From f1f081fd1ddf00f86f0c561293715ead931887a2 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 26 Jul 2019 13:43:48 -0400
Subject: initial commit

---
 .gitmodules     |   3 +
 randutils       |   1 +
 space_wolff.cpp | 446 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 450 insertions(+)
 create mode 100644 .gitmodules
 create mode 160000 randutils
 create mode 100644 space_wolff.cpp

diff --git a/.gitmodules b/.gitmodules
new file mode 100644
index 0000000..0a97926
--- /dev/null
+++ b/.gitmodules
@@ -0,0 +1,3 @@
+[submodule "randutils"]
+	path = randutils
+	url = https://gist.github.com/imneme/540829265469e673d045/
diff --git a/randutils b/randutils
new file mode 160000
index 0000000..8486a61
--- /dev/null
+++ b/randutils
@@ -0,0 +1 @@
+Subproject commit 8486a610a954a8248c12485fb4cfc390a5f5f854
diff --git a/space_wolff.cpp b/space_wolff.cpp
new file mode 100644
index 0000000..b88944e
--- /dev/null
+++ b/space_wolff.cpp
@@ -0,0 +1,446 @@
+
+#include <vector>
+#include <list>
+#include <set>
+#include <iostream>
+#include <functional>
+#include <random>
+#include <queue>
+#include <eigen3/Eigen/Dense>
+#include "randutils/randutils.hpp"
+
+const std::array<std::array<unsigned, 16>, 16> smiley = 
+  {{
+    {{0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0}},
+    {{0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0}},
+    {{0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0}},
+    {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}},
+    {{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}},
+    {{1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1}},
+    {{1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1}},
+    {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}},
+    {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}},
+    {{1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1}},
+    {{1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1}},
+    {{1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1}},
+    {{0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0}},
+    {{0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0}},
+    {{0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0}},
+    {{0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0}}
+  }};
+
+template <class T, int D>
+using vector = Eigen::Matrix<T, D, 1>;
+
+template <class T, int D>
+using matrix = Eigen::Matrix<T, D, D>;
+
+template <class T, int D, class state>
+class spin {
+  public:
+    vector<T, D> x;
+    state s;
+};
+
+template <class T, int D>
+class euclidean {
+  private:
+    unsigned L;
+
+  public:
+    vector<T, D> t;
+    matrix<T, D> r;
+    euclidean(unsigned L) : L(L) {
+      for (unsigned i = 0; i < D; i++) {
+        t(i) = 0;
+        r(i, i) = 1;
+        for (unsigned j = 1; j < D; j++) {
+          r(i, (i + j) % D) = 0;
+        }
+      }
+    }
+
+    euclidean(unsigned L, vector<T, D> t0, matrix<T, D> r0) : L(L) {
+      t = t0;
+      r = r0;
+    }
+
+    template <class state>
+    spin<T, D, state> act(spin<T, D, state> s) {
+      spin<T, D, state> s_new;
+
+      s_new.x = t + r * s.x;
+      s_new.s = s.s;
+
+      for (unsigned i = 0; i < D; i++) {
+        s_new.x(i) = fmod(L + s_new.x(i), L);
+      }
+
+      return s_new;
+    }
+
+    euclidean act(const euclidean& x) {
+      vector<T, D> tnew = r * x.t + t;
+      matrix<T, D> rnew = r * x.r;
+
+      euclidean pnew(this->L, tnew, rnew);
+
+      return pnew;
+    }
+
+    euclidean inverse() {
+      vector<T, D> tnew = - r.transpose() * t;
+      matrix<T, D> rnew = r.transpose();
+
+      euclidean pnew(this->L, tnew, rnew);
+
+      return pnew;
+    }
+};
+
+template <int D>
+class dictionary {
+  private:
+    unsigned L;
+    std::vector<std::set<unsigned>> d;
+
+  public:
+    dictionary(unsigned Li) : L(Li), d(pow(Li, D)) {};
+
+    template <class T>
+    unsigned dictionary_index(vector<T, D> x) {
+      unsigned pos_ind = 0;
+
+      for (unsigned i = 0; i < D; i++) {
+        pos_ind += pow(L, i) * (unsigned)x(i);
+      };
+
+      return pos_ind;
+    }
+
+    template <class T>
+    void record(vector<T, D> x, unsigned ind) {
+      d[dictionary_index<T>(x)].insert(ind);
+    };
+
+    template <class T>
+    void remove(vector<T, D> x, unsigned ind) {
+      d[dictionary_index<T>(x)].erase(ind);
+    };
+
+    template <class T>
+    std::set<unsigned> on_site(vector<T, D> x) {
+      return d[dictionary_index<T>(x)];
+    };
+
+    template <class T>
+    std::set<unsigned> nearest_neighbors(vector<T, D> x) {
+      unsigned ind = dictionary_index<T>(x);
+      std::set<unsigned> ns;
+
+      for (unsigned i = 0; i < D; i++) {
+        for (signed j : {-1, 1}) {
+          unsigned ni = pow(L, i + 1) * (ind / ((unsigned)pow(L, i + 1))) + fmod(pow(L, i + 1) + ind + j * pow(L, i), pow(L, i + 1));
+          for (unsigned nii : d[ni]) {
+            ns.insert(nii);
+          }
+        }
+      }
+
+      return ns;
+    };
+
+    template <class T>
+    std::set<unsigned> next_nearest_neighbors(vector<T, D> x) {
+      unsigned ind = dictionary_index<T>(x);
+      std::set<unsigned> ns;
+
+      for (unsigned i = 0; i < D; i++) {
+        for (signed j : {-1, 1}) {
+          unsigned ni = pow(L, i + 1) * (ind / ((unsigned)pow(L, i + 1))) + fmod(pow(L, i + 1) + ind + j * pow(L, i), pow(L, i + 1));
+          for (unsigned k = 0; k < D; k++) {
+            if (k != i) {
+              for (signed l : {-1, 1}) {
+                unsigned nni = pow(L, k + 1) * (ni / ((unsigned)pow(L, k + 1))) + fmod(pow(L, k + 1) + ni + l * pow(L, k), pow(L, k + 1));
+                for (unsigned nnii : d[nni]) {
+                  ns.insert(nnii);
+                }
+              }
+            }
+          }
+        }
+      }
+
+      return ns;
+    };
+
+    template <class T>
+    std::set<unsigned> next_next_nearest_neighbors(vector<T, D> x) {
+      unsigned ind = dictionary_index<T>(x);
+      std::set<unsigned> ns;
+
+      for (unsigned i = 0; i < D; i++) {
+        for (signed j : {-1, 1}) {
+          unsigned ni = pow(L, i + 1) * (ind / ((unsigned)pow(L, i + 1))) + fmod(pow(L, i + 1) + ind + j * pow(L, i), pow(L, i + 1));
+          for (unsigned k = 0; k < D; k++) {
+            if (k != i) {
+              for (signed l : {-1, 1}) {
+                unsigned nni = pow(L, k + 1) * (ni / ((unsigned)pow(L, k + 1))) + fmod(pow(L, k + 1) + ni + l * pow(L, k), pow(L, k + 1));
+                for (unsigned m = 0; m < D; m++) {
+                  if (m != i && m != k) {
+                    for (signed n : {-1, 1}) {
+                      unsigned nnni = pow(L, m + 1) * (nni / ((unsigned)pow(L, m + 1))) + fmod(pow(L, m + 1) + nni + n * pow(L, m), pow(L, m + 1));
+                      for (unsigned nnnii : d[nnni]) {
+                        ns.insert(nnnii);
+                      }
+                    }
+                  }
+                }
+              }
+            }
+          }
+        }
+      }
+
+      return ns;
+    };
+};
+
+template <class U, int D, class state>
+class model {
+  public:
+    unsigned L;
+    euclidean<U, D> s0;
+    std::vector<spin<U, D, state>> s;
+    dictionary<D> dict;
+    std::function<std::set<unsigned>(model<U, D, state>&, unsigned, spin<U, D, state>)> neighbors;
+    std::function<double(spin<U, D, state>, spin<U, D, state>)> Z;
+    std::function<double(spin<U, D, state>)> B;
+    double E;
+
+    model(unsigned L, std::function<double(spin<U, D, state>, spin<U, D, state>)> Z,
+        std::function<double(spin<U, D, state>)> B,
+        std::function<std::set<unsigned>(model<U, D, state>&, unsigned, spin<U, D, state>)> ns) : 
+      L(L), s0(L), dict(L), neighbors(ns), Z(Z), B(B) {
+        }
+
+    void step(double T, unsigned ind, euclidean<U, D> r, std::mt19937& rng) {
+      std::uniform_real_distribution<double> dist(0.0, 1.0);
+
+      std::queue<unsigned> queue;
+      queue.push(ind);
+
+      std::vector<bool> visited(s.size() + 1, false);
+
+      while (!queue.empty()) {
+        unsigned i = queue.front();
+        queue.pop();
+
+        if (!visited[i]) {
+          visited[i] = true;
+
+          bool we_are_ghost = i == s.size();
+
+          spin<U, D, state> si_new;
+          euclidean<U, D> s0_new(L);
+
+          if (we_are_ghost) {
+            s0_new = r.act(s0);
+          } else {
+            si_new = r.act(s[i]);
+          }
+
+          for (unsigned j : neighbors(*this, i, si_new)) {
+            if (j != i) {
+              double dE;
+              bool neighbor_is_ghost = j == s.size();
+
+              if (we_are_ghost || neighbor_is_ghost) {
+                spin<U, D, state> s0s_old, s0s_new;
+                unsigned non_ghost;
+
+                if (neighbor_is_ghost) {
+                  non_ghost = i;
+                  s0s_old = s0.inverse().act(s[i]);
+                  s0s_new = s0.inverse().act(si_new);
+                } else {
+                  non_ghost = j;
+                  s0s_old = s0.inverse().act(s[j]);
+                  s0s_new = s0_new.inverse().act(s[j]);
+                }
+
+                dE = B(s0s_old) - B(s0s_new);
+              } else {
+                dE = Z(s[i], s[j]) - Z(si_new, s[j]);
+              }
+
+              double p = 1.0 - exp(-dE / T);
+
+              if (dist(rng) < p) {
+                queue.push(j);
+              }
+            }
+          }
+
+          if (we_are_ghost) {
+            s0 = s0_new;
+          } else {
+            dict.remove(s[i].x, i);
+            s[i] = si_new;
+            dict.record(s[i].x, i);
+          }
+        }
+      }
+    }
+
+    void wolff(double T, unsigned N, std::mt19937& rng) {
+      std::uniform_real_distribution<double> t_dist(0, L);
+      std::uniform_int_distribution<unsigned> r_dist(0, D - 1);
+      std::uniform_int_distribution<unsigned> ind_dist(0, s.size() - 1);
+
+      for (unsigned i = 0; i < N; i++) {
+        vector<U, D> t;
+        matrix<U, D> m;
+        for (unsigned j = 0; j < D; j++) {
+          t(j) = (U)t_dist(rng);
+        }
+
+        unsigned flip_D1 = r_dist(rng);
+        unsigned flip_D2 = r_dist(rng);
+
+        for (unsigned j = 0; j < D; j++) {
+          for (unsigned k = 0; k < D; k++) {
+            if ((j == flip_D1 && k == flip_D2) || (j == flip_D2 && k == flip_D1)) {
+              if (flip_D1 <= flip_D2) {
+                m(j, k) = -1;
+              } else {
+                m(j, k) = 1;
+              }
+            } else if ((j == k && j != flip_D1) && j != flip_D2) {
+              m(j, k) = 1;
+            } else {
+              m(j, k) = 0;
+            }
+          }
+        }
+
+        euclidean<U, D> g(L, t, m);
+
+        this->step(T, ind_dist(rng), g, rng);
+      }
+    }
+};
+
+int main(int argc, char* argv[]) {
+  unsigned L = 32;
+  const unsigned D = 2;
+
+  std::function<double(spin<signed, D, signed>, spin<signed, D, signed>)> Z =
+    [] (spin<signed, D, signed> s1, spin<signed, D, signed> s2) -> double {
+      bool one_one = false;
+      bool many_ones = false;
+      bool any_two = false;
+      
+      for (unsigned i = 0; i < D; i++) {
+        unsigned diff = abs(s1.x(i) - s2.x(i));
+        if (diff == 1 && !one_one) {
+          one_one = true;
+        } else if (diff == 1 && one_one) {
+          many_ones = true;
+          break;
+        } else if (diff > 1) {
+          any_two = true;
+          break;
+        }
+      }
+
+      if (!one_one && !any_two) {
+        return -std::numeric_limits<double>::infinity();
+      } else if (one_one && !many_ones && !any_two) {
+        return s1.s * s2.s;
+      } else {
+        return 0;
+      }
+    };
+
+  std::function<double(spin<signed, D, signed>)> B =
+    [] (spin<signed, D, signed> s) -> double {
+      return 100 * s.s * smiley[s.x(0) / 2][s.x(1) / 2];
+    };
+
+  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> os1 = m.dict.on_site(s1.x);
+        std::set<unsigned> nn0 = m.dict.nearest_neighbors(m.s[i0].x);
+        std::set<unsigned> nn1 = m.dict.nearest_neighbors(s1.x);
+        nn.insert(nn0.begin(), nn0.end());
+        nn.insert(nn1.begin(), nn1.end());
+        nn.insert(os1.begin(), os1.end());
+        nn.insert(m.s.size());
+      } else {
+        for (unsigned i = 0; i < m.s.size(); i++) {
+          nn.insert(i);
+        }
+      }
+      return nn;
+    };
+
+  model<signed, D, signed> ising(L, Z, B, neighbors);
+
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+  std::uniform_int_distribution<unsigned> coin(0, 1);
+
+  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) / 2) || down >= pow(L, 2) / 2) {
+        ising.s.push_back({{i, j}, 1});
+        up++;
+      } else {
+        ising.s.push_back({{i, j}, -1});
+        down++;
+      }
+      ising.dict.record<signed>({i, j}, n);
+      n++;
+    }
+  }
+  /*
+  for (unsigned i = 0; i < L; i++) {
+    for (unsigned j = 0; j < L; j++) {
+      if (i < L / 2) {
+        ising.s.push_back({{i, j}, 1});
+      } else {
+        ising.s.push_back({{i, j}, -1});
+      }
+      ising.dict.record<signed>({i, j}, n);
+      n++;
+    }
+  }
+  */
+
+  ising.wolff(2.0 / log(1.0 + sqrt(2.0)), 5000, rng);
+
+  std::vector<signed> output(pow(L, D));
+
+  for (spin<signed, D, signed> s : ising.s) {
+    spin<signed, D, signed> rs = ising.s0.inverse().act(s);
+    output[L * rs.x(1) + rs.x(0)] = s.s;
+  }
+
+  for (unsigned i = 0; i < L; i++) {
+    for (unsigned j = 0; j < L; j++) {
+      unsigned out = output[L * i + j] == 1 ? 1 : 0;
+      std::cout << out;
+    }
+    std::cout << "\n";
+  }
+
+  return 0;
+}
+
-- 
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