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include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp

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+/*
+ [auto_generated]
+ boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp
+ 
+ [begin_description]
+ Implementation of the symplectic MacLachlan stepper for separable Hamiltonian system.
+ [end_description]
+ 
+ Copyright 2011-2013 Karsten Ahnert
+ Copyright 2011-2013 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_MCLACHLAN_HPP_INCLUDED
+#define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
+
+
+#include <boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp>
+
+#include <boost/numeric/odeint/algebra/range_algebra.hpp>
+#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>
+
+#include <array>
+
+namespace boost {
+namespace numeric {
+namespace odeint {
+
+
+#ifndef DOXYGEN_SKIP
+namespace detail {
+namespace symplectic_rkn_sb3a_mclachlan {
+
+    /*
+      exp( a1 t A ) exp( b1 t B )
+      exp( a2 t A ) exp( b2 t B )
+      exp( a3 t A ) exp( b3 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 std::array< Value , 6 >
+    {
+        coef_a_type( void )
+        {
+            (*this)[0] = static_cast< Value >( 0.40518861839525227722 );
+            (*this)[1] = static_cast< Value >( -0.28714404081652408900 );
+            (*this)[2] = static_cast< Value >( 1 ) / static_cast< Value >( 2 ) - ( (*this)[0] + (*this)[1] );
+            (*this)[3] = (*this)[2];
+            (*this)[4] = (*this)[1];
+            (*this)[5] = (*this)[0];
+
+        }
+    };
+
+    template< class Value >
+    struct coef_b_type : public std::array< Value , 6 >
+    {
+        coef_b_type( void )
+        {
+            (*this)[0] = static_cast< Value >( -3 ) / static_cast< Value >( 73 );
+            (*this)[1] = static_cast< Value >( 17 ) / static_cast< Value >( 59 );
+            (*this)[2] = static_cast< Value >( 1 ) - static_cast< Value >( 2 ) * ( (*this)[0] + (*this)[1] );
+            (*this)[3] = (*this)[1];
+            (*this)[4] = (*this)[0];
+            (*this)[5] = static_cast< Value >( 0 );
+        }
+    };
+
+} // namespace symplectic_rkn_sb3a_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_mclachlan :
+        public symplectic_nystroem_stepper_base
+<
+    6 , 4 ,
+    Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
+    >
+#else
+class symplectic_rkn_sb3a_mclachlan : public symplectic_nystroem_stepper_base
+#endif
+{
+public:
+#ifndef DOXYGEN_SKIP
+    typedef symplectic_nystroem_stepper_base
+    <
+    6 , 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_mclachlan( const algebra_type &algebra = algebra_type() )
+        : stepper_base_type(
+            detail::symplectic_rkn_sb3a_mclachlan::coef_a_type< value_type >() ,
+            detail::symplectic_rkn_sb3a_mclachlan::coef_b_type< value_type >() ,
+            algebra )
+    { }
+};
+
+
+/************* DOXYGEN ***********/
+
+/**
+ * \class symplectic_rkn_sb3a_mclachlan
+ * \brief Implement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order.
+ *
+ * The method is of fourth order and has six stages. It is described HERE. This method cannot be used
+ * with multiprecision types since the coefficients are not defined analytically.
+ *
+ * ToDo Add reference to the 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_mclachlan::symplectic_rkn_sb3a_mclachlan( const algebra_type &algebra )
+     * \brief Constructs the symplectic_rkn_sb3a_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_MCLACHLAN_HPP_INCLUDED