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