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/*
Copyright 2011-2012 Karsten Ahnert
Copyright 2011-2013 Mario Mulansky
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 <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.hpp>
#include <boost/random/mersenne_twister.hpp>
#include <boost/random/uniform_real.hpp>
#include <boost/random/variate_generator.hpp>
using namespace std;
using namespace boost::numeric::odeint;
//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::device_vector< size_t > index_vector_type;
// typedef thrust::host_vector< value_type > state_type;
// typedef thrust::host_vector< size_t > index_vector_type;
const value_type sigma = 10.0;
const value_type b = 8.0 / 3.0;
//[ thrust_lorenz_parameters_define_simple_system
struct lorenz_system
{
struct lorenz_functor
{
template< class T >
__host__ __device__
void operator()( T t ) const
{
// unpack the parameter we want to vary and the Lorenz variables
value_type R = thrust::get< 3 >( t );
value_type x = thrust::get< 0 >( t );
value_type y = thrust::get< 1 >( t );
value_type z = thrust::get< 2 >( t );
thrust::get< 4 >( t ) = sigma * ( y - x );
thrust::get< 5 >( t ) = R * x - y - x * z;
thrust::get< 6 >( t ) = -b * z + x * y ;
}
};
lorenz_system( size_t N , const state_type &beta )
: m_N( N ) , m_beta( beta ) { }
template< class State , class Deriv >
void operator()( const State &x , Deriv &dxdt , value_type t ) const
{
thrust::for_each(
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( x ) ,
boost::begin( x ) + m_N ,
boost::begin( x ) + 2 * m_N ,
m_beta.begin() ,
boost::begin( dxdt ) ,
boost::begin( dxdt ) + m_N ,
boost::begin( dxdt ) + 2 * m_N ) ) ,
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( x ) + m_N ,
boost::begin( x ) + 2 * m_N ,
boost::begin( x ) + 3 * m_N ,
m_beta.begin() ,
boost::begin( dxdt ) + m_N ,
boost::begin( dxdt ) + 2 * m_N ,
boost::begin( dxdt ) + 3 * m_N ) ) ,
lorenz_functor() );
}
size_t m_N;
const state_type &m_beta;
};
//]
struct lorenz_perturbation_system
{
struct lorenz_perturbation_functor
{
template< class T >
__host__ __device__
void operator()( T t ) const
{
value_type R = thrust::get< 1 >( t );
value_type x = thrust::get< 0 >( thrust::get< 0 >( t ) );
value_type y = thrust::get< 1 >( thrust::get< 0 >( t ) );
value_type z = thrust::get< 2 >( thrust::get< 0 >( t ) );
value_type dx = thrust::get< 3 >( thrust::get< 0 >( t ) );
value_type dy = thrust::get< 4 >( thrust::get< 0 >( t ) );
value_type dz = thrust::get< 5 >( thrust::get< 0 >( t ) );
thrust::get< 0 >( thrust::get< 2 >( t ) ) = sigma * ( y - x );
thrust::get< 1 >( thrust::get< 2 >( t ) ) = R * x - y - x * z;
thrust::get< 2 >( thrust::get< 2 >( t ) ) = -b * z + x * y ;
thrust::get< 3 >( thrust::get< 2 >( t ) ) = sigma * ( dy - dx );
thrust::get< 4 >( thrust::get< 2 >( t ) ) = ( R - z ) * dx - dy - x * dz;
thrust::get< 5 >( thrust::get< 2 >( t ) ) = y * dx + x * dy - b * dz;
}
};
lorenz_perturbation_system( size_t N , const state_type &beta )
: m_N( N ) , m_beta( beta ) { }
template< class State , class Deriv >
void operator()( const State &x , Deriv &dxdt , value_type t ) const
{
thrust::for_each(
thrust::make_zip_iterator( thrust::make_tuple(
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( x ) ,
boost::begin( x ) + m_N ,
boost::begin( x ) + 2 * m_N ,
boost::begin( x ) + 3 * m_N ,
boost::begin( x ) + 4 * m_N ,
boost::begin( x ) + 5 * m_N ) ) ,
m_beta.begin() ,
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( dxdt ) ,
boost::begin( dxdt ) + m_N ,
boost::begin( dxdt ) + 2 * m_N ,
boost::begin( dxdt ) + 3 * m_N ,
boost::begin( dxdt ) + 4 * m_N ,
boost::begin( dxdt ) + 5 * m_N ) )
) ) ,
thrust::make_zip_iterator( thrust::make_tuple(
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( x ) + m_N ,
boost::begin( x ) + 2 * m_N ,
boost::begin( x ) + 3 * m_N ,
boost::begin( x ) + 4 * m_N ,
boost::begin( x ) + 5 * m_N ,
boost::begin( x ) + 6 * m_N ) ) ,
m_beta.begin() ,
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( dxdt ) + m_N ,
boost::begin( dxdt ) + 2 * m_N ,
boost::begin( dxdt ) + 3 * m_N ,
boost::begin( dxdt ) + 4 * m_N ,
boost::begin( dxdt ) + 5 * m_N ,
boost::begin( dxdt ) + 6 * m_N ) )
) ) ,
lorenz_perturbation_functor() );
}
size_t m_N;
const state_type &m_beta;
};
struct lyap_observer
{
//[thrust_lorenz_parameters_observer_functor
struct lyap_functor
{
template< class T >
__host__ __device__
void operator()( T t ) const
{
value_type &dx = thrust::get< 0 >( t );
value_type &dy = thrust::get< 1 >( t );
value_type &dz = thrust::get< 2 >( t );
value_type norm = sqrt( dx * dx + dy * dy + dz * dz );
dx /= norm;
dy /= norm;
dz /= norm;
thrust::get< 3 >( t ) += log( norm );
}
};
//]
lyap_observer( size_t N , size_t every = 100 )
: m_N( N ) , m_lyap( N ) , m_every( every ) , m_count( 0 )
{
thrust::fill( m_lyap.begin() , m_lyap.end() , 0.0 );
}
template< class Lyap >
void fill_lyap( Lyap &lyap )
{
thrust::copy( m_lyap.begin() , m_lyap.end() , lyap.begin() );
for( size_t i=0 ; i<lyap.size() ; ++i )
lyap[i] /= m_t_overall;
}
template< class State >
void operator()( State &x , value_type t )
{
if( ( m_count != 0 ) && ( ( m_count % m_every ) == 0 ) )
{
thrust::for_each(
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( x ) + 3 * m_N ,
boost::begin( x ) + 4 * m_N ,
boost::begin( x ) + 5 * m_N ,
m_lyap.begin() ) ) ,
thrust::make_zip_iterator( thrust::make_tuple(
boost::begin( x ) + 4 * m_N ,
boost::begin( x ) + 5 * m_N ,
boost::begin( x ) + 6 * m_N ,
m_lyap.end() ) ) ,
lyap_functor() );
clog << t << "\n";
}
++m_count;
m_t_overall = t;
}
size_t m_N;
state_type m_lyap;
size_t m_every;
size_t m_count;
value_type m_t_overall;
};
const size_t N = 1024*2;
const value_type dt = 0.01;
int main( int arc , char* argv[] )
{
int driver_version , runtime_version;
cudaDriverGetVersion( &driver_version );
cudaRuntimeGetVersion ( &runtime_version );
cout << driver_version << "\t" << runtime_version << endl;
//[ thrust_lorenz_parameters_define_beta
vector< value_type > beta_host( N );
const value_type beta_min = 0.0 , beta_max = 56.0;
for( size_t i=0 ; i<N ; ++i )
beta_host[i] = beta_min + value_type( i ) * ( beta_max - beta_min ) / value_type( N - 1 );
state_type beta = beta_host;
//]
//[ thrust_lorenz_parameters_integration
state_type x( 6 * N );
// initialize x,y,z
thrust::fill( x.begin() , x.begin() + 3 * N , 10.0 );
// initial dx
thrust::fill( x.begin() + 3 * N , x.begin() + 4 * N , 1.0 );
// initialize dy,dz
thrust::fill( x.begin() + 4 * N , x.end() , 0.0 );
// create error stepper, can be used with make_controlled or make_dense_output
typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type > stepper_type;
lorenz_system lorenz( N , beta );
lorenz_perturbation_system lorenz_perturbation( N , beta );
lyap_observer obs( N , 1 );
// calculate transients
integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz , std::make_pair( x.begin() , x.begin() + 3 * N ) , 0.0 , 10.0 , dt );
// calculate the Lyapunov exponents -- the main loop
double t = 0.0;
while( t < 10000.0 )
{
integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz_perturbation , x , t , t + 1.0 , 0.1 );
t += 1.0;
obs( x , t );
}
vector< value_type > lyap( N );
obs.fill_lyap( lyap );
for( size_t i=0 ; i<N ; ++i )
cout << beta_host[i] << "\t" << lyap[i] << "\n";
//]
return 0;
}
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