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/*
libs/numeric/odeint/examples/stochastic_euler.hpp
Copyright 2012 Karsten Ahnert
Copyright 2012 Mario Mulansky
Stochastic euler stepper example and Ornstein-Uhlenbeck process
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 <vector>
#include <iostream>
#include <boost/random.hpp>
#include <boost/array.hpp>
#include <boost/numeric/odeint.hpp>
/*
//[ stochastic_euler_class_definition
template< size_t N > class stochastic_euler
{
public:
typedef boost::array< double , N > state_type;
typedef boost::array< double , N > deriv_type;
typedef double value_type;
typedef double time_type;
typedef unsigned short order_type;
typedef boost::numeric::odeint::stepper_tag stepper_category;
static order_type order( void ) { return 1; }
// ...
};
//]
*/
/*
//[ stochastic_euler_do_step
template< size_t N > class stochastic_euler
{
public:
// ...
template< class System >
void do_step( System system , state_type &x , time_type t , time_type dt ) const
{
deriv_type det , stoch ;
system.first( x , det );
system.second( x , stoch );
for( size_t i=0 ; i<x.size() ; ++i )
x[i] += dt * det[i] + sqrt( dt ) * stoch[i];
}
};
//]
*/
//[ stochastic_euler_class
template< size_t N >
class stochastic_euler
{
public:
typedef boost::array< double , N > state_type;
typedef boost::array< double , N > deriv_type;
typedef double value_type;
typedef double time_type;
typedef unsigned short order_type;
typedef boost::numeric::odeint::stepper_tag stepper_category;
static order_type order( void ) { return 1; }
template< class System >
void do_step( System system , state_type &x , time_type t , time_type dt ) const
{
deriv_type det , stoch ;
system.first( x , det );
system.second( x , stoch );
for( size_t i=0 ; i<x.size() ; ++i )
x[i] += dt * det[i] + sqrt( dt ) * stoch[i];
}
};
//]
//[ stochastic_euler_ornstein_uhlenbeck_def
const static size_t N = 1;
typedef boost::array< double , N > state_type;
struct ornstein_det
{
void operator()( const state_type &x , state_type &dxdt ) const
{
dxdt[0] = -x[0];
}
};
struct ornstein_stoch
{
boost::mt19937 &m_rng;
boost::normal_distribution<> m_dist;
ornstein_stoch( boost::mt19937 &rng , double sigma ) : m_rng( rng ) , m_dist( 0.0 , sigma ) { }
void operator()( const state_type &x , state_type &dxdt )
{
dxdt[0] = m_dist( m_rng );
}
};
//]
struct streaming_observer
{
template< class State >
void operator()( const State &x , double t ) const
{
std::cout << t << "\t" << x[0] << "\n";
}
};
int main( int argc , char **argv )
{
using namespace std;
using namespace boost::numeric::odeint;
//[ ornstein_uhlenbeck_main
boost::mt19937 rng;
double dt = 0.1;
state_type x = {{ 1.0 }};
integrate_const( stochastic_euler< N >() , make_pair( ornstein_det() , ornstein_stoch( rng , 1.0 ) ),
x , 0.0 , 10.0 , dt , streaming_observer() );
//]
return 0;
}
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