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/examples/phase_oscillator_ensemble.cpp b/examples/phase_oscillator_ensemble.cpp
new file mode 100644
index 0000000..090fd58
--- /dev/null
+++ b/examples/phase_oscillator_ensemble.cpp
@@ -0,0 +1,151 @@
+/*
+ * phase_oscillator_ensemble.cpp
+ *
+ * Demonstrates the phase transition from an unsynchronized to an synchronized state.
+ *
+ * Copyright 2011-2012 Karsten Ahnert
+ * Copyright 2011-2012 Mario Mulansky
+ * 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 <utility>
+
+#include <boost/numeric/odeint.hpp>
+
+#ifndef M_PI //not there on windows
+#define M_PI 3.141592653589793 //...
+#endif
+
+#include <boost/random.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+//[ phase_oscillator_ensemble_system_function
+typedef vector< double > container_type;
+
+
+pair< double , double > calc_mean_field( const container_type &x )
+{
+    size_t n = x.size();
+    double cos_sum = 0.0 , sin_sum = 0.0;
+    for( size_t i=0 ; i<n ; ++i )
+    {
+        cos_sum += cos( x[i] );
+        sin_sum += sin( x[i] );
+    }
+    cos_sum /= double( n );
+    sin_sum /= double( n );
+
+    double K = sqrt( cos_sum * cos_sum + sin_sum * sin_sum );
+    double Theta = atan2( sin_sum , cos_sum );
+
+    return make_pair( K , Theta );
+}
+
+
+struct phase_ensemble
+{
+    container_type m_omega;
+    double m_epsilon;
+
+    phase_ensemble( const size_t n , double g = 1.0 , double epsilon = 1.0 )
+    : m_omega( n , 0.0 ) , m_epsilon( epsilon )
+    {
+        create_frequencies( g );
+    }
+
+    void create_frequencies( double g )
+    {
+        boost::mt19937 rng;
+        boost::cauchy_distribution<> cauchy( 0.0 , g );
+        boost::variate_generator< boost::mt19937&, boost::cauchy_distribution<> > gen( rng , cauchy );
+        generate( m_omega.begin() , m_omega.end() , gen );
+    }
+
+    void set_epsilon( double epsilon ) { m_epsilon = epsilon; }
+
+    double get_epsilon( void ) const { return m_epsilon; }
+
+    void operator()( const container_type &x , container_type &dxdt , double /* t */ ) const
+    {
+        pair< double , double > mean = calc_mean_field( x );
+        for( size_t i=0 ; i<x.size() ; ++i )
+            dxdt[i] = m_omega[i] + m_epsilon * mean.first * sin( mean.second - x[i] );
+    }
+};
+//]
+
+
+
+//[ phase_oscillator_ensemble_observer
+struct statistics_observer
+{
+    double m_K_mean;
+    size_t m_count;
+
+    statistics_observer( void )
+    : m_K_mean( 0.0 ) , m_count( 0 ) { }
+
+    template< class State >
+    void operator()( const State &x , double t )
+    {
+        pair< double , double > mean = calc_mean_field( x );
+        m_K_mean += mean.first;
+        ++m_count;
+    }
+
+    double get_K_mean( void ) const { return ( m_count != 0 ) ? m_K_mean / double( m_count ) : 0.0 ; }
+
+    void reset( void ) { m_K_mean = 0.0; m_count = 0; }
+};
+//]
+
+
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+    //[ phase_oscillator_ensemble_integration
+    const size_t n = 16384;
+    const double dt = 0.1;
+
+    container_type x( n );
+
+    boost::mt19937 rng;
+    boost::uniform_real<> unif( 0.0 , 2.0 * M_PI );
+    boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
+
+    // gamma = 1, the phase transition occurs at epsilon = 2
+    phase_ensemble ensemble( n , 1.0 );
+    statistics_observer obs;
+
+    for( double epsilon = 0.0 ; epsilon < 5.0 ; epsilon += 0.1 )
+    {
+        ensemble.set_epsilon( epsilon );
+        obs.reset();
+
+        // start with random initial conditions
+        generate( x.begin() , x.end() , gen );
+
+        // calculate some transients steps
+        integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 10.0 , dt );
+
+        // integrate and compute the statistics
+        integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 100.0 , dt , boost::ref( obs ) );
+        cout << epsilon << "\t" << obs.get_K_mean() << endl;
+    }
+
+
+    //]
+
+    return 0;
+}