Chris@16: /*
Chris@16:  [auto_generated]
Chris@16:  boost/numeric/odeint/stepper/implicit_euler.hpp
Chris@16: 
Chris@16:  [begin_description]
Chris@16:  Impementation of the implicit Euler method. Works with ublas::vector as state type.
Chris@16:  [end_description]
Chris@16: 
Chris@101:  Copyright 2010-2012 Mario Mulansky
Chris@101:  Copyright 2010-2012 Karsten Ahnert
Chris@101:  Copyright 2012 Christoph Koke
Chris@16: 
Chris@16:  Distributed under the Boost Software License, Version 1.0.
Chris@16:  (See accompanying file LICENSE_1_0.txt or
Chris@16:  copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: #ifndef BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
Chris@16: #define BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED
Chris@16: 
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/util/bind.hpp>
Chris@16: #include <boost/numeric/odeint/util/unwrap_reference.hpp>
Chris@16: #include <boost/numeric/odeint/stepper/stepper_categories.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/util/ublas_wrapper.hpp>
Chris@16: #include <boost/numeric/odeint/util/is_resizeable.hpp>
Chris@16: #include <boost/numeric/odeint/util/resizer.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/ublas/vector.hpp>
Chris@16: #include <boost/numeric/ublas/matrix.hpp>
Chris@16: #include <boost/numeric/ublas/lu.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace numeric {
Chris@16: namespace odeint {
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: template< class ValueType , class Resizer = initially_resizer >
Chris@16: class implicit_euler
Chris@16: {
Chris@16: 
Chris@16: public:
Chris@16: 
Chris@16:     typedef ValueType value_type;
Chris@16:     typedef value_type time_type;
Chris@16:     typedef boost::numeric::ublas::vector< value_type > state_type;
Chris@16:     typedef state_wrapper< state_type > wrapped_state_type;
Chris@16:     typedef state_type deriv_type;
Chris@16:     typedef state_wrapper< deriv_type > wrapped_deriv_type;
Chris@16:     typedef boost::numeric::ublas::matrix< value_type > matrix_type;
Chris@16:     typedef state_wrapper< matrix_type > wrapped_matrix_type;
Chris@16:     typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type;
Chris@16:     typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type;
Chris@16:     typedef Resizer resizer_type;
Chris@16:     typedef stepper_tag stepper_category;
Chris@16:     typedef implicit_euler< ValueType , Resizer > stepper_type;
Chris@16: 
Chris@16:     implicit_euler( value_type epsilon = 1E-6 )
Chris@16:     : m_epsilon( epsilon ) 
Chris@16:     { }
Chris@16: 
Chris@16: 
Chris@16:     template< class System >
Chris@16:     void do_step( System system , state_type &x , time_type t , time_type dt )
Chris@16:     {
Chris@16:         typedef typename odeint::unwrap_reference< System >::type system_type;
Chris@16:         typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
Chris@16:         typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
Chris@16:         system_type &sys = system;
Chris@16:         deriv_func_type &deriv_func = sys.first;
Chris@16:         jacobi_func_type &jacobi_func = sys.second;
Chris@16: 
Chris@16:         m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<state_type> , detail::ref( *this ) , detail::_1 ) );
Chris@16: 
Chris@16:         for( size_t i=0 ; i<x.size() ; ++i )
Chris@16:             m_pm.m_v[i] = i;
Chris@16: 
Chris@16:         t += dt;
Chris@16: 
Chris@16:         // apply first Newton step
Chris@16:         deriv_func( x , m_dxdt.m_v , t );
Chris@16: 
Chris@16:         m_b.m_v = dt * m_dxdt.m_v;
Chris@16: 
Chris@16:         jacobi_func( x , m_jacobi.m_v  , t );
Chris@16:         m_jacobi.m_v *= dt;
Chris@16:         m_jacobi.m_v -= boost::numeric::ublas::identity_matrix< value_type >( x.size() );
Chris@16: 
Chris@16:         solve( m_b.m_v , m_jacobi.m_v );
Chris@16: 
Chris@16:         m_x.m_v = x - m_b.m_v;
Chris@16: 
Chris@16:         // iterate Newton until some precision is reached
Chris@16:         // ToDo: maybe we should apply only one Newton step -> linear implicit one-step scheme
Chris@16:         while( boost::numeric::ublas::norm_2( m_b.m_v ) > m_epsilon )
Chris@16:         {
Chris@16:             deriv_func( m_x.m_v , m_dxdt.m_v , t );
Chris@16:             m_b.m_v = x - m_x.m_v + dt*m_dxdt.m_v;
Chris@16: 
Chris@16:             // simplified version, only the first Jacobian is used
Chris@16:             //            jacobi( m_x , m_jacobi , t );
Chris@16:             //            m_jacobi *= dt;
Chris@16:             //            m_jacobi -= boost::numeric::ublas::identity_matrix< value_type >( x.size() );
Chris@16: 
Chris@16:             solve( m_b.m_v , m_jacobi.m_v );
Chris@16: 
Chris@16:             m_x.m_v -= m_b.m_v;
Chris@16:         }
Chris@16:         x = m_x.m_v;
Chris@16:     }
Chris@16: 
Chris@16:     template< class StateType >
Chris@16:     void adjust_size( const StateType &x )
Chris@16:     {
Chris@16:         resize_impl( x );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     bool resize_impl( const StateIn &x )
Chris@16:     {
Chris@16:         bool resized = false;
Chris@16:         resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_x , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_b , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_jacobi , x , typename is_resizeable<matrix_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() );
Chris@16:         return resized;
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     void solve( state_type &x , matrix_type &m )
Chris@16:     {
Chris@16:         int res = boost::numeric::ublas::lu_factorize( m , m_pm.m_v );
Chris@101:         if( res != 0 ) std::exit(0);
Chris@16:         boost::numeric::ublas::lu_substitute( m , m_pm.m_v , x );
Chris@16:     }
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     value_type m_epsilon;
Chris@16:     resizer_type m_resizer;
Chris@16:     wrapped_deriv_type m_dxdt;
Chris@16:     wrapped_state_type m_x;
Chris@16:     wrapped_deriv_type m_b;
Chris@16:     wrapped_matrix_type m_jacobi;
Chris@16:     wrapped_pmatrix_type m_pm;
Chris@16: 
Chris@16: 
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: } // odeint
Chris@16: } // numeric
Chris@16: } // boost
Chris@16: 
Chris@16: 
Chris@16: #endif // BOOST_NUMERIC_ODEINT_STEPPER_IMPLICIT_EULER_HPP_INCLUDED