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#pragma once
#include "matrix.hpp"
#include "spin.hpp"
#include "vector.hpp"
typedef double Radius;
typedef signed IsingSpin;
template <class T, int D> class Dimer {
public:
double radius;
Vector<T, D> relativePosition;
};
template <class T, int D> class Euclidean {
public:
Vector<T, D> t;
Matrix<T, D> r;
Euclidean(T 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(Vector<T, D> t0, Matrix<T, D> r0) {
t = t0;
r = r0;
}
Vector<T, D> act(const Vector<T, D>& x) const { return t + r * x; }
template <typename U> Vector<U, D> act(const Vector<U, D>& x) const {
return t.template cast<U>() + r.template cast<U>() * x;
}
Radius act(Radius r) const { return r; }
IsingSpin act(IsingSpin s) const { return s; }
Dimer<T, D> act(const Dimer<T, D>& d) const {
return {.radius = d.radius, .relativePosition = r * d.relativePosition};
}
template <class S> Spin<T, D, S> act(const Spin<T, D, S>& s) const {
return {.x = act(s.x), .s = act(s.s)};
}
Euclidean act(const Euclidean& x) const { return Euclidean(r * x.t + t, r * x.r); }
Euclidean inverse() const { return Euclidean(-r.transpose() * t, r.transpose()); }
};
template <class T, int D> class TorusGroup {
private:
T L;
public:
Vector<T, D> t;
Matrix<T, D> r;
/** brief TorusGroup - default constructor, constructs the identity
*/
TorusGroup(T 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;
}
}
}
TorusGroup(T L, Vector<T, D> t0, Matrix<T, D> r0) : L(L) {
t = t0;
r = r0;
}
template <class S> Spin<T, D, S> act(const Spin<T, D, S>& s) const {
Spin<T, D, S> 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;
}
Vector<T, D> act(const Vector<T, D>& s) const {
Vector<T, D> s_new = t + r * s;
for (unsigned i = 0; i < D; i++) {
s_new(i) = fmod(L + s_new(i), L);
}
return s_new;
}
template <typename U> Vector<U, D> act(const Vector<U, D>& s) const {
Vector<U, D> s_new = t.template cast<U>() + r.template cast<U>() * s;
for (unsigned i = 0; i < D; i++) {
s_new(i) = fmod(L + s_new(i), L);
}
return s_new;
}
TorusGroup act(const TorusGroup& x) const {
Vector<T, D> tnew = r * x.t + t;
Matrix<T, D> rnew = r * x.r;
for (unsigned i = 0; i < D; i++) {
tnew(i) = fmod(L + tnew(i), L);
}
TorusGroup pnew(this->L, tnew, rnew);
return pnew;
}
TorusGroup inverse() const {
Vector<T, D> tnew = -r.transpose() * t;
Matrix<T, D> rnew = r.transpose();
TorusGroup pnew(this->L, tnew, rnew);
return pnew;
}
};
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