text: /*
   [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 ) std::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
  