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123 lines
3.6 KiB
C++
123 lines
3.6 KiB
C++
/*
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Copyright 2011 Mario Mulansky
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Copyright 2012 Karsten Ahnert
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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/*
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* Example of a 2D simulation of nonlinearly coupled oscillators.
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* Program just prints final energy which should be close to the initial energy (1.0).
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* No parallelization is employed here.
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* Run time on a 2.3GHz Intel Core-i5: about 10 seconds for 100 steps.
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* Compile simply via bjam or directly:
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* g++ -O3 -I${BOOST_ROOT} -I../../../../.. spreading.cpp
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*/
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#include <iostream>
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#include <fstream>
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#include <vector>
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#include <cstdlib>
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#include <sys/time.h>
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#include <boost/ref.hpp>
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#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>
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// we use a vector< vector< double > > as state type,
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// for that some functionality has to be added for odeint to work
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#include "nested_range_algebra.hpp"
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#include "vector_vector_resize.hpp"
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// defines the rhs of our dynamical equation
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#include "lattice2d.hpp"
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/* dynamical equations (Hamiltonian structure):
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dqdt_{i,j} = p_{i,j}
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dpdt_{i,j} = - omega_{i,j}*q_{i,j} - \beta*[ (q_{i,j} - q_{i,j-1})^3
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+(q_{i,j} - q_{i,j+1})^3
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+(q_{i,j} - q_{i-1,j})^3
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+(q_{i,j} - q_{i+1,j})^3 ]
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*/
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using namespace std;
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static const int MAX_N = 1024;//2048;
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static const size_t KAPPA = 2;
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static const size_t LAMBDA = 4;
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static const double W = 1.0;
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static const double gap = 0.0;
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static const size_t steps = 100;
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static const double dt = 0.1;
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double initial_e = 1.0;
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double beta = 1.0;
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int realization_index = 0;
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//the state type
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typedef vector< vector< double > > state_type;
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//the stepper, choose a symplectic one to account for hamiltonian structure
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//use nested_range_algebra for calculations on vector< vector< ... > >
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typedef boost::numeric::odeint::symplectic_rkn_sb3a_mclachlan<
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state_type , state_type , double , state_type , state_type , double ,
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nested_range_algebra< boost::numeric::odeint::range_algebra > ,
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boost::numeric::odeint::default_operations > stepper_type;
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double time_diff_in_ms( timeval &t1 , timeval &t2 )
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{ return (t2.tv_sec - t1.tv_sec)*1000.0 + (t2.tv_usec - t1.tv_usec)/1000.0 + 0.5; }
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int main( int argc, const char* argv[] ) {
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srand( time(NULL) );
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lattice2d< KAPPA , LAMBDA > lattice( beta );
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lattice.generate_pot( W , gap , MAX_N );
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state_type q( MAX_N , vector< double >( MAX_N , 0.0 ) );
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state_type p( q );
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state_type energy( q );
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p[MAX_N/2][MAX_N/2] = sqrt( 0.5*initial_e );
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p[MAX_N/2+1][MAX_N/2] = sqrt( 0.5*initial_e );
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p[MAX_N/2][MAX_N/2+1] = sqrt( 0.5*initial_e );
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p[MAX_N/2+1][MAX_N/2+1] = sqrt( 0.5*initial_e );
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cout.precision(10);
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lattice.local_energy( q , p , energy );
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double e=0.0;
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for( size_t i=0 ; i<energy.size() ; ++i )
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for( size_t j=0 ; j<energy[i].size() ; ++j )
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{
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e += energy[i][j];
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}
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cout << "initial energy: " << lattice.energy( q , p ) << endl;
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timeval elapsed_time_start , elapsed_time_end;
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gettimeofday(&elapsed_time_start , NULL);
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stepper_type stepper;
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for( size_t step=0 ; step<=steps ; ++step )
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{
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stepper.do_step( boost::ref( lattice ) ,
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make_pair( boost::ref( q ) , boost::ref( p ) ) ,
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0.0 , 0.1 );
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}
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gettimeofday(&elapsed_time_end , NULL);
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double elapsed_time = time_diff_in_ms( elapsed_time_start , elapsed_time_end );
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cout << steps << " steps in " << elapsed_time/1000 << " s (energy: " << lattice.energy( q , p ) << ")" << endl;
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}
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