size_t integrate_adaptive( Stepper stepper , System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer , dense_output_stepper_tag ) { typename omplext_odeint::unwrap_reference< Observer >::type &obs = observer; size_t count = 0; stepper.initialize( start_state , start_time , dt ); while( less_with_sign( stepper.current_time() , end_time , stepper.current_time_step() ) ) { while( less_eq_with_sign( stepper.current_time() + stepper.current_time_step() , end_time , stepper.current_time_step() ) ) { //make sure we don't go beyond the end_time obs( stepper.current_state() , stepper.current_time() ); stepper.do_step( system ); ++count; } stepper.initialize( stepper.current_state() , stepper.current_time() , end_time - stepper.current_time() ); } obs( stepper.current_state() , stepper.current_time() ); // overwrite start_state with the final point boost::numeric::omplext_odeint::copy( stepper.current_state() , start_state ); return count; }
Time integrate_n_steps( Stepper stepper , System system , State &start_state , Time start_time , Time dt , size_t num_of_steps , Observer observer , dense_output_stepper_tag ) { typename odeint::unwrap_reference< Observer >::type &obs = observer; Time time = start_time; const Time end_time = start_time + static_cast< typename unit_value_type<Time>::type >(num_of_steps) * dt; stepper.initialize( start_state , time , dt ); size_t step = 0; while( step < num_of_steps ) { while( less_with_sign( time , stepper.current_time() , stepper.current_time_step() ) ) { stepper.calc_state( time , start_state ); obs( start_state , time ); ++step; // direct computation of the time avoids error propagation happening when using time += dt // we need clumsy type analysis to get boost units working here time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * dt; } // we have not reached the end, do another real step if( less_with_sign( stepper.current_time()+stepper.current_time_step() , end_time , stepper.current_time_step() ) ) { stepper.do_step( system ); } else if( less_with_sign( stepper.current_time() , end_time , stepper.current_time_step() ) ) { // do the last step ending exactly on the end point stepper.initialize( stepper.current_state() , stepper.current_time() , end_time - stepper.current_time() ); stepper.do_step( system ); } } while( stepper.current_time() < end_time ) { if( less_with_sign( end_time , stepper.current_time()+stepper.current_time_step() , stepper.current_time_step() ) ) stepper.initialize( stepper.current_state() , stepper.current_time() , end_time - stepper.current_time() ); stepper.do_step( system ); } // observation at end point, only if we ended exactly on the end-point (or above due to finite precision) obs( stepper.current_state() , end_time ); return time; }
void operator()( void ) { Stepper stepper; initializing_stepper init_stepper; const int o = stepper.order()+1; //order of the error is order of approximation + 1 const state_type x0 = {{ 0.0 , 1.0 }}; state_type x1 = x0; double t = 0.0; double dt = 0.2; // initialization, does a number of steps already to fill internal buffer, t is increased // we use the rk78 as initializing stepper stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt ); double A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] ); double phi = std::asin(x1[0]/A) - t; // do a number of steps to fill the buffer with results from adams bashforth for( size_t n=0 ; n < stepper.steps ; ++n ) { stepper.do_step( osc() , x1 , t , dt ); t += dt; } // now we do the actual step stepper.do_step( osc() , x1 , t , dt ); // only examine the error of the adams-bashforth step, not the initialization const double f = 2.0 * std::abs( A*sin(t+dt+phi) - x1[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 ) { x1 = x0; t = 0.0; stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt ); A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] ); phi = std::asin(x1[0]/A) - t; // now we do the actual step stepper.do_step( osc() , x1 , t , dt ); // only examine the error of the adams-bashforth step, not the initialization std::cout << "Testing dt=" << dt << " , " << std::abs( A*sin(t+dt+phi) - x1[0] ) << std::endl; BOOST_CHECK_LT( std::abs( A*sin(t+dt+phi) - x1[0] ) , f*std::pow( dt , o ) ); dt *= 0.5; } }
size_t integrate_adaptive( Stepper stepper , System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer , dense_output_stepper_tag ) { typename boost::unwrap_reference< Observer >::type &obs = observer; size_t count = 0; stepper.initialize( start_state , start_time , dt ); while( stepper.current_time() < end_time ) { while( stepper.current_time() + stepper.current_time_step() <= end_time ) { //make sure we don't go beyond the end_time obs( stepper.current_state() , stepper.current_time() ); stepper.do_step( system ); ++count; } stepper.initialize( stepper.current_state() , stepper.current_time() , end_time - stepper.current_time() ); } obs( stepper.current_state() , stepper.current_time() ); return count; }
void operator()( void ) { double t = 0; const double dt = 0.1; state_type x = 0; Stepper stepper; InitStepper init_stepper; stepper.initialize( init_stepper, rhs, x, t, dt ); // ab-stepper needs order-1 init steps: t and x should be (order-1)*dt BOOST_CHECK_CLOSE( t , (stepper.order()-1)*dt , 1E-16 ); BOOST_CHECK_CLOSE( x, ( stepper.order() - 1 ) * dt, 2E-14 ); }
void check_dense_output_stepper( Stepper &stepper ) { typedef Stepper stepper_type; typedef typename stepper_type::state_type state_type; typedef typename stepper_type::value_type value_type; typedef typename stepper_type::deriv_type deriv_type; typedef typename stepper_type::time_type time_type; // typedef typename stepper_type::order_type order_type; time_type t( 0.0 * si::second ); time_type dt( 0.1 * si::second ); state_type x( 1.0 * si::meter , 0.0 * si::meter_per_second ) , x2; stepper.initialize( x , t , dt ); stepper.do_step( oscillator ); stepper.calc_state( dt / 2.0 , x2 ); }