Merge commit '4ebe6417a5fce5f0994fc0c31bebf732be96a07c' as 'boost'

boost/libs/numeric/odeint/examples/harmonic_oscillator.cpp

@@ -0,0 +1,211 @@
+/*
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2011-2013 Mario Mulansky
+ Copyright 2013 Pascal Germroth
+
+ 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)
+ */
+
+
+#include <iostream>
+#include <vector>
+
+#include <boost/numeric/odeint.hpp>
+
+
+
+//[ rhs_function
+/* The type of container used to hold the state vector */
+typedef std::vector< double > state_type;
+
+const double gam = 0.15;
+
+/* The rhs of x' = f(x) */
+void harmonic_oscillator( const state_type &x , state_type &dxdt , const double /* t */ )
+{
+    dxdt[0] = x[1];
+    dxdt[1] = -x[0] - gam*x[1];
+}
+//]
+
+
+
+
+
+//[ rhs_class
+/* The rhs of x' = f(x) defined as a class */
+class harm_osc {
+
+    double m_gam;
+
+public:
+    harm_osc( double gam ) : m_gam(gam) { }
+
+    void operator() ( const state_type &x , state_type &dxdt , const double /* t */ )
+    {
+        dxdt[0] = x[1];
+        dxdt[1] = -x[0] - m_gam*x[1];
+    }
+};
+//]
+
+
+
+
+
+//[ integrate_observer
+struct push_back_state_and_time
+{
+    std::vector< state_type >& m_states;
+    std::vector< double >& m_times;
+
+    push_back_state_and_time( std::vector< state_type > &states , std::vector< double > &times )
+    : m_states( states ) , m_times( times ) { }
+
+    void operator()( const state_type &x , double t )
+    {
+        m_states.push_back( x );
+        m_times.push_back( t );
+    }
+};
+//]
+
+struct write_state
+{
+    void operator()( const state_type &x ) const
+    {
+        std::cout << x[0] << "\t" << x[1] << "\n";
+    }
+};
+
+
+int main(int /* argc */ , char** /* argv */ )
+{
+    using namespace std;
+    using namespace boost::numeric::odeint;
+
+
+    //[ state_initialization
+    state_type x(2);
+    x[0] = 1.0; // start at x=1.0, p=0.0
+    x[1] = 0.0;
+    //]
+
+
+
+    //[ integration
+    size_t steps = integrate( harmonic_oscillator ,
+            x , 0.0 , 10.0 , 0.1 );
+    //]
+
+
+
+    //[ integration_class
+    harm_osc ho(0.15);
+    steps = integrate( ho ,
+            x , 0.0 , 10.0 , 0.1 );
+    //]
+
+
+
+
+
+    //[ integrate_observ
+    vector<state_type> x_vec;
+    vector<double> times;
+
+    steps = integrate( harmonic_oscillator ,
+            x , 0.0 , 10.0 , 0.1 ,
+            push_back_state_and_time( x_vec , times ) );
+
+    /* output */
+    for( size_t i=0; i<=steps; i++ )
+    {
+        cout << times[i] << '\t' << x_vec[i][0] << '\t' << x_vec[i][1] << '\n';
+    }
+    //]
+
+
+
+
+
+
+
+    //[ define_const_stepper
+    runge_kutta4< state_type > stepper;
+    integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+    //]
+
+
+
+
+    //[ integrate_const_loop
+    const double dt = 0.01;
+    for( double t=0.0 ; t<10.0 ; t+= dt )
+        stepper.do_step( harmonic_oscillator , x , t , dt );
+    //]
+
+
+
+
+    //[ define_adapt_stepper
+    typedef runge_kutta_cash_karp54< state_type > error_stepper_type;
+    //]
+
+
+
+    //[ integrate_adapt
+    typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
+    controlled_stepper_type controlled_stepper;
+    integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+    //]
+
+    {
+    //[integrate_adapt_full
+    double abs_err = 1.0e-10 , rel_err = 1.0e-6 , a_x = 1.0 , a_dxdt = 1.0;
+    controlled_stepper_type controlled_stepper( 
+        default_error_checker< double , range_algebra , default_operations >( abs_err , rel_err , a_x , a_dxdt ) );
+    integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+    //]
+    }
+
+
+    //[integrate_adapt_make_controlled
+    integrate_adaptive( make_controlled< error_stepper_type >( 1.0e-10 , 1.0e-6 ) , 
+                        harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+    //]
+
+
+
+
+    //[integrate_adapt_make_controlled_alternative
+    integrate_adaptive( make_controlled( 1.0e-10 , 1.0e-6 , error_stepper_type() ) , 
+                        harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
+    //]
+
+    #ifdef BOOST_NUMERIC_ODEINT_CXX11
+    //[ define_const_stepper_cpp11
+    {
+    runge_kutta4< state_type > stepper;
+    integrate_const( stepper , []( const state_type &x , state_type &dxdt , double t ) {
+            dxdt[0] = x[1]; dxdt[1] = -x[0] - gam*x[1]; }
+        , x , 0.0 , 10.0 , 0.01 );
+    }
+    //]
+    
+    
+    
+    //[ harm_iterator_const_step]
+    std::for_each( make_const_step_time_iterator_begin( stepper , harmonic_oscillator, x , 0.0 , 0.1 , 10.0 ) ,
+                   make_const_step_time_iterator_end( stepper , harmonic_oscillator, x ) ,
+                   []( std::pair< const state_type & , const double & > x ) {
+                       cout << x.second << " " << x.first[0] << " " << x.first[1] << "\n"; } );
+    //]
+    #endif
+    
+    
+
+
+}