整理

include/boost/numeric/odeint/stepper/implicit_euler.hpp

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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, [this](auto&& arg) { return this->resize_impl<state_type>(std::forward<decltype(arg)>(arg)); });
+
+        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