375 lines
15 KiB
Plaintext
375 lines
15 KiB
Plaintext
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/*
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[auto_generated]
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boost/numeric/odeint/stepper/runge_kutta_fehlberg87.hpp
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[begin_description]
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Implementation of the Runge-Kutta-Fehlberg stepper with the generic stepper.
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[end_description]
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Copyright 2011-2013 Mario Mulansky
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Copyright 2012-2013 Karsten Ahnert
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED
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#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED
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#include <boost/fusion/container/vector.hpp>
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#include <boost/fusion/container/generation/make_vector.hpp>
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#include <boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp>
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#include <boost/numeric/odeint/algebra/range_algebra.hpp>
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#include <boost/numeric/odeint/algebra/default_operations.hpp>
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#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
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#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
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#include <boost/array.hpp>
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#include <boost/numeric/odeint/util/state_wrapper.hpp>
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#include <boost/numeric/odeint/util/is_resizeable.hpp>
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#include <boost/numeric/odeint/util/resizer.hpp>
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namespace boost {
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namespace numeric {
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namespace odeint {
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#ifndef DOXYGEN_SKIP
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template< class Value = double >
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struct rk78_coefficients_a1 : boost::array< Value , 1 >
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{
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rk78_coefficients_a1( void )
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{
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(*this)[0] = static_cast< Value >( 2 )/static_cast< Value >( 27 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a2 : boost::array< Value , 2 >
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{
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rk78_coefficients_a2( void )
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{
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(*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 36 );
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(*this)[1] = static_cast< Value >( 1 )/static_cast< Value >( 12 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a3 : boost::array< Value , 3 >
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{
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rk78_coefficients_a3( void )
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{
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(*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 24 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 8 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a4 : boost::array< Value , 4 >
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{
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rk78_coefficients_a4( void )
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{
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(*this)[0] = static_cast< Value >( 5 )/static_cast< Value >( 12 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( -25 )/static_cast< Value >( 16 );
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(*this)[3] = static_cast< Value >( 25 )/static_cast< Value >( 16 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a5 : boost::array< Value , 5 >
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{
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rk78_coefficients_a5( void )
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{
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(*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 20 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 1 )/static_cast< Value >( 4 );
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(*this)[4] = static_cast< Value >( 1 )/static_cast< Value >( 5 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a6 : boost::array< Value , 6 >
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{
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rk78_coefficients_a6( void )
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{
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(*this)[0] = static_cast< Value >( -25 )/static_cast< Value >( 108 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 125 )/static_cast< Value >( 108 );
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(*this)[4] = static_cast< Value >( -65 )/static_cast< Value >( 27 );
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(*this)[5] = static_cast< Value >( 125 )/static_cast< Value >( 54 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a7 : boost::array< Value , 7 >
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{
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rk78_coefficients_a7( void )
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{
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(*this)[0] = static_cast< Value >( 31 )/static_cast< Value >( 300 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 0 );
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(*this)[4] = static_cast< Value >( 61 )/static_cast< Value >( 225 );
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(*this)[5] = static_cast< Value >( -2 )/static_cast< Value >( 9 );
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(*this)[6] = static_cast< Value >( 13 )/static_cast< Value >( 900 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a8 : boost::array< Value , 8 >
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{
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rk78_coefficients_a8( void )
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{
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(*this)[0] = static_cast< Value >( 2 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( -53 )/static_cast< Value >( 6 );
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(*this)[4] = static_cast< Value >( 704 )/static_cast< Value >( 45 );
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(*this)[5] = static_cast< Value >( -107 )/static_cast< Value >( 9 );
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(*this)[6] = static_cast< Value >( 67 )/static_cast< Value >( 90 );
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(*this)[7] = static_cast< Value >( 3 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a9 : boost::array< Value , 9 >
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{
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rk78_coefficients_a9( void )
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{
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(*this)[0] = static_cast< Value >( -91 )/static_cast< Value >( 108 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 23 )/static_cast< Value >( 108 );
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(*this)[4] = static_cast< Value >( -976 )/static_cast< Value >( 135 );
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(*this)[5] = static_cast< Value >( 311 )/static_cast< Value >( 54 );
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(*this)[6] = static_cast< Value >( -19 )/static_cast< Value >( 60 );
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(*this)[7] = static_cast< Value >( 17 )/static_cast< Value >( 6 );
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(*this)[8] = static_cast< Value >( -1 )/static_cast< Value >( 12 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a10 : boost::array< Value , 10 >
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{
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rk78_coefficients_a10( void )
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{
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(*this)[0] = static_cast< Value >( 2383 )/static_cast< Value >( 4100 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 );
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(*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 );
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(*this)[5] = static_cast< Value >( -301 )/static_cast< Value >( 82 );
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(*this)[6] = static_cast< Value >( 2133 )/static_cast< Value >( 4100 );
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(*this)[7] = static_cast< Value >( 45 )/static_cast< Value >( 82 );
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(*this)[8] = static_cast< Value >( 45 )/static_cast< Value >( 164 );
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(*this)[9] = static_cast< Value >( 18 )/static_cast< Value >( 41 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a11 : boost::array< Value , 11 >
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{
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rk78_coefficients_a11( void )
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{
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(*this)[0] = static_cast< Value >( 3 )/static_cast< Value >( 205 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 0 );
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(*this)[4] = static_cast< Value >( 0 );
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(*this)[5] = static_cast< Value >( -6 )/static_cast< Value >( 41 );
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(*this)[6] = static_cast< Value >( -3 )/static_cast< Value >( 205 );
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(*this)[7] = static_cast< Value >( -3 )/static_cast< Value >( 41 );
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(*this)[8] = static_cast< Value >( 3 )/static_cast< Value >( 41 );
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(*this)[9] = static_cast< Value >( 6 )/static_cast< Value >( 41 );
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(*this)[10] = static_cast< Value >( 0 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_a12 : boost::array< Value , 12 >
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{
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rk78_coefficients_a12( void )
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{
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(*this)[0] = static_cast< Value >( -1777 )/static_cast< Value >( 4100 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 );
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(*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 );
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(*this)[5] = static_cast< Value >( -289 )/static_cast< Value >( 82 );
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(*this)[6] = static_cast< Value >( 2193 )/static_cast< Value >( 4100 );
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(*this)[7] = static_cast< Value >( 51 )/static_cast< Value >( 82 );
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(*this)[8] = static_cast< Value >( 33 )/static_cast< Value >( 164 );
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(*this)[9] = static_cast< Value >( 12 )/static_cast< Value >( 41 );
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(*this)[10] = static_cast< Value >( 0 );
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(*this)[11] = static_cast< Value >( 1 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_b : boost::array< Value , 13 >
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{
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rk78_coefficients_b( void )
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{
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(*this)[0] = static_cast< Value >( 0 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 0 );
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(*this)[4] = static_cast< Value >( 0 );
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(*this)[5] = static_cast< Value >( 34 )/static_cast<Value>( 105 );
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(*this)[6] = static_cast< Value >( 9 )/static_cast<Value>( 35 );
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(*this)[7] = static_cast< Value >( 9 )/static_cast<Value>( 35 );
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(*this)[8] = static_cast< Value >( 9 )/static_cast<Value>( 280 );
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(*this)[9] = static_cast< Value >( 9 )/static_cast<Value>( 280 );
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(*this)[10] = static_cast< Value >( 0 );
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(*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
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(*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_db : boost::array< Value , 13 >
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{
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rk78_coefficients_db( void )
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{
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(*this)[0] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 );
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(*this)[1] = static_cast< Value >( 0 );
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(*this)[2] = static_cast< Value >( 0 );
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(*this)[3] = static_cast< Value >( 0 );
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(*this)[4] = static_cast< Value >( 0 );
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(*this)[5] = static_cast< Value >( 0 );
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(*this)[6] = static_cast< Value >( 0 );
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(*this)[7] = static_cast< Value >( 0 );
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(*this)[8] = static_cast< Value >( 0 );
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(*this)[9] = static_cast< Value >( 0 );
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(*this)[10] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 );
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(*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
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(*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 );
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}
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};
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template< class Value = double >
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struct rk78_coefficients_c : boost::array< Value , 13 >
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{
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rk78_coefficients_c( void )
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{
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(*this)[0] = static_cast< Value >( 0 );
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(*this)[1] = static_cast< Value >( 2 )/static_cast< Value >( 27 );
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(*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 9 );
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(*this)[3] = static_cast< Value >( 1 )/static_cast<Value>( 6 );
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(*this)[4] = static_cast< Value >( 5 )/static_cast<Value>( 12 );
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(*this)[5] = static_cast< Value >( 1 )/static_cast<Value>( 2 );
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(*this)[6] = static_cast< Value >( 5 )/static_cast<Value>( 6 );
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(*this)[7] = static_cast< Value >( 1 )/static_cast<Value>( 6 );
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(*this)[8] = static_cast< Value >( 2 )/static_cast<Value>( 3 );
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(*this)[9] = static_cast< Value >( 1 )/static_cast<Value>( 3 );
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(*this)[10] = static_cast< Value >( 1 );
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(*this)[11] = static_cast< Value >( 0 );
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(*this)[12] = static_cast< Value >( 1 );
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}
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};
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#endif // DOXYGEN_SKIP
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template<
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class State ,
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class Value = double ,
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class Deriv = State ,
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class Time = Value ,
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class Algebra = typename algebra_dispatcher< State >::algebra_type ,
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class Operations = typename operations_dispatcher< State >::operations_type ,
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class Resizer = initially_resizer
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>
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#ifndef DOXYGEN_SKIP
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class runge_kutta_fehlberg78 : public explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time ,
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Algebra , Operations , Resizer >
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#else
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class runge_kutta_fehlberg78 : public explicit_error_generic_rk
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#endif
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{
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public:
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#ifndef DOXYGEN_SKIP
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typedef explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time ,
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Algebra , Operations , Resizer > stepper_base_type;
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#endif
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typedef typename stepper_base_type::state_type state_type;
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typedef typename stepper_base_type::value_type value_type;
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typedef typename stepper_base_type::deriv_type deriv_type;
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typedef typename stepper_base_type::time_type time_type;
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typedef typename stepper_base_type::algebra_type algebra_type;
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typedef typename stepper_base_type::operations_type operations_type;
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typedef typename stepper_base_type::resizer_type resizer_type;
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#ifndef DOXYGEN_SKIP
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typedef typename stepper_base_type::stepper_type stepper_type;
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typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
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typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
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#endif // DOXYGEN_SKIP
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runge_kutta_fehlberg78( const algebra_type &algebra = algebra_type() ) : stepper_base_type(
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boost::fusion::make_vector( rk78_coefficients_a1<Value>() , rk78_coefficients_a2<Value>() , rk78_coefficients_a3<Value>() ,
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rk78_coefficients_a4<Value>() , rk78_coefficients_a5<Value>() , rk78_coefficients_a6<Value>() ,
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rk78_coefficients_a7<Value>() , rk78_coefficients_a8<Value>() , rk78_coefficients_a9<Value>() ,
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rk78_coefficients_a10<Value>() , rk78_coefficients_a11<Value>() , rk78_coefficients_a12<Value>() ) ,
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rk78_coefficients_b<Value>() , rk78_coefficients_db<Value>() , rk78_coefficients_c<Value>() , algebra )
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{ }
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};
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/************* DOXYGEN *************/
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/**
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* \class runge_kutta_fehlberg78
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* \brief The Runge-Kutta Fehlberg 78 method.
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*
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* The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications.
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* The method is explicit and fulfills the Error Stepper concept. Step size control
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* is provided but continuous output is not available for this method.
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*
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* This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern).
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* Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation.
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* For more details see explicit_error_stepper_base and explicit_error_generic_rk.
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*
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* \tparam State The state type.
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* \tparam Value The value type.
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* \tparam Deriv The type representing the time derivative of the state.
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* \tparam Time The time representing the independent variable - the time.
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* \tparam Algebra The algebra type.
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* \tparam Operations The operations type.
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* \tparam Resizer The resizer policy type.
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*/
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/**
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* \fn runge_kutta_fehlberg78::runge_kutta_fehlberg78( const algebra_type &algebra )
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* \brief Constructs the runge_kutta_cash_fehlberg78 class. This constructor can be used as a default
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* constructor if the algebra has a default constructor.
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||
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* \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
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||
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*/
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||
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}
|
||
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}
|
||
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}
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#endif //BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED
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