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+/*
+ [auto_generated]
+ libs/numeric/odeint/test/integrate_implicit.cpp
+
+ [begin_description]
+ This file tests the integrate function and its variants with the implicit steppers.
+ [end_description]
+
+ Copyright 2011 Mario Mulansky
+ Copyright 2011-2013 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_implicit
+
+#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/numeric/ublas/vector.hpp>
+#include <boost/numeric/ublas/matrix.hpp>
+
+#include <boost/test/unit_test.hpp>
+
+#include <boost/mpl/vector.hpp>
+
+#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/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_dense_output.hpp>
+
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+namespace ublas = boost::numeric::ublas;
+
+typedef double value_type;
+typedef ublas::vector< value_type > state_type;
+typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+
+struct sys
+{
+ void operator()( const state_type &x , state_type &dxdt , const value_type &t ) const
+ {
+ dxdt( 0 ) = x( 0 ) + 2 * x( 1 );
+ dxdt( 1 ) = x( 1 );
+ }
+};
+
+struct jacobi
+{
+ void operator()( const state_type &x , matrix_type &jacobi , const value_type &t , state_type &dfdt ) const
+ {
+ jacobi( 0 , 0 ) = 1;
+ jacobi( 0 , 1 ) = 2;
+ jacobi( 1 , 0 ) = 0;
+ jacobi( 1 , 1 ) = 1;
+ dfdt( 0 ) = 0.0;
+ dfdt( 1 ) = 0.0;
+ }
+};
+
+struct push_back_time
+{
+ std::vector< double >& m_times;
+
+ push_back_time( std::vector< double > &times )
+ : m_times( times ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_times.push_back( t );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_const_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+ const value_type dt = 0.03;
+ const value_type t_end = 10.0;
+
+ std::vector< value_type > times;
+
+ integrate_const( Stepper() , std::make_pair( sys() , jacobi() ) , x , 0.0 , t_end ,
+ dt , push_back_time( times ) );
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , static_cast<int>(std::floor(t_end/dt))+1 );
+
+ for( size_t i=0 ; i<times.size() ; ++i )
+ {
+ //std::cout << i << 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) * 2.0e-16 );
+ }
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_adaptive_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+ const value_type dt = 0.03;
+ const value_type t_end = 10.0;
+
+ std::vector< value_type > times;
+
+ size_t steps = integrate_adaptive( Stepper() , std::make_pair( sys() , jacobi() ) , x , 0.0 , t_end ,
+ dt , push_back_time( times ) );
+
+ BOOST_CHECK_EQUAL( times.size() , steps+1 );
+
+ BOOST_CHECK_SMALL( times[0] - 0.0 , 2.0e-16 );
+ BOOST_CHECK_SMALL( times[times.size()-1] - t_end , times.size() * 3.0e-16 );
+ }
+};
+
+
+template< class Stepper >
+struct perform_integrate_times_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+
+ const value_type dt = 0.03;
+
+ std::vector< double > times;
+
+ // simple stepper
+ integrate_times( Stepper() , std::make_pair( sys() , jacobi() ) , x ,
+ boost::counting_iterator<int>(0) , boost::counting_iterator<int>(10) ,
+ dt , push_back_time( times ) );
+
+ BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , 10 );
+
+ 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) );
+ }
+};
+
+template< class Stepper >
+struct perform_integrate_n_steps_test
+{
+ void operator()( void )
+ {
+ state_type x( 2 , 1.0 );
+
+ const value_type dt = 0.03;
+ const int n = 200;
+
+ std::vector< double > times;
+
+ // simple stepper
+ value_type end_time = integrate_n_steps( Stepper() , std::make_pair( sys() , jacobi() ) , x , 0.0 , dt , n , push_back_time( times ) );
+
+ BOOST_CHECK_SMALL( end_time - n*dt , 3.0e-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 , (i+1) * 2.0e-16 );
+ }
+};
+
+
+
+class stepper_methods : public mpl::vector<
+ rosenbrock4< value_type > ,
+ rosenbrock4_controller< rosenbrock4< value_type > > ,
+ rosenbrock4_dense_output< rosenbrock4_controller< rosenbrock4< value_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();
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_adaptive_test< Stepper > tester;
+ tester();
+}
+
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_times_test_case , Stepper, stepper_methods )
+{
+ perform_integrate_times_test< Stepper > tester;
+ tester();
+}
+
+
+class simple_stepper_methods : public mpl::vector<
+ rosenbrock4< value_type >
+> { };
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_n_steps_test_case , Stepper, simple_stepper_methods )
+{
+ perform_integrate_n_steps_test< Stepper > tester;
+ tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()