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+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp
+
+ [begin_description]
+ tba.
+ [end_description]
+
+ Copyright 2012-2013 Karsten Ahnert
+ Copyright 2012-2013 Mario Mulansky
+
+ 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_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED
+#define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED
+
+#include <boost/numeric/odeint/algebra/default_operations.hpp>
+#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
+#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
+
+#include <boost/numeric/odeint/util/resizer.hpp>
+
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+#ifndef DOXYGEN_SKIP
+namespace detail {
+namespace symplectic_rkn_sb3a_m4_mclachlan {
+
+ /*
+ exp( a1 t A ) exp( b1 t B )
+ exp( a2 t A ) exp( b2 t B )
+ exp( a3 t A )
+ exp( b2 t B ) exp( a2 t A )
+ exp( b1 t B ) exp( a1 t A )
+ */
+
+
+
+ template< class Value >
+ struct coef_a_type : public boost::array< Value , 5 >
+ {
+ coef_a_type( void )
+ {
+ using std::sqrt;
+
+ Value z = sqrt( static_cast< Value >( 7 ) / static_cast< Value >( 8 ) ) / static_cast< Value >( 3 );
+ (*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 2 ) - z ;
+ (*this)[1] = static_cast< Value >( -1 ) / static_cast< Value >( 3 ) + z ;
+ (*this)[2] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
+ (*this)[3] = (*this)[1];
+ (*this)[4] = (*this)[0];
+ }
+ };
+
+ template< class Value >
+ struct coef_b_type : public boost::array< Value , 5 >
+ {
+ coef_b_type( void )
+ {
+ (*this)[0] = static_cast< Value >( 1 );
+ (*this)[1] = static_cast< Value >( -1 ) / static_cast< Value >( 2 );
+ (*this)[2] = (*this)[1];
+ (*this)[3] = (*this)[0];
+ (*this)[4] = static_cast< Value >( 0 );
+ }
+ };
+
+} // namespace symplectic_rkn_sb3a_m4_mclachlan
+} // namespace detail
+#endif // DOXYGEN_SKIP
+
+
+
+
+template<
+ class Coor ,
+ class Momentum = Coor ,
+ class Value = double ,
+ class CoorDeriv = Coor ,
+ class MomentumDeriv = Coor ,
+ class Time = Value ,
+ class Algebra = typename algebra_dispatcher< Coor >::algebra_type ,
+ class Operations = typename operations_dispatcher< Coor >::operations_type ,
+ class Resizer = initially_resizer
+ >
+#ifndef DOXYGEN_SKIP
+class symplectic_rkn_sb3a_m4_mclachlan :
+ public symplectic_nystroem_stepper_base
+<
+ 5 , 4 ,
+ Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+ >
+#else
+class symplectic_rkn_sb3a_m4_mclachlan : public symplectic_nystroem_stepper_base
+#endif
+{
+public:
+#ifndef DOXYGEN_SKIP
+ typedef symplectic_nystroem_stepper_base
+ <
+ 5 , 4 ,
+ Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+ > stepper_base_type;
+#endif
+ typedef typename stepper_base_type::algebra_type algebra_type;
+ typedef typename stepper_base_type::value_type value_type;
+
+
+ symplectic_rkn_sb3a_m4_mclachlan( const algebra_type &algebra = algebra_type() )
+ : stepper_base_type(
+ detail::symplectic_rkn_sb3a_m4_mclachlan::coef_a_type< value_type >() ,
+ detail::symplectic_rkn_sb3a_m4_mclachlan::coef_b_type< value_type >() ,
+ algebra )
+ { }
+};
+
+
+/***************** DOXYGEN ***************/
+
+/**
+ * \class symplectic_rkn_sb3a_m4_mclachlan
+ * \brief Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order.
+ *
+ * The method is of fourth order and has five stages. It is described HERE. This method can be used
+ * with multiprecision types since the coefficients are defined analytically.
+ *
+ * ToDo: add reference to paper.
+ *
+ * \tparam Order The order of the stepper.
+ * \tparam Coor The type representing the coordinates q.
+ * \tparam Momentum The type representing the coordinates p.
+ * \tparam Value The basic value type. Should be something like float, double or a high-precision type.
+ * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt.
+ * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt.
+ * \tparam Time The type representing the time t.
+ * \tparam Algebra The algebra.
+ * \tparam Operations The operations.
+ * \tparam Resizer The resizer policy.
+ */
+
+ /**
+ * \fn symplectic_rkn_sb3a_m4_mclachlan::symplectic_rkn_sb3a_m4_mclachlan( const algebra_type &algebra )
+ * \brief Constructs the symplectic_rkn_sb3a_m4_mclachlan. This constructor can be used as a default
+ * constructor if the algebra has a default constructor.
+ * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
+ */
+
+} // namespace odeint
+} // namespace numeric
+} // namespace boost
+
+
+#endif // BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED