/*
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boost/numeric/odeint/stepper/detail/controlled_adams_bashforth_moulton.hpp
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[begin_description]
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Implemetation of an controlled adams bashforth moulton stepper.
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[end_description]
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Copyright 2017 Valentin Noah Hartmann
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_ADAMS_BASHFORTH_MOULTON_HPP_INCLUDED
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#define BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_ADAMS_BASHFORTH_MOULTON_HPP_INCLUDED
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#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
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#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
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#include <boost/numeric/odeint/stepper/adaptive_adams_bashforth_moulton.hpp>
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#include <boost/numeric/odeint/stepper/detail/pid_step_adjuster.hpp>
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#include <boost/numeric/odeint/util/unwrap_reference.hpp>
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#include <boost/numeric/odeint/util/is_resizeable.hpp>
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#include <boost/numeric/odeint/util/resizer.hpp>
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#include <boost/numeric/odeint/util/copy.hpp>
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#include <boost/numeric/odeint/util/bind.hpp>
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#include <iostream>
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namespace boost {
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namespace numeric {
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namespace odeint {
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template<
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size_t MaxOrder,
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class State,
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class Value = double,
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class Algebra = typename algebra_dispatcher< State >::algebra_type
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>
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class default_order_adjuster
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{
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public:
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typedef State state_type;
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typedef Value value_type;
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typedef state_wrapper< state_type > wrapped_state_type;
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typedef Algebra algebra_type;
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default_order_adjuster( const algebra_type &algebra = algebra_type() )
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: m_algebra( algebra )
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{};
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size_t adjust_order(size_t order, size_t init, boost::array<wrapped_state_type, 4> &xerr)
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{
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using std::abs;
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value_type errc = abs(m_algebra.norm_inf(xerr[2].m_v));
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value_type errm1 = 3*errc;
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value_type errm2 = 3*errc;
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if(order > 2)
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{
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errm2 = abs(m_algebra.norm_inf(xerr[0].m_v));
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}
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if(order >= 2)
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{
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errm1 = abs(m_algebra.norm_inf(xerr[1].m_v));
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}
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size_t o_new = order;
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if(order == 2 && errm1 <= 0.5*errc)
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{
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o_new = order - 1;
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}
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else if(order > 2 && errm2 < errc && errm1 < errc)
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{
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o_new = order - 1;
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}
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if(init < order)
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{
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return order+1;
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}
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else if(o_new == order - 1)
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{
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return order-1;
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}
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else if(order <= MaxOrder)
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{
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value_type errp = abs(m_algebra.norm_inf(xerr[3].m_v));
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if(order > 1 && errm1 < errc && errp)
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{
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return order-1;
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}
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else if(order < MaxOrder && errp < (0.5-0.25*order/MaxOrder) * errc)
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{
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return order+1;
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}
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}
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return order;
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};
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private:
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algebra_type m_algebra;
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};
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template<
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class ErrorStepper,
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class StepAdjuster = detail::pid_step_adjuster< typename ErrorStepper::state_type,
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typename ErrorStepper::value_type,
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typename ErrorStepper::deriv_type,
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typename ErrorStepper::time_type,
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typename ErrorStepper::algebra_type,
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typename ErrorStepper::operations_type,
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detail::H211PI
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>,
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class OrderAdjuster = default_order_adjuster< ErrorStepper::order_value,
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typename ErrorStepper::state_type,
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typename ErrorStepper::value_type,
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typename ErrorStepper::algebra_type
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>,
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class Resizer = initially_resizer
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>
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class controlled_adams_bashforth_moulton
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{
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public:
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typedef ErrorStepper stepper_type;
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static const typename stepper_type::order_type order_value = stepper_type::order_value;
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typedef typename stepper_type::state_type state_type;
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typedef typename stepper_type::value_type value_type;
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typedef typename stepper_type::deriv_type deriv_type;
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typedef typename stepper_type::time_type time_type;
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typedef typename stepper_type::algebra_type algebra_type;
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typedef typename stepper_type::operations_type operations_type;
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typedef Resizer resizer_type;
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typedef StepAdjuster step_adjuster_type;
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typedef OrderAdjuster order_adjuster_type;
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typedef controlled_stepper_tag stepper_category;
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typedef typename stepper_type::wrapped_state_type wrapped_state_type;
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typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
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typedef boost::array< wrapped_state_type , 4 > error_storage_type;
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typedef typename stepper_type::coeff_type coeff_type;
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typedef controlled_adams_bashforth_moulton< ErrorStepper , StepAdjuster , OrderAdjuster , Resizer > controlled_stepper_type;
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controlled_adams_bashforth_moulton(step_adjuster_type step_adjuster = step_adjuster_type())
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:m_stepper(),
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m_dxdt_resizer(), m_xerr_resizer(), m_xnew_resizer(),
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m_step_adjuster( step_adjuster ), m_order_adjuster()
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{};
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template< class ExplicitStepper, class System >
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void initialize(ExplicitStepper stepper, System system, state_type &inOut, time_type &t, time_type dt)
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{
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m_stepper.initialize(stepper, system, inOut, t, dt);
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};
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template< class System >
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void initialize(System system, state_type &inOut, time_type &t, time_type dt)
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{
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m_stepper.initialize(system, inOut, t, dt);
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};
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template< class ExplicitStepper, class System >
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void initialize_controlled(ExplicitStepper stepper, System system, state_type &inOut, time_type &t, time_type &dt)
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{
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reset();
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coeff_type &coeff = m_stepper.coeff();
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m_dxdt_resizer.adjust_size( inOut , detail::bind( &controlled_stepper_type::template resize_dxdt_impl< state_type > , detail::ref( *this ) , detail::_1 ) );
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controlled_step_result res = fail;
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for( size_t i=0 ; i<order_value; ++i )
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{
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do
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{
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res = stepper.try_step( system, inOut, t, dt );
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}
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while(res != success);
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system( inOut , m_dxdt.m_v , t );
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coeff.predict(t-dt, dt);
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coeff.do_step(m_dxdt.m_v);
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coeff.confirm();
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if(coeff.m_eo < order_value)
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{
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++coeff.m_eo;
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}
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}
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}
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template< class System >
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controlled_step_result try_step(System system, state_type & inOut, time_type &t, time_type &dt)
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{
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m_xnew_resizer.adjust_size( inOut , detail::bind( &controlled_stepper_type::template resize_xnew_impl< state_type > , detail::ref( *this ) , detail::_1 ) );
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controlled_step_result res = try_step(system, inOut, t, m_xnew.m_v, dt);
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if(res == success)
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{
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boost::numeric::odeint::copy( m_xnew.m_v , inOut);
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}
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return res;
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};
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template< class System >
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controlled_step_result try_step(System system, const state_type & in, time_type &t, state_type & out, time_type &dt)
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{
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m_xerr_resizer.adjust_size( in , detail::bind( &controlled_stepper_type::template resize_xerr_impl< state_type > , detail::ref( *this ) , detail::_1 ) );
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m_dxdt_resizer.adjust_size( in , detail::bind( &controlled_stepper_type::template resize_dxdt_impl< state_type > , detail::ref( *this ) , detail::_1 ) );
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m_stepper.do_step_impl(system, in, t, out, dt, m_xerr[2].m_v);
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coeff_type &coeff = m_stepper.coeff();
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time_type dtPrev = dt;
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dt = m_step_adjuster.adjust_stepsize(coeff.m_eo, dt, m_xerr[2].m_v, out, m_stepper.dxdt() );
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if(dt / dtPrev >= step_adjuster_type::threshold())
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{
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system(out, m_dxdt.m_v, t+dtPrev);
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coeff.do_step(m_dxdt.m_v);
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coeff.confirm();
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t += dtPrev;
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size_t eo = coeff.m_eo;
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// estimate errors for next step
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double factor = 1;
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algebra_type m_algebra;
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m_algebra.for_each2(m_xerr[2].m_v, coeff.phi[1][eo].m_v,
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typename operations_type::template scale_sum1<double>(factor*dt*(coeff.gs[eo])));
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if(eo > 1)
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{
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m_algebra.for_each2(m_xerr[1].m_v, coeff.phi[1][eo-1].m_v,
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typename operations_type::template scale_sum1<double>(factor*dt*(coeff.gs[eo-1])));
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}
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if(eo > 2)
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{
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m_algebra.for_each2(m_xerr[0].m_v, coeff.phi[1][eo-2].m_v,
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typename operations_type::template scale_sum1<double>(factor*dt*(coeff.gs[eo-2])));
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}
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if(eo < order_value && coeff.m_eo < coeff.m_steps_init-1)
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{
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m_algebra.for_each2(m_xerr[3].m_v, coeff.phi[1][eo+1].m_v,
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typename operations_type::template scale_sum1<double>(factor*dt*(coeff.gs[eo+1])));
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}
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// adjust order
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coeff.m_eo = m_order_adjuster.adjust_order(coeff.m_eo, coeff.m_steps_init-1, m_xerr);
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return success;
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}
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else
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{
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return fail;
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}
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};
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void reset() { m_stepper.reset(); };
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private:
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template< class StateType >
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bool resize_dxdt_impl( const StateType &x )
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{
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return adjust_size_by_resizeability( m_dxdt, x, typename is_resizeable<deriv_type>::type() );
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};
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template< class StateType >
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bool resize_xerr_impl( const StateType &x )
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{
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bool resized( false );
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for(size_t i=0; i<m_xerr.size(); ++i)
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{
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resized |= adjust_size_by_resizeability( m_xerr[i], x, typename is_resizeable<state_type>::type() );
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}
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return resized;
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};
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template< class StateType >
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bool resize_xnew_impl( const StateType &x )
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{
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return adjust_size_by_resizeability( m_xnew, x, typename is_resizeable<state_type>::type() );
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};
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stepper_type m_stepper;
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wrapped_deriv_type m_dxdt;
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error_storage_type m_xerr;
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wrapped_state_type m_xnew;
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resizer_type m_dxdt_resizer;
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resizer_type m_xerr_resizer;
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resizer_type m_xnew_resizer;
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step_adjuster_type m_step_adjuster;
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order_adjuster_type m_order_adjuster;
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};
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} // odeint
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} // numeric
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} // boost
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#endif
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