From 2242fd6f8b7f16b706d49a2288da3aa20f12314b Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 13 Feb 2020 15:00:31 -0500
Subject: Added gitignore and fixed Ising to work with new paradigm

---
 .gitignore           |   7 ++
 ising.cpp            | 250 +++++++++++++++++++++++++++++++--------------------
 octree.hpp           |  19 +++-
 random.hpp           |   6 ++
 space_wolff.hpp      | 172 +----------------------------------
 spheres_infinite.cpp |  46 +++++-----
 spin.hpp             |   2 +
 torus_symmetries.hpp |   2 +-
 transformation.hpp   | 201 +++++++++++++++++++++++++++++++++++++++++
 9 files changed, 412 insertions(+), 293 deletions(-)
 create mode 100644 .gitignore
 create mode 100644 random.hpp
 create mode 100644 transformation.hpp

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..dac4c22
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,7 @@
+*
+!*.hpp
+!*.cpp
+!.gitignore
+!.gitmodules
+*/
+
diff --git a/ising.cpp b/ising.cpp
index 1987a8f..38dce3b 100644
--- a/ising.cpp
+++ b/ising.cpp
@@ -1,14 +1,53 @@
 
+#include "smiley.hpp"
 #include "space_wolff.hpp"
+#include "torus_symmetries.hpp"
+#include <GL/glut.h>
+
+const unsigned D = 2;
+typedef Model<signed, D, TorusGroup<signed, D>, signed> model;
+
+class animation : public measurement<signed, D, TorusGroup<signed, D>, signed> {
+private:
+  uint64_t t1;
+  uint64_t t2;
+  unsigned n;
+  unsigned tmp;
+
+public:
+  animation(double L, unsigned w, int argc, char* argv[]) {
+    t1 = 0;
+    t2 = 0;
+    n = 0;
+
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(w, w);
+    glutCreateWindow("wolff");
+    glClearColor(0.0, 0.0, 0.0, 0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0, L, 0, L);
+  }
 
-std::function<double(spin<signed, 2, signed>)> B_sin(unsigned L, unsigned n, double H) {
-  return [n, H, L] (spin<signed, 2, signed> s) -> double {
-    return H * s.s * cos(2 * M_PI * n * s.x(0) / ((double)L));
-  };
-}
+  void post_cluster(const model& m) override {
+    glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
+    glClear(GL_COLOR_BUFFER_BIT);
+    glClearColor(0.0, 1.0, 0.0, 0.0);
+    for (const Spin<signed, 2, signed>* s : m.s) {
+      if (s->s == 1) {
+        glColor3f(0.0, 0.0, 0.0);
+      } else if (s->s == -1) {
+        glColor3f(1.0, 1.0, 1.0);
+      }
+      Vector<signed, 2> xx = m.s0.inverse().act(*s).x;
+      glRecti(xx(0), xx(1), xx(0) + 1, xx(1) + 1);
+    }
+    glFlush();
+  }
+};
 
 int main(int argc, char* argv[]) {
-  const unsigned D = 2;
 
   unsigned L = 32;
   unsigned N = 1000;
@@ -23,120 +62,133 @@ int main(int argc, char* argv[]) {
 
   while ((opt = getopt(argc, argv, "N:L:T:H:e:m:M:n:")) != -1) {
     switch (opt) {
-      case 'N': 
-        N = (unsigned)atof(optarg);
-        break;
-      case 'L':
-        L = atoi(optarg);
-        break;
-      case 'T':
-        T = atof(optarg);
-        break;
-      case 'H':
-        H = atof(optarg);
-        break;
-      case 'e':
-        ε = atof(optarg);
-        break;
-      case 'm':
-        mod = atoi(optarg);
-        break;
-      case 'M':
-        multi = atoi(optarg);
-        break;
-      case 'n':
-        mag = atof(optarg);
-        break;
-      default:
-        exit(1);
+    case 'N':
+      N = (unsigned)atof(optarg);
+      break;
+    case 'L':
+      L = atoi(optarg);
+      break;
+    case 'T':
+      T = atof(optarg);
+      break;
+    case 'H':
+      H = atof(optarg);
+      break;
+    case 'e':
+      ε = atof(optarg);
+      break;
+    case 'm':
+      mod = atoi(optarg);
+      break;
+    case 'M':
+      multi = atoi(optarg);
+      break;
+    case 'n':
+      mag = atof(optarg);
+      break;
+    default:
+      exit(1);
     }
   }
 
   double pZ = 1.0 - exp(-1.0 / T);
 
-  std::function<double(spin<signed, D, signed>, spin<signed, D, signed>)> Z =
-    [L, pZ] (spin<signed, D, signed> s1, spin<signed, D, signed> s2) -> double {
-      bool old_one_one = false;
-      bool old_many_ones = false;
-      bool old_any_two = false;
-
-      vector<signed, D> old_diff = diff<signed, D>(L, s1.x, s2.x);
-      
-      for (unsigned i = 0; i < D; i++) {
-        if (old_diff(i) == 1 && !old_one_one) {
-          old_one_one = true;
-        } else if (old_diff(i) == 1 && old_one_one) {
-          old_many_ones = true;
-        } else if (old_diff(i) > 1) {
-          old_any_two = true;
-        }
+  std::function<double(const Spin<signed, D, signed>&, const Spin<signed, D, signed>&)> Z =
+      [L, pZ](const Spin<signed, D, signed>& s1, const Spin<signed, D, signed>& s2) -> double {
+    bool old_one_one = false;
+    bool old_many_ones = false;
+    bool old_any_two = false;
+
+    Vector<signed, D> old_diff = diff<signed, D>(L, s1.x, s2.x);
+
+    for (unsigned i = 0; i < D; i++) {
+      if (old_diff(i) == 1 && !old_one_one) {
+        old_one_one = true;
+      } else if (old_diff(i) == 1 && old_one_one) {
+        old_many_ones = true;
+      } else if (old_diff(i) > 1) {
+        old_any_two = true;
       }
+    }
 
-      bool were_on_someone = !old_one_one && !old_any_two;
-      bool were_nearest_neighbors = old_one_one && !old_many_ones && !old_any_two;
-
-      if (were_on_someone) {
-        return -std::numeric_limits<double>::infinity();;
-      } else if (were_nearest_neighbors) {
-        return s1.s * s2.s;
-      } else {
-        return 0.0;
-      }
-    };
-
-  std::function<double(spin<signed, D, signed>)> B_face =
-    [L, H] (spin<signed, D, signed> s) -> double {
-      return H * s.s * smiley[s.x(0) * 16 / L][s.x(1) * 16 / L];
-    };
-
-  std::function<double(spin<signed, D, signed>)> B;
+    bool were_on_someone = !old_one_one && !old_any_two;
+    bool were_nearest_neighbors = old_one_one && !old_many_ones && !old_any_two;
 
-  if (mod > 0) {
-    B = B_sin(L, mod, H);
-  } else {
-    B = B_face;
-  }
+    if (were_on_someone) {
+      return -std::numeric_limits<double>::infinity();
+      ;
+    } else if (were_nearest_neighbors) {
+      return s1.s * s2.s;
+    } else {
+      return 0.0;
+    }
+  };
 
-  std::function<std::set<unsigned>(model<signed, D, signed>&, unsigned, spin<signed, D, signed>)> neighbors =
-    [] (model<signed, D, signed>& m, unsigned i0, spin<signed, D, signed> s1) -> std::set<unsigned> {
-      std::set<unsigned> nn;
-      if (i0 < m.s.size()) {
-        std::set<unsigned> nn0 = m.dict.neighbors(m.s[i0].x, 1);
-        std::set<unsigned> nn1 = m.dict.neighbors(s1.x, 1);
-        nn.insert(nn0.begin(), nn0.end());
-        nn.insert(nn1.begin(), nn1.end());
-        nn.insert(m.s.size());
-      } else {
-        for (unsigned i = 0; i < m.s.size(); i++) {
-          nn.insert(i);
-        }
-      }
-      return nn;
-    };
+  std::function<double(const Spin<signed, D, signed>&)> B_face =
+      [L, H](const Spin<signed, D, signed>& s) -> double {
+    return H * s.s * smiley[15 - s.x(1) * 16 / L][s.x(0) * 16 / L];
+  };
 
-  model<signed, D, signed> ising(L, L, Z, B, neighbors);
+  std::function<double(Spin<signed, D, signed>)> B = B_face;
 
-  randutils::auto_seed_128 seeds;
-  std::mt19937 rng{seeds};
+  Model<signed, D, TorusGroup<signed, D>, signed> ising(L, Z, B);
 
-  std::uniform_int_distribution<unsigned> coin(0, 1);
+  Rng rng;
 
   unsigned n = 0;
   unsigned up = 0;
   unsigned down = 0;
   for (unsigned i = 0; i < L; i++) {
     for (unsigned j = 0; j < L; j++) {
-      if ((coin(rng) && up < pow(L, 2) * mag) || down >= pow(L, 2) * mag) {
-        ising.s.push_back({{i, j}, 1});
+      Spin<signed, D, signed>* ss = new Spin<signed, D, signed>();
+      ss->x = {i, j};
+      if (rng.uniform<double>(0, 1) < mag) {
+        ss->s = 1;
         up++;
       } else {
-        ising.s.push_back({{i, j}, -1});
+        ss->s = -1;
         down++;
       }
-      ising.dict.record({i, j}, n);
+      ising.s.push_back(ss);
+      ising.dict.insert(ss);
       n++;
     }
   }
+
+  std::vector<Vector<signed, 2>> torusVectors = torus_vecs<signed, 2>(L);
+  std::vector<Matrix<signed, 2>> torusMatrices = torus_mats<signed, 2>();
+
+  Gen<signed, D, TorusGroup<signed, D>, signed> g =
+      [L, &torusVectors,
+       &torusMatrices](Model<signed, D, TorusGroup<signed, D>, signed>& M,
+                       Rng& r) -> Transformation<signed, D, TorusGroup<signed, D>, signed>* {
+    Matrix<signed, 2> m;
+    Vector<signed, 2> t;
+
+    m = r.pick(torusMatrices);
+    t(0) = r.uniform<signed>(0, L);
+    t(1) = r.uniform<signed>(0, L);
+    t = t - m * t;
+
+    TorusGroup<signed, 2> g = TorusGroup<signed, 2>({(signed)L, t, m});
+
+    Spin<signed, 2, signed>* ss = r.pick(M.s);
+    Spin<signed, 2, signed> s2 = g.act(*ss);
+
+    while (ss->x(0) == s2.x(0) && ss->x(1) == s2.x(1)) {
+      ss = r.pick(M.s);
+      s2 = g.act(*ss);
+    }
+
+    std::set<Spin<signed, 2, signed>*> s2s = M.dict.at(s2.x);
+
+    return new PairFlip<signed, 2, TorusGroup<signed, 2>, signed>(M, g, ss, *s2s.begin());
+  };
+
+  animation A(L, 750, argc, argv);
+
+  ising.wolff(T, {g}, A, N);
+
   /*
   for (unsigned i = 0; i < L; i++) {
     for (unsigned j = 0; j < L; j++) {
@@ -151,8 +203,7 @@ int main(int argc, char* argv[]) {
   }
   */
 
-  ising.update_energy();
-
+  /*
   while (true) {
     ising.wolff(T, N, rng);
     std::array<double, 2> τ = ising.Eq.τ();
@@ -168,8 +219,8 @@ int main(int argc, char* argv[]) {
   std::array<double, 2> act = ising.Eq.τ();
   std::vector<double> ρ = ising.Eq.ρ();
 
-  outfile << L << " " << T << " " << mod << " " << H << " " << ising.Eq.num_added() << " " << ising.Cq.avg() << " " << ising.Cq.serr() << " " << act[0] << " " << act[1];
-  for (double ρi : ρ) {
+  outfile << L << " " << T << " " << mod << " " << H << " " << ising.Eq.num_added() << " " <<
+  ising.Cq.avg() << " " << ising.Cq.serr() << " " << act[0] << " " << act[1]; for (double ρi : ρ) {
     outfile << " " << ρi;
   }
   outfile << "\n";
@@ -195,6 +246,7 @@ int main(int argc, char* argv[]) {
   }
 
   snapfile.close();
+  */
 
   return 0;
 }
diff --git a/octree.hpp b/octree.hpp
index 1be6e0a..bb13242 100644
--- a/octree.hpp
+++ b/octree.hpp
@@ -5,6 +5,8 @@
 #include <set>
 #include <unordered_map>
 
+#include <iostream>
+
 #include "spin.hpp"
 #include "vector.hpp"
 
@@ -31,16 +33,16 @@ private:
   std::unordered_map<std::array<signed, D>, std::set<Spin<T, D, S>*>> data;
 
 public:
-  Octree(T L, unsigned N) {
-    L = L;
-    N = N;
+  Octree(T L_tmp, unsigned N_tmp) {
+    L = L_tmp;
+    N = N_tmp;
   }
 
   std::array<signed, D> ind(Vector<T, D> x) const {
     std::array<signed, D> ind;
 
     for (unsigned i = 0; i < D; i++) {
-      ind[i] = (signed)std::floor(N * x(i) / L);
+      ind[i] = std::floor(N * x(i) / L);
     }
 
     return ind;
@@ -55,6 +57,15 @@ public:
     }
   };
 
+  std::set<Spin<T, D, S>*> at(const Vector<T, D>& x) const {
+    auto it = data.find(ind(x));
+    if (it == data.end()) {
+      return {};
+    } else {
+      return it->second;
+    }
+  }
+
   std::set<Spin<T, D, S>*> neighbors(const Vector<T, D>& x) const {
     std::array<signed, D> i0 = ind(x);
     std::set<Spin<T, D, S>*> ns;
diff --git a/random.hpp b/random.hpp
new file mode 100644
index 0000000..9f1d33d
--- /dev/null
+++ b/random.hpp
@@ -0,0 +1,6 @@
+#pragma once
+
+#include "pcg-cpp/include/pcg_random.hpp"
+#include "randutils/randutils.hpp"
+
+using Rng = randutils::random_generator<pcg32>;
diff --git a/space_wolff.hpp b/space_wolff.hpp
index 8ea7dfb..c4a7a21 100644
--- a/space_wolff.hpp
+++ b/space_wolff.hpp
@@ -7,15 +7,12 @@
 #include <queue>
 #include <vector>
 
-#include "pcg-cpp/include/pcg_random.hpp"
-#include "randutils/randutils.hpp"
-
 #include "euclidean.hpp"
 #include "octree.hpp"
 #include "quantity.hpp"
 #include "spin.hpp"
-
-using Rng = randutils::random_generator<pcg32>;
+#include "random.hpp"
+#include "transformation.hpp"
 
 template <class U, int D, class R, class S> class Model;
 
@@ -35,175 +32,12 @@ public:
 };
 
 
-template <class U, int D, class R, class S> class Transformation {
-  public:
-    virtual std::set<Spin<U, D, S>*> current() const {return {NULL};}
-    virtual std::set<Spin<U, D, S>*> toConsider() const {return {};}
-    virtual double ΔE(const Spin<U, D, S>*) const {return 0;}
-    virtual Transformation* createNew(Spin<U, D, S>*) const {return new Transformation();}
-    virtual void apply();
-};
-
-template <class U, int D, class R, class S> using Gen = std::function<Transformation<U, D, R, S>*(Model<U, D, R, S>&, Rng&)>;
-
-template <class U, int D, class R, class S> class SpinFlip : public Transformation<U, D, R, S> {
-  private:
-    Model<U, D, R, S>& M;
-    Spin<U, D, S>& sOld;
-    const R r;
-    Spin<U, D, S>  sNew;
-  public:
-    SpinFlip(Model<U, D, R, S>& M, const R& r, Spin<U, D, S>& s) : M(M), r(r), sOld(s) {
-      sNew = r.act(s);
-    }
-
-    std::set<Spin<U, D, S>*> current() const override {
-      return {&sOld};
-    }
-
-    std::set<Spin<U, D, S>*> toConsider() const override {
-      std::set<Spin<U, D, S>*> neighbors;
-      std::set<Spin<U, D, S>*> current_neighbors = M.dict.neighbors(sOld.x);
-      std::set<Spin<U, D, S>*> new_neighbors = M.dict.neighbors(sNew.x);
-
-      neighbors.insert(current_neighbors.begin(), current_neighbors.end());
-      neighbors.insert(new_neighbors.begin(), new_neighbors.end());
-      neighbors.insert(NULL);
-
-      return neighbors;
-    }
-
-    double ΔE(const Spin<U, D, S>* s) const override {
-      if (s == NULL) {
-        Spin<U, D, S> s0s_old = M.s0.inverse().act(sOld);
-        Spin<U, D, S> s0s_new = M.s0.inverse().act(sNew);
-        return M.B(s0s_new) - M.B(s0s_old);
-      } else {
-        return M.Z(sOld, *s) - M.Z(sNew, *s);
-      }
-    }
-
-    Transformation<U, D, R, S>* createNew(Spin<U, D, S>* s) const override;
-
-    void apply() override {
-      M.dict.remove(&sOld);
-      sOld = sNew;
-      M.dict.insert(&sOld);
-    }
-};
-
-template <class U, int D, class R, class S> class PairFlip : public Transformation<U, D, R, S> {
-  private:
-    Model<U, D, R, S>& M;
-    Spin<U, D, S>& s1Old;
-    Spin<U, D, S>& s2Old;
-    const R r;
-    Spin<U, D, S>  s1New;
-    Spin<U, D, S>  s2New;
-  public:
-    PairFlip(Model<U, D, R, S>& M, const R& r, Spin<U, D, S>& s1, Spin<U, D, S>& s2) : M(M), r(r), s1Old(s1), s2Old(s2) {
-      s1New = r.act(s1);
-      s2New = r.act(s2);
-    }
-
-    std::set<Spin<U, D, S>*> current() const override {
-      return {&s1Old, &s2Old};
-    }
-
-    std::set<Spin<U, D, S>*> toConsider() const override {
-      std::set<Spin<U, D, S>*> neighbors;
-      std::set<Spin<U, D, S>*> current_neighbors_1 = M.dict.neighbors(s1Old.x);
-      std::set<Spin<U, D, S>*> current_neighbors_2 = M.dict.neighbors(s2Old.x);
-      std::set<Spin<U, D, S>*> new_neighbors_1 = M.dict.neighbors(s1New.x);
-      std::set<Spin<U, D, S>*> new_neighbors_2 = M.dict.neighbors(s2New.x);
-
-      neighbors.insert(current_neighbors_1.begin(), current_neighbors_1.end());
-      neighbors.insert(current_neighbors_2.begin(), current_neighbors_2.end());
-      neighbors.insert(new_neighbors_1.begin(), new_neighbors_1.end());
-      neighbors.insert(new_neighbors_2.begin(), new_neighbors_2.end());
-      neighbors.insert(NULL);
-
-      return neighbors;
-    }
-
-    double ΔE(const Spin<U, D, S>* s) const override {
-      if (s == NULL) {
-        Spin<U, D, S> s0s1_old = M.s0.inverse().act(s1Old);
-        Spin<U, D, S> s0s1_new = M.s0.inverse().act(s1New);
-        Spin<U, D, S> s0s2_old = M.s0.inverse().act(s2Old);
-        Spin<U, D, S> s0s2_new = M.s0.inverse().act(s2New);
-        return M.B(s0s1_new) + M.B(s0s2_new) - M.B(s0s1_old) - M.B(s0s2_old);
-      } else {
-        return M.Z(s1Old, *s) + M.Z(s2Old, *s) - M.Z(s1New, *s) - M.Z(s2New, *s);
-      }
-    }
-
-    Transformation<U, D, R, S>* createNew(Spin<U, D, S>* s) const override;
-
-    void apply() override {
-      M.dict.remove(&s1Old);
-      M.dict.remove(&s2Old);
-      s1Old = s1New;
-      s2Old = s2New;
-      M.dict.insert(&s1Old);
-      M.dict.insert(&s2Old);
-    }
-};
-
-template <class U, int D, class R, class S> class FieldFlip : public Transformation<U, D, R, S> {
-  private:
-    Model<U, D, R, S>& M;
-    const R r;
-    R s0New;
-  public:
-    FieldFlip(Model<U, D, R, S>& M, const R& r) : M(M), r(r), s0New(r.act(M.s0)) {}
-
-    std::set<Spin<U, D, S>*> toConsider() const override {
-      std::set<Spin<U, D, S>*> neighbors;
-
-      for (Spin<U, D, S>& s : M.s) {
-        neighbors.insert(&s);
-      }
-
-      return neighbors;
-    }
-
-    double ΔE(const Spin<U, D, S>* s) const override {
-      Spin<U, D, S> s0s_old = M.s0.inverse().act(*s);
-      Spin<U, D, S> s0s_new = s0New.inverse().act(*s);
-      return M.B(s0s_new) - M.B(s0s_old);
-    }
-
-    Transformation<U, D, R, S>* createNew(Spin<U, D, S>* s) const override {
-      return new SpinFlip<U, D, R, S>(M, r, *s);
-    }
-
-    void apply() override {
-      M.s0 = s0New;
-    }
-};
-
-template<class U, int D, class R, class S> Transformation<U, D, R, S>* SpinFlip<U, D, R, S>::createNew(Spin<U, D, S>* s) const {
-  if (s == NULL) {
-    return new FieldFlip<U, D, R, S>(M, r);
-  } else {
-    return new SpinFlip(M, r, *s);
-  }
-}
-
-template<class U, int D, class R, class S> Transformation<U, D, R, S>* PairFlip<U, D, R, S>::createNew(Spin<U, D, S>* s) const {
-  if (s == NULL) {
-    return new FieldFlip<U, D, R, S>(M, r);
-  } else {
-    return new SpinFlip<U, D, R, S>(M, r, *s);
-  }
-}
 
 template <class U, int D, class R, class S> class Model {
 public:
   U L;
   R s0;
-  std::vector<Spin<U, D, S>> s;
+  std::vector<Spin<U, D, S>*> s;
   Octree<U, D, S> dict;
   std::function<double(const Spin<U, D, S>&, const Spin<U, D, S>&)> Z;
   std::function<double(const Spin<U, D, S>&)> B;
diff --git a/spheres_infinite.cpp b/spheres_infinite.cpp
index 3505d6d..026486e 100644
--- a/spheres_infinite.cpp
+++ b/spheres_infinite.cpp
@@ -41,13 +41,13 @@ public:
   void post_cluster(const model& m) override {
     glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
     glClear(GL_COLOR_BUFFER_BIT);
-    for (const Spin<double, 2, double>& s : m.s) {
+    for (const Spin<double, 2, double>* s : m.s) {
       glBegin(GL_POLYGON);
       unsigned n_points = 50;
       glColor3f(0.0f, 0.0f, 0.0f);
       for (unsigned i = 0; i < n_points; i++) {
-        glVertex2d(m.s0.inverse().act(s).x(0) + s.s * cos(2 * i * M_PI / n_points),
-                   m.s0.inverse().act(s).x(1) + s.s * sin(2 * i * M_PI / n_points));
+        glVertex2d(m.s0.inverse().act(*s).x(0) + s->s * cos(2 * i * M_PI / n_points),
+                   m.s0.inverse().act(*s).x(1) + s->s * sin(2 * i * M_PI / n_points));
       }
       glEnd();
     }
@@ -78,14 +78,14 @@ Gen<double, D, Euclidean<double, D>, double> eGen(double ε) {
     m(0, 1) = -2 * cos(θ) * sin(θ);
     m(1, 0) = -2 * cos(θ) * sin(θ);
 
-    unsigned f_ind = rng.uniform((unsigned)0, (unsigned)M.s.size());
-    t =  M.s[f_ind].x;
+    Spin<double, D, double>* s = rng.pick(M.s);
+    t = s->x;
     for (unsigned j = 0; j < D; j++) {
       t(j) += rng.variate<double, std::normal_distribution>(0.0, ε);
     }
 
     Euclidean<double, D> g(t - m * t, m);
-    return new SpinFlip<double, D, Euclidean<double, D>, double>(M, g, M.s[f_ind]);
+    return new SpinFlip<double, D, Euclidean<double, D>, double>(M, g, s);
   };
 }
 
@@ -93,12 +93,15 @@ Gen<double, D, Euclidean<double, D>, double> mGen(double ε) {
   return [ε](model& M, Rng& rng) -> Transformation<double, D, Euclidean<double, D>, double>* {
     Matrix<double, D> m;
 
-    unsigned f_ind1 = rng.uniform((unsigned)0, (unsigned)M.s.size());
-    unsigned f_ind2 = rng.uniform((unsigned)0, (unsigned)M.s.size() - 1);
-    if (f_ind2 >= f_ind1) f_ind2++;
+    Spin<double, D, double>* s1 = rng.pick(M.s);
+    Spin<double, D, double>* s2 = rng.pick(M.s);
 
-    Vector<double, D> t1 = M.s[f_ind1].x;
-    Vector<double, D> t2 = M.s[f_ind2].x;
+    while (s1 == s2) {
+      s2 = rng.pick(M.s);
+    }
+
+    Vector<double, D> t1 = s1->x;
+    Vector<double, D> t2 = s2->x;
     Vector<double, D> t12 = t1 - t2;
     Vector<double, D> t = (t1 + t2) / 2;
 
@@ -110,7 +113,7 @@ Gen<double, D, Euclidean<double, D>, double> mGen(double ε) {
     m(1, 0) = -2 * cos(θ) * sin(θ);
 
     Euclidean<double, D> g(t - m * t, m);
-    return new PairFlip<double, D, Euclidean<double, D>, double>(M, g, M.s[f_ind1], M.s[f_ind2]);
+    return new PairFlip<double, D, Euclidean<double, D>, double>(M, g, s1, s2);
   };
 }
 
@@ -179,17 +182,19 @@ int main(int argc, char* argv[]) {
   auto g1 = eGen(0.5);
   auto g2 = mGen(0.2);
   animation A(L, 750, argc, argv);
-  model sphere(1, Z, B);
+  model sphere(1.0, Z, B);
 
   Rng rng;
 
-  sphere.s.reserve(n);
+  sphere.s.resize(n);
 
   unsigned nx = floor(sqrt(n));
-  for (unsigned i = 0; i < n; i++) {
-    Vector<double, D> pos = {(i / nx) * L / nx, (i % nx) * L / nx};
-    sphere.s.push_back({pos, rng.uniform<double>(0.25, 0.45)});
-    sphere.dict.insert(&sphere.s.back());
+  for (unsigned i = 0; i < sphere.s.size(); i++) {
+    Spin<double, 2, double>* ss = new Spin<double, 2, double>();
+    ss->x = {(i / nx) * L / nx, (i % nx) * L / nx};
+    ss->s = rng.uniform<double>(0.25, 0.45);
+    sphere.s[i] = ss;
+    sphere.dict.insert(ss);
   }
 
   sphere.wolff(T, {g1, g2}, A, N);
@@ -212,9 +217,10 @@ int main(int argc, char* argv[]) {
   std::ofstream snapfile;
   snapfile.open("sphere_snap.dat");
 
-  for (Spin<double, D, double> s : sphere.s) {
-    Spin<double, D, double> rs = sphere.s0.inverse().act(s);
+  for (Spin<double, D, double>* s : sphere.s) {
+    Spin<double, D, double> rs = sphere.s0.inverse().act(*s);
     snapfile << rs.x.transpose() << "\n";
+    delete s;
   }
 
   snapfile.close();
diff --git a/spin.hpp b/spin.hpp
index d4d39cc..bb8369b 100644
--- a/spin.hpp
+++ b/spin.hpp
@@ -7,5 +7,7 @@ template <class T, int D, class S> class Spin {
 public:
   Vector<T, D> x;
   S s;
+
+  Spin() { x = Vector<T, D>::Zero(); }
 };
 
diff --git a/torus_symmetries.hpp b/torus_symmetries.hpp
index 17772de..7bcb70b 100644
--- a/torus_symmetries.hpp
+++ b/torus_symmetries.hpp
@@ -56,7 +56,7 @@ template <class U, int D> std::vector<Matrix<U, D>> torus_mats() {
 
   one_sequences<D>(sequences, D);
 
-  sequences.pop_front(); // don't want the identity matrix!
+  sequences.pop_back(); // don't want the identity matrix!
 
   for (std::array<double, D> sequence : sequences) {
     Matrix<U, D> m;
diff --git a/transformation.hpp b/transformation.hpp
new file mode 100644
index 0000000..0731ec9
--- /dev/null
+++ b/transformation.hpp
@@ -0,0 +1,201 @@
+#pragma once
+
+#include <set>
+
+#include "random.hpp"
+#include "spin.hpp"
+
+template <class U, int D, class R, class S> class Model;
+
+template <class U, int D, class R, class S> class Transformation {
+public:
+  virtual std::set<Spin<U, D, S>*> current() const { return {NULL}; }
+  virtual std::set<Spin<U, D, S>*> toConsider() const { return {}; }
+  virtual double ΔE(const Spin<U, D, S>*) const { return 0; }
+  virtual Transformation* createNew(Spin<U, D, S>*) const { return new Transformation(); }
+  virtual void apply(){};
+};
+
+template <class U, int D, class R, class S>
+using Gen = std::function<Transformation<U, D, R, S>*(Model<U, D, R, S>&, Rng&)>;
+
+template <class U, int D, class R, class S> class SpinFlip : public Transformation<U, D, R, S> {
+private:
+  Model<U, D, R, S>& M;
+  Spin<U, D, S>* sOld;
+  const R r;
+  Spin<U, D, S> sNew;
+
+public:
+  SpinFlip(Model<U, D, R, S>& M, const R& r, Spin<U, D, S>* s) : M(M), r(r) {
+    sOld = s;
+    sNew = r.act(*s);
+  }
+
+  std::set<Spin<U, D, S>*> current() const override { return {sOld}; }
+
+  std::set<Spin<U, D, S>*> toConsider() const override {
+    std::set<Spin<U, D, S>*> neighbors;
+    std::set<Spin<U, D, S>*> current_neighbors = M.dict.neighbors(sOld->x);
+    std::set<Spin<U, D, S>*> new_neighbors = M.dict.neighbors(sNew.x);
+
+    neighbors.insert(current_neighbors.begin(), current_neighbors.end());
+    neighbors.insert(new_neighbors.begin(), new_neighbors.end());
+    neighbors.insert(NULL);
+
+    return neighbors;
+  }
+
+  double ΔE(const Spin<U, D, S>* s) const override {
+    if (s == NULL) {
+      Spin<U, D, S> s0s_old = M.s0.inverse().act(*sOld);
+      Spin<U, D, S> s0s_new = M.s0.inverse().act(sNew);
+      return M.B(s0s_new) - M.B(s0s_old);
+    } else {
+      return M.Z(*sOld, *s) - M.Z(sNew, *s);
+    }
+  }
+
+  Transformation<U, D, R, S>* createNew(Spin<U, D, S>* s) const override;
+
+  void apply() override {
+    M.dict.remove(sOld);
+    *sOld = sNew;
+    M.dict.insert(sOld);
+  }
+};
+
+template <class U, int D, class R, class S> class PairFlip : public Transformation<U, D, R, S> {
+private:
+  Model<U, D, R, S>& M;
+  Spin<U, D, S>* s1Old;
+  Spin<U, D, S>* s2Old;
+  const R r;
+  Spin<U, D, S> s1New;
+  Spin<U, D, S> s2New;
+
+public:
+  PairFlip(Model<U, D, R, S>& M, const R& r, Spin<U, D, S>* s1, Spin<U, D, S>* s2) : M(M), r(r) {
+    s1Old = s1;
+    s2Old = s2;
+    s1New = r.act(*s1);
+    s2New = r.act(*s2);
+  }
+
+  std::set<Spin<U, D, S>*> current() const override { return {s1Old, s2Old}; }
+
+  std::set<Spin<U, D, S>*> toConsider() const override {
+    std::set<Spin<U, D, S>*> neighbors;
+    std::set<Spin<U, D, S>*> current_neighbors_1 = M.dict.neighbors(s1Old->x);
+    std::set<Spin<U, D, S>*> current_neighbors_2 = M.dict.neighbors(s2Old->x);
+    std::set<Spin<U, D, S>*> new_neighbors_1 = M.dict.neighbors(s1New.x);
+    std::set<Spin<U, D, S>*> new_neighbors_2 = M.dict.neighbors(s2New.x);
+
+    neighbors.insert(current_neighbors_1.begin(), current_neighbors_1.end());
+    neighbors.insert(current_neighbors_2.begin(), current_neighbors_2.end());
+    neighbors.insert(new_neighbors_1.begin(), new_neighbors_1.end());
+    neighbors.insert(new_neighbors_2.begin(), new_neighbors_2.end());
+    neighbors.insert(NULL);
+
+    return neighbors;
+  }
+
+  double ΔE(const Spin<U, D, S>* s) const override {
+    if (s == NULL) {
+      Spin<U, D, S> s0s1_old = M.s0.inverse().act(*s1Old);
+      Spin<U, D, S> s0s1_new = M.s0.inverse().act(s1New);
+      Spin<U, D, S> s0s2_old = M.s0.inverse().act(*s2Old);
+      Spin<U, D, S> s0s2_new = M.s0.inverse().act(s2New);
+      return M.B(s0s1_new) + M.B(s0s2_new) - M.B(s0s1_old) - M.B(s0s2_old);
+    } else {
+      return M.Z(*s1Old, *s) + M.Z(*s2Old, *s) - M.Z(s1New, *s) - M.Z(s2New, *s);
+    }
+  }
+
+  Transformation<U, D, R, S>* createNew(Spin<double, D, S>* s) const;
+  Transformation<U, D, R, S>* createNew(Spin<signed, D, S>* s) const;
+
+  void apply() override {
+    M.dict.remove(s1Old);
+    M.dict.remove(s2Old);
+    *s1Old = s1New;
+    *s2Old = s2New;
+    M.dict.insert(s1Old);
+    M.dict.insert(s2Old);
+  }
+};
+
+template <class U, int D, class R, class S> class FieldFlip : public Transformation<U, D, R, S> {
+private:
+  Model<U, D, R, S>& M;
+  const R r;
+  R s0New;
+
+public:
+  FieldFlip(Model<U, D, R, S>& M, const R& r) : M(M), r(r), s0New(r.act(M.s0)) {}
+
+  std::set<Spin<U, D, S>*> toConsider() const override {
+    std::set<Spin<U, D, S>*> neighbors;
+
+    for (Spin<U, D, S>* s : M.s) {
+      neighbors.insert(s);
+    }
+
+    return neighbors;
+  }
+
+  double ΔE(const Spin<U, D, S>* s) const override {
+    Spin<U, D, S> s0s_old = M.s0.inverse().act(*s);
+    Spin<U, D, S> s0s_new = s0New.inverse().act(*s);
+    return M.B(s0s_new) - M.B(s0s_old);
+  }
+
+  Transformation<double, D, R, S>* createNew(Spin<double, D, S>* s) const {
+    return new SpinFlip<U, D, R, S>(M, r, s);
+  }
+
+  Transformation<signed, D, R, S>* createNew(Spin<signed, D, S>* s) const {
+    Vector<signed, 2> v = r.act(*s).x;
+    std::set<Spin<U, D, S>*> on_site = M.dict.at(v);
+    if (on_site.empty()) {
+      return new SpinFlip<U, D, R, S>(M, r, s);
+    } else {
+      return new PairFlip<U, D, R, S>(M, r, s, *on_site.begin());
+    }
+  }
+
+  void apply() override { M.s0 = s0New; }
+};
+
+template <class U, int D, class R, class S>
+Transformation<U, D, R, S>* SpinFlip<U, D, R, S>::createNew(Spin<U, D, S>* s) const {
+  if (s == NULL) {
+    return new FieldFlip<U, D, R, S>(M, r);
+  } else {
+    return new SpinFlip(M, r, s);
+  }
+}
+
+template <class U, int D, class R, class S>
+Transformation<U, D, R, S>* PairFlip<U, D, R, S>::createNew(Spin<double, D, S>* s) const {
+  if (s == NULL) {
+    return new FieldFlip<U, D, R, S>(M, r);
+  } else {
+    return new SpinFlip<U, D, R, S>(M, r, s);
+  }
+}
+
+template <class U, int D, class R, class S>
+Transformation<U, D, R, S>* PairFlip<U, D, R, S>::createNew(Spin<signed, D, S>* s) const {
+  if (s == NULL) {
+    return new FieldFlip<U, D, R, S>(M, r);
+  } else {
+    Vector<signed, 2> v = r.act(*s).x;
+    std::set<Spin<U, D, S>*> on_site = M.dict.at(v);
+    if (on_site.empty()) {
+      return new SpinFlip<U, D, R, S>(M, r, s);
+    } else {
+      return new PairFlip<U, D, R, S>(M, r, s, *on_site.begin());
+    }
+  }
+}
-- 
cgit v1.2.3-54-g00ecf