/* 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; }