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