| /* |
| [auto_generated] |
| boost/numeric/odeint/stepper/rosenbrock4.hpp |
| |
| [begin_description] |
| Implementation of the Rosenbrock 4 method for solving stiff ODEs. Note, that a |
| controller and a dense-output stepper exist for this method, |
| [end_description] |
| |
| Copyright 2011-2013 Karsten Ahnert |
| Copyright 2011-2012 Mario Mulansky |
| 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_ROSENBROCK4_HPP_INCLUDED |
| #define BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED |
| |
| |
| #include <boost/numeric/odeint/util/bind.hpp> |
| #include <boost/numeric/odeint/util/unwrap_reference.hpp> |
| #include <boost/numeric/ublas/vector.hpp> |
| #include <boost/numeric/ublas/matrix.hpp> |
| #include <boost/numeric/ublas/lu.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 { |
| |
| |
| /* |
| * ToDo: |
| * |
| * 2. Interfacing for odeint, check if controlled_error_stepper can be used |
| * 3. dense output |
| */ |
| |
| |
| |
| template< class Value > |
| struct default_rosenbrock_coefficients |
| { |
| typedef Value value_type; |
| typedef unsigned short order_type; |
| |
| default_rosenbrock_coefficients( void ) |
| : gamma ( static_cast< value_type >( 0.25 ) ) , |
| d1 ( static_cast< value_type >( 0.25 ) ) , |
| d2 ( static_cast< value_type >( -0.1043 ) ) , |
| d3 ( static_cast< value_type >( 0.1035 ) ) , |
| d4 ( static_cast< value_type >( 0.3620000000000023e-01 ) ) , |
| c2 ( static_cast< value_type >( 0.386 ) ) , |
| c3 ( static_cast< value_type >( 0.21 ) ) , |
| c4 ( static_cast< value_type >( 0.63 ) ) , |
| c21 ( static_cast< value_type >( -0.5668800000000000e+01 ) ) , |
| a21 ( static_cast< value_type >( 0.1544000000000000e+01 ) ) , |
| c31 ( static_cast< value_type >( -0.2430093356833875e+01 ) ) , |
| c32 ( static_cast< value_type >( -0.2063599157091915e+00 ) ) , |
| a31 ( static_cast< value_type >( 0.9466785280815826e+00 ) ) , |
| a32 ( static_cast< value_type >( 0.2557011698983284e+00 ) ) , |
| c41 ( static_cast< value_type >( -0.1073529058151375e+00 ) ) , |
| c42 ( static_cast< value_type >( -0.9594562251023355e+01 ) ) , |
| c43 ( static_cast< value_type >( -0.2047028614809616e+02 ) ) , |
| a41 ( static_cast< value_type >( 0.3314825187068521e+01 ) ) , |
| a42 ( static_cast< value_type >( 0.2896124015972201e+01 ) ) , |
| a43 ( static_cast< value_type >( 0.9986419139977817e+00 ) ) , |
| c51 ( static_cast< value_type >( 0.7496443313967647e+01 ) ) , |
| c52 ( static_cast< value_type >( -0.1024680431464352e+02 ) ) , |
| c53 ( static_cast< value_type >( -0.3399990352819905e+02 ) ) , |
| c54 ( static_cast< value_type >( 0.1170890893206160e+02 ) ) , |
| a51 ( static_cast< value_type >( 0.1221224509226641e+01 ) ) , |
| a52 ( static_cast< value_type >( 0.6019134481288629e+01 ) ) , |
| a53 ( static_cast< value_type >( 0.1253708332932087e+02 ) ) , |
| a54 ( static_cast< value_type >( -0.6878860361058950e+00 ) ) , |
| c61 ( static_cast< value_type >( 0.8083246795921522e+01 ) ) , |
| c62 ( static_cast< value_type >( -0.7981132988064893e+01 ) ) , |
| c63 ( static_cast< value_type >( -0.3152159432874371e+02 ) ) , |
| c64 ( static_cast< value_type >( 0.1631930543123136e+02 ) ) , |
| c65 ( static_cast< value_type >( -0.6058818238834054e+01 ) ) , |
| d21 ( static_cast< value_type >( 0.1012623508344586e+02 ) ) , |
| d22 ( static_cast< value_type >( -0.7487995877610167e+01 ) ) , |
| d23 ( static_cast< value_type >( -0.3480091861555747e+02 ) ) , |
| d24 ( static_cast< value_type >( -0.7992771707568823e+01 ) ) , |
| d25 ( static_cast< value_type >( 0.1025137723295662e+01 ) ) , |
| d31 ( static_cast< value_type >( -0.6762803392801253e+00 ) ) , |
| d32 ( static_cast< value_type >( 0.6087714651680015e+01 ) ) , |
| d33 ( static_cast< value_type >( 0.1643084320892478e+02 ) ) , |
| d34 ( static_cast< value_type >( 0.2476722511418386e+02 ) ) , |
| d35 ( static_cast< value_type >( -0.6594389125716872e+01 ) ) |
| {} |
| |
| const value_type gamma; |
| const value_type d1 , d2 , d3 , d4; |
| const value_type c2 , c3 , c4; |
| const value_type c21 ; |
| const value_type a21; |
| const value_type c31 , c32; |
| const value_type a31 , a32; |
| const value_type c41 , c42 , c43; |
| const value_type a41 , a42 , a43; |
| const value_type c51 , c52 , c53 , c54; |
| const value_type a51 , a52 , a53 , a54; |
| const value_type c61 , c62 , c63 , c64 , c65; |
| const value_type d21 , d22 , d23 , d24 , d25; |
| const value_type d31 , d32 , d33 , d34 , d35; |
| |
| static const order_type stepper_order = 4; |
| static const order_type error_order = 3; |
| }; |
| |
| |
| |
| template< class Value , class Coefficients = default_rosenbrock_coefficients< Value > , class Resizer = initially_resizer > |
| class rosenbrock4 |
| { |
| private: |
| |
| public: |
| |
| typedef Value value_type; |
| typedef boost::numeric::ublas::vector< value_type > state_type; |
| typedef state_type deriv_type; |
| typedef value_type time_type; |
| typedef boost::numeric::ublas::matrix< value_type > matrix_type; |
| typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type; |
| typedef Resizer resizer_type; |
| typedef Coefficients rosenbrock_coefficients; |
| typedef stepper_tag stepper_category; |
| typedef unsigned short order_type; |
| |
| typedef state_wrapper< state_type > wrapped_state_type; |
| typedef state_wrapper< deriv_type > wrapped_deriv_type; |
| typedef state_wrapper< matrix_type > wrapped_matrix_type; |
| typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type; |
| |
| typedef rosenbrock4< Value , Coefficients , Resizer > stepper_type; |
| |
| const static order_type stepper_order = rosenbrock_coefficients::stepper_order; |
| const static order_type error_order = rosenbrock_coefficients::error_order; |
| |
| rosenbrock4( void ) |
| : m_resizer() , m_x_err_resizer() , |
| m_jac() , m_pm() , |
| m_dfdt() , m_dxdt() , m_dxdtnew() , |
| m_g1() , m_g2() , m_g3() , m_g4() , m_g5() , |
| m_cont3() , m_cont4() , m_xtmp() , m_x_err() , |
| m_coef() |
| { } |
| |
| |
| order_type order() const { return stepper_order; } |
| |
| template< class System > |
| void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt , state_type &xerr ) |
| { |
| // get the system and jacobi function |
| 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; |
| |
| const size_t n = x.size(); |
| |
| 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<n ; ++i ) |
| m_pm.m_v( i ) = i; |
| |
| deriv_func( x , m_dxdt.m_v , t ); |
| jacobi_func( x , m_jac.m_v , t , m_dfdt.m_v ); |
| |
| m_jac.m_v *= -1.0; |
| m_jac.m_v += 1.0 / m_coef.gamma / dt * boost::numeric::ublas::identity_matrix< value_type >( n ); |
| boost::numeric::ublas::lu_factorize( m_jac.m_v , m_pm.m_v ); |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| m_g1.m_v[i] = m_dxdt.m_v[i] + dt * m_coef.d1 * m_dfdt.m_v[i]; |
| boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g1.m_v ); |
| |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| m_xtmp.m_v[i] = x[i] + m_coef.a21 * m_g1.m_v[i]; |
| deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c2 * dt ); |
| for( size_t i=0 ; i<n ; ++i ) |
| m_g2.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d2 * m_dfdt.m_v[i] + m_coef.c21 * m_g1.m_v[i] / dt; |
| boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g2.m_v ); |
| |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| m_xtmp.m_v[i] = x[i] + m_coef.a31 * m_g1.m_v[i] + m_coef.a32 * m_g2.m_v[i]; |
| deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c3 * dt ); |
| for( size_t i=0 ; i<n ; ++i ) |
| m_g3.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d3 * m_dfdt.m_v[i] + ( m_coef.c31 * m_g1.m_v[i] + m_coef.c32 * m_g2.m_v[i] ) / dt; |
| boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g3.m_v ); |
| |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| m_xtmp.m_v[i] = x[i] + m_coef.a41 * m_g1.m_v[i] + m_coef.a42 * m_g2.m_v[i] + m_coef.a43 * m_g3.m_v[i]; |
| deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c4 * dt ); |
| for( size_t i=0 ; i<n ; ++i ) |
| m_g4.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d4 * m_dfdt.m_v[i] + ( m_coef.c41 * m_g1.m_v[i] + m_coef.c42 * m_g2.m_v[i] + m_coef.c43 * m_g3.m_v[i] ) / dt; |
| boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g4.m_v ); |
| |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| m_xtmp.m_v[i] = x[i] + m_coef.a51 * m_g1.m_v[i] + m_coef.a52 * m_g2.m_v[i] + m_coef.a53 * m_g3.m_v[i] + m_coef.a54 * m_g4.m_v[i]; |
| deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt ); |
| for( size_t i=0 ; i<n ; ++i ) |
| m_g5.m_v[i] = m_dxdtnew.m_v[i] + ( m_coef.c51 * m_g1.m_v[i] + m_coef.c52 * m_g2.m_v[i] + m_coef.c53 * m_g3.m_v[i] + m_coef.c54 * m_g4.m_v[i] ) / dt; |
| boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g5.m_v ); |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| m_xtmp.m_v[i] += m_g5.m_v[i]; |
| deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt ); |
| for( size_t i=0 ; i<n ; ++i ) |
| xerr[i] = m_dxdtnew.m_v[i] + ( m_coef.c61 * m_g1.m_v[i] + m_coef.c62 * m_g2.m_v[i] + m_coef.c63 * m_g3.m_v[i] + m_coef.c64 * m_g4.m_v[i] + m_coef.c65 * m_g5.m_v[i] ) / dt; |
| boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , xerr ); |
| |
| for( size_t i=0 ; i<n ; ++i ) |
| xout[i] = m_xtmp.m_v[i] + xerr[i]; |
| } |
| |
| template< class System > |
| void do_step( System system , state_type &x , time_type t , time_type dt , state_type &xerr ) |
| { |
| do_step( system , x , t , x , dt , xerr ); |
| } |
| |
| /* |
| * do_step without error output - just calls above functions with and neglects the error estimate |
| */ |
| template< class System > |
| void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt ) |
| { |
| m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) ); |
| do_step( system , x , t , xout , dt , m_x_err.m_v ); |
| } |
| |
| template< class System > |
| void do_step( System system , state_type &x , time_type t , time_type dt ) |
| { |
| m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) ); |
| do_step( system , x , t , dt , m_x_err.m_v ); |
| } |
| |
| void prepare_dense_output() |
| { |
| const size_t n = m_g1.m_v.size(); |
| for( size_t i=0 ; i<n ; ++i ) |
| { |
| m_cont3.m_v[i] = m_coef.d21 * m_g1.m_v[i] + m_coef.d22 * m_g2.m_v[i] + m_coef.d23 * m_g3.m_v[i] + m_coef.d24 * m_g4.m_v[i] + m_coef.d25 * m_g5.m_v[i]; |
| m_cont4.m_v[i] = m_coef.d31 * m_g1.m_v[i] + m_coef.d32 * m_g2.m_v[i] + m_coef.d33 * m_g3.m_v[i] + m_coef.d34 * m_g4.m_v[i] + m_coef.d35 * m_g5.m_v[i]; |
| } |
| } |
| |
| |
| void calc_state( time_type t , state_type &x , |
| const state_type &x_old , time_type t_old , |
| const state_type &x_new , time_type t_new ) |
| { |
| const size_t n = m_g1.m_v.size(); |
| time_type dt = t_new - t_old; |
| time_type s = ( t - t_old ) / dt; |
| time_type s1 = 1.0 - s; |
| for( size_t i=0 ; i<n ; ++i ) |
| x[i] = x_old[i] * s1 + s * ( x_new[i] + s1 * ( m_cont3.m_v[i] + s * m_cont4.m_v[i] ) ); |
| } |
| |
| |
| |
| template< class StateType > |
| void adjust_size( const StateType &x ) |
| { |
| resize_impl( x ); |
| resize_x_err( x ); |
| } |
| |
| |
| protected: |
| |
| 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_dfdt , x , typename is_resizeable<deriv_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_dxdtnew , x , typename is_resizeable<deriv_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_xtmp , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_g1 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_g2 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_g3 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_g4 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_g5 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_cont3 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_cont4 , x , typename is_resizeable<state_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_jac , x , typename is_resizeable<matrix_type>::type() ); |
| resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() ); |
| return resized; |
| } |
| |
| template< class StateIn > |
| bool resize_x_err( const StateIn &x ) |
| { |
| return adjust_size_by_resizeability( m_x_err , x , typename is_resizeable<state_type>::type() ); |
| } |
| |
| private: |
| |
| |
| resizer_type m_resizer; |
| resizer_type m_x_err_resizer; |
| |
| wrapped_matrix_type m_jac; |
| wrapped_pmatrix_type m_pm; |
| wrapped_deriv_type m_dfdt , m_dxdt , m_dxdtnew; |
| wrapped_state_type m_g1 , m_g2 , m_g3 , m_g4 , m_g5; |
| wrapped_state_type m_cont3 , m_cont4; |
| wrapped_state_type m_xtmp; |
| wrapped_state_type m_x_err; |
| |
| const rosenbrock_coefficients m_coef; |
| }; |
| |
| |
| } // namespace odeint |
| } // namespace numeric |
| } // namespace boost |
| |
| #endif // BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED |