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+/*
+ [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
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-24 02:53:49 +0000