From 7548abd44c37d4495dd498193ea15b0df757b904 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 9 Jun 2021 16:32:27 +0200
Subject: Lots of work.

---
 ciamarra.cpp | 489 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 480 insertions(+), 9 deletions(-)

(limited to 'ciamarra.cpp')

diff --git a/ciamarra.cpp b/ciamarra.cpp
index 6b932bf..f2f44c1 100644
--- a/ciamarra.cpp
+++ b/ciamarra.cpp
@@ -1,10 +1,477 @@
+#include <eigen3/Eigen/Dense>
+#include <eigen3/Eigen/src/Core/CwiseNullaryOp.h>
 #include <iostream>
+#include <list>
+#include <vector>
+#include <queue>
 
-#include "glass.hpp"
+#include "pcg-cpp/include/pcg_random.hpp"
+#include "randutils/randutils.hpp"
 
+using Rng = randutils::random_generator<pcg32>;
 
-void print(const CiamarraSystem<2>& s) {
-  for (const Vertex<2, CiamarraState<2>>& v : s.vertices) {
+template <int D> using Vector = Eigen::Matrix<int, D, 1>;
+template <int D> using Matrix = Eigen::Matrix<int, D, D>;
+
+int iPow(int x, unsigned p) {
+  if (p == 0)
+    return 1;
+  if (p == 1)
+    return x;
+
+  int tmp = iPow(x, p / 2);
+  if (p % 2 == 0)
+    return tmp * tmp;
+  else
+    return x * tmp * tmp;
+}
+
+unsigned mod(signed a, unsigned b) {
+  return ((a < 0) ? (a + (1 - a / (signed)b) * b) : a) % b;
+}
+
+template <int D, typename Derived> Vector<D> mod(const Eigen::MatrixBase<Derived>& v, unsigned b) {
+  Vector<D> u;
+  for (unsigned i = 0; i < D; i++) {
+    u(i) = mod(v(i), b);
+  }
+  return u;
+}
+
+template <int D> void one_sequences(std::list<std::array<double, D>>& sequences, unsigned level) {
+  if (level > 0) {
+    unsigned new_level = level - 1;
+    unsigned old_length = sequences.size();
+    for (std::array<double, D>& sequence : sequences) {
+      std::array<double, D> new_sequence = sequence;
+      new_sequence[new_level] = -1;
+      sequences.push_front(new_sequence);
+    }
+    one_sequences<D>(sequences, new_level);
+  }
+}
+
+template <unsigned D> std::vector<Matrix<D>> generateTorusMatrices() {
+  std::vector<Matrix<D>> mats;
+
+  std::array<double, D> ini_sequence;
+  ini_sequence.fill(1);
+  std::list<std::array<double, D>> sequences;
+  sequences.push_back(ini_sequence);
+
+  one_sequences<D>(sequences, D);
+
+  sequences.pop_back(); // don't want the identity matrix!
+
+  for (std::array<double, D> sequence : sequences) {
+    Matrix<D> m;
+    for (unsigned i = 0; i < D; i++) {
+      for (unsigned j = 0; j < D; j++) {
+        if (i == j) {
+          m(i, j) = sequence[i];
+        } else {
+          m(i, j) = 0;
+        }
+      }
+    }
+
+    mats.push_back(m);
+  }
+
+  for (unsigned i = 0; i < D; i++) {
+    for (unsigned j = 0; j < D; j++) {
+      if (i != j) {
+        Matrix<D> m;
+        for (unsigned k = 0; k < D; k++) {
+          for (unsigned l = 0; l < D; l++) {
+            if ((k == i && l == j) || (k == j && l == i)) {
+              if (i < j) {
+                m(k, l) = 1;
+              } else {
+                m(k, l) = -1;
+              }
+            } else if (k == l && (k != i && k != j)) {
+              m(k, l) = 1;
+            } else {
+              m(k, l) = 0;
+            }
+          }
+        }
+        mats.push_back(m);
+      }
+    }
+  }
+
+  return mats;
+}
+
+template <unsigned D> class State : public Vector<D> {
+public:
+  State() : Vector<D>(Vector<D>::Zero()) {}
+
+  State(const Vector<D>& v) : Vector<D>(v) {}
+
+  State(unsigned a, signed b) : Vector<D>(Vector<D>::Zero()) { this->operator()(a) = b; }
+
+  State(Rng& r) : State(r.uniform((unsigned)0, D - 1), r.pick({-1, 1})) {}
+
+  bool isEmpty() const { return this->squaredNorm() == 0; }
+
+  void remove() { this->setZero(); }
+
+  State<D> flip() const {
+    State<D> s;
+    for (unsigned i = 0; i < D; i++) {
+      s(i) = -this->operator()(i);
+    }
+    return s;
+  }
+};
+
+template <unsigned D> class Transformation {
+  public:
+    unsigned L;
+    Matrix<D> m;
+    Vector<D> v;
+
+    Transformation(unsigned L) : L(L) {
+      m.setIdentity();
+      v.setZero();
+    }
+
+    Transformation(unsigned L, const Matrix<D>& m, const Vector<D>& v) : L(L), m(m), v(v) {}
+
+    Transformation(unsigned L, const std::vector<Matrix<D>>& ms, Rng& r) : m(r.pick(ms)), L(L) {
+      for (unsigned i = 0; i < D; i++) {
+        v[i] = r.uniform((unsigned)0, L - 1);
+      }
+
+      v = v - m * v;
+    }
+
+    Vector<D> apply(const Vector<D>& x) const {
+      return mod<D>(v + m * x, L);
+    }
+
+    Transformation<D> apply(const Transformation<D>& t) const {
+      Transformation<D> tNew(L);
+
+      tNew.m = m * t.m;
+      tNew.v = apply(t.v);
+
+      return tNew;
+    }
+
+    State<D> apply(const State<D>& x) const {
+      return State<D>(m * x);
+    }
+
+    Transformation<D> inverse() const {
+      return Transformation<D>(L, m.transpose(), -m.transpose() * v);
+    }
+};
+
+template <unsigned D> class HalfEdge;
+
+template <unsigned D> class Vertex {
+public:
+  Vector<D> position;
+  State<D> state;
+  std::vector<HalfEdge<D>> adjacentEdges;
+  bool marked;
+
+  bool isEmpty() const { return state.isEmpty(); }
+};
+
+template <unsigned D> class HalfEdge {
+public:
+  Vertex<D>& neighbor;
+  Vector<D> Δx;
+
+  HalfEdge(Vertex<D>& n, const Vector<D>& d) : neighbor(n), Δx(d) {}
+};
+
+template <unsigned D> class System {
+public:
+  const unsigned L;
+  unsigned N;
+  std::vector<Vertex<D>> vertices;
+  Transformation<D> orientation;
+
+  unsigned vectorToIndex(const Vector<D>& x) const {
+    unsigned i = 0;
+    for (unsigned d = 0; d < D; d++) {
+      i += x[d] * iPow(L, d);
+    }
+    return i;
+  }
+
+  Vector<D> indexToVector(unsigned i) const {
+    Vector<D> x;
+    for (unsigned d = 0; d < D; d++) {
+      x[d] = (i / iPow(L, d)) % L;
+    }
+    return x;
+  }
+
+  System(unsigned L) : L(L), N(0), vertices(iPow(L, D)), orientation(L) {
+    for (unsigned i = 0; i < iPow(L, D); i++) {
+      vertices[i].position = indexToVector(i);
+      vertices[i].adjacentEdges.reserve(2 * D);
+      vertices[i].marked = false;
+    }
+
+    for (unsigned d = 0; d < D; d++) {
+      Vector<D> Δx = Vector<D>::Zero();
+      Δx[d] = 1;
+      for (signed i = 0; i < iPow(L, D); i++) {
+        unsigned j = iPow(L, d + 1) * (i / iPow(L, d + 1)) + mod(i + iPow(L, d), pow(L, d + 1));
+        vertices[i].adjacentEdges.push_back(HalfEdge<D>(vertices[j], Δx));
+        vertices[j].adjacentEdges.push_back(HalfEdge<D>(vertices[i], -Δx));
+      }
+    }
+  }
+
+  std::list<std::reference_wrapper<Vertex<D>>> overlaps(Vertex<D>& v, const State<D>& s,
+                                                        bool excludeSelf = false) {
+    std::list<std::reference_wrapper<Vertex<D>>> o;
+
+    if (s.isEmpty()) {
+      return o;
+    }
+
+    if (!v.isEmpty() && !excludeSelf) {
+      o.push_back(v);
+    }
+
+    for (const HalfEdge<D>& e : v.adjacentEdges) {
+      if (!e.neighbor.isEmpty()) {
+        if (s.dot(e.Δx) == 1 || e.neighbor.state.dot(e.Δx) == -1) {
+          o.push_back(e.neighbor);
+        }
+      }
+    }
+
+    return o;
+  }
+
+  bool insert(Vertex<D>& v, const State<D>& s) {
+    if (overlaps(v, s).empty()) {
+      v.state = s;
+      N++;
+      return true;
+    } else {
+      return false;
+    }
+  }
+
+  bool tryDeletion(Vertex<D>& v) {
+    if (v.isEmpty()) {
+      return false;
+    } else {
+      v.state.remove();
+      N--;
+      return true;
+    }
+  }
+
+  bool tryRandomMove(Rng& r) {
+    Vertex<D>& v = r.pick(vertices);
+    State<D> oldState = v.state;
+
+    if (!tryDeletion(v)) {
+      return false;
+    }
+
+    if (1.0 / (2.0 * D) > r.uniform(0.0, 1.0)) {
+      for (HalfEdge<D>& e : v.adjacentEdges) {
+        if (1 == e.Δx.dot(oldState)) {
+          if (insert(e.neighbor, oldState.flip())) {
+            return true;
+          }
+          break;
+        }
+      }
+    } else {
+      State<D> newState(r);
+      while (newState.dot(oldState) == 1) {
+        newState = State<D>(r);
+      }
+      if (insert(v, newState)) {
+        return true;
+      }
+    }
+    v.state = oldState;
+    N++;
+    return false;
+  }
+
+  bool trySwap(Vertex<D>& v1, Vertex<D>& v2) {
+    if (overlaps(v1, v2.state, true).size() == 0 && overlaps(v2, v1.state, true).size() == 0) {
+      std::swap(v1.state, v2.state);
+      return true;
+    } else {
+      return false;
+    }
+  }
+
+  bool tryRandomSwap(Rng& r) {
+    Vertex<D>& v1 = r.pick(vertices);
+    Vertex<D>& v2 = r.pick(vertices);
+
+    return trySwap(v1, v2);
+  }
+
+  void setGroundState() {
+    N = 0;
+
+    for (Vertex<D>& v : vertices) {
+      unsigned a = 0;
+      for (unsigned d = 0; d < D; d++) {
+        a += (d + 1) * v.position(d);
+      }
+      a %= 2 * D + 1;
+
+      v.state.setZero() = Vector<D>::Zero();
+
+      if (0 < a && a <= D) {
+        v.state(a - 1) = -1;
+        N++;
+      } else if (D < a) {
+        v.state(2 * D - a) = 1;
+        N++;
+      }
+    }
+  }
+
+  bool compatible() {
+    for (Vertex<D>& v : vertices) {
+      if (overlaps(v, v.state, true).size() > 0) {
+        return false;
+      }
+    }
+
+    return true;
+  }
+
+  double density() const { return N / pow(L, D); }
+
+  unsigned maxOccupation() const {
+    //      return (2 * D * iPow(L, D)) / (2 * D + 1);
+    return iPow(L, D);
+  }
+
+  void sweepGrandCanonical(double z, Rng& r) {
+    for (unsigned i = 0; i < iPow(L, D); i++) {
+      if (0.5 < r.uniform(0.0, 1.0)) {
+        double pIns = maxOccupation() * z / (N + 1);
+
+        if (pIns > r.uniform(0.0, 1.0)) {
+          while (true) {
+            Vertex<D>& v = r.pick(vertices);
+            if (v.isEmpty()) {
+              insert(v, State<D>(r));
+              break;
+            }
+          }
+        }
+      } else {
+
+        double pDel = N / (z * maxOccupation());
+
+        if (pDel > r.uniform(0.0, 1.0)) {
+          tryDeletion(r.pick(vertices));
+        }
+      }
+
+      tryRandomMove(r);
+    }
+  }
+
+  void sweepLocal(Rng& r) {
+    for (unsigned i = 0; i < iPow(L, D); i++) {
+      tryRandomMove(r);
+    }
+  }
+
+  void sweepSwap(Rng& r) {
+    for (unsigned i = 0; i < iPow(L, D); i++) {
+      tryRandomSwap(r);
+    }
+  }
+
+  unsigned flipCluster(const Transformation<D>& R, Vertex<D>& v0, Rng& r, bool dry = false) {
+    std::queue<std::reference_wrapper<Vertex<D>>> q;
+    q.push(v0);
+
+    unsigned n = 0;
+
+    while (!q.empty()) {
+      Vertex<D>& v = q.front();
+      q.pop();
+
+      if (!v.marked) {
+        Vector<D> xNew = R.apply(v.position);
+        Vertex<D>& vNew = vertices[vectorToIndex(xNew)];
+
+        v.marked = true;
+        vNew.marked = true;
+
+        State<D> s = R.apply(v.state);
+        State<D> sNew = R.apply(vNew.state);
+
+        std::list<std::reference_wrapper<Vertex<D>>> overlaps1 = overlaps(vNew, s, true);
+        std::list<std::reference_wrapper<Vertex<D>>> overlaps2 = overlaps(v, sNew, true);
+        overlaps1.splice(overlaps1.begin(), overlaps2);
+
+        for (Vertex<D>& vn : overlaps1) {
+          if (!vn.marked) {
+            q.push(vn);
+          }
+        }
+
+        if (!dry) {
+          v.state = sNew;
+          vNew.state = s;
+        }
+
+        n += 1;
+      }
+    }
+
+    return n;
+  }
+
+  void swendsenWang(const Transformation<D>& R, Rng& r) {
+    for (Vertex<D>& v : vertices) {
+      if (!v.marked) {
+        bool dry = 0.5 < r.uniform(0.0, 1.0);
+        unsigned n = flipCluster(R, v, r, dry);
+        if (n > pow(L, D) / 4 && !dry) {
+          orientation = R.apply(orientation);
+        }
+      }
+    }
+
+    for (Vertex<D>& v : vertices) {
+      v.marked = false;
+    }
+  }
+
+  int overlap(const System<D>& s) const {
+    int o = 0;
+
+    for (unsigned i = 0; i < vertices.size(); i++) {
+      State<D> s2 = orientation.apply(s.vertices[vectorToIndex(orientation.inverse().apply(indexToVector(i)))].state);
+      o += vertices[i].state.dot(s2);
+    }
+
+    return o;
+  }
+};
+
+void print(const System<2>& s) {
+  for (const Vertex<2>& v : s.vertices) {
     if (v.state(0) == 1 && v.state(1) == 0) {
       std::cerr << "▶";
     } else if (v.state(0) == -1 && v.state(1) == 0) {
@@ -42,7 +509,7 @@ int main() {
   double Tmax = 0.2;
   double δT = 0.02;
 
-  CiamarraSystem<D> s(L);
+  System<D> s(L);
 
   Rng r;
 
@@ -58,11 +525,8 @@ int main() {
   } 
 
   std::cerr << "Found state with appropriate density." << std::endl;
-    if (!s.compatible()) {
-      std::cerr <<"whoops!" << std::endl;
-    }
 
-  CiamarraSystem<D> s0 = s;
+  System<D> s0 = s;
 
   std::vector<Matrix<D>> ms = generateTorusMatrices<D>();
 
@@ -72,9 +536,16 @@ int main() {
       n++;
       std::cout << i << " " << s.overlap(s0) << std::endl;
     }
+    Matrix<D> m = r.pick(ms);
+    Vertex<D>& v = r.pick(s.vertices);
+    unsigned nC = s.flipCluster(Transformation<D>(L, m, v.position - m * v.position), v, r);
+    std::cerr << nC << std::endl;
+    for (Vertex<D>& v : s.vertices) {
+      v.marked = false;
+    }
 //    s.sweepLocal(r);
 //    s.sweepSwap(r);
-    s.swendsenWang(Transformation<D>(L, ms, r), r);
+//    s.swendsenWang(Transformation<D>(L, ms, r), r);
   }
 
   return 0;
-- 
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