    typedef typename stepper_base_type::value_type value_type;
    typedef typename stepper_base_type::deriv_type deriv_type;
    typedef typename stepper_base_type::time_type time_type;
    typedef typename stepper_base_type::algebra_type algebra_type;
    typedef typename stepper_base_type::operations_type operations_type;
    typedef typename stepper_base_type::resizer_type resizer_type;

#ifndef DOXYGEN_SKIP
    typedef typename stepper_base_type::stepper_type stepper_type;
    typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
    typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;

    typedef std::vector< value_type > value_vector;
    typedef std::vector< value_vector > value_matrix;
    typedef std::vector< size_t > int_vector;
    typedef std::vector< wrapped_state_type > state_table_type;
    typedef modified_midpoint< state_type, value_type, deriv_type, time_type,
                               algebra_type, operations_type,
                               resizer_type > midpoint_stepper_type;

#endif // DOXYGEN_SKIP

    typedef unsigned short order_type;
    static const order_type order_value = stepper_base_type::order_value;
    static const order_type stepper_order_value =
        stepper_base_type::stepper_order_value;
    static const order_type error_order_value =
        stepper_base_type::error_order_value;

    const static size_t m_k_max = ( order_value - 2 ) / 2;

    extrapolation_stepper( const algebra_type &algebra = algebra_type() )
        : stepper_base_type( algebra ), m_interval_sequence( m_k_max + 1 ),
          m_coeff( m_k_max + 1 ), m_table( m_k_max )
    {
        for ( unsigned short i = 0; i < m_k_max + 1; i++ )
        {
            m_interval_sequence[i] = 2 * ( i + 1 );
            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] =
                    static_cast< value_type >( 1 ) /
                    ( r * r - static_cast< value_type >(
                                  1 ) ); // coefficients for extrapolation
            }
        }
    }

    template < class System, class StateIn, class DerivIn, class StateOut,
               class Err >
    void do_step_impl( System system, const StateIn &in, const DerivIn &dxdt,
                       time_type t, StateOut &out, time_type dt, Err &xerr )
    {
        // std::cout << "dt: " << dt << std::endl;
        // normal step
        do_step_impl( system, in, dxdt, t, out, dt );

        static const value_type val1( 1.0 );
        // additionally, perform the error calculation
        stepper_base_type::m_algebra.for_each3(
            xerr, out, m_table[0].m_v,
            typename operations_type::template scale_sum2<
                value_type, value_type >( val1, -val1 ) );
    }

    template < class System, class StateInOut, class DerivIn, class Err >
    void do_step_impl_io( System system, StateInOut &inout, const DerivIn &dxdt,
                          time_type t, time_type dt, Err &xerr )
    {
        // normal step
        do_step_impl_io( system, inout, dxdt, t, dt );

        static const value_type val1( 1.0 );
        // additionally, perform the error calculation
        stepper_base_type::m_algebra.for_each3(
            xerr, inout, m_table[0].m_v,
            typename operations_type::template scale_sum2<
                value_type, value_type >( val1, -val1 ) );
    }

    template < class System, class StateIn, class DerivIn, class StateOut >
    void do_step_impl( System system, const StateIn &in, const DerivIn &dxdt,
                       time_type t, StateOut &out, time_type dt )
    {
        m_resizer.adjust_size(
            in, detail::bind( &stepper_type::template resize_impl< StateIn >,
                              detail::ref( *this ), detail::_1 ) );
        size_t k = 0;
        m_midpoint.set_steps( m_interval_sequence[k] );
        m_midpoint.do_step( system, in, dxdt, t, out, dt );
        for ( k = 1; k <= m_k_max; ++k )
        {
            m_midpoint.set_steps( m_interval_sequence[k] );
            m_midpoint.do_step( system, in, dxdt, t, m_table[k - 1].m_v, dt );
            extrapolate( k, m_table, m_coeff, out );
        }
    }

    template < class System, class StateInOut, class DerivIn >
    void do_step_impl_io( System system, StateInOut &inout, const DerivIn &dxdt,
                          time_type t, time_type dt )
    {
        // special care for inout
        m_xout_resizer.adjust_size(
            inout,
            detail::bind( &stepper_type::template resize_m_xout< StateInOut >,
                          detail::ref( *this ), detail::_1 ) );
        do_step_impl( system, inout, dxdt, t, m_xout.m_v, dt );
        boost::numeric::odeint::copy( m_xout.m_v, inout );
    }

    template < class System, class StateInOut, class DerivIn >
    void do_step_dxdt_impl( System system, StateInOut &x, const DerivIn &dxdt,
                            time_type t, time_type dt )
    {
        do_step_impl_io( system , x , dxdt , t , dt );
    }

    template < class System, class StateIn, class DerivIn, class StateOut >
    void do_step_dxdt_impl( System system, const StateIn &in,
                            const DerivIn &dxdt, time_type t, StateOut &out,
                            time_type dt )
    {
        do_step_impl( system , in , dxdt , t , out , dt );
    }


    template < class StateIn > void adjust_size( const StateIn &x )
    {
        resize_impl( x );
        m_midpoint.adjust_size( x );
    }

  private:
    template < class StateIn > bool resize_impl( const StateIn &x )
    {
        bool resized( false );
        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() );
        return resized;
    }

    template < class StateIn > bool resize_m_xout( const StateIn &x )
    {
        return adjust_size_by_resizeability(
            m_xout, x, typename is_resizeable< state_type >::type() );
    }

    template < class StateInOut >
    void extrapolate( size_t k, state_table_type &table,
                      const value_matrix &coeff, StateInOut &xest )
    /* polynomial extrapolation, see http://www.nr.com/webnotes/nr3web21.pdf
       uses the obtained intermediate results to extrapolate to dt->0
    */
    {
        static const value_type val1 = static_cast< value_type >( 1.0 );

        for ( int j = k - 1; j > 0; --j )
        {
            stepper_base_type::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][j],
                                              -coeff[k][j] ) );
        }
        stepper_base_type::m_algebra.for_each3(
            xest, table[0].m_v, xest,
            typename operations_type::template scale_sum2<
                value_type, value_type >( val1 + coeff[k][0], -coeff[k][0] ) );
    }

  private:
    midpoint_stepper_type m_midpoint;

    resizer_type m_resizer;
    resizer_type m_xout_resizer;

    int_vector m_interval_sequence; // stores the successive interval counts
    value_matrix m_coeff;

    wrapped_state_type m_xout;
    state_table_type m_table; // sequence of states for extrapolation
};

/******** DOXYGEN *******/

/**
 * \class extrapolation_stepper
 * \brief Extrapolation stepper with configurable order, and error estimation.
 *
 * The extrapolation stepper is a stepper with error estimation and configurable
 * order. The order is given as template parameter and needs to be an _odd_
 * number. The stepper is based on several executions of the modified midpoint
 * method and a Richardson extrapolation. This is essentially the same technique
 * as for bulirsch_stoer, but without the variable order.
 *
 * \note The Order parameter has to be an even number greater 2.
 */
}
}
}
#endif