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//==============================================================================
// Copyright 2011-2014 Karsten Ahnert
// Copyright 2011-2014 Mario Mulansky
// Copyright 2014 LRI UMR 8623 CNRS/Univ Paris Sud XI
// Copyright 2014 NumScale SAS
//
// Distributed under the Boost Software License, Version 1.0.
// See accompanying file LICENSE.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt
//==============================================================================
#include <iostream>
#include <utility>
#include <boost/numeric/odeint.hpp>
#ifndef M_PI //not there on windows
#define M_PI 3.141592653589793 //...
#endif
#include <boost/random.hpp>
#include <boost/dispatch/meta/as_integer.hpp>
#include <nt2/include/functions/cos.hpp>
#include <nt2/include/functions/sin.hpp>
#include <nt2/include/functions/atan2.hpp>
#include <nt2/table.hpp>
#include <nt2/include/functions/zeros.hpp>
#include <nt2/include/functions/sum.hpp>
#include <nt2/include/functions/mean.hpp>
#include <nt2/arithmetic/include/functions/hypot.hpp>
#include <nt2/include/functions/tie.hpp>
#include <boost/numeric/odeint/external/nt2/nt2_algebra_dispatcher.hpp>
using namespace std;
using namespace boost::numeric::odeint;
template <typename container_type, typename T>
pair< T, T > calc_mean_field( const container_type &x )
{
T cos_sum = 0.0 , sin_sum = 0.0;
nt2::tie(cos_sum,sin_sum) = nt2::tie(nt2::mean( nt2::cos(x) ), nt2::mean( nt2::sin(x) ));
T K = nt2::hypot(sin_sum,cos_sum);
T Theta = nt2::atan2( sin_sum , cos_sum );
return make_pair( K , Theta );
}
template <typename container_type, typename T>
struct phase_ensemble
{
typedef typename boost::dispatch::meta::as_integer<T,unsigned>::type int_type;
container_type m_omega;
T m_epsilon;
phase_ensemble( const int_type n , T g = 1.0 , T epsilon = 1.0 )
: m_epsilon( epsilon )
{
m_omega = nt2::zeros(nt2::of_size(n), nt2::meta::as_<T>());
create_frequencies( g );
}
void create_frequencies( T g )
{
boost::mt19937 rng;
boost::cauchy_distribution<> cauchy( 0.0 , g );
boost::variate_generator< boost::mt19937&, boost::cauchy_distribution<> > gen( rng , cauchy );
generate( m_omega.begin() , m_omega.end() , gen );
}
void set_epsilon( T epsilon ) { m_epsilon = epsilon; }
T get_epsilon( void ) const { return m_epsilon; }
void operator()( const container_type &x , container_type &dxdt , T ) const
{
pair< T, T > mean = calc_mean_field<container_type,T>( x );
dxdt = m_omega + m_epsilon * mean.first * nt2::sin( mean.second - x );
}
};
template<typename T>
struct statistics_observer
{
typedef typename boost::dispatch::meta::as_integer<T,unsigned>::type int_type;
T m_K_mean;
int_type m_count;
statistics_observer( void )
: m_K_mean( 0.0 ) , m_count( 0 ) { }
template< class State >
void operator()( const State &x , T t )
{
pair< T, T > mean = calc_mean_field<State,T>( x );
m_K_mean += mean.first;
++m_count;
}
T get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / T( m_count ) : 0.0 ; }
void reset( void ) { m_K_mean = 0.0; m_count = 0; }
};
template<typename T>
struct test_ode_table
{
typedef nt2::table<T> array_type;
typedef void experiment_is_immutable;
typedef typename boost::dispatch::meta::as_integer<T,unsigned>::type int_type;
test_ode_table ( )
: size_(16384), ensemble( size_ , 1.0 ), unif( 0.0 , 2.0 * M_PI ), gen( rng , unif ), obs()
{
x.resize(nt2::of_size(size_));
}
void operator()()
{
for( T epsilon = 0.0 ; epsilon < 5.0 ; epsilon += 0.1 )
{
ensemble.set_epsilon( epsilon );
obs.reset();
// start with random initial conditions
generate( x.begin() , x.end() , gen );
// calculate some transients steps
integrate_const( runge_kutta4< array_type, T >() , boost::ref( ensemble ) , x , T(0.0) , T(10.0) , dt );
// integrate and compute the statistics
integrate_const( runge_kutta4< array_type, T >() , boost::ref( ensemble ) , x , T(0.0) , T(100.0) , dt , boost::ref( obs ) );
cout << epsilon << "\t" << obs.get_K_mean() << endl;
}
}
friend std::ostream& operator<<(std::ostream& os, test_ode_table<T> const& p)
{
return os << "(" << p.size() << ")";
}
std::size_t size() const { return size_; }
private:
std::size_t size_;
phase_ensemble<array_type,T> ensemble;
boost::uniform_real<> unif;
array_type x;
boost::mt19937 rng;
boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen;
statistics_observer<T> obs;
static const T dt = 0.1;
};
int main()
{
std::cout<< " With T = [double] \n";
test_ode_table<double> test_double;
test_double();
std::cout<< " With T = [float] \n";
test_ode_table<float> test_float;
test_float();
}
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