From 02bff5563d5a0150bde4ae3de9222a1837aefa98 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 10 Oct 2022 20:49:04 +0200
Subject: Merged Graph and AztecDiamond classes.

---
 rbmp.hpp | 162 ++++++++++++++++++++++++++++++++++++---------------------------
 1 file changed, 93 insertions(+), 69 deletions(-)

(limited to 'rbmp.hpp')

diff --git a/rbmp.hpp b/rbmp.hpp
index 02ca5ad..15b7e97 100644
--- a/rbmp.hpp
+++ b/rbmp.hpp
@@ -3,6 +3,7 @@
 #include <random>
 #include <vector>
 #include <limits>
+#include <stack>
 
 #include "randutils/randutils.hpp"
 #include "pcg-cpp/include/pcg_random.hpp"
@@ -10,97 +11,120 @@
 #include "blossom5-v2.05.src/PerfectMatching.h"
 
 using Rng = randutils::random_generator<pcg32>;
+using Real = long double;
 
-
-class Graph {
+class AztecDiamond {
 public:
-class Edge;
-class HalfEdge;
-
-class Coordinate {
-  std::array<int, 2> r;
-  public:
-  void operator=(const std::array<int, 2>& rp) {
-    r = rp;
-  }
-  void operator+=(const Coordinate& x) {
-    r[0] += x.r[0];
-    r[1] += x.r[1];
-  }
-  void operator-=(const Coordinate& x) {
-    r[0] -= x.r[0];
-    r[1] -= x.r[1];
-  }
-  int operator[](unsigned i) const {
-    return r[i];
-  }
-};
+  using Coordinate = std::array<int, 2>;
 
-class Vertex {
-public:
-  unsigned index;
-  std::vector<std::reference_wrapper<HalfEdge>> neighbors;
-  Coordinate coordinate;
+  typedef struct Vertex {
+    unsigned index;
+    Coordinate coordinate;
+  } Vertex;
 
-  void addEdge(HalfEdge& e) {
-    neighbors.push_back(e);
-  }
-};
+  typedef struct Edge {
+    Vertex* tail;
+    Vertex* head;
+    double weight;
+    std::stack<Real> weights;
+    Real probability = 0;
+  } Edge;
 
-class HalfEdge {
 private:
-  Vertex* tail;
-  Vertex* head;
+  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);
 
-public:
-  const Edge& edge;
+    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];
 
-  HalfEdge(const Edge& e) : edge(e) {}
-  void setVertices(Vertex& vt, Vertex& vh) {
-    tail = &vt;
-    head = &vh;
+    return {e1, e2, e3, e4};
   }
-  const Vertex& getHead() const {
-    return *head;
-  }
-  const Vertex& getTail() const {
-    return *tail;
-  }
-};
 
-class Edge {
 public:
-  std::array<HalfEdge, 2> halfedges;
-  double weight;
-
-  Edge() : halfedges{*this, *this} {};
-  void setVertices(Vertex& red, Vertex& blue) {
-    halfedges[0].setVertices(red, blue);
-    halfedges[1].setVertices(blue, red);
-    red.addEdge(halfedges[0]);
-    blue.addEdge(halfedges[1]);
-  }
-};
+  unsigned n;
   std::vector<Vertex> vertices;
   std::vector<Edge> edges;
 
-  Graph(int n, Rng& r) : vertices(2 * n * (n + 1)), edges(pow(2 * n, 2)) {
+  AztecDiamond(int n, Rng& r) : 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[i].coordinate = {2 * (i % (n + 1)), 2 * (i / (n + 1)) + 1};
       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++) {
-      Vertex& redVertex = vertices[(1 + (i % (2 * n))) / 2 + (n + 1) * ((i / 4) / n)];
-      Vertex& blueVertex = vertices[M + (i % (2 * n)) / 2 + n * (((i + 2 * n) / 4) / n)];
-      edges[i].setVertices(redVertex, blueVertex);
+      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)];
       edges[i].weight = r.variate<double, std::exponential_distribution>(1);
     }
   }
-};
 
-bool edgeMatched(PerfectMatching& pm, const Graph::Edge& e) {
-  return e.halfedges[0].getTail().index == pm.GetMatch(e.halfedges[0].getHead().index);
-}
+  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;
+  }
+};
-- 
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