Chris@16: /*
Chris@16:  [auto_generated]
Chris@16:  boost/numeric/odeint/stepper/rosenbrock4.hpp
Chris@16: 
Chris@16:  [begin_description]
Chris@16:  Implementation of the Rosenbrock 4 method for solving stiff ODEs. Note, that a
Chris@16:  controller and a dense-output stepper exist for this method,
Chris@16:  [end_description]
Chris@16: 
Chris@101:  Copyright 2011-2013 Karsten Ahnert
Chris@101:  Copyright 2011-2012 Mario Mulansky
Chris@101:  Copyright 2012 Christoph Koke
Chris@16: 
Chris@16:  Distributed under the Boost Software License, Version 1.0.
Chris@16:  (See accompanying file LICENSE_1_0.txt or
Chris@16:  copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: #ifndef BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
Chris@16: #define BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
Chris@16: 
Chris@16: 
Chris@16: #include <boost/numeric/odeint/util/bind.hpp>
Chris@16: #include <boost/numeric/odeint/util/unwrap_reference.hpp>
Chris@16: #include <boost/numeric/ublas/vector.hpp>
Chris@16: #include <boost/numeric/ublas/matrix.hpp>
Chris@16: #include <boost/numeric/ublas/lu.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/stepper/stepper_categories.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/util/ublas_wrapper.hpp>
Chris@16: #include <boost/numeric/odeint/util/is_resizeable.hpp>
Chris@16: #include <boost/numeric/odeint/util/resizer.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/ublas/vector.hpp>
Chris@16: #include <boost/numeric/ublas/matrix.hpp>
Chris@16: #include <boost/numeric/ublas/lu.hpp>
Chris@16: 
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace numeric {
Chris@16: namespace odeint {
Chris@16: 
Chris@16: 
Chris@16: /*
Chris@16:  * ToDo:
Chris@16:  *
Chris@16:  * 2. Interfacing for odeint, check if controlled_error_stepper can be used
Chris@16:  * 3. dense output
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: template< class Value >
Chris@16: struct default_rosenbrock_coefficients
Chris@16: {
Chris@16:     typedef Value value_type;
Chris@16:     typedef unsigned short order_type;
Chris@16: 
Chris@16:     default_rosenbrock_coefficients( void )
Chris@16:     : gamma ( static_cast< value_type >( 0.25 ) ) ,
Chris@16:       d1 ( static_cast< value_type >( 0.25 ) ) ,
Chris@16:       d2 ( static_cast< value_type >( -0.1043 ) ) ,
Chris@16:       d3 ( static_cast< value_type >( 0.1035 ) ) ,
Chris@16:       d4 ( static_cast< value_type >( 0.3620000000000023e-01 ) ) ,
Chris@16:       c2 ( static_cast< value_type >( 0.386 ) ) ,
Chris@16:       c3 ( static_cast< value_type >( 0.21 ) ) ,
Chris@16:       c4 ( static_cast< value_type >( 0.63 ) ) ,
Chris@16:       c21 ( static_cast< value_type >( -0.5668800000000000e+01 ) ) ,
Chris@16:       a21 ( static_cast< value_type >( 0.1544000000000000e+01 ) ) ,
Chris@16:       c31 ( static_cast< value_type >( -0.2430093356833875e+01 ) ) ,
Chris@16:       c32 ( static_cast< value_type >( -0.2063599157091915e+00 ) ) ,
Chris@16:       a31 ( static_cast< value_type >( 0.9466785280815826e+00 ) ) ,
Chris@16:       a32 ( static_cast< value_type >( 0.2557011698983284e+00 ) ) ,
Chris@16:       c41 ( static_cast< value_type >( -0.1073529058151375e+00 ) ) ,
Chris@16:       c42 ( static_cast< value_type >( -0.9594562251023355e+01 ) ) ,
Chris@16:       c43 ( static_cast< value_type >( -0.2047028614809616e+02 ) ) ,
Chris@16:       a41 ( static_cast< value_type >( 0.3314825187068521e+01 ) ) ,
Chris@16:       a42 ( static_cast< value_type >( 0.2896124015972201e+01 ) ) ,
Chris@16:       a43 ( static_cast< value_type >( 0.9986419139977817e+00 ) ) ,
Chris@16:       c51 ( static_cast< value_type >( 0.7496443313967647e+01 ) ) ,
Chris@16:       c52 ( static_cast< value_type >( -0.1024680431464352e+02 ) ) ,
Chris@16:       c53 ( static_cast< value_type >( -0.3399990352819905e+02 ) ) ,
Chris@16:       c54 ( static_cast< value_type >(  0.1170890893206160e+02 ) ) ,
Chris@16:       a51 ( static_cast< value_type >( 0.1221224509226641e+01 ) ) ,
Chris@16:       a52 ( static_cast< value_type >( 0.6019134481288629e+01 ) ) ,
Chris@16:       a53 ( static_cast< value_type >( 0.1253708332932087e+02 ) ) ,
Chris@16:       a54 ( static_cast< value_type >( -0.6878860361058950e+00 ) ) ,
Chris@16:       c61 ( static_cast< value_type >( 0.8083246795921522e+01 ) ) ,
Chris@16:       c62 ( static_cast< value_type >( -0.7981132988064893e+01 ) ) ,
Chris@16:       c63 ( static_cast< value_type >( -0.3152159432874371e+02 ) ) ,
Chris@16:       c64 ( static_cast< value_type >( 0.1631930543123136e+02 ) ) ,
Chris@16:       c65 ( static_cast< value_type >( -0.6058818238834054e+01 ) ) ,
Chris@16:       d21 ( static_cast< value_type >( 0.1012623508344586e+02 ) ) ,
Chris@16:       d22 ( static_cast< value_type >( -0.7487995877610167e+01 ) ) ,
Chris@16:       d23 ( static_cast< value_type >( -0.3480091861555747e+02 ) ) ,
Chris@16:       d24 ( static_cast< value_type >( -0.7992771707568823e+01 ) ) ,
Chris@16:       d25 ( static_cast< value_type >( 0.1025137723295662e+01 ) ) ,
Chris@16:       d31 ( static_cast< value_type >( -0.6762803392801253e+00 ) ) ,
Chris@16:       d32 ( static_cast< value_type >( 0.6087714651680015e+01 ) ) ,
Chris@16:       d33 ( static_cast< value_type >( 0.1643084320892478e+02 ) ) ,
Chris@16:       d34 ( static_cast< value_type >( 0.2476722511418386e+02 ) ) ,
Chris@16:       d35 ( static_cast< value_type >( -0.6594389125716872e+01 ) )
Chris@16:     {}
Chris@16: 
Chris@16:     const value_type gamma;
Chris@16:     const value_type d1 , d2 , d3 , d4;
Chris@16:     const value_type c2 , c3 , c4;
Chris@16:     const value_type c21 ;
Chris@16:     const value_type a21;
Chris@16:     const value_type c31 , c32;
Chris@16:     const value_type a31 , a32;
Chris@16:     const value_type c41 , c42 , c43;
Chris@16:     const value_type a41 , a42 , a43;
Chris@16:     const value_type c51 , c52 , c53 , c54;
Chris@16:     const value_type a51 , a52 , a53 , a54;
Chris@16:     const value_type c61 , c62 , c63 , c64 , c65;
Chris@16:     const value_type d21 , d22 , d23 , d24 , d25;
Chris@16:     const value_type d31 , d32 , d33 , d34 , d35;
Chris@16: 
Chris@16:     static const order_type stepper_order = 4;
Chris@16:     static const order_type error_order = 3;
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: template< class Value , class Coefficients = default_rosenbrock_coefficients< Value > , class Resizer = initially_resizer >
Chris@16: class rosenbrock4
Chris@16: {
Chris@16: private:
Chris@16: 
Chris@16: public:
Chris@16: 
Chris@16:     typedef Value value_type;
Chris@16:     typedef boost::numeric::ublas::vector< value_type > state_type;
Chris@16:     typedef state_type deriv_type;
Chris@16:     typedef value_type time_type;
Chris@16:     typedef boost::numeric::ublas::matrix< value_type > matrix_type;
Chris@16:     typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type;
Chris@16:     typedef Resizer resizer_type;
Chris@16:     typedef Coefficients rosenbrock_coefficients;
Chris@16:     typedef stepper_tag stepper_category;
Chris@16:     typedef unsigned short order_type;
Chris@16: 
Chris@16:     typedef state_wrapper< state_type > wrapped_state_type;
Chris@16:     typedef state_wrapper< deriv_type > wrapped_deriv_type;
Chris@16:     typedef state_wrapper< matrix_type > wrapped_matrix_type;
Chris@16:     typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type;
Chris@16: 
Chris@16:     typedef rosenbrock4< Value , Coefficients , Resizer > stepper_type;
Chris@16: 
Chris@16:     const static order_type stepper_order = rosenbrock_coefficients::stepper_order;
Chris@16:     const static order_type error_order = rosenbrock_coefficients::error_order;
Chris@16: 
Chris@16:     rosenbrock4( void )
Chris@16:     : m_resizer() , m_x_err_resizer() ,
Chris@16:       m_jac() , m_pm() ,
Chris@16:       m_dfdt() , m_dxdt() , m_dxdtnew() ,
Chris@16:       m_g1() , m_g2() , m_g3() , m_g4() , m_g5() ,
Chris@16:       m_cont3() , m_cont4() , m_xtmp() , m_x_err() ,
Chris@16:       m_coef()
Chris@16:     { }
Chris@16: 
Chris@16: 
Chris@16:     order_type order() const { return stepper_order; } 
Chris@16: 
Chris@16:     template< class System >
Chris@16:     void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt , state_type &xerr )
Chris@16:     {
Chris@16:         // get the system and jacobi function
Chris@16:         typedef typename odeint::unwrap_reference< System >::type system_type;
Chris@16:         typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
Chris@16:         typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
Chris@16:         system_type &sys = system;
Chris@16:         deriv_func_type &deriv_func = sys.first;
Chris@16:         jacobi_func_type &jacobi_func = sys.second;
Chris@16: 
Chris@16:         const size_t n = x.size();
Chris@16: 
Chris@16:         m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<state_type> , detail::ref( *this ) , detail::_1 ) );
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             m_pm.m_v( i ) = i;
Chris@16: 
Chris@16:         deriv_func( x , m_dxdt.m_v , t );
Chris@16:         jacobi_func( x , m_jac.m_v , t , m_dfdt.m_v );
Chris@16: 
Chris@16:         m_jac.m_v *= -1.0;
Chris@16:         m_jac.m_v += 1.0 / m_coef.gamma / dt * boost::numeric::ublas::identity_matrix< value_type >( n );
Chris@16:         boost::numeric::ublas::lu_factorize( m_jac.m_v , m_pm.m_v );
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             m_g1.m_v[i] = m_dxdt.m_v[i] + dt * m_coef.d1 * m_dfdt.m_v[i];
Chris@16:         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g1.m_v );
Chris@16: 
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             m_xtmp.m_v[i] = x[i] + m_coef.a21 * m_g1.m_v[i];
Chris@16:         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c2 * dt );
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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;
Chris@16:         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g2.m_v );
Chris@16: 
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             m_xtmp.m_v[i] = x[i] + m_coef.a31 * m_g1.m_v[i] + m_coef.a32 * m_g2.m_v[i];
Chris@16:         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c3 * dt );
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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;
Chris@16:         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g3.m_v );
Chris@16: 
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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];
Chris@16:         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c4 * dt );
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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;
Chris@16:         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g4.m_v );
Chris@16: 
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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];
Chris@16:         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt );
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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;
Chris@16:         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g5.m_v );
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             m_xtmp.m_v[i] += m_g5.m_v[i];
Chris@16:         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt );
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             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;
Chris@16:         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , xerr );
Chris@16: 
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             xout[i] = m_xtmp.m_v[i] + xerr[i];
Chris@16:     }
Chris@16: 
Chris@16:     template< class System >
Chris@16:     void do_step( System system , state_type &x , time_type t , time_type dt , state_type &xerr )
Chris@16:     {
Chris@16:         do_step( system , x , t , x , dt , xerr );
Chris@16:     }
Chris@16: 
Chris@16:     /*
Chris@16:      * do_step without error output - just calls above functions with and neglects the error estimate
Chris@16:      */
Chris@16:     template< class System >
Chris@16:     void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt )
Chris@16:     {
Chris@16:         m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) );
Chris@16:         do_step( system , x , t , xout , dt , m_x_err.m_v );
Chris@16:     }
Chris@16: 
Chris@16:     template< class System >
Chris@16:     void do_step( System system , state_type &x , time_type t , time_type dt )
Chris@16:     {
Chris@16:         m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) );
Chris@16:         do_step( system , x , t , dt , m_x_err.m_v );
Chris@16:     }
Chris@16: 
Chris@16:     void prepare_dense_output()
Chris@16:     {
Chris@16:         const size_t n = m_g1.m_v.size();
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:         {
Chris@16:             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];
Chris@16:             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];
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     void calc_state( time_type t , state_type &x ,
Chris@16:             const state_type &x_old , time_type t_old ,
Chris@16:             const state_type &x_new , time_type t_new )
Chris@16:     {
Chris@16:         const size_t n = m_g1.m_v.size();
Chris@16:         time_type dt = t_new - t_old;
Chris@16:         time_type s = ( t - t_old ) / dt;
Chris@16:         time_type s1 = 1.0 - s;
Chris@16:         for( size_t i=0 ; i<n ; ++i )
Chris@16:             x[i] = x_old[i] * s1 + s * ( x_new[i] + s1 * ( m_cont3.m_v[i] + s * m_cont4.m_v[i] ) );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16:     template< class StateType >
Chris@16:     void adjust_size( const StateType &x )
Chris@16:     {
Chris@16:         resize_impl( x );
Chris@16:         resize_x_err( x );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16: protected:
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     bool resize_impl( const StateIn &x )
Chris@16:     {
Chris@16:         bool resized = false;
Chris@16:         resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_dfdt , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_dxdtnew , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_xtmp , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_g1 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_g2 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_g3 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_g4 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_g5 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_cont3 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_cont4 , x , typename is_resizeable<state_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_jac , x , typename is_resizeable<matrix_type>::type() );
Chris@16:         resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() );
Chris@16:         return resized;
Chris@16:     }
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     bool resize_x_err( const StateIn &x )
Chris@16:     {
Chris@16:         return adjust_size_by_resizeability( m_x_err , x , typename is_resizeable<state_type>::type() );
Chris@16:     }
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16: 
Chris@16:     resizer_type m_resizer;
Chris@16:     resizer_type m_x_err_resizer;
Chris@16: 
Chris@16:     wrapped_matrix_type m_jac;
Chris@16:     wrapped_pmatrix_type m_pm;
Chris@16:     wrapped_deriv_type m_dfdt , m_dxdt , m_dxdtnew;
Chris@16:     wrapped_state_type m_g1 , m_g2 , m_g3 , m_g4 , m_g5;
Chris@16:     wrapped_state_type m_cont3 , m_cont4;
Chris@16:     wrapped_state_type m_xtmp;
Chris@16:     wrapped_state_type m_x_err;
Chris@16: 
Chris@16:     const rosenbrock_coefficients m_coef;
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: } // namespace odeint
Chris@16: } // namespace numeric
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED