Merge commit '4ebe6417a5fce5f0994fc0c31bebf732be96a07c' as 'boost'

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

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+/* Boost libs/numeric/odeint/examples/solar_system.cpp
+
+ Copyright 2010-2012 Karsten Ahnert
+ Copyright 2011 Mario Mulansky
+
+ Solar system example for Hamiltonian stepper
+
+ 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 <boost/array.hpp>
+
+#include <boost/numeric/odeint.hpp>
+
+#include "point_type.hpp"
+
+//[ container_type_definition
+// we simulate 5 planets and the sun
+const size_t n = 6;
+
+typedef point< double , 3 > point_type;
+typedef boost::array< point_type , n > container_type;
+typedef boost::array< double , n > mass_type;
+//]
+
+
+
+
+
+
+
+//[ coordinate_function
+const double gravitational_constant = 2.95912208286e-4;
+
+struct solar_system_coor
+{
+    const mass_type &m_masses;
+
+    solar_system_coor( const mass_type &masses ) : m_masses( masses ) { }
+
+    void operator()( const container_type &p , container_type &dqdt ) const
+    {
+        for( size_t i=0 ; i<n ; ++i )
+            dqdt[i] = p[i] / m_masses[i];
+    }
+};
+//]
+
+
+//[ momentum_function
+struct solar_system_momentum
+{
+    const mass_type &m_masses;
+
+    solar_system_momentum( const mass_type &masses ) : m_masses( masses ) { }
+
+    void operator()( const container_type &q , container_type &dpdt ) const
+    {
+        const size_t n = q.size();
+        for( size_t i=0 ; i<n ; ++i )
+        {
+            dpdt[i] = 0.0;
+            for( size_t j=0 ; j<i ; ++j )
+            {
+                point_type diff = q[j] - q[i];
+                double d = abs( diff );
+                diff *= ( gravitational_constant * m_masses[i] * m_masses[j] / d / d / d );
+                dpdt[i] += diff;
+                dpdt[j] -= diff;
+
+            }
+        }
+    }
+};
+//]
+
+
+
+
+
+
+
+//[ some_helpers
+point_type center_of_mass( const container_type &x , const mass_type &m )
+{
+    double overall_mass = 0.0;
+    point_type mean( 0.0 );
+    for( size_t i=0 ; i<x.size() ; ++i )
+    {
+        overall_mass += m[i];
+        mean += m[i] * x[i];
+    }
+    if( !x.empty() ) mean /= overall_mass;
+    return mean;
+}
+
+
+double energy( const container_type &q , const container_type &p , const mass_type &masses )
+{
+    const size_t n = q.size();
+    double en = 0.0;
+    for( size_t i=0 ; i<n ; ++i )
+    {
+        en += 0.5 * norm( p[i] ) / masses[i];
+        for( size_t j=0 ; j<i ; ++j )
+        {
+            double diff = abs( q[i] - q[j] );
+            en -= gravitational_constant * masses[j] * masses[i] / diff;
+        }
+    }
+    return en;
+}
+//]
+
+
+//[ streaming_observer
+struct streaming_observer
+{
+    std::ostream& m_out;
+
+    streaming_observer( std::ostream &out ) : m_out( out ) { }
+
+    template< class State >
+    void operator()( const State &x , double t ) const
+    {
+        container_type &q = x.first;
+        m_out << t;
+        for( size_t i=0 ; i<q.size() ; ++i ) m_out << "\t" << q[i];
+        m_out << "\n";
+    }
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+
+    using namespace std;
+    using namespace boost::numeric::odeint;
+
+    mass_type masses = {{
+            1.00000597682 ,      // sun
+            0.000954786104043 ,  // jupiter
+            0.000285583733151 ,  // saturn
+            0.0000437273164546 , // uranus
+            0.0000517759138449 , // neptune
+            1.0 / ( 1.3e8 )      // pluto
+    }};
+
+    container_type q = {{
+            point_type( 0.0 , 0.0 , 0.0 ) ,                        // sun
+            point_type( -3.5023653 , -3.8169847 , -1.5507963 ) ,   // jupiter
+            point_type( 9.0755314 , -3.0458353 , -1.6483708 ) ,    // saturn
+            point_type( 8.3101420 , -16.2901086 , -7.2521278 ) ,   // uranus
+            point_type( 11.4707666 , -25.7294829 , -10.8169456 ) , // neptune
+            point_type( -15.5387357 , -25.2225594 , -3.1902382 )   // pluto
+    }};
+
+    container_type p = {{
+            point_type( 0.0 , 0.0 , 0.0 ) ,                        // sun
+            point_type( 0.00565429 , -0.00412490 , -0.00190589 ) , // jupiter
+            point_type( 0.00168318 , 0.00483525 , 0.00192462 ) ,   // saturn
+            point_type( 0.00354178 , 0.00137102 , 0.00055029 ) ,   // uranus
+            point_type( 0.00288930 , 0.00114527 , 0.00039677 ) ,   // neptune
+            point_type( 0.00276725 , -0.00170702 , -0.00136504 )   // pluto
+    }};
+
+    point_type qmean = center_of_mass( q , masses );
+    point_type pmean = center_of_mass( p , masses );
+    for( size_t i=0 ; i<n ; ++i )
+    {
+        q[i] -= qmean ;
+        p[i] -= pmean;
+    }
+
+    for( size_t i=0 ; i<n ; ++i ) p[i] *= masses[i];
+
+    //[ integration_solar_system
+    typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
+    const double dt = 100.0;
+    
+    integrate_const(
+            stepper_type() ,
+            make_pair( solar_system_coor( masses ) , solar_system_momentum( masses ) ) ,
+            make_pair( boost::ref( q ) , boost::ref( p ) ) ,
+            0.0 , 200000.0 , dt , streaming_observer( cout ) );
+    //]
+
+
+    return 0;
+}
+
+
+/*
+Plot with gnuplot:
+p "solar_system.dat" u 2:4 w l,"solar_system.dat" u 5:7 w l,"solar_system.dat" u 8:10 w l,"solar_system.dat" u 11:13 w l,"solar_system.dat" u 14:16 w l,"solar_system.dat" u 17:19 w l
+ */