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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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