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#include <iostream>
#include <vector>
#include <cmath>
#include <random>
#include <fstream>
#include <chrono>
struct coordinate{
double x{0};
double y{0};
};
double compute_sq_distances(const coordinate& pos1, const coordinate& pos2, const double& L,
double& dx, double& dy){
// box volume = [L,L]^n
static double two_L = 2*L;
dx = pos1.x  pos2.x;
dx = dx > L ? dxtwo_L : (dx < L ? dx+two_L : dx);
dy = pos1.y  pos2.y;
dy = dy > L ? dytwo_L : (dy < L ? dy+two_L : dy);
return dx*dx + dy*dy;
}
double force_term(double& dist2, const double& kappa, const double& sigma_2){
static double pref {kappa/(2*sigma_2)};
static double expo;
expo = exp(dist2/(2*sigma_2));
return pref*expo;
}
void compute_force(std:: vector<coordinate>& forces, const std:: vector<coordinate>& positions,
const double& L, const double& kappa, const double& sigma_2){
static double dx, dy;
static double dist2;
static int n_part = forces.size();
static double force;
for (int i=0; i<n_part; ++i){
forces[i].x = forces[i].y = 0;
}
for (int i=0; i<n_part; ++i){
for(int j=i+1; j<n_part; ++j){
dist2 = compute_sq_distances(positions[i], positions[j], L, dx, dy);
force = force_term(dist2, kappa, sigma_2);
forces[i].x += force*dx;
forces[i].y += force*dy;
forces[j].x += force*dx;
forces[j].y += force*dy;
}
}
return;
}
void B_step(const std:: vector <coordinate>& positions, std:: vector <coordinate>& velocities, std:: vector <coordinate>& forces,
const double& stepsize, const double& L, const double& kappa, const double& sigma_2){
static const int n_part = positions.size();
// Update velocities.
for (int i=0; i<n_part; ++i){
velocities[i].x += stepsize*forces[i].x;
velocities[i].y += stepsize*forces[i].y;
}
return;
}
void A_step(std:: vector <coordinate>& positions, const std:: vector <coordinate>& velocities, const double& stepsize, const double& L){
static int n_part = positions.size();
for (int i=0; i<n_part; ++i){
positions[i].x += stepsize*velocities[i].x;
positions[i].y += stepsize*velocities[i].y;
}
return;
}
void O_step(std:: vector <coordinate>& velocities, const double& stepsize,
const double& gamma, const double& beta, std:: mt19937& RNG){
static std:: normal_distribution<> normal{0,1};
static const int n_part = velocities.size();
static const double a = exp(gamma*stepsize);
static const double pref = sqrt(1/beta *(1a*a));
for (int i=0; i<n_part; ++i){
velocities[i].x = a*velocities[i].x + pref*normal(RNG);
velocities[i].y = a*velocities[i].y + pref*normal(RNG);
}
return;
}
void apply_periodic_boundaries(std:: vector <coordinate>& positions, const double& L){
static const int n_part = positions.size();
static const double two_L = 2*L;
static double x, y;
for (int i=0; i<n_part; ++i){
x = positions[i].x;
positions[i].x = x>L ? xtwo_L : (x<L ? x + two_L : x);
y = positions[i].y;
positions[i].y = y>L ? ytwo_L : (y<L ? y + two_L : y);
}
return;
}
int main(int argc, char* argv[]){
// Hyperparameters.
const double L {10};
const int N_iter {20000};
const int n_meas {10};
const int n_part {1000};
const double beta {300};
const double gamma {0.05};
const double kappa {1./n_part};
const double sigma_2 {1};
const double stepsize {0.1};
const int randomseed {1};
// Prepare simulation.
// Prepare RNG.
std:: mt19937 twister;
std:: seed_seq seq{1,20,3200,403,5*randomseed+1,12000,73667,9474+randomseed,19151randomseed};
std:: vector < std::uint32_t > seeds(1);
seq.generate(seeds.begin(), seeds.end());
twister.seed(seeds.at(0));
// Set positions.
std:: uniform_real_distribution<double> box_uniform(L, L);
std:: vector <coordinate> positions(n_part);
for (int i=0; i<n_part; ++i){
positions[i].x = box_uniform(twister);
positions[i].y = box_uniform(twister);
}
// Set forces.
std:: vector <coordinate> forces(n_part);
compute_force(forces, positions, L, kappa, sigma_2);
// Set velocities.
std:: vector <coordinate> velocities(n_part);
// Main loop.
const double stepsize_half = 0.5 * stepsize;
std:: normal_distribution<> normal{0,1};
auto t1 = std:: chrono::high_resolution_clock::now();
for (int i=0; i<=N_iter; ++i){
B_step(positions, velocities, forces, stepsize_half, L, kappa, sigma_2);
A_step(positions, velocities, stepsize_half, L);
apply_periodic_boundaries(positions, L);
O_step(velocities, stepsize, gamma, beta, twister);
A_step(positions, velocities, stepsize_half, L);
apply_periodic_boundaries(positions, L);
compute_force(forces, positions, L, kappa, sigma_2);
B_step(positions, velocities, forces, stepsize_half, L, kappa, sigma_2);
if (i%1000==0) std::cout << "Iteration "<<i<< " done!\n";
}
auto t2 = std:: chrono:: high_resolution_clock:: now();
auto ms_int = std:: chrono:: duration_cast < std:: chrono:: seconds > (t2  t1);
std:: cout << "Execution took " << ms_int.count() << " seconds!\n";
return 0;
}
