test/numeric/velocity_verlet.cpp

/* Boost numeric test of the runge kutta steppers test file

 Copyright 2012 Mario Mulansky
 Copyright 2012 Karsten Ahnert

 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)
*/

// disable checked iterator warning for msvc
#include <boost/config.hpp>
#ifdef BOOST_MSVC
    #pragma warning(disable:4996)
#endif

#define BOOST_TEST_MODULE numeric_runge_kutta

#include <iostream>
#include <cmath>

#include <boost/array.hpp>

#include <boost/test/unit_test.hpp>

#include <boost/mpl/vector.hpp>

#include <boost/numeric/odeint.hpp>

using namespace boost::unit_test;
using namespace boost::numeric::odeint;
namespace mpl = boost::mpl;

typedef double value_type;

typedef boost::array< double , 1 > state_type;

// harmonic oscillator, analytic solution x[0] = sin( t )
struct osc
{
    void operator()( const state_type &x, const state_type &v, state_type &a,
                     const double t ) const
    {
        a[0] = -x[0];
    }
};

BOOST_AUTO_TEST_SUITE( velocity_verlet_test )

BOOST_AUTO_TEST_CASE( numeric_velocity_verlet_test )
{
   
    velocity_verlet<state_type> stepper;
    const int steps = 10;
    // order of the error is order of approximation + 1
    const int o = stepper.order() + 1;

    const state_type x0 = {{ 0.0 }};
    const state_type v0 = {{ 1.0 }};
    state_type x = x0;
    state_type v = v0;
    const double t = 0.0;
    /* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
    double dt = 0.5;
    for ( int step = 0; step < steps; ++step )
    {
        stepper.do_step(
            osc(), std::make_pair( boost::ref( x ), boost::ref( v ) ), t, dt );
    }
    const double f = steps * std::abs( sin( steps * dt ) - x[0] ) /
                     std::pow( dt, o ); // upper bound

    std::cout << o << " , " << f << std::endl;

    /* as long as we have errors above machine precision */
    while( f*std::pow( dt , o ) > 1E-16 )
    {
        x = x0;
        v = v0;
        stepper.reset();
        for ( int step = 0; step < steps; ++step )
        {
            stepper.do_step( osc() , std::make_pair(boost::ref(x), boost::ref(v)) , t , dt );
        }
        std::cout << "Testing dt=" << dt << std::endl;
        BOOST_CHECK_LT( std::abs( sin( steps * dt ) - x[0] ),
                        f * std::pow( dt, o ) );
        dt *= 0.5;
    }
};


BOOST_AUTO_TEST_SUITE_END()