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/*
[auto_generated]
boost/numeric/odeint/stepper/implicit_euler.hpp
[begin_description]
Impementation of the implicit Euler method. Works with ublas::vector as state type.
[end_description]
Copyright 2010-2012 Mario Mulansky
Copyright 2010-2012 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_IMPLICIT_EULER_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
#include <utility>
#include <boost/numeric/odeint/util/bind.hpp>
#include <boost/numeric/odeint/util/unwrap_reference.hpp>
#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/util/ublas_wrapper.hpp>
#include <boost/numeric/odeint/util/is_resizeable.hpp>
#include <boost/numeric/odeint/util/resizer.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/lu.hpp>
namespace boost {
namespace numeric {
namespace odeint {
template< class ValueType , class Resizer = initially_resizer >
class implicit_euler
{
public:
typedef ValueType value_type;
typedef value_type time_type;
typedef boost::numeric::ublas::vector< value_type > state_type;
typedef state_wrapper< state_type > wrapped_state_type;
typedef state_type deriv_type;
typedef state_wrapper< deriv_type > wrapped_deriv_type;
typedef boost::numeric::ublas::matrix< value_type > matrix_type;
typedef state_wrapper< matrix_type > wrapped_matrix_type;
typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type;
typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type;
typedef Resizer resizer_type;
typedef stepper_tag stepper_category;
typedef implicit_euler< ValueType , Resizer > stepper_type;
implicit_euler( value_type epsilon = 1E-6 )
: m_epsilon( epsilon )
{ }
template< class System >
void do_step( System system , state_type &x , time_type t , time_type dt )
{
typedef typename odeint::unwrap_reference< System >::type system_type;
typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
system_type &sys = system;
deriv_func_type &deriv_func = sys.first;
jacobi_func_type &jacobi_func = sys.second;
m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<state_type> , detail::ref( *this ) , detail::_1 ) );
for( size_t i=0 ; i<x.size() ; ++i )
m_pm.m_v[i] = i;
t += dt;
// apply first Newton step
deriv_func( x , m_dxdt.m_v , t );
m_b.m_v = dt * m_dxdt.m_v;
jacobi_func( x , m_jacobi.m_v , t );
m_jacobi.m_v *= dt;
m_jacobi.m_v -= boost::numeric::ublas::identity_matrix< value_type >( x.size() );
solve( m_b.m_v , m_jacobi.m_v );
m_x.m_v = x - m_b.m_v;
// iterate Newton until some precision is reached
// ToDo: maybe we should apply only one Newton step -> linear implicit one-step scheme
while( boost::numeric::ublas::norm_2( m_b.m_v ) > m_epsilon )
{
deriv_func( m_x.m_v , m_dxdt.m_v , t );
m_b.m_v = x - m_x.m_v + dt*m_dxdt.m_v;
// simplified version, only the first Jacobian is used
// jacobi( m_x , m_jacobi , t );
// m_jacobi *= dt;
// m_jacobi -= boost::numeric::ublas::identity_matrix< value_type >( x.size() );
solve( m_b.m_v , m_jacobi.m_v );
m_x.m_v -= m_b.m_v;
}
x = m_x.m_v;
}
template< class StateType >
void adjust_size( const StateType &x )
{
resize_impl( x );
}
private:
template< class StateIn >
bool resize_impl( const StateIn &x )
{
bool resized = false;
resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
resized |= adjust_size_by_resizeability( m_x , x , typename is_resizeable<state_type>::type() );
resized |= adjust_size_by_resizeability( m_b , x , typename is_resizeable<deriv_type>::type() );
resized |= adjust_size_by_resizeability( m_jacobi , x , typename is_resizeable<matrix_type>::type() );
resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() );
return resized;
}
void solve( state_type &x , matrix_type &m )
{
int res = boost::numeric::ublas::lu_factorize( m , m_pm.m_v );
if( res != 0 ) exit(0);
boost::numeric::ublas::lu_substitute( m , m_pm.m_v , x );
}
private:
value_type m_epsilon;
resizer_type m_resizer;
wrapped_deriv_type m_dxdt;
wrapped_state_type m_x;
wrapped_deriv_type m_b;
wrapped_matrix_type m_jacobi;
wrapped_pmatrix_type m_pm;
};
} // odeint
} // numeric
} // boost
#endif // BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
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