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/*
* two_dimensional_phase_lattice.cpp
*
* This example show how one can use matrices as state types in odeint.
*
* 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 <map>
#include <string>
#include <fstream>
#ifndef M_PI //not there on windows
#define M_PI 3.1415927 //...
#endif
#include <boost/numeric/odeint.hpp>
using namespace std;
using namespace boost::numeric::odeint;
//[ two_dimensional_phase_lattice_definition
typedef boost::numeric::ublas::matrix< double > state_type;
struct two_dimensional_phase_lattice
{
two_dimensional_phase_lattice( double gamma = 0.5 )
: m_gamma( gamma ) { }
void operator()( const state_type &x , state_type &dxdt , double /* t */ ) const
{
size_t size1 = x.size1() , size2 = x.size2();
for( size_t i=1 ; i<size1-1 ; ++i )
{
for( size_t j=1 ; j<size2-1 ; ++j )
{
dxdt( i , j ) =
coupling_func( x( i + 1 , j ) - x( i , j ) ) +
coupling_func( x( i - 1 , j ) - x( i , j ) ) +
coupling_func( x( i , j + 1 ) - x( i , j ) ) +
coupling_func( x( i , j - 1 ) - x( i , j ) );
}
}
for( size_t i=0 ; i<x.size1() ; ++i ) dxdt( i , 0 ) = dxdt( i , x.size2() -1 ) = 0.0;
for( size_t j=0 ; j<x.size2() ; ++j ) dxdt( 0 , j ) = dxdt( x.size1() -1 , j ) = 0.0;
}
double coupling_func( double x ) const
{
return sin( x ) - m_gamma * ( 1.0 - cos( x ) );
}
double m_gamma;
};
//]
struct write_for_gnuplot
{
size_t m_every , m_count;
write_for_gnuplot( size_t every = 10 )
: m_every( every ) , m_count( 0 ) { }
void operator()( const state_type &x , double t )
{
if( ( m_count % m_every ) == 0 )
{
clog << t << endl;
cout << "sp '-'" << endl;
for( size_t i=0 ; i<x.size1() ; ++i )
{
for( size_t j=0 ; j<x.size2() ; ++j )
{
cout << i << "\t" << j << "\t" << sin( x( i , j ) ) << "\n";
}
cout << "\n";
}
cout << "e" << endl;
}
++m_count;
}
};
class write_snapshots
{
public:
typedef std::map< size_t , std::string > map_type;
write_snapshots( void ) : m_count( 0 ) { }
void operator()( const state_type &x , double t )
{
map< size_t , string >::const_iterator it = m_snapshots.find( m_count );
if( it != m_snapshots.end() )
{
ofstream fout( it->second.c_str() );
for( size_t i=0 ; i<x.size1() ; ++i )
{
for( size_t j=0 ; j<x.size2() ; ++j )
{
fout << i << "\t" << j << "\t" << x( i , j ) << "\t" << sin( x( i , j ) ) << "\n";
}
fout << "\n";
}
}
++m_count;
}
map_type& snapshots( void ) { return m_snapshots; }
const map_type& snapshots( void ) const { return m_snapshots; }
private:
size_t m_count;
map_type m_snapshots;
};
int main( int argc , char **argv )
{
size_t size1 = 128 , size2 = 128;
state_type x( size1 , size2 , 0.0 );
for( size_t i=(size1/2-10) ; i<(size1/2+10) ; ++i )
for( size_t j=(size2/2-10) ; j<(size2/2+10) ; ++j )
x( i , j ) = static_cast<double>( rand() ) / RAND_MAX * 2.0 * M_PI;
write_snapshots snapshots;
snapshots.snapshots().insert( make_pair( size_t( 0 ) , string( "lat_0000.dat" ) ) );
snapshots.snapshots().insert( make_pair( size_t( 100 ) , string( "lat_0100.dat" ) ) );
snapshots.snapshots().insert( make_pair( size_t( 1000 ) , string( "lat_1000.dat" ) ) );
observer_collection< state_type , double > obs;
obs.observers().push_back( write_for_gnuplot( 10 ) );
obs.observers().push_back( snapshots );
cout << "set term x11" << endl;
cout << "set pm3d map" << endl;
integrate_const( runge_kutta4<state_type>() , two_dimensional_phase_lattice( 1.2 ) ,
x , 0.0 , 1001.0 , 0.1 , boost::ref( obs ) );
// controlled steppers work only after ublas bugfix
//integrate_const( make_dense_output< runge_kutta_dopri5< state_type > >( 1E-6 , 1E-6 ) , two_dimensional_phase_lattice( 1.2 ) ,
// x , 0.0 , 1001.0 , 0.1 , boost::ref( obs ) );
return 0;
}
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