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-rw-r--r--glass.cpp553
1 files changed, 0 insertions, 553 deletions
diff --git a/glass.cpp b/glass.cpp
deleted file mode 100644
index f2f44c1..0000000
--- a/glass.cpp
+++ /dev/null
@@ -1,553 +0,0 @@
-#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;
-}
-
-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;
- 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;
- }
-
- 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;
- }
-
- 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;
-
- if (s.isEmpty()) {
- return o;
- }
-
- if (!v.isEmpty() && !excludeSelf) {
- o.push_back(v);
- }
-
- for (const HalfEdge<D>& e : v.adjacentEdges) {
- if (!e.neighbor.isEmpty()) {
- if (s.dot(e.Δx) == 1 || e.neighbor.state.dot(e.Δx) == -1) {
- o.push_back(e.neighbor);
- }
- }
- }
-
- 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;
-
- for (Vertex<D>& v : vertices) {
- unsigned a = 0;
- for (unsigned d = 0; d < D; d++) {
- a += (d + 1) * v.position(d);
- }
- a %= 2 * D + 1;
-
- v.state.setZero() = Vector<D>::Zero();
-
- if (0 < a && a <= D) {
- v.state(a - 1) = -1;
- N++;
- } else if (D < a) {
- v.state(2 * D - a) = 1;
- 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) {
- if (v.state(0) == 1 && v.state(1) == 0) {
- std::cerr << "▶";
- } else if (v.state(0) == -1 && v.state(1) == 0) {
- std::cerr << "◀";
- } else if (v.state(0) == 0 && v.state(1) == -1) {
- std::cerr << "▲";
- } else if (v.state(0) == 0 && v.state(1) == 1) {
- std::cerr << "▼";
- } else if (v.state(0) == 0 && v.state(1) == 0) {
- std::cerr << " ";
- } else {
- std::cerr << "X";
- }
-
- if (v.position(0) == s.L - 1) {
- std::cerr << std::endl;
- }
- }
-}
-
-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;
- unsigned Nmin = 2e2;
- unsigned Nmax = 2e5;
- double Tmin = 0.04;
- double Tmax = 0.2;
- double δT = 0.02;
-
- System<D> s(L);
-
- Rng r;
-
- double z = exp(1 / 0.08);
-
- while (s.density() < 0.818) {
- s.sweepGrandCanonical(z, r);
- }
-
- if (!s.compatible()) {
- std::cerr << "Net compatible!" << std::endl;
- return 1;
- }
-
- std::cerr << "Found state with appropriate density." << std::endl;
-
- System<D> s0 = s;
-
- std::vector<Matrix<D>> ms = generateTorusMatrices<D>();
-
- unsigned n = 1;
- for (unsigned i = 0; i < 1e5; i++) {
- if (n < 20 * log(i + 1)) {
- n++;
- std::cout << i << " " << s.overlap(s0) << std::endl;
- }
- Matrix<D> m = r.pick(ms);
- Vertex<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) {
- v.marked = false;
- }
-// s.sweepLocal(r);
-// s.sweepSwap(r);
-// s.swendsenWang(Transformation<D>(L, ms, r), r);
- }
-
- return 0;
-}
-