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+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate.cpp
+
+ [begin_description]
+ This file tests the integrate function and its variants.
+ [end_description]
+
+ Copyright 2011-2012 Mario Mulansky
+ Copyright 2011-2012 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)
+ */
+
+
+#define BOOST_TEST_MODULE odeint_integrate_functions
+
+#include <boost/type_traits.hpp>
+
+#include <vector>
+#include <cmath>
+#include <iostream>
+
+#include <boost/numeric/odeint/config.hpp>
+
+#include <boost/array.hpp>
+#include <boost/ref.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+// nearly everything from odeint is used in these tests
+#ifndef ODEINT_INTEGRATE_ITERATOR
+#include <boost/numeric/odeint/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/integrate/integrate_n_steps.hpp>
+#else
+#include <boost/numeric/odeint/iterator/integrate/integrate_const.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_times.hpp>
+#include <boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp>
+#endif
+#include <boost/numeric/odeint/stepper/euler.hpp>
+#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
+#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
+#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
+#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
+#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
+
+#include <boost/numeric/odeint/stepper/adaptive_adams_bashforth_moulton.hpp>
+#include <boost/numeric/odeint/stepper/controlled_adams_bashforth_moulton.hpp>
+
+#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+
+typedef double value_type;
+typedef std::vector< value_type > state_type;
+
+void lorenz( const state_type &x , state_type &dxdt , const value_type t )
+{
+ //const value_type sigma( 10.0 );
+ const value_type R( 28.0 );
+ const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
+
+ // first component trivial
+ dxdt[0] = 1.0; //sigma * ( x[1] - x[0] );
+ dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
+ dxdt[2] = -b * x[2] + x[0] * x[1];
+}
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ state_type& m_x;
+
+ push_back_time( std::vector< double > &times , state_type &x )
+ : m_times( times ) , m_x( x ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ boost::numeric::odeint::copy( x , m_x );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_const_test
+{
+ void operator()( const value_type t_end , const value_type dt )
+ {
+ // std::cout << "Testing integrate_const with " << typeid( Stepper ).name() << std::endl;
+
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ size_t steps = integrate_const( Stepper() , lorenz , x , 0.0 , t_end ,
+ dt , push_back_time( times , x_end ) );
+
+ std::cout.precision(16);
+ std::cout << t_end << " (" << dt << "), " << steps << " , " << times.size() << " , " << 10.0+dt*steps << "=" << x_end[0] << std::endl;
+
+ std::cout << static_cast<int>(floor(t_end/dt)) << " , " << t_end/dt << std::endl;
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , static_cast<int>(floor(t_end/dt))+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ {
+ //std::cout << i << " , " << times[i] << " , " << static_cast< value_type >(i)*dt << std::endl;
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL( times[i] - static_cast< value_type >(i)*dt , (i+1) * 2E-16 );
+ }
+
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + times[times.size()-1]) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+ //BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+ //BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_adaptive_test
+{
+ void operator()( const value_type t_end = 10.0 , const value_type dt = 0.03 )
+ {
+ // std::cout << "Testing integrate_adaptive with " << typeid( Stepper ).name() << std::endl;
+
+ state_type x( 3 , 10.0 ) , x_end( 3 );
+
+ std::vector< value_type > times;
+
+ size_t steps = integrate_adaptive( Stepper() , lorenz , x , 0.0 , t_end ,
+ dt , push_back_time( times , x_end ) );
+
+ // std::cout << t_end << " , " << steps << " , " << times.size() << " , " << dt << " , " << 10.0+t_end << "=" << x_end[0] << std::endl;
+
+ BOOST_CHECK_EQUAL( times.size() , steps+1 );
+
+ BOOST_CHECK_SMALL( times[0] - 0.0 , 2E-16 );
+ BOOST_CHECK_SMALL( times[times.size()-1] - t_end , times.size() * 2E-16 );
+
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + t_end) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+ }
+};
+
+
+template< class Stepper >
+struct perform_integrate_times_test
+{
+ void operator()( const int n = 10 , const int dn=1 , const value_type dt = 0.03 )
+ {
+ // std::cout << "Testing integrate_times with " << typeid( Stepper ).name() << std::endl;
+
+ state_type x( 3 ) , x_end( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+
+ std::vector< double > times;
+
+ std::vector< double > obs_times( abs(n) );
+ for( int i=0 ; boost::numeric::odeint::detail::less_with_sign( static_cast<double>(i) ,
+ static_cast<double>(obs_times.size()) ,
+ dt ) ; i+=dn )
+ {
+ obs_times[i] = i;
+ }
+ // simple stepper
+ integrate_times( Stepper() , lorenz , x , obs_times.begin() , obs_times.end() ,
+ dt , push_back_time( times , x_end ) );
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , abs(n) );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
+
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + 1.0*times[times.size()-1]) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_n_steps_test
+{
+ void operator()( const int n = 200 , const value_type dt = 0.01 )
+ {
+ // std::cout << "Testing integrate_n_steps with " << typeid( Stepper ).name() << ". ";
+ // std::cout << "dt=" << dt << std::endl;
+
+ state_type x( 3 ) , x_end( 3 );
+ x[0] = x[1] = x[2] = 10.0;
+
+ std::vector< double > times;
+
+ // simple stepper
+ value_type end_time = integrate_n_steps( Stepper() , lorenz , x , 0.0 , dt , n , push_back_time( times , x_end ) );
+
+ BOOST_CHECK_SMALL( end_time - n*dt , 2E-16 );
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , n+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ {
+ // check if observer was called at times 0,1,2,...
+ BOOST_CHECK_SMALL(times[i] - static_cast< value_type >(i) * dt, 2E-16);
+ }
+ // check first, trivial, component
+ BOOST_CHECK_SMALL( (10.0 + end_time) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
+// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
+// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
+
+ }
+};
+
+
+
+class stepper_methods : public mpl::vector<
+ euler< state_type > ,
+ modified_midpoint< state_type > ,
+ runge_kutta4< state_type > ,
+ runge_kutta_cash_karp54< state_type > ,
+ runge_kutta_dopri5< state_type > ,
+ runge_kutta_fehlberg78< state_type > ,
+ controlled_runge_kutta< runge_kutta_cash_karp54< state_type > > ,
+ controlled_runge_kutta< runge_kutta_dopri5< state_type > > ,
+ controlled_runge_kutta< runge_kutta_fehlberg78< state_type > > ,
+ bulirsch_stoer< state_type > ,
+ dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > >,
+ adaptive_adams_bashforth_moulton<3, state_type>,
+ adaptive_adams_bashforth_moulton<5, state_type>,
+ adaptive_adams_bashforth_moulton<7, state_type>,
+ controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<3, state_type> >,
+ controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<5, state_type> >
+ //bulirsch_stoer_dense_out< state_type >
+> { };
+
+
+
+BOOST_AUTO_TEST_SUITE( integrate_test )
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_const_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_const_test< Stepper > tester;
+ tester( 1.005 , 0.01 );
+ tester( 1.0 , 0.01 );
+ tester( 1.1 , 0.01 );
+ tester( -1.005 , -0.01 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_adaptive_test< Stepper > tester;
+ tester( 1.005 , 0.01 );
+ tester( 1.0 , 0.01 );
+ tester( 1.1 , 0.01 );
+ tester( -1.005 , -0.01 );
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_times_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_times_test< Stepper > tester;
+ tester();
+ //tester( -10 , -0.01 );
+}
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_n_steps_test_case , Stepper, stepper_methods )
+{
+ if(!boost::is_same<Stepper, controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<3, state_type> > >::value &&
+ !boost::is_same<Stepper, controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<5, state_type> > >::value)
+ {
+ perform_integrate_n_steps_test< Stepper > tester;
+ tester();
+ tester( 200 , 0.01 );
+ tester( 200 , 0.01 );
+ tester( 200 , 0.01 );
+ tester( 200 , -0.01 );
+ }
+}
+
+BOOST_AUTO_TEST_SUITE_END()
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