Squashed 'third_party/boostorg/odeint/' content from commit 6ff2719

Change-Id: If4892e29c1a5e6cf3a7aa51486a2725c251b0c7d
git-subtree-dir: third_party/boostorg/odeint
git-subtree-split: 6ff2719b6907b86596c3d43e88c1bcfdf29df560
diff --git a/test/numeric/runge_kutta.cpp b/test/numeric/runge_kutta.cpp
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+/* 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>
+#include <boost/numeric/odeint/stepper/extrapolation_stepper.hpp>
+
+using namespace boost::unit_test;
+using namespace boost::numeric::odeint;
+namespace mpl = boost::mpl;
+
+typedef double value_type;
+
+typedef boost::array< double , 2 > state_type;
+
+// harmonic oscillator, analytic solution x[0] = sin( t )
+struct osc
+{
+    void operator()( const state_type &x , state_type &dxdt , const double t ) const
+    {
+        dxdt[0] = x[1];
+        dxdt[1] = -x[0];
+    }
+};
+
+/* reset dispatcher */
+template< class StepperCategory >
+struct resetter
+{
+    template< class Stepper >
+    static void reset( Stepper &stepper ) { }
+};
+
+template< >
+struct resetter< explicit_error_stepper_fsal_tag >
+{
+    template< class Stepper >
+    static void reset( Stepper &stepper ) 
+    { stepper.reset(); }
+};
+
+
+BOOST_AUTO_TEST_SUITE( numeric_runge_kutta_test )
+
+
+/* generic test for all runge kutta steppers */
+template< class Stepper >
+struct perform_runge_kutta_test
+{
+    void operator()( void )
+    {
+   
+        Stepper 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;
+        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;
+        stepper.do_step( osc() , x0 , t , x1 , dt );
+        const double f = 2.0 * std::abs( sin(dt) - 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 )
+        {
+            // reset stepper which require resetting (fsal steppers)
+            resetter< typename Stepper::stepper_category >::reset( stepper );
+            
+            stepper.do_step( osc() , x0 , t , x1 , dt );
+            std::cout << "Testing dt=" << dt << std::endl;
+            BOOST_CHECK_LT( std::abs( sin(dt) - x1[0] ) , f*std::pow( dt , o ) );
+            dt *= 0.5;
+        }
+    }
+};
+
+
+/* generic error test for all runge kutta steppers */
+template< class Stepper >
+struct perform_runge_kutta_error_test
+{
+    void operator()( void )
+    {
+        Stepper stepper;
+        const int o = stepper.error_order()+1; //order of the error is order of approximation + 1
+
+        const state_type x0 = {{ 0.0 , 1.0 }};
+        state_type x1 , x_err;
+        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;
+        stepper.do_step( osc() , x0 , t , x1 , dt , x_err );
+        const double f = 2.0 * std::abs( x_err[0] ) / std::pow( dt , o );
+
+        std::cout << o << " , " << f << " , " << x0[0] << std::endl;
+
+        /* as long as we have errors above machine precision */
+        while( f*std::pow( dt , o ) > 1E-16 )
+        {
+            // reset stepper which require resetting (fsal steppers)
+            resetter< typename Stepper::stepper_category >::reset( stepper );
+            
+            stepper.do_step( osc() , x0 , t , x1 , dt , x_err );
+            std::cout << "Testing dt=" << dt << ": " << x_err[1] << std::endl;
+            BOOST_CHECK_SMALL( std::abs( x_err[0] ) , f*std::pow( dt , o ) );
+            dt *= 0.5;
+        }
+    }
+};
+
+
+typedef mpl::vector<
+    euler< state_type > ,
+    modified_midpoint< state_type > ,
+    runge_kutta4< state_type > ,
+    runge_kutta4_classic< state_type > ,
+    runge_kutta_cash_karp54_classic< state_type > ,
+    runge_kutta_cash_karp54< state_type > ,
+    runge_kutta_dopri5< state_type > ,
+    runge_kutta_fehlberg78< state_type > ,
+    extrapolation_stepper< 4, state_type > ,
+    extrapolation_stepper< 6, state_type > ,
+    extrapolation_stepper< 8, state_type > ,
+    extrapolation_stepper< 10, state_type >
+    > runge_kutta_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_test , Stepper, runge_kutta_steppers )
+{
+    perform_runge_kutta_test< Stepper > tester;
+    tester();
+}
+
+
+typedef mpl::vector<
+    runge_kutta_cash_karp54_classic< state_type > ,
+    runge_kutta_cash_karp54< state_type > ,
+    runge_kutta_dopri5< state_type > ,
+    runge_kutta_fehlberg78< state_type > ,
+    extrapolation_stepper< 4, state_type > ,
+    extrapolation_stepper< 6, state_type > ,
+    extrapolation_stepper< 8, state_type > ,
+    extrapolation_stepper< 10, state_type >
+    > runge_kutta_error_steppers;
+
+BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_error_test , Stepper, runge_kutta_error_steppers )
+{
+    perform_runge_kutta_error_test< Stepper > tester;
+    tester();
+}
+
+BOOST_AUTO_TEST_SUITE_END()