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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;
private:
std::tuple<Edge&, Edge&, Edge&, Edge&> face(unsigned i, unsigned j) {
unsigned x0 = n - i;
unsigned xx = 2 * (j % i);
unsigned yy = 2 * (j / i);
Edge& e1 = edges[2 * n * (x0 + yy) + x0 + xx];
Edge& e2 = edges[2 * n * (x0 + yy) + x0 + xx + 1];
Edge& e3 = edges[2 * n * (x0 + yy + 1) + x0 + xx];
Edge& e4 = edges[2 * n * (x0 + yy + 1) + x0 + xx + 1];
return {e1, e2, e3, e4};
}
public:
unsigned n;
std::vector<Edge> edges;
AztecDiamond(unsigned n) : edges(pow(2 * n, 2)), n(n) {}
void computeWeights() {
for (unsigned i = n; i > 0; i--) {
#pragma omp parallel for
for (unsigned j = 0; j < pow(i, 2); j++) {
auto [e1, e2, e3, e4] = face(i, j);
Real w = e1.weights.top();
Real x = e2.weights.top();
Real y = e3.weights.top();
Real z = e4.weights.top();
Real cellFactor = w * z + x * y;
e1.weights.push(z / cellFactor);
e2.weights.push(y / cellFactor);
e3.weights.push(x / cellFactor);
e4.weights.push(w / cellFactor);
}
}
// This process computes one extra weight per edge.
for (Edge& e : edges) {
e.weights.pop();
}
}
Real computeProbabilities() { // destroys *all* weights
Real partitionFunction = 1;
for (unsigned i = 1; i <= n; i++) {
#pragma omp parallel for
for (unsigned j = 0; j < pow(i, 2); j++) {
auto [e1, e2, e3, e4] = face(i, j);
Real p = e1.probability;
Real q = e2.probability;
Real r = e3.probability;
Real s = e4.probability;
Real w = e1.weights.top();
Real x = e2.weights.top();
Real y = e3.weights.top();
Real z = e4.weights.top();
Real cellFactor = w * z + x * y;
Real deficit = 1 - p - q - r - s;
e1.probability = s + deficit * w * z / cellFactor;
e2.probability = r + deficit * x * y / cellFactor;
e3.probability = q + deficit * x * y / cellFactor;
e4.probability = p + deficit * w * z / cellFactor;
e1.weights.pop();
e2.weights.pop();
e3.weights.pop();
e4.weights.pop();
partitionFunction *= cellFactor;
}
}
return partitionFunction;
}
};
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";
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 Graph::Edge& e = G.edges[i];
const Graph::Vertex& vt = e.halfedges[0].getTail();
const Graph::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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