/* * fpu.cpp * * This example demonstrates how one can use odeint to solve the Fermi-Pasta-Ulam system. * Created on: July 13, 2011 * * Copyright 2009 Karsten Ahnert and 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 <numeric> #include <cmath> #include <vector> #include <boost/numeric/odeint.hpp> #ifndef M_PI //not there on windows #define M_PI 3.1415927 //... #endif using namespace std; using namespace boost::numeric::odeint; //[ fpu_system_function typedef vector< double > container_type; struct fpu { const double m_beta; fpu( const double beta = 1.0 ) : m_beta( beta ) { } // system function defining the ODE void operator()( const container_type &q , container_type &dpdt ) const { size_t n = q.size(); double tmp = q[0] - 0.0; double tmp2 = tmp + m_beta * tmp * tmp * tmp; dpdt[0] = -tmp2; for( size_t i=0 ; i<n-1 ; ++i ) { tmp = q[i+1] - q[i]; tmp2 = tmp + m_beta * tmp * tmp * tmp; dpdt[i] += tmp2; dpdt[i+1] = -tmp2; } tmp = - q[n-1]; tmp2 = tmp + m_beta * tmp * tmp * tmp; dpdt[n-1] += tmp2; } // calculates the energy of the system double energy( const container_type &q , const container_type &p ) const { // ... //<- double energy = 0.0; size_t n = q.size(); double tmp = q[0]; energy += 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp; for( size_t i=0 ; i<n-1 ; ++i ) { tmp = q[i+1] - q[i]; energy += 0.5 * ( p[i] * p[i] + tmp * tmp ) + 0.25 * m_beta * tmp * tmp * tmp * tmp; } energy += 0.5 * p[n-1] * p[n-1]; tmp = q[n-1]; energy += 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp; return energy; //-> } // calculates the local energy of the system void local_energy( const container_type &q , const container_type &p , container_type &e ) const { // ... //<- size_t n = q.size(); double tmp = q[0]; double tmp2 = 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp; e[0] = tmp2; for( size_t i=0 ; i<n-1 ; ++i ) { tmp = q[i+1] - q[i]; tmp2 = 0.25 * tmp * tmp + 0.125 * m_beta * tmp * tmp * tmp * tmp; e[i] += 0.5 * p[i] * p[i] + tmp2 ; e[i+1] = tmp2; } tmp = q[n-1]; tmp2 = 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp; e[n-1] += 0.5 * p[n-1] * p[n-1] + tmp2; //-> } }; //] //[ fpu_observer struct streaming_observer { std::ostream& m_out; const fpu &m_fpu; size_t m_write_every; size_t m_count; streaming_observer( std::ostream &out , const fpu &f , size_t write_every = 100 ) : m_out( out ) , m_fpu( f ) , m_write_every( write_every ) , m_count( 0 ) { } template< class State > void operator()( const State &x , double t ) { if( ( m_count % m_write_every ) == 0 ) { container_type &q = x.first; container_type &p = x.second; container_type energy( q.size() ); m_fpu.local_energy( q , p , energy ); for( size_t i=0 ; i<q.size() ; ++i ) { m_out << t << "\t" << i << "\t" << q[i] << "\t" << p[i] << "\t" << energy[i] << "\n"; } m_out << "\n"; clog << t << "\t" << accumulate( energy.begin() , energy.end() , 0.0 ) << "\n"; } ++m_count; } }; //] int main( int argc , char **argv ) { //[ fpu_integration const size_t n = 64; container_type q( n , 0.0 ) , p( n , 0.0 ); for( size_t i=0 ; i<n ; ++i ) { p[i] = 0.0; q[i] = 32.0 * sin( double( i + 1 ) / double( n + 1 ) * M_PI ); } const double dt = 0.1; typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type; fpu fpu_instance( 8.0 ); integrate_const( stepper_type() , fpu_instance , make_pair( boost::ref( q ) , boost::ref( p ) ) , 0.0 , 1000.0 , dt , streaming_observer( cout , fpu_instance , 10 ) ); //] return 0; }