text: /*
   * resizing_lattice.cpp
   *
   * Demonstrates the usage of resizing of the state type during integration.
   * Examplary system is a strongly nonlinear, disordered Hamiltonian lattice
   * where the spreading of energy is investigated
   *
   * Copyright 2011-2012 Mario Mulansky
   * Copyright 2012-2013 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)
   *
   */
  
  #include <iostream>
  #include <utility>
  
  #include <boost/numeric/odeint.hpp>
  
  #include <boost/ref.hpp>
  #include <boost/random.hpp>
  
  using namespace std;
  using namespace boost::numeric::odeint;
  
  //[ resizing_lattice_system_class
  typedef vector< double > coord_type;
  typedef pair< coord_type , coord_type > state_type;
  
  struct compacton_lattice
  {
      const int m_max_N;
      const double m_beta;
      int m_pot_start_index;
      vector< double > m_pot;
  
      compacton_lattice( int max_N , double beta , int pot_start_index )
          : m_max_N( max_N ) , m_beta( beta ) , m_pot_start_index( pot_start_index ) , m_pot( max_N )
      {
          srand( time( NULL ) );
          // fill random potential with iid values from [0,1]
          boost::mt19937 rng;
          boost::uniform_real<> unif( 0.0 , 1.0 );
          boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
          generate( m_pot.begin() , m_pot.end() , gen );
      }
  
      void operator()( const coord_type &q , coord_type &dpdt )
      {
          // calculate dpdt = -dH/dq of this hamiltonian system
          // dp_i/dt = - V_i * q_i^3 - beta*(q_i - q_{i-1})^3 + beta*(q_{i+1} - q_i)^3
          const int N = q.size();
          double diff = q[0] - q[N-1];
          for( int i=0 ; i<N ; ++i )
          {
              dpdt[i] = - m_pot[m_pot_start_index+i] * q[i]*q[i]*q[i] -
                      m_beta * diff*diff*diff;
              diff = q[(i+1) % N] - q[i];
              dpdt[i] += m_beta * diff*diff*diff;
          }
      }
  
      void energy_distribution( const coord_type &q , const coord_type &p , coord_type &energies )
      {
          // computes the energy per lattice site normalized by total energy
          const size_t N = q.size();
          double en = 0.0;
          for( size_t i=0 ; i<N ; i++ )
          {
              const double diff = q[(i+1) % N] - q[i];
              energies[i] = p[i]*p[i]/2.0
                  + m_pot[m_pot_start_index+i]*q[i]*q[i]*q[i]*q[i]/4.0
                  + m_beta/4.0 * diff*diff*diff*diff;
              en += energies[i];
          }
          en = 1.0/en;
          for( size_t i=0 ; i<N ; i++ )
          {
              energies[i] *= en;
          }
      }
  
      double energy( const coord_type &q , const coord_type &p )
      {
          // calculates the total energy of the excitation
          const size_t N = q.size();
          double en = 0.0;
          for( size_t i=0 ; i<N ; i++ )
          {
              const double diff = q[(i+1) % N] - q[i];
              en += p[i]*p[i]/2.0
                  + m_pot[m_pot_start_index+i]*q[i]*q[i]*q[i]*q[i] / 4.0
                  + m_beta/4.0 * diff*diff*diff*diff;
          }
          return en;
      }
  
      void change_pot_start( const int delta )
      {
          m_pot_start_index += delta;
      }
  };
  //]
  
  //[ resizing_lattice_resize_function
  void do_resize( coord_type &q , coord_type &p , coord_type &distr , const int N )
  {
      q.resize( N );
      p.resize( N );
      distr.resize( N );
  }
  //]
  
  const int max_N = 1024;
  const double beta = 1.0;
  
  int main()
  {
      //[ resizing_lattice_initialize
      //start with 60 sites
      const int N_start = 60;
      coord_type q( N_start , 0.0 );
      q.reserve( max_N );
      coord_type p( N_start , 0.0 );
      p.reserve( max_N );
      // start with uniform momentum distribution over 20 sites
      fill( p.begin()+20 , p.end()-20 , 1.0/sqrt(20.0) );
  
      coord_type distr( N_start , 0.0 );
      distr.reserve( max_N );
  
      // create the system
      compacton_lattice lattice( max_N , beta , (max_N-N_start)/2 );
  
      //create the stepper, note that we use an always_resizer because state size might change during steps
      typedef symplectic_rkn_sb3a_mclachlan< coord_type , coord_type , double , coord_type , coord_type , double ,
              range_algebra , default_operations , always_resizer > hamiltonian_stepper;
      hamiltonian_stepper stepper;
      hamiltonian_stepper::state_type state = make_pair( q , p );
      //]
  
      //[ resizing_lattice_steps_loop
      double t = 0.0;
      const double dt = 0.1;
      const int steps = 10000;
      for( int step = 0 ; step < steps ; ++step )
      {
          stepper.do_step( boost::ref(lattice) , state , t , dt );
          lattice.energy_distribution( state.first , state.second , distr );
          if( distr[10] > 1E-150 )
          {
              do_resize( state.first , state.second , distr , state.first.size()+20 );
              rotate( state.first.begin() , state.first.end()-20 , state.first.end() );
              rotate( state.second.begin() , state.second.end()-20 , state.second.end() );
              lattice.change_pot_start( -20 );
              cout << t << ": resized left to " << distr.size() << ", energy = " << lattice.energy( state.first , state.second ) << endl;
          }
          if( distr[distr.size()-10] > 1E-150 )
          {
              do_resize( state.first , state.second , distr , state.first.size()+20 );
              cout << t << ": resized right to " << distr.size() << ", energy = " << lattice.energy( state.first , state.second ) << endl;
          }
          t += dt;
      }
      //]
  
      cout << "final lattice size: " << distr.size() << ", final energy: " << lattice.energy( state.first , state.second ) << endl;
  }
  