96 lines
2.5 KiB
C++
96 lines
2.5 KiB
C++
/* Boost numeric test of the symplectic steppers test file
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Copyright 2012 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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// disable checked iterator warning for msvc
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#include <boost/config.hpp>
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#ifdef BOOST_MSVC
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#pragma warning(disable:4996)
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#endif
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#define BOOST_TEST_MODULE numeric_symplectic
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#include <iostream>
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#include <cmath>
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#include <boost/array.hpp>
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#include <boost/test/unit_test.hpp>
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#include <boost/mpl/vector.hpp>
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#include <boost/numeric/odeint.hpp>
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using namespace boost::unit_test;
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using namespace boost::numeric::odeint;
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namespace mpl = boost::mpl;
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typedef double value_type;
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typedef boost::array< double ,1 > state_type;
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// harmonic oscillator, analytic solution x[0] = sin( t )
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struct osc
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{
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void operator()( const state_type &q , state_type &dpdt ) const
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{
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dpdt[0] = -q[0];
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}
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};
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BOOST_AUTO_TEST_SUITE( numeric_symplectic_test )
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/* generic test for all symplectic steppers */
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template< class Stepper >
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struct perform_symplectic_test
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{
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void operator()( void )
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{
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Stepper stepper;
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const int o = stepper.order()+1; //order of the error is order of approximation + 1
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const state_type q0 = {{ 0.0 }};
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const state_type p0 = {{ 1.0 }};
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state_type q1,p1;
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std::pair< state_type , state_type >x1( q1 , p1 );
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const double t = 0.0;
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/* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
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double dt = 0.5;
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stepper.do_step( osc() , std::make_pair( q0 , p0 ) , t , x1 , dt );
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const double f = 2.0 * std::abs( sin(dt) - x1.first[0] ) / std::pow( dt , o );
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std::cout << o << " , " << f << std::endl;
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/* as long as we have errors above machine precision */
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while( f*std::pow( dt , o ) > 1E-16 )
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{
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stepper.do_step( osc() , std::make_pair( q0 , p0 ) , t , x1 , dt );
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std::cout << "Testing dt=" << dt << std::endl;
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BOOST_CHECK_SMALL( std::abs( sin(dt) - x1.first[0] ) , f*std::pow( dt , o ) );
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dt *= 0.5;
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}
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}
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};
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typedef mpl::vector<
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symplectic_euler< state_type > ,
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symplectic_rkn_sb3a_mclachlan< state_type >
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> symplectic_steppers;
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BOOST_AUTO_TEST_CASE_TEMPLATE( symplectic_test , Stepper, symplectic_steppers )
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{
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perform_symplectic_test< Stepper > tester;
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tester();
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}
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BOOST_AUTO_TEST_SUITE_END()
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