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#include <vector>
#include <stack>
#include "randutils/randutils.hpp"
#include "pcg-cpp/include/pcg_random.hpp"
#include "blossom5-v2.05.src/PerfectMatching.h"
using Rng = randutils::random_generator<pcg32>;
using Real = long double;
class AztecDiamond {
public:
using Coordinate = std::array<int, 2>;
typedef struct Vertex {
unsigned index;
Coordinate coordinate;
} Vertex;
typedef struct Edge {
Vertex* tail;
Vertex* head;
Real weight;
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 x = x0 + 2 * (j % i);
unsigned y = x0 + 2 * (j / i);
Edge& e1 = edges[2 * n * y + x];
Edge& e2 = edges[2 * n * y + x + 1];
Edge& e3 = edges[2 * n * (y + 1) + x];
Edge& e4 = edges[2 * n * (y + 1) + x + 1];
return {e1, e2, e3, e4};
}
public:
unsigned n;
std::vector<Vertex> vertices;
std::vector<Edge> edges;
AztecDiamond(int n) : n(n), vertices(2 * n * (n + 1)), edges(pow(2 * n, 2)) {
unsigned M = vertices.size() / 2;
for (int i = 0; i < M; i++) {
vertices[i].index = i;
vertices[M + i].index = M + i;
vertices[i].coordinate = {2 * (i % (n + 1)), 2 * (i / (n + 1)) + 1};
vertices[M + i].coordinate = {2 * (i % n) + 1, 2 * (i / n)};
}
for (unsigned i = 0; i < edges.size(); i++) {
edges[i].tail = &vertices[(1 + (i % (2 * n))) / 2 + (n + 1) * ((i / 4) / n)];
edges[i].head = &vertices[M + (i % (2 * n)) / 2 + n * (((i + 2 * n) / 4) / n)];
}
}
void setWeights(Rng& r) {
for (Edge& e : edges) {
e.weight = r.variate<Real, std::exponential_distribution>(1);
}
}
void computeWeights(Real T) {
for (Edge& e : edges) {
e.weights.push(exp(-e.weight / T));
}
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 = std::max(std::numeric_limits<Real>::min(), 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
for (Edge& e : edges) {
e.probability = 0;
}
Real logPartitionFunction = 0;
for (unsigned i = 1; i <= n; i++) {
#pragma omp parallel for reduction(+:logPartitionFunction)
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();
logPartitionFunction += log(cellFactor);
}
}
return logPartitionFunction;
}
};
bool edgeMatched(PerfectMatching& pm, const AztecDiamond::Edge& e);
PerfectMatching findGroundState(const AztecDiamond& a);
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