Partial progress towards merging BM model into global objects.

5 files changed, 268 insertions, 596 deletions

diff --git a/biroli-mezard.cpp b/biroli-mezard.cpp
index e2fb71a..5b6213f 100644
--- a/biroli-mezard.cpp
+++ b/biroli-mezard.cpp
@@ -1,149 +1,30 @@
 #include <fstream>
 #include <iostream>
-#include <limits>
-#include <list>
-#include <queue>
-#include <vector>
-#include <chrono>
 #include <unordered_set>
 
-#include <eigen3/Eigen/Dense>
-
-#include "pcg-cpp/include/pcg_random.hpp"
-#include "randutils/randutils.hpp"
-
-using Rng = randutils::random_generator<pcg32>;
-
-template <int D> using Vector = Eigen::Matrix<int, D, 1>;
-template <int D> using Matrix = Eigen::Matrix<int, D, D>;
+#include "glass.hpp"
 
 const unsigned Empty = std::numeric_limits<unsigned>::max();
 
-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;
-    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 <int 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 <int D> class Transformation {
+class BiroliState {
 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);
-    }
+  unsigned maximumNeighbors;
+  unsigned occupiedNeighbors;
 
-    v = v - m * v;
+  BiroliState() {
+    maximumNeighbors = Empty;
+    occupiedNeighbors = 0;
   }
 
-  Transformation<D> inverse() const {
-    return Transformation<D>(L, m.transpose(), -m.transpose() * v);
+  bool empty() const { return maximumNeighbors == Empty; }
+  bool frustrated() const { return occupiedNeighbors > maximumNeighbors; }
+  bool operator==(const BiroliState& s) const {
+    return s.maximumNeighbors == maximumNeighbors;
   }
-
-  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;
+  void remove() {
+    maximumNeighbors = Empty;
   }
-};
+}
 
 template <int D> class Vertex {
 public:
@@ -156,8 +37,6 @@ public:
   bool visited;
 
   Vertex() {
-    occupiedNeighbors = 0;
-    maximumNeighbors = Empty;
     marked = false;
   }
 
@@ -179,20 +58,15 @@ public:
   }
 };
 
-template <int D> class System {
+template <int D> class BiroliSystem : public HardSystem<D, BiroliState> {
 public:
-  const unsigned L;
   std::vector<unsigned> N;
-  std::unordered_set<Vertex<D>*> occupants;
-  std::vector<Vertex<D>> vertices;
-  Transformation<D> orientation;
-
-  unsigned size() const { return vertices.size(); }
+  std::unordered_set<Vertex<D, BiroliState>*> occupants;
 
   unsigned types() const { return N.size() - 1; }
 
   unsigned occupancy() const {
-    return size() - N[0];
+    return BiroliSystem::size() - N[0];
   }
 
   double density() const { return (double)occupancy() / size(); }
@@ -217,23 +91,7 @@ public:
     return true;
   }
 
-  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, unsigned T) : L(L), N(T + 1, 0), vertices(iPow(L, D)), orientation(L) {
+  BiroliSystem(unsigned L, unsigned T) : L(L), N(T + 1, 0), vertices(iPow(L, D)), orientation(L) {
     N[0] = size();
 
     for (unsigned i = 0; i < size(); i++) {
diff --git a/ciamarra.cpp b/ciamarra.cpp
index f2f44c1..7d7c8af 100644
--- a/ciamarra.cpp
+++ b/ciamarra.cpp
@@ -1,251 +1,58 @@
-#include <eigen3/Eigen/Dense>
-#include <eigen3/Eigen/src/Core/CwiseNullaryOp.h>
-#include <iostream>
-#include <list>
-#include <vector>
-#include <queue>
-
 #include "pcg-cpp/include/pcg_random.hpp"
 #include "randutils/randutils.hpp"
 
-using Rng = randutils::random_generator<pcg32>;
-
-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;
-}
+#include "glass.hpp"
 
-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> class CiamarraState : public Vector<D> {
+public:
+  CiamarraState() : Vector<D>(Vector<D>::Zero()) {}
 
-template <unsigned D> std::vector<Matrix<D>> generateTorusMatrices() {
-  std::vector<Matrix<D>> mats;
+  CiamarraState(const Vector<D>& v) : Vector<D>(v) {}
 
-  std::array<double, D> ini_sequence;
-  ini_sequence.fill(1);
-  std::list<std::array<double, D>> sequences;
-  sequences.push_back(ini_sequence);
+  CiamarraState(unsigned a, signed b) : Vector<D>(Vector<D>::Zero()) { CiamarraState::operator()(a) = b; }
 
-  one_sequences<D>(sequences, D);
+  CiamarraState(Rng& r) : CiamarraState(r.uniform((unsigned)0, D - 1), r.pick({-1, 1})) {}
 
-  sequences.pop_back(); // don't want the identity matrix!
+  bool empty() const { return CiamarraState::squaredNorm() == 0; }
 
-  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;
-        }
-      }
-    }
+  void remove() { CiamarraState::setZero(); }
 
-    mats.push_back(m);
+  bool operator==(const CiamarraState<D>& s) const {
+    return CiamarraState::dot(s) == 1;
   }
 
-  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;
+  CiamarraState<D> flip() const {
+    CiamarraState<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;
+  CiamarraState<D> transform(const Transformation<D>& m) const {
+    return m * *this;
   }
+};
 
-  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;
-    }
+template <unsigned D>
+class CiamarraSystem : public HardSystem<D, CiamarraState<D>> {
+  using HardSystem<D, CiamarraState<D>>::HardSystem;
 
-    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;
+  std::list<std::reference_wrapper<Vertex<D, CiamarraState<D>>>>
+    overlaps(Vertex<D, CiamarraState<D>>& v, const CiamarraState<D>& s, bool
+        excludeSelf = false) override {
+    std::list<std::reference_wrapper<Vertex<D, CiamarraState<D>>>> o;
 
-    if (s.isEmpty()) {
+    if (s.empty()) {
       return o;
     }
 
-    if (!v.isEmpty() && !excludeSelf) {
+    if (!v.empty() && !excludeSelf) {
       o.push_back(v);
     }
 
-    for (const HalfEdge<D>& e : v.adjacentEdges) {
-      if (!e.neighbor.isEmpty()) {
+    for (const HalfEdge<D, CiamarraState<D>>& e : v.adjacentEdges) {
+      if (!e.neighbor.empty()) {
         if (s.dot(e.Δx) == 1 || e.neighbor.state.dot(e.Δx) == -1) {
           o.push_back(e.neighbor);
         }
@@ -255,77 +62,10 @@ public:
     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;
+    CiamarraSystem::N = 0;
 
-    for (Vertex<D>& v : vertices) {
+    for (Vertex<D, CiamarraState<D>>& v : CiamarraSystem::vertices) {
       unsigned a = 0;
       for (unsigned d = 0; d < D; d++) {
         a += (d + 1) * v.position(d);
@@ -336,142 +76,18 @@ public:
 
       if (0 < a && a <= D) {
         v.state(a - 1) = -1;
-        N++;
+        CiamarraSystem::N++;
       } else if (D < a) {
         v.state(2 * D - a) = 1;
-        N++;
+        CiamarraSystem::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) {
+
+void print(const CiamarraSystem<2>& s) {
+  for (const Vertex<2, CiamarraState<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) {
@@ -492,14 +108,6 @@ void print(const System<2>& s) {
   }
 }
 
-template <unsigned D> Vector<D> randomVector(unsigned L, Rng& r) {
-  Vector<D> x;
-  for (unsigned i = 0; i < D; i++) {
-    x[i] = r.uniform((unsigned)0, L - 1);
-  }
-  return x;
-}
-
 int main() {
   const unsigned D = 3;
   unsigned L = 15;
@@ -509,7 +117,7 @@ int main() {
   double Tmax = 0.2;
   double δT = 0.02;
 
-  System<D> s(L);
+  CiamarraSystem<D> s(L);
 
   Rng r;
 
@@ -526,7 +134,7 @@ int main() {
 
   std::cerr << "Found state with appropriate density." << std::endl;
 
-  System<D> s0 = s;
+  CiamarraSystem<D> s0 = s;
 
   std::vector<Matrix<D>> ms = generateTorusMatrices<D>();
 
@@ -537,10 +145,10 @@ int main() {
       std::cout << i << " " << s.overlap(s0) << std::endl;
     }
     Matrix<D> m = r.pick(ms);
-    Vertex<D>& v = r.pick(s.vertices);
+    Vertex<D, CiamarraState<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) {
+    for (Vertex<D, CiamarraState<D>>& v : s.vertices) {
       v.marked = false;
     }
 //    s.sweepLocal(r);
diff --git a/compile_flags.txt b/compile_flags.txt
new file mode 100644
index 0000000..02d9f07
--- /dev/null
+++ b/compile_flags.txt
@@ -0,0 +1,3 @@
+-std=c++20
+-O3
+-I/usr/include/eigen3
diff --git a/distinguishable.cpp b/distinguishable.cpp
index 0b70cf2..22f228a 100644
--- a/distinguishable.cpp
+++ b/distinguishable.cpp
@@ -16,12 +16,14 @@ public:
 };
 
 template <unsigned D>
-class DistinguishableSystem : public FiniteEnergySystem<D, DistinguishableState> {
+class DistinguishableSystem : public SoftSystem<D, DistinguishableState> {
 public:
   std::vector<double> interaction;
 
   DistinguishableSystem(unsigned L, unsigned N, Rng& r)
-      : FiniteEnergySystem<D, DistinguishableState>(L, N), interaction(N * N) {
+      : SoftSystem<D, DistinguishableState>(L), interaction(N * N) {
+    DistinguishableSystem::N = N;
+
     for (double& V : interaction) {
       V = r.uniform(-0.5, 0.5);
     }
diff --git a/glass.hpp b/glass.hpp
index 64fe8b7..d313ced 100644
--- a/glass.hpp
+++ b/glass.hpp
@@ -180,6 +180,7 @@ public:
   const unsigned L;
   unsigned N;
   std::vector<Vertex<D, S>> vertices;
+  Transformation<D> orientation;
 
   unsigned vectorToIndex(const Vector<D>& x) const {
     unsigned i = 0;
@@ -197,7 +198,7 @@ public:
     return x;
   }
 
-  System(unsigned L, unsigned N) : L(L), N(N), vertices(iPow(L, D)) {
+  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].initialPosition = vertices[i].position;
@@ -216,8 +217,14 @@ public:
     }
   }
 
+  unsigned size() const { return vertices.size(); }
+
   double density() const { return N / pow(L, D); }
 
+  unsigned maxOccupation() const {
+    return iPow(L, D);
+  }
+
   void setInitialPosition() {
     for (Vertex<D, S>& v : vertices) {
       v.initialPosition = v.position;
@@ -240,7 +247,7 @@ public:
   }
 };
 
-template <unsigned D, State S> class FiniteEnergySystem : public System<D, S> {
+template <unsigned D, State S> class SoftSystem : public System<D, S> {
 public:
   using System<D, S>::System;
 
@@ -326,7 +333,7 @@ public:
                        bool dry = false) {
     std::queue<std::array<std::reference_wrapper<Vertex<D, S>>, 2>> q;
     Vector<D> x0New = R.apply(v0.position);
-    Vertex<D, S>& v0New = this->vertices[this->vectorToIndex(x0New)];
+    Vertex<D, S>& v0New = SoftSystem::vertices[SoftSystem::vectorToIndex(x0New)];
     q.push({v0, v0New});
 
     unsigned n = 0;
@@ -346,7 +353,7 @@ public:
           Vertex<D, S>& vn = e.neighbor;
 
           Vector<D> xnNew = R.apply(vn.position);
-          Vertex<D, S>& vnNew = this->vertices[this->vectorToIndex(xnNew)];
+          Vertex<D, S>& vnNew = SoftSystem::vertices[SoftSystem::vectorToIndex(xnNew)];
 
           if (!vn.marked && !vnNew.marked) {
             double E0 = pairEnergy(v.state, vn.state) + pairEnergy(vNew.state, vnNew.state);
@@ -393,3 +400,197 @@ public:
   }
 };
 
+template <unsigned D, State S> class HardSystem : public System<D, S> {
+public:
+
+  HardSystem(unsigned L) : System<D, S>(L) {}
+
+  virtual std::list<std::reference_wrapper<Vertex<D, S>>> overlaps(Vertex<D, S>&, const S&,
+                                                        bool = false) { return {}; }
+
+  bool insert(Vertex<D, S>& v, const S& s) {
+    if (overlaps(v, s).empty()) {
+      v.state = s;
+      HardSystem::N++;
+      return true;
+    } else {
+      return false;
+    }
+  }
+
+  bool tryDeletion(Vertex<D, S>& v) {
+    if (v.empty()) {
+      return false;
+    } else {
+      v.state.remove();
+      HardSystem::N--;
+      return true;
+    }
+  }
+
+  bool tryRandomMove(Rng& r) {
+    Vertex<D, S>& v = r.pick(HardSystem::vertices);
+    S oldState = v.state;
+
+    if (!tryDeletion(v)) {
+      return false;
+    }
+
+    if (1.0 / (2.0 * D) > r.uniform(0.0, 1.0)) {
+      for (HalfEdge<D, S>& e : v.adjacentEdges) {
+        if (1 == e.Δx.dot(oldState)) {
+          if (insert(e.neighbor, oldState.flip())) {
+            return true;
+          }
+          break;
+        }
+      }
+    } else {
+      S newState(r);
+      while (newState == oldState) {
+        newState = S(r);
+      }
+      if (insert(v, newState)) {
+        return true;
+      }
+    }
+    v.state = oldState;
+    HardSystem::N++;
+    return false;
+  }
+
+  bool trySwap(Vertex<D, S>& v1, Vertex<D, S>& 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, S>& v1 = r.pick(HardSystem::vertices);
+    Vertex<D, S>& v2 = r.pick(HardSystem::vertices);
+
+    return trySwap(v1, v2);
+  }
+
+
+  bool compatible() {
+    for (Vertex<D, S>& v : HardSystem::vertices) {
+      if (overlaps(v, v.state, true).size() > 0) {
+        return false;
+      }
+    }
+
+    return true;
+  }
+
+  void sweepGrandCanonical(double z, Rng& r) {
+    for (unsigned i = 0; i < iPow(HardSystem::L, D); i++) {
+      if (0.5 < r.uniform(0.0, 1.0)) {
+        double pIns = HardSystem::maxOccupation() * z / (HardSystem::N + 1);
+
+        if (pIns > r.uniform(0.0, 1.0)) {
+          while (true) {
+            Vertex<D, S>& v = r.pick(HardSystem::vertices);
+            if (v.empty()) {
+              insert(v, S(r));
+              break;
+            }
+          }
+        }
+      } else {
+
+        double pDel = HardSystem::N / (z * HardSystem::maxOccupation());
+
+        if (pDel > r.uniform(0.0, 1.0)) {
+          tryDeletion(r.pick(HardSystem::vertices));
+        }
+      }
+
+      tryRandomMove(r);
+    }
+  }
+
+  void sweepLocal(Rng& r) {
+    for (unsigned i = 0; i < iPow(HardSystem::L, D); i++) {
+      tryRandomMove(r);
+    }
+  }
+
+  void sweepSwap(Rng& r) {
+    for (unsigned i = 0; i < iPow(HardSystem::L, D); i++) {
+      tryRandomSwap(r);
+    }
+  }
+
+  unsigned flipCluster(const Transformation<D>& R, Vertex<D, S>& v0, Rng& r, bool dry = false) {
+    std::queue<std::reference_wrapper<Vertex<D, S>>> q;
+    q.push(v0);
+
+    unsigned n = 0;
+
+    while (!q.empty()) {
+      Vertex<D, S>& v = q.front();
+      q.pop();
+
+      if (!v.marked) {
+        Vector<D> xNew = R.apply(v.position);
+        Vertex<D, S>& vNew = HardSystem::vertices[HardSystem::vectorToIndex(xNew)];
+
+        v.marked = true;
+        vNew.marked = true;
+
+        S s = R.apply(v.state);
+        S sNew = R.apply(vNew.state);
+
+        std::list<std::reference_wrapper<Vertex<D, S>>> overlaps1 = overlaps(vNew, s, true);
+        std::list<std::reference_wrapper<Vertex<D, S>>> overlaps2 = overlaps(v, sNew, true);
+        overlaps1.splice(overlaps1.begin(), overlaps2);
+
+        for (Vertex<D, S>& 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, S>& v : HardSystem::vertices) {
+      if (!v.marked) {
+        bool dry = 0.5 < r.uniform(0.0, 1.0);
+        unsigned n = flipCluster(R, v, r, dry);
+        if (n > pow(HardSystem::L, D) / 4 && !dry) {
+          orientation = R.apply(orientation);
+        }
+      }
+    }
+
+    for (Vertex<D, S>& v : HardSystem::vertices) {
+      v.marked = false;
+    }
+  }
+
+  int overlap(const System<D, S>& s) const {
+    int o = 0;
+
+    for (unsigned i = 0; i < HardSystem::vertices.size(); i++) {
+      S s2 = orientation.apply(s.vertices[HardSystem::vectorToIndex(orientation.inverse().apply(HardSystem::indexToVector(i)))].state);
+      o += HardSystem::vertices[i].state.dot(s2);
+    }
+
+    return o;
+  }
+};