WSJT-X/boost/libs/numeric/odeint/examples/fpu.cpp

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/*
* fpu.cpp
*
* This example demonstrates how one can use odeint to solve the Fermi-Pasta-Ulam system.
* Created on: July 13, 2011
*
* Copyright 2011-2012 Karsten Ahnert
* Copyright 2011 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;
}