Starting implementing collective moves.

4 files changed, 538 insertions, 25 deletions

diff --git a/animation.hpp b/animation.hpp
index b1ff815..31a466e 100644
--- a/animation.hpp
+++ b/animation.hpp
@@ -28,12 +28,16 @@ void initializeAnimation(int argc, char** argv, unsigned window_size = 1000) {
 template <Particle<2> T> void draw(const Model<2, T>& m) {
   glClear(GL_COLOR_BUFFER_BIT);
   for (const Sphere<2>& p : m.particles) {
+    std::array<double, 3> color = {0, 0, 0};
+    if (p.m) {
+      color = {0, 1, 0};
+    }
     Sphere<2> pTmp = p;
     pTmp.x = m.orientation.inverse().act(p.x);
-    draw(pTmp);
+    draw(pTmp, color);
     if (pTmp.intersectsBoundary()) {
       for (Vector<2> Δy : {(Vector<2>){1,0}, {-1,0}, {0,1}, {0,-1}, {-1,1}, {1,1}, {1,-1},{-1,-1}}) {
-        draw({(Vector<2>)pTmp.x + Δy, p.r});
+        draw({(Vector<2>)pTmp.x + Δy, p.r}, color);
       }
     }
   }
diff --git a/shear.hpp b/shear.hpp
new file mode 100644
index 0000000..5e1f73f
--- /dev/null
+++ b/shear.hpp
@@ -0,0 +1,426 @@
+#pragma once
+
+#include <assert.h>
+#include <set>
+#include <vector>
+#include <queue>
+
+#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<double, D, 1>;
+template <int D> using Matrix = Eigen::Matrix<double, D, D>;
+
+template <int D> class Position : public Vector<D> {
+private:
+
+  void recenter() {
+    for (unsigned i = 0; i < D; i++) {
+      double& vi = Vector<D>::operator()(i);
+      signed n = floor(vi);
+      vi -= n;
+      if (i == D - 2) {
+        Vector<D>::operator()(D - 1) += γ * n;
+      }
+    }
+  }
+
+public:
+  const double& γ;
+  Position(const double& γ) : γ(γ) {}
+
+  Position(const Position<D>& p) : Vector<D>(p), γ(p.γ) {}
+  Position(const Vector<D>& v, const double& γ) : Vector<D>(v), γ(γ) {}
+
+  Position<D>& operator=(const Position<D>& p) {
+    Vector<D>::operator=(p);
+    return *this;
+  }
+
+  Position<D>& operator+=(const Vector<D>& u) {
+    Vector<D>::operator+=(u);
+    recenter();
+    return *this;
+  }
+
+  friend Position<D> operator+(Position<D> v, const Vector<D>& u) {
+    v += u;
+    return v;
+  }
+
+  Position<D>& operator-=(const Vector<D>& u) {
+    Vector<D>::operator-=(u);
+    recenter();
+    return *this;
+  }
+
+  friend Vector<D> operator-(const Position<D>& v, const Position<D>& u) {
+    std::vector<Vector<2>> ds;
+    ds.reserve(9);
+
+    unsigned iCur  = 0;
+    unsigned iMin;
+    double dMin = std::numeric_limits<double>::infinity();
+
+    Position<2> v2(v.γ);
+    v2(0) = v(D - 2);
+    v2(1) = v(D - 1);
+
+    for (signed i : {-1, 0, 1}) {
+      for (signed j : {-1, 0, 1}) {
+        Vector<2> u2;
+        u2(0) = u(0) + i;
+        u2(1) = u(1) + j + v.γ * i;
+
+        ds.push_back(v2 - u2);
+
+        double d = ds.back().squaredNorm();
+
+        if (d < dMin) {
+          iMin = iCur;
+          dMin = d;
+        }
+
+        iCur++;
+      }
+    }
+
+    Vector<D> w = v - (Vector<D>)u;
+
+    for (unsigned i = 0; i < D - 2; i++) {
+      double& wi = w(i);
+      if (wi > 0.5) {
+        wi = 1 - wi;
+      }
+    }
+
+    w(D - 2) = ds[iMin](0); 
+    w(D - 1) = ds[iMin](1); 
+
+    return (Vector<D>)w;
+  }
+};
+
+template <int D> class Euclidean {
+public:
+  Vector<D> t;
+  Matrix<D> r;
+
+  Euclidean() {
+    t.setZero();
+    r.setIdentity();
+  }
+
+  Euclidean(const Vector<D>& t0, const Matrix<D>& r0) : t(t0), r(r0) {}
+
+  Euclidean inverse() const { return Euclidean(-r.transpose() * t, r.transpose()); }
+
+  Vector<D> act(const Vector<D>& x) const { return r * x + t; }
+  Position<D> act(const Position<D>& x) const { return Position<D>(r * x, x.γ) + t; }
+  Euclidean<D> act(const Euclidean<D>& R) const { return {act(R.t), r * R.r}; }
+};
+
+template <typename T, int D> concept Particle = requires(T v, const Position<D>& x, double r) {
+  { v.x } -> std::same_as<Position<D>>;
+  { v.r } -> std::same_as<double>;
+  { v.m } -> std::same_as<bool>;
+  { v.U(x, r) } -> std::same_as<double>;
+};
+
+template <int D, Particle<D> T> class NeighborLists {
+private:
+  unsigned n;
+  const double& γ;
+  std::vector<std::set<T*>> lists;
+
+  unsigned mod(signed a, unsigned b) const {
+    if (a >= 0) {
+      return a % b;
+    } else {
+      return (a + b * ((b - a) / b)) % b;
+    }
+  }
+
+  int iPow(int x, unsigned p) const {
+    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 index(Position<D> x) const {
+    unsigned ind = 0;
+    for (unsigned i = 0; i < D; i++) {
+      ind += pow(n, i) * std::floor(n * x(i));
+    }
+    assert(ind < lists.size());
+    return ind;
+  }
+
+  std::pair<typename std::set<T*>::iterator, bool> insert(T& p, unsigned ind) {
+    return lists[ind].insert(&p);
+  }
+
+  size_t erase(T& p, unsigned ind) {
+    return lists[ind].erase(&p);
+  }
+
+  void neighborsOfHelper(signed i0, unsigned d, std::set<T*>& ns, signed overEdge = 0) const {
+    if (d == 0) {
+      const std::set<T*>& a = lists[i0];
+      ns.insert(a.begin(), a.end());
+    } else {
+      for (signed j : {-1, 0, 1}) {
+        signed i1 = iPow(n, d) * (i0 / iPow(n, d)) + mod(i0 + (signed)round(overEdge * n * γ) + j * iPow(n, d-1), iPow(n, d));
+        signed newEdge = 0;
+        if (d == 2) {
+          if (i0 - i1 == n)
+            newEdge = -1;
+          if (i1 - i0 == n) {
+            newEdge = 1;
+          }
+        }
+        neighborsOfHelper(i1, d - 1, ns, newEdge);
+      }
+    }
+  }
+
+public:
+  NeighborLists(const double& γ, unsigned m) : n(m), γ(γ), lists(pow(n, D)) {}
+  NeighborLists(const double& γ, double l) : NeighborLists(γ, (unsigned)floor(1 / l)) {}
+
+  std::pair<typename std::set<T*>::iterator, bool> insert(T& p, const Position<D>& x) {
+    return insert(p, index(x));
+  }
+
+  std::pair<typename std::set<T*>::iterator, bool> insert(T& p) {
+    return insert(p, p.x);
+  }
+
+  size_t erase(T& p, const Position<D>& x) {
+    return erase(p, index(x));
+  }
+
+  size_t erase(T& p) {
+    return erase(p, p.x);
+  }
+
+  void move(T& p, const Position<D>& xNew) {
+    unsigned iOld = index(p.x);
+    unsigned iNew = index(xNew);
+    if (iNew != iOld) {
+      erase(p, iOld);
+      insert(p, iNew);
+    }
+  }
+
+  std::set<T*> neighborsOf(const Position<D>& x) const {
+    std::set<T*> neighbors;
+    neighborsOfHelper(index(x), D, neighbors);
+    return neighbors;
+  }
+};
+
+template <int D, Particle<D> T> class Model {
+private:
+  bool metropolisAccept(double β, double ΔE, Rng& r) const {
+    return ΔE < 0 || exp(-β * ΔE) > r.uniform(0.0, 1.0);
+  }
+
+  bool swapAccept(const T& p1, const T& p2) const {
+    double rat = p1.r / p2.r;
+    return (rat < 1.2 && rat > 0.83);
+  }
+
+public:
+  double γ;
+  NeighborLists<D, T> nl;
+  std::vector<T> particles;
+  Euclidean<D> orientation;
+
+  Model(unsigned N, double l, std::function<double(Rng& r)> g, Rng& r) : γ(0), nl(γ, l) {
+    particles.reserve(N);
+    for (unsigned i = 0; i < N; i++) {
+      Position<D> x(γ);
+      for (double& xi : x) {
+        xi = r.uniform(0.0, 1.0);
+      }
+      particles.push_back(T(x, g(r)));
+      nl.insert(particles.back());
+    }
+  };
+
+  void shear(double Δγ) {
+    γ += Δγ;
+  }
+
+  void move(T& p, const Position<D>& x) {
+    nl.move(p, x);
+    p.x = x;
+  }
+
+  bool move(double β, T& p, const Vector<D>& Δx, Rng& r) {
+    Position<D> xNew = p.x + Δx;
+    double ΔE = 0;
+
+    for (const T* neighbor : nl.neighborsOf(p.x)) {
+      if (neighbor != &p) {
+        ΔE -= neighbor->U(p.x, p.r);
+      }
+    }
+
+    for (const T* neighbor : nl.neighborsOf(xNew)) {
+      if (neighbor != &p) {
+        ΔE += neighbor->U(xNew, p.r);
+      }
+    }
+
+    if (metropolisAccept(β, ΔE, r)) {
+      move(p, xNew);
+      return true;
+    } else {
+      return false;
+    }
+  }
+
+  bool swap(double β, T& p1, T& p2, Rng& r) {
+    if (!swapAccept(p1, p2))
+      return false;
+
+    double ΔE = 0;
+
+    for (const T* neighbor : nl.neighborsOf(p1.x)) {
+      if (neighbor != &p1 && neighbor != &p2) {
+        ΔE += neighbor->U(p1.x, p2.r) - neighbor->U(p1.x, p1.r);
+      }
+    }
+
+    for (const T* neighbor : nl.neighborsOf(p2.x)) {
+      if (neighbor != &p1 && neighbor != &p2) {
+        ΔE += neighbor->U(p2.x, p1.r) - neighbor->U(p2.x, p2.r);
+      }
+    }
+
+    if (metropolisAccept(β, ΔE, r)) {
+      std::swap(p1.r, p2.r);
+      return true;
+    } else {
+      return false;
+    }
+  }
+
+  bool randomSwap(double β, Rng& r) {
+    return swap(β, r.pick(particles), r.pick(particles), r);
+  }
+
+  bool randomMove(double β, double δ, Rng& r) {
+    Vector<D> Δx;
+    for (double& Δxi : Δx) {
+      Δxi = r.variate<double, std::normal_distribution>(0, δ);
+    }
+    return move(β, r.pick(particles), Δx, r);
+  }
+
+  unsigned clusterFlip(double β, const Euclidean<D>& R, T& p0, Rng& r) {
+    unsigned n = 0;
+    std::queue<T*> q;
+    q.push(&p0);
+
+    while (!q.empty()) {
+      T* p = q.front();
+      q.pop();
+
+      if (!p->m) {
+        p->m = true;
+        Position<D> xNew = R.act(p->x);
+
+        for (T* neighbor : nl.neighborsOf(xNew)) {
+          if (!neighbor->m) {
+            double ΔE = neighbor->U(xNew, p->r) - neighbor->U(p->x, p->r);
+            if (1 - exp(-β * ΔE) > r.uniform(0.0, 1.0)) {
+              q.push(neighbor);
+            }
+          }
+        }
+
+        move(*p, xNew);
+        n++;
+      }
+    }
+
+    for (T& p : particles) {
+      p.m = false;
+    }
+
+    if (n > particles.size() / 2) {
+      orientation = R.act(orientation);
+    }
+
+    return n;
+  }
+
+  unsigned clusterSwap(double β, T& s1, T& s2, Rng& r) {
+    if (!swapAccept(s1, s2))
+      return 0;
+
+    Vector<2> t1 = s1.x;
+    Vector<2> t2 = s2.x;
+    Vector<2> t = (t1 + t2) / 2;
+
+    Matrix<2> mat;
+
+    mat(0, 0) = -1;
+    mat(1, 1) = -1;
+    mat(0, 1) = 0;
+    mat(1, 0) = 0;
+
+    Euclidean<2> g(t - mat * t, mat);
+
+    return clusterFlip(β, g, s1, r);
+  }
+
+  unsigned randomClusterSwap(double β, Rng& r) {
+    return clusterSwap(β, r.pick(particles), r.pick(particles), r);
+  }
+};
+
+template <int D> class Sphere {
+public:
+  Position<D> x;
+  bool m;
+  double r;
+
+  Sphere() : m(false) {};
+
+  Sphere(const Position<D>& x, double r) : x(x), m(false), r(r) {};
+
+  double regularizedDistanceSquared(const Position<D>& y, double ry) const {
+    return (x - y).squaredNorm() / pow(r + ry, 2);
+  } 
+
+  bool intersectsBoundary() const {
+    for (double xi : x) {
+      if (xi < r || 1 - xi < r) {
+        return true;
+      }
+    }
+    return false;
+  }
+};
+
+std::function<double(Rng&)> gContinuousPolydisperse(double Rmax) {
+  return [Rmax] (Rng& r) -> double {
+    return pow(r.uniform(pow(2.219, -2), 1.0), -0.5) * Rmax / 2.219;
+  };
+}
diff --git a/soft_spheres.cpp b/soft_spheres.cpp
index 148812f..10e90c7 100644
--- a/soft_spheres.cpp
+++ b/soft_spheres.cpp
@@ -24,7 +24,7 @@ int main(int argc, char* argv[]) {
   unsigned N = 1200;
   double R = 0.025;
   double ε = 0.005;
-  unsigned steps = 1e4;
+  unsigned steps = 1e2;
   double β = 0.5;
 
   initializeAnimation(argc, argv);
@@ -40,7 +40,7 @@ int main(int argc, char* argv[]) {
     }
 
 //    std::cout << m.randomClusterSwap(β, r) << std::endl;
-    
+
     if (i % 3 == 0)
       draw(m);
   }
@@ -51,10 +51,17 @@ int main(int argc, char* argv[]) {
     }
 
     unsigned k = m.randomClusterSwap(β, r);
-    if (k != 0 && k != N) {
-      std::cout << k << std::endl;
+    std::cout << k << std::endl;
+
+    if (k > 0 && k < N) {
+      draw(m);
+      getchar();
     }
-    
+
+    for (SoftSphere<2, n>& p : m.particles) {
+      p.m = false;
+    }
+
     if (i % 3 == 0)
       draw(m);
   }
diff --git a/spheres.hpp b/spheres.hpp
index 6dd5b04..161ef9c 100644
--- a/spheres.hpp
+++ b/spheres.hpp
@@ -177,9 +177,57 @@ public:
   }
 };
 
+template <int D, Particle<D> T> class Move {
+public:
+  const Euclidean<D> g;
+  std::vector<T*> ps;
+  std::vector<Position<D>> xNews;
+
+  Move(const Euclidean<D>& g, std::vector<T*> ps) : g(g), ps(ps) {
+    xNews.reserve(ps.size());
+    for (T* p : ps) {
+      xNews.push_back(g.act((Position<D>)p->x));
+    }
+  }
+
+  void insert(T* p) {
+    ps.push_back(p);
+    xNews.push_back(g.act(p->x));
+  }
+
+  bool anyMarked() const {
+    for (const T* p : ps) {
+      if (p->m) {
+        return true;
+      }
+    }
+
+    return false;
+  }
+
+  unsigned size() const {
+    return ps.size();
+  }
+
+  double ΔE(const T& n) const {
+    double e = 0;
+
+    for (unsigned i = 0; i < ps.size(); i++) {
+      if (&n == ps[i]) {
+        return 0;
+      } else {
+        e += n.U(xNews[i], ps[i]->r) - n.U(ps[i]->x, ps[i]->r);
+      }
+    }
+
+    return e;
+  }
+};
+
+
 template <int D, Particle<D> T> class Model {
 private:
-  bool metropolisAccept(double β, double ΔE, Rng& r) const {
+  bool metropolisAccept(double β, double ΔE, Rng& r, double a = 1.0) const {
     return ΔE < 0 || exp(-β * ΔE) > r.uniform(0.0, 1.0);
   }
 
@@ -208,6 +256,13 @@ public:
     p.x = x;
   }
 
+  void execute(Move<D, T>& m) {
+    for (unsigned i = 0; i < m.size(); i++) {
+      move(*(m.ps[i]), m.xNews[i]);
+      m.ps[i]->m = true;
+    }
+  }
+
   bool move(double β, T& p, const Vector<D>& Δx, Rng& r) {
     Position<D> xNew = p.x + Δx;
     double ΔE = 0;
@@ -270,37 +325,56 @@ public:
     return move(β, r.pick(particles), Δx, r);
   }
 
-  unsigned clusterFlip(double β, const Euclidean<D>& R, T& p0, Rng& r) {
+  unsigned clusterFlip(double β, const Euclidean<D>& R, Move<D, T>& m0, Rng& r) {
     unsigned n = 0;
-    std::queue<T*> q;
-    q.push(&p0);
+    std::queue<Move<D, T>> q;
+    q.push(m0);
 
     while (!q.empty()) {
-      T* p = q.front();
+      Move<D, T> m = q.front();
       q.pop();
 
-      if (!p->m) {
-        p->m = true;
-        Position<D> xNew = R.act(p->x);
+      if (!m.anyMarked()) {
+        std::set<T*> neighbors = {};
+        for (unsigned i = 0; i < m.ps.size(); i++) {
+          std::set<T*> pNeighbors = nl.neighborsOf(m.ps[i]->x);
+          std::set<T*> pNeighborsNew = nl.neighborsOf(m.xNews[i]);
+          neighbors.insert(pNeighbors.begin(), pNeighbors.end());
+          neighbors.insert(pNeighborsNew.begin(), pNeighborsNew.end());
+        }
+        double ΔEmax = 0;
+        T* pMax = NULL;
 
-        for (T* neighbor : nl.neighborsOf(xNew)) {
+        for (T* neighbor : neighbors) {
           if (!neighbor->m) {
-            double ΔE = neighbor->U(xNew, p->r) - neighbor->U(p->x, p->r);
+            double ΔE = m.ΔE(*neighbor);
+            if (ΔE > ΔEmax) {
+              ΔEmax = ΔE;
+              pMax = neighbor;
+            }
+          }
+        }
+
+        if (pMax != NULL) {
+          if (1 - 1e2 * exp(-β * ΔEmax) > r.uniform(0.0, 1.0)) {
+            m.insert(pMax);
+          }
+        }
+        
+        for (T* neighbor : neighbors) {
+          if (!neighbor->m) {
+            double ΔE = m.ΔE(*neighbor);
             if (1 - exp(-β * ΔE) > r.uniform(0.0, 1.0)) {
-              q.push(neighbor);
+              q.push(Move<D, T>(R, {neighbor}));
             }
           }
         }
 
-        move(*p, xNew);
-        n++;
+        execute(m);
+        n += m.size();;
       }
     }
 
-    for (T& p : particles) {
-      p.m = false;
-    }
-
     if (n > particles.size() / 2) {
       orientation = R.act(orientation);
     }
@@ -325,7 +399,9 @@ public:
 
     Euclidean<2> g(t - mat * t, mat);
 
-    return clusterFlip(β, g, s1, r);
+    Move<D, T> m(g, {&s1, &s2});
+
+    return clusterFlip(β, g, m, r);
   }
 
   unsigned randomClusterSwap(double β, Rng& r) {