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/*
* stepper_details.cpp
*
* This example demonstrates some details about the steppers in odeint.
*
*
* Copyright 2011-2012 Karsten Ahnert
* Copyright 2012 Mario Mulansky
* Copyright 2013 Pascal Germroth
*
* 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/array.hpp>
#include <boost/bind.hpp>
#include <boost/numeric/odeint.hpp>
using namespace std;
using namespace boost::numeric::odeint;
const size_t N = 3;
typedef boost::array< double , N > state_type;
//[ system_function_structure
void sys( const state_type & /*x*/ , state_type & /*dxdt*/ , const double /*t*/ )
{
// ...
}
//]
void sys1( const state_type &/*x*/ , state_type &/*dxdt*/ , const double /*t*/ )
{
}
void sys2( const state_type &/*x*/ , state_type &/*dxdt*/ , const double /*t*/ )
{
}
//[ symplectic_stepper_detail_system_function
typedef boost::array< double , 1 > vector_type;
struct harm_osc_f1
{
void operator()( const vector_type &p , vector_type &dqdt )
{
dqdt[0] = p[0];
}
};
struct harm_osc_f2
{
void operator()( const vector_type &q , vector_type &dpdt )
{
dpdt[0] = -q[0];
}
};
//]
//[ symplectic_stepper_detail_system_class
struct harm_osc
{
void f1( const vector_type &p , vector_type &dqdt ) const
{
dqdt[0] = p[0];
}
void f2( const vector_type &q , vector_type &dpdt ) const
{
dpdt[0] = -q[0];
}
};
//]
int main( int argc , char **argv )
{
using namespace std;
// Explicit stepper example
{
double t( 0.0 ) , dt( 0.1 );
state_type in , out , dxdtin , inout;
//[ explicit_stepper_detail_example
runge_kutta4< state_type > rk;
rk.do_step( sys1 , inout , t , dt ); // In-place transformation of inout
rk.do_step( sys2 , inout , t , dt ); // call with different system: Ok
rk.do_step( sys1 , in , t , out , dt ); // Out-of-place transformation
rk.do_step( sys1 , inout , dxdtin , t , dt ); // In-place tranformation of inout
rk.do_step( sys1 , in , dxdtin , t , out , dt ); // Out-of-place transformation
//]
}
// FSAL stepper example
{
double t( 0.0 ) , dt( 0.1 );
state_type in , in2 , in3 , out , dxdtin , dxdtout , inout , dxdtinout;
//[ fsal_stepper_detail_example
runge_kutta_dopri5< state_type > rk;
rk.do_step( sys1 , in , t , out , dt );
rk.do_step( sys2 , in , t , out , dt ); // DONT do this, sys1 is assumed
rk.do_step( sys2 , in2 , t , out , dt );
rk.do_step( sys2 , in3 , t , out , dt ); // DONT do this, in2 is assumed
rk.do_step( sys1 , inout , dxdtinout , t , dt );
rk.do_step( sys2 , inout , dxdtinout , t , dt ); // Ok, internal derivative is not used, dxdtinout is updated
rk.do_step( sys1 , in , dxdtin , t , out , dxdtout , dt );
rk.do_step( sys2 , in , dxdtin , t , out , dxdtout , dt ); // Ok, internal derivative is not used
//]
}
// Symplectic harmonic oscillator example
{
double t( 0.0 ) , dt( 0.1 );
//[ symplectic_stepper_detail_example
pair< vector_type , vector_type > x;
x.first[0] = 1.0; x.second[0] = 0.0;
symplectic_rkn_sb3a_mclachlan< vector_type > rkn;
rkn.do_step( make_pair( harm_osc_f1() , harm_osc_f2() ) , x , t , dt );
//]
//[ symplectic_stepper_detail_system_class_example
harm_osc h;
rkn.do_step( make_pair( boost::bind( &harm_osc::f1 , h , _1 , _2 ) , boost::bind( &harm_osc::f2 , h , _1 , _2 ) ) ,
x , t , dt );
//]
}
// Simplified harmonic oscillator example
{
double t = 0.0, dt = 0.1;
//[ simplified_symplectic_stepper_example
pair< vector_type , vector_type > x;
x.first[0] = 1.0; x.second[0] = 0.0;
symplectic_rkn_sb3a_mclachlan< vector_type > rkn;
rkn.do_step( harm_osc_f1() , x , t , dt );
//]
vector_type q = {{ 1.0 }} , p = {{ 0.0 }};
//[ symplectic_stepper_detail_ref_usage
rkn.do_step( harm_osc_f1() , make_pair( boost::ref( q ) , boost::ref( p ) ) , t , dt );
rkn.do_step( harm_osc_f1() , q , p , t , dt );
rkn.do_step( make_pair( harm_osc_f1() , harm_osc_f2() ) , q , p , t , dt );
//]
}
// adams_bashforth_moulton stepper example
{
double t = 0.0 , dt = 0.1;
state_type inout;
//[ multistep_detail_example
adams_bashforth_moulton< 5 , state_type > abm;
abm.initialize( sys , inout , t , dt );
abm.do_step( sys , inout , t , dt );
//]
//[ multistep_detail_own_stepper_initialization
abm.initialize( runge_kutta_fehlberg78< state_type >() , sys , inout , t , dt );
//]
}
// dense output stepper examples
{
double t = 0.0 , dt = 0.1;
state_type in;
//[ dense_output_detail_example
dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > > dense;
dense.initialize( in , t , dt );
pair< double , double > times = dense.do_step( sys );
(void)times;
//]
state_type inout;
double t_start = 0.0 , t_end = 1.0;
//[ dense_output_detail_generation1
typedef boost::numeric::odeint::result_of::make_dense_output<
runge_kutta_dopri5< state_type > >::type dense_stepper_type;
dense_stepper_type dense2 = make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() );
(void)dense2;
//]
//[ dense_output_detail_generation2
integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() ) , sys , inout , t_start , t_end , dt );
//]
}
return 0;
}
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