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/*
Copyright 2010-2012 Karsten Ahnert
Copyright 2011-2013 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 <vector>
#include <boost/numeric/odeint.hpp>
//[ rhs_function
/* The type of container used to hold the state vector */
typedef std::vector< double > state_type;
const double gam = 0.15;
/* The rhs of x' = f(x) */
void harmonic_oscillator( const state_type &x , state_type &dxdt , const double /* t */ )
{
dxdt[0] = x[1];
dxdt[1] = -x[0] - gam*x[1];
}
//]
//[ rhs_class
/* The rhs of x' = f(x) defined as a class */
class harm_osc {
double m_gam;
public:
harm_osc( double gam ) : m_gam(gam) { }
void operator() ( const state_type &x , state_type &dxdt , const double /* t */ )
{
dxdt[0] = x[1];
dxdt[1] = -x[0] - m_gam*x[1];
}
};
//]
//[ integrate_observer
struct push_back_state_and_time
{
std::vector< state_type >& m_states;
std::vector< double >& m_times;
push_back_state_and_time( std::vector< state_type > &states , std::vector< double > &times )
: m_states( states ) , m_times( times ) { }
void operator()( const state_type &x , double t )
{
m_states.push_back( x );
m_times.push_back( t );
}
};
//]
struct write_state
{
void operator()( const state_type &x ) const
{
std::cout << x[0] << "\t" << x[1] << "\n";
}
};
int main(int /* argc */ , char** /* argv */ )
{
using namespace std;
using namespace boost::numeric::odeint;
//[ state_initialization
state_type x(2);
x[0] = 1.0; // start at x=1.0, p=0.0
x[1] = 0.0;
//]
//[ integration
size_t steps = integrate( harmonic_oscillator ,
x , 0.0 , 10.0 , 0.1 );
//]
//[ integration_class
harm_osc ho(0.15);
steps = integrate( ho ,
x , 0.0 , 10.0 , 0.1 );
//]
//[ integrate_observ
vector<state_type> x_vec;
vector<double> times;
steps = integrate( harmonic_oscillator ,
x , 0.0 , 10.0 , 0.1 ,
push_back_state_and_time( x_vec , times ) );
/* output */
for( size_t i=0; i<=steps; i++ )
{
cout << times[i] << '\t' << x_vec[i][0] << '\t' << x_vec[i][1] << '\n';
}
//]
//[ define_const_stepper
runge_kutta4< state_type > stepper;
integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
//]
//[ integrate_const_loop
const double dt = 0.01;
for( double t=0.0 ; t<10.0 ; t+= dt )
stepper.do_step( harmonic_oscillator , x , t , dt );
//]
//[ define_adapt_stepper
typedef runge_kutta_cash_karp54< state_type > error_stepper_type;
//]
//[ integrate_adapt
typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
controlled_stepper_type controlled_stepper;
integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
//]
{
//[integrate_adapt_full
double abs_err = 1.0e-10 , rel_err = 1.0e-6 , a_x = 1.0 , a_dxdt = 1.0;
controlled_stepper_type controlled_stepper(
default_error_checker< double , range_algebra , default_operations >( abs_err , rel_err , a_x , a_dxdt ) );
integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
//]
}
//[integrate_adapt_make_controlled
integrate_adaptive( make_controlled< error_stepper_type >( 1.0e-10 , 1.0e-6 ) ,
harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
//]
//[integrate_adapt_make_controlled_alternative
integrate_adaptive( make_controlled( 1.0e-10 , 1.0e-6 , error_stepper_type() ) ,
harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
//]
#ifdef BOOST_NUMERIC_ODEINT_CXX11
//[ define_const_stepper_cpp11
{
runge_kutta4< state_type > stepper;
integrate_const( stepper , []( const state_type &x , state_type &dxdt , double t ) {
dxdt[0] = x[1]; dxdt[1] = -x[0] - gam*x[1]; }
, x , 0.0 , 10.0 , 0.01 );
}
//]
//[ harm_iterator_const_step]
std::for_each( make_const_step_time_iterator_begin( stepper , harmonic_oscillator, x , 0.0 , 0.1 , 10.0 ) ,
make_const_step_time_iterator_end( stepper , harmonic_oscillator, x ) ,
[]( std::pair< const state_type & , const double & > x ) {
cout << x.second << " " << x.first[0] << " " << x.first[1] << "\n"; } );
//]
#endif
}