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#include <functional>
#include <fstream>
#include <stack>
#include "rbmp.hpp"
using Real = long double;
class AztecDiamond {
public:
typedef struct Edge {
std::stack<Real> weights;
Real probability = 0;
} Edge;
using Face = std::array<std::reference_wrapper<Edge>, 4>;
std::vector<Edge> edges;
std::vector<std::vector<Face>> lattices;
AztecDiamond(unsigned n) : edges(pow(2 * n, 2)), lattices(n) {
for (unsigned i = 1; i <= n; i++) {
lattices[n - i].reserve(pow(i, 2));
unsigned x0 = n - i;
for (unsigned j = 0; j < pow(i, 2); j++) {
unsigned x = 2 * (j % i);
unsigned y = 2 * (j / i);
lattices[n - i].push_back({
edges[2 * n * (x0 + y) + x0 + x],
edges[2 * n * (x0 + y) + x0 + x + 1],
edges[2 * n * (x0 + y + 1) + x0 + x],
edges[2 * n * (x0 + y + 1) + x0 + x + 1]
});
}
}
}
void computeWeights() {
for (std::vector<Face>& faces : lattices) {
#pragma omp parallel for
for (Face& f : faces) {
Real w = f[0].get().weights.top();
Real x = f[1].get().weights.top();
Real y = f[2].get().weights.top();
Real z = f[3].get().weights.top();
Real cellFactor = w * z + x * y;
f[0].get().weights.push(z / cellFactor);
f[1].get().weights.push(y / cellFactor);
f[2].get().weights.push(x / cellFactor);
f[3].get().weights.push(w / cellFactor);
}
}
// This process computes one extra weight per edge.
for (Edge& e : edges) {
e.weights.pop();
}
}
void computeProbabilities() { // destroys *all* weights
for (auto it = lattices.rbegin(); it != lattices.rend(); it++) {
#pragma omp parallel for
for (Face& f : *it) {
Real p = f[0].get().probability;
Real q = f[1].get().probability;
Real r = f[2].get().probability;
Real s = f[3].get().probability;
Real w = f[0].get().weights.top();
Real x = f[1].get().weights.top();
Real y = f[2].get().weights.top();
Real z = f[3].get().weights.top();
Real cellFactor = w * z + x * y;
Real deficit = 1 - p - q - r - s;
f[0].get().probability = s + deficit * w * z / cellFactor;
f[1].get().probability = r + deficit * x * y / cellFactor;
f[2].get().probability = q + deficit * x * y / cellFactor;
f[3].get().probability = p + deficit * w * z / cellFactor;
for (Edge& e : f) {
e.weights.pop();
}
}
}
}
};
int main(int argc, char* argv[]) {
unsigned n = 100;
unsigned m = 100;
Real T = 1;
int opt;
while ((opt = getopt(argc, argv, "n:m:T:")) != -1) {
switch (opt) {
case 'n':
n = atoi(optarg);
break;
case 'm':
m = (unsigned)atof(optarg);
break;
case 'T':
T = atof(optarg);
break;
default:
exit(1);
}
}
std::string filename = "order_" + std::to_string(n) + "_" + std::to_string(T) + ".dat";
std::ifstream input(filename);
Rng r;
AztecDiamond a(n);
std::vector<Real> avgProbabilities(a.edges.size());
for (unsigned i = 0; i < m; i++) {
for (AztecDiamond::Edge& e : a.edges) {
e.weights.push(exp(- r.variate<Real, std::exponential_distribution>(1) / T));
e.probability = 0;
}
a.computeWeights();
a.computeProbabilities();
for (unsigned j = 0; j < a.edges.size(); j++) {
avgProbabilities[j] += a.edges[j].probability;
}
}
Graph G(n, r);
std::vector<Real> data_x(G.vertices.size());
std::vector<Real> data_y(G.vertices.size());
for (unsigned i = 0; i < G.edges.size(); i++) {
const Edge& e = G.edges[i];
const Vertex& vt = e.halfedges[0].getTail();
const Vertex& vh = e.halfedges[0].getHead();
data_x[vt.index] += avgProbabilities[i] * (vt.coordinate[0] - vh.coordinate[0]);
data_y[vt.index] += avgProbabilities[i] * (vt.coordinate[1] - vh.coordinate[1]);
data_x[vh.index] += avgProbabilities[i] * (vt.coordinate[0] - vh.coordinate[0]);
data_y[vh.index] += avgProbabilities[i] * (vt.coordinate[1] - vh.coordinate[1]);
}
std::ofstream output(filename);
for (unsigned i = 0; i < G.vertices.size(); i++) {
output << data_x[i] << " " << data_y[i] << std::endl;
}
output.close();
return 0;
}
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