From 3c02310b3aced22ebe0fdd172cf3070f8a49d412 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 24 Jun 2021 10:26:33 +0200
Subject: Added new model.

---
 distinguishable.cpp | 497 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 497 insertions(+)
 create mode 100644 distinguishable.cpp

diff --git a/distinguishable.cpp b/distinguishable.cpp
new file mode 100644
index 0000000..d9f51ea
--- /dev/null
+++ b/distinguishable.cpp
@@ -0,0 +1,497 @@
+#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;
+}
+
+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;
+}
+
+class State {
+public:
+  unsigned type;
+
+  State() {
+    type = 0;
+  }
+
+  State(unsigned t) {
+    type = t;
+  }
+
+  bool isEmpty() const { return type == 0; }
+
+  void remove() { type = 0; }
+};
+
+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;
+    }
+
+    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;
+  Vector<D> initialPosition;
+  State 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;
+  std::vector<double> interaction;
+
+  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 N, Rng& r) : L(L), N(N), vertices(iPow(L, D)), interaction(N * N) {
+    for (unsigned i = 0; i < iPow(L, D); i++) {
+      vertices[i].position = indexToVector(i);
+      vertices[i].initialPosition = vertices[i].position;
+      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));
+      }
+    }
+
+    for (double& V : interaction) {
+      V = r.uniform(-0.5, 0.5);
+    }
+
+    for (unsigned i = 0; i < N; i++) {
+      vertices[i].state.type = i + 1;
+    }
+  }
+
+  double pairEnergy(const State& s1, const State& s2) const {
+    if (s1.isEmpty() || s2.isEmpty()) {
+      return 0;
+    } else {
+      if (s1.type < s2.type) {
+        return interaction[(s1.type - 1) * N + (s2.type - 1)];
+      } else {
+        return interaction[(s2.type - 1) * N + (s1.type - 1)];
+      }
+    }
+  }
+
+  double siteEnergy(const Vertex<D>& v) const {
+    double E = 0;
+
+    for (const HalfEdge<D>& e : v.adjacentEdges) {
+      E += pairEnergy(v.state, e.neighbor.state);
+    }
+
+    return E;
+  }
+
+  double energy() const {
+    double E = 0;
+
+    for (const Vertex<D>& v : vertices) {
+      E += siteEnergy(v);
+    }
+
+    return E / 2;
+  }
+
+  bool trySwap(Vertex<D>& v1, Vertex<D>& v2, double T, Rng& r) {
+    double E0 = siteEnergy(v1) + siteEnergy(v2);
+    std::swap(v1.state, v2.state);
+    double E1 = siteEnergy(v1) + siteEnergy(v2);
+    double ΔE = E1 - E0;
+
+    if (exp(-ΔE / T) > r.uniform(0.0, 1.0)) {
+      /* Accept the swap. */
+      std::swap(v1.initialPosition, v2.initialPosition);
+      return true;
+    } else {
+      /* Revert the swap. */
+      std::swap(v1.state, v2.state);
+      return false;
+    }
+  }
+
+  bool tryRandomMove(double T, Rng& r) {
+    Vertex<D>& v1 = r.pick(vertices);
+
+    if (v1.isEmpty()) {
+      return false;
+    }
+
+    Vertex<D>& v2 = (r.pick(v1.adjacentEdges)).neighbor;
+
+    if (!v2.isEmpty()) {
+      return false;
+    }
+
+    return trySwap(v1, v2, T, r);
+  }
+
+  bool tryRandomSwap(double T, Rng& r) {
+    Vertex<D>& v1 = r.pick(vertices);
+    Vertex<D>& v2 = r.pick(vertices);
+
+    if (v1.state.type != v2.state.type) {
+      return trySwap(v1, v2, T, r);
+    } else {
+      return false;
+    }
+  }
+
+  double density() const { return N / pow(L, D); }
+
+  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, double T, Rng& r, bool dry = false) {
+    std::queue<std::array<std::reference_wrapper<Vertex<D>>, 2>> q;
+    Vector<D> x0New = R.apply(v0.position);
+    Vertex<D>& v0New = vertices[vectorToIndex(x0New)];
+    q.push({v0, v0New});
+
+    unsigned n = 0;
+
+    while (!q.empty()) {
+      auto [vR, vNewR] = q.front();
+      q.pop();
+
+      Vertex<D>& v = vR;
+      Vertex<D>& vNew = vNewR;
+
+      if (!v.marked && !vNew.marked) {
+        v.marked = true;
+        vNew.marked = true;
+
+        for (HalfEdge<D>& e : v.adjacentEdges) {
+          Vertex<D>& vn = e.neighbor;
+
+          Vector<D> xnNew = R.apply(vn.position);
+          Vertex<D>& vnNew = vertices[vectorToIndex(xnNew)];
+
+          if (!vn.marked && !vnNew.marked) {
+            double E0 = pairEnergy(v.state, vn.state) + pairEnergy(vNew.state, vnNew.state);
+            double E1 = pairEnergy(vNew.state, vn.state) + pairEnergy(v.state, vnNew.state);
+            double ΔE = E1 - E0;
+            
+            if (exp(-ΔE / T) < r.uniform(0.0, 1.0)) {
+              q.push({vn, vnNew});
+            }
+          }
+        }
+
+        if (!dry) {
+          std::swap(v.state, vNew.state);
+          std::swap(v.initialPosition, vNew.initialPosition);
+        }
+
+        n += 1;
+      }
+    }
+
+    return n;
+  }
+
+  unsigned wolff(const Transformation<D>& R, double T, Rng& r) {
+    unsigned n = flipCluster(R, r.pick(vertices), T, r);
+    for (Vertex<D>& v : vertices) {
+      v.marked = false;
+    }
+    return n;
+  }
+
+  void swendsenWang(const Transformation<D>& R, double T, Rng& r) {
+    for (Vertex<D>& v : vertices) {
+      if (!v.marked) {
+        bool dry = 0.5 < r.uniform(0.0, 1.0);
+        flipCluster(R, v, T, r, dry);
+      }
+    }
+
+    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 setInitialPosition() {
+    for (Vertex<D>& v: vertices) {
+      v.initialPosition = v.position;
+    }
+  }
+
+  double selfIntermediateScattering() const {
+    double F = 0;
+
+    Vector<D> k1 = {M_PI, 0};
+    Vector<D> k2 = {0, M_PI};
+    for (const Vertex<D>& v : vertices) {
+      if (!v.isEmpty()) {
+        F += cos(k1.dot(v.position - v.initialPosition));
+        F += cos(k2.dot(v.position - v.initialPosition));
+      }
+    }
+
+    return F / (2 * N);
+  }
+};
+
+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 = 2;
+  unsigned L = 40;
+  unsigned N = 1560;
+  double Tmin = 0;
+  double Tmax = 0.4;
+  double δT = 0.02;
+
+  Rng r;
+
+  System<D> s(L, N, r);
+
+  std::vector<Matrix<D>> ms = generateTorusMatrices<D>();
+
+  for (unsigned j = 0; j < 10 * s.vertices.size(); j++) {
+    //unsigned nC = s.wolff(Transformation<D>(L, m, v.position - m * v.position), T, r);
+    s.tryRandomSwap(1000, r);
+  }
+
+  for (unsigned i = 0; i < 1e5; i++) {
+    for (unsigned j = 0; j < s.vertices.size(); j++) {
+      s.tryRandomMove(Tmax, r);
+    }
+  }
+
+  unsigned n = 1;
+  for (double T = Tmax; T > Tmin; T -= δT) {
+
+    /*
+    for (unsigned i = 0; i < 1e5; i++) {
+      Matrix<D> m = r.pick(ms);
+      Vertex<D>& v = r.pick(s.vertices);
+      s.wolff(Transformation<D>(L, m, v.position - m * v.position), T, r);
+    }
+    */
+    /*
+    */
+    s.setInitialPosition();
+    std::cout << T << " ";
+    for (unsigned i = 0; i < 1e4; i++) {
+      Matrix<D> m = r.pick(ms);
+      Vertex<D>& v = r.pick(s.vertices);
+      s.wolff(Transformation<D>(L, m, v.position - m * v.position), T, r);
+      std::cout << s.selfIntermediateScattering() << " ";
+    }
+    /*
+    for (unsigned i = 0; i < 1e5; i++) {
+      for (unsigned j = 0; j < s.vertices.size(); j++) {
+        s.tryRandomMove(T, r);
+      }
+      std::cout << s.selfIntermediateScattering() << " ";
+    }
+    */
+    std::cout << std::endl;
+    std::cerr << T << " " << s.energy() / N << std::endl;
+//    s.sweepLocal(r);
+//    s.sweepSwap(r);
+//    s.swendsenWang(Transformation<D>(L, ms, r), r);
+  }
+
+  return 0;
+}
+
-- 
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