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/*
[auto_generated]
libs/numeric/odeint/examples/heun.cpp
[begin_description]
Examplary implementation of the method of Heun.
[end_description]
Copyright 2012 Karsten Ahnert
Copyright 2012 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)
*/
#include <iostream>
#include <boost/fusion/container/vector.hpp>
#include <boost/fusion/container/generation/make_vector.hpp>
#include <boost/array.hpp>
#include <boost/numeric/odeint.hpp>
namespace fusion = boost::fusion;
//[ heun_define_coefficients
template< class Value = double >
struct heun_a1 : boost::array< Value , 1 > {
heun_a1( void )
{
(*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 3 );
}
};
template< class Value = double >
struct heun_a2 : boost::array< Value , 2 >
{
heun_a2( void )
{
(*this)[0] = static_cast< Value >( 0 );
(*this)[1] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
}
};
template< class Value = double >
struct heun_b : boost::array< Value , 3 >
{
heun_b( void )
{
(*this)[0] = static_cast<Value>( 1 ) / static_cast<Value>( 4 );
(*this)[1] = static_cast<Value>( 0 );
(*this)[2] = static_cast<Value>( 3 ) / static_cast<Value>( 4 );
}
};
template< class Value = double >
struct heun_c : boost::array< Value , 3 >
{
heun_c( void )
{
(*this)[0] = static_cast< Value >( 0 );
(*this)[1] = static_cast< Value >( 1 ) / static_cast< Value >( 3 );
(*this)[2] = static_cast< Value >( 2 ) / static_cast< Value >( 3 );
}
};
//]
//[ heun_stepper_definition
template<
class State ,
class Value = double ,
class Deriv = State ,
class Time = Value ,
class Algebra = boost::numeric::odeint::range_algebra ,
class Operations = boost::numeric::odeint::default_operations ,
class Resizer = boost::numeric::odeint::initially_resizer
>
class heun : public
boost::numeric::odeint::explicit_generic_rk< 3 , 3 , State , Value , Deriv , Time ,
Algebra , Operations , Resizer >
{
public:
typedef boost::numeric::odeint::explicit_generic_rk< 3 , 3 , State , Value , Deriv , Time ,
Algebra , Operations , Resizer > stepper_base_type;
typedef typename stepper_base_type::state_type state_type;
typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
typedef typename stepper_base_type::value_type value_type;
typedef typename stepper_base_type::deriv_type deriv_type;
typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
typedef typename stepper_base_type::time_type time_type;
typedef typename stepper_base_type::algebra_type algebra_type;
typedef typename stepper_base_type::operations_type operations_type;
typedef typename stepper_base_type::resizer_type resizer_type;
typedef typename stepper_base_type::stepper_type stepper_type;
heun( const algebra_type &algebra = algebra_type() )
: stepper_base_type(
fusion::make_vector(
heun_a1<Value>() ,
heun_a2<Value>() ) ,
heun_b<Value>() , heun_c<Value>() , algebra )
{ }
};
//]
const double sigma = 10.0;
const double R = 28.0;
const double b = 8.0 / 3.0;
struct lorenz
{
template< class State , class Deriv >
void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
{
typename boost::range_iterator< const State >::type x = boost::begin( x_ );
typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
dxdt[0] = sigma * ( x[1] - x[0] );
dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
dxdt[2] = -b * x[2] + x[0] * x[1];
}
};
struct streaming_observer
{
std::ostream &m_out;
streaming_observer( std::ostream &out ) : m_out( out ) { }
template< typename State , typename Value >
void operator()( const State &x , Value t ) const
{
m_out << t;
for( size_t i=0 ; i<x.size() ; ++i ) m_out << "\t" << x[i];
m_out << "\n";
}
};
int main( int argc , char **argv )
{
using namespace std;
using namespace boost::numeric::odeint;
//[ heun_example
typedef boost::array< double , 3 > state_type;
heun< state_type > h;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
integrate_const( h , lorenz() , x , 0.0 , 100.0 , 0.01 ,
streaming_observer( std::cout ) );
//]
return 0;
}
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