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/resizing_lattice.cpp b/examples/resizing_lattice.cpp
new file mode 100644
index 0000000..f77f26e
--- /dev/null
+++ b/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;
+}