/* [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