/*
* phase_oscillator_ensemble.cu
*
* The example how the phase_oscillator ensemble can be implemented using CUDA and thrust
*
* Created on: July 15, 2011
* Author: karsten
*/
#include <iostream>
#include <fstream>
#include <cmath>
#include <utility>
#include <thrust/device_vector.h>
#include <thrust/reduce.h>
#include <thrust/functional.h>
#include <boost/numeric/odeint.hpp>
#include <boost/numeric/odeint/external/thrust/thrust_algebra.hpp>
#include <boost/numeric/odeint/external/thrust/thrust_operations.hpp>
#include <boost/numeric/odeint/external/thrust/thrust_resize.hpp>
#include <boost/timer.hpp>
#include <boost/random/cauchy_distribution.hpp>
using namespace std;
using namespace boost::numeric::odeint;
/*
* Sorry for that dirty hack, but nvcc has large problems with boost::random.
*
* Nevertheless we need the cauchy distribution from boost::random, and therefore
* we need a generator. Here it is:
*/
struct drand48_generator
{
typedef double result_type;
result_type operator()( void ) const { return drand48(); }
result_type min( void ) const { return 0.0; }
result_type max( void ) const { return 1.0; }
};
//[ thrust_phase_ensemble_state_type
//change this to float if your device does not support double computation
typedef double value_type;
//change this to host_vector< ... > of you want to run on CPU
typedef thrust::device_vector< value_type > state_type;
// typedef thrust::host_vector< value_type > state_type;
//]
//[ thrust_phase_ensemble_mean_field_calculator
struct mean_field_calculator
{
struct sin_functor : public thrust::unary_function< value_type , value_type >
{
__host__ __device__
value_type operator()( value_type x) const
{
return sin( x );
}
};
struct cos_functor : public thrust::unary_function< value_type , value_type >
{
__host__ __device__
value_type operator()( value_type x) const
{
return cos( x );
}
};
static std::pair< value_type , value_type > get_mean( const state_type &x )
{
//[ thrust_phase_ensemble_sin_sum
value_type sin_sum = thrust::reduce(
thrust::make_transform_iterator( x.begin() , sin_functor() ) ,
thrust::make_transform_iterator( x.end() , sin_functor() ) );
//]
value_type cos_sum = thrust::reduce(
thrust::make_transform_iterator( x.begin() , cos_functor() ) ,
thrust::make_transform_iterator( x.end() , cos_functor() ) );
cos_sum /= value_type( x.size() );
sin_sum /= value_type( x.size() );
value_type K = sqrt( cos_sum * cos_sum + sin_sum * sin_sum );
value_type Theta = atan2( sin_sum , cos_sum );
return std::make_pair( K , Theta );
}
};
//]
//[ thrust_phase_ensemble_sys_function
class phase_oscillator_ensemble
{
public:
struct sys_functor
{
value_type m_K , m_Theta , m_epsilon;
sys_functor( value_type K , value_type Theta , value_type epsilon )
: m_K( K ) , m_Theta( Theta ) , m_epsilon( epsilon ) { }
template< class Tuple >
__host__ __device__
void operator()( Tuple t )
{
thrust::get<2>(t) = thrust::get<1>(t) + m_epsilon * m_K * sin( m_Theta - thrust::get<0>(t) );
}
};
// ...
//<-
phase_oscillator_ensemble( size_t N , value_type g = 1.0 , value_type epsilon = 1.0 )
: m_omega() , m_N( N ) , m_epsilon( epsilon )
{
create_frequencies( g );
}
void create_frequencies( value_type g )
{
boost::cauchy_distribution< value_type > cauchy( 0.0 , g );
// boost::variate_generator< boost::mt19937&, boost::cauchy_distribution< value_type > > gen( rng , cauchy );
drand48_generator d48;
vector< value_type > omega( m_N );
for( size_t i=0 ; i<m_N ; ++i )
omega[i] = cauchy( d48 );
// generate( omega.begin() , omega.end() , gen );
m_omega = omega;
}
void set_epsilon( value_type epsilon ) { m_epsilon = epsilon; }
value_type get_epsilon( void ) const { return m_epsilon; }
//->
void operator() ( const state_type &x , state_type &dxdt , const value_type dt ) const
{
std::pair< value_type , value_type > mean_field = mean_field_calculator::get_mean( x );
thrust::for_each(
thrust::make_zip_iterator( thrust::make_tuple( x.begin() , m_omega.begin() , dxdt.begin() ) ),
thrust::make_zip_iterator( thrust::make_tuple( x.end() , m_omega.end() , dxdt.end()) ) ,
sys_functor( mean_field.first , mean_field.second , m_epsilon )
);
}
// ...
//<-
private:
state_type m_omega;
const size_t m_N;
value_type m_epsilon;
//->
};
//]
//[ thrust_phase_ensemble_observer
struct statistics_observer
{
value_type m_K_mean;
size_t m_count;
statistics_observer( void )
: m_K_mean( 0.0 ) , m_count( 0 ) { }
template< class State >
void operator()( const State &x , value_type t )
{
std::pair< value_type , value_type > mean = mean_field_calculator::get_mean( x );
m_K_mean += mean.first;
++m_count;
}
value_type get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / value_type( m_count ) : 0.0 ; }
void reset( void ) { m_K_mean = 0.0; m_count = 0; }
};
//]
// const size_t N = 16384 * 128;
const size_t N = 16384;
const value_type pi = 3.1415926535897932384626433832795029;
const value_type dt = 0.1;
const value_type d_epsilon = 0.1;
const value_type epsilon_min = 0.0;
const value_type epsilon_max = 5.0;
const value_type t_transients = 10.0;
const value_type t_max = 100.0;
int main( int arc , char* argv[] )
{
// initial conditions on host
vector< value_type > x_host( N );
for( size_t i=0 ; i<N ; ++i ) x_host[i] = 2.0 * pi * drand48();
//[ thrust_phase_ensemble_system_instance
phase_oscillator_ensemble ensemble( N , 1.0 );
//]
boost::timer timer;
boost::timer timer_local;
double dopri5_time = 0.0 , rk4_time = 0.0;
{
//[thrust_phase_ensemble_define_dopri5
typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
//]
ofstream fout( "phase_ensemble_dopri5.dat" );
timer.restart();
for( value_type epsilon = epsilon_min ; epsilon < epsilon_max ; epsilon += d_epsilon )
{
ensemble.set_epsilon( epsilon );
statistics_observer obs;
state_type x = x_host;
timer_local.restart();
// calculate some transients steps
//[ thrust_phase_ensemble_integration
size_t steps1 = integrate_const( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , boost::ref( ensemble ) , x , 0.0 , t_transients , dt );
//]
// integrate and compute the statistics
size_t steps2 = integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , stepper_type() ) , boost::ref( ensemble ) , x , 0.0 , t_max , dt , boost::ref( obs ) );
fout << epsilon << "\t" << obs.get_K_mean() << endl;
cout << "Dopri5 : " << epsilon << "\t" << obs.get_K_mean() << "\t" << timer_local.elapsed() << "\t" << steps1 << "\t" << steps2 << endl;
}
dopri5_time = timer.elapsed();
}
{
//[ thrust_phase_ensemble_define_rk4
typedef runge_kutta4< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
//]
ofstream fout( "phase_ensemble_rk4.dat" );
timer.restart();
for( value_type epsilon = epsilon_min ; epsilon < epsilon_max ; epsilon += d_epsilon )
{
ensemble.set_epsilon( epsilon );
statistics_observer obs;
state_type x = x_host;
timer_local.restart();
// calculate some transients steps
size_t steps1 = integrate_const( stepper_type() , boost::ref( ensemble ) , x , 0.0 , t_transients , dt );
// integrate and compute the statistics
size_t steps2 = integrate_const( stepper_type() , boost::ref( ensemble ) , x , 0.0 , t_max , dt , boost::ref( obs ) );
fout << epsilon << "\t" << obs.get_K_mean() << endl;
cout << "RK4 : " << epsilon << "\t" << obs.get_K_mean() << "\t" << timer_local.elapsed() << "\t" << steps1 << "\t" << steps2 << endl;
}
rk4_time = timer.elapsed();
}
cout << "Dopri 5 : " << dopri5_time << " s\n";
cout << "RK4 : " << rk4_time << "\n";
return 0;
}
