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Diffstat (limited to 'src/boost/libs/numeric/odeint/examples/resizing_lattice.cpp')
-rw-r--r-- | src/boost/libs/numeric/odeint/examples/resizing_lattice.cpp | 169 |
1 files changed, 169 insertions, 0 deletions
diff --git a/src/boost/libs/numeric/odeint/examples/resizing_lattice.cpp b/src/boost/libs/numeric/odeint/examples/resizing_lattice.cpp new file mode 100644 index 00000000..f77f26e5 --- /dev/null +++ b/src/boost/libs/numeric/odeint/examples/resizing_lattice.cpp @@ -0,0 +1,169 @@ +/* + * 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; +} |