1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
|
#pragma once
#include "matrix.hpp"
#include "spin.hpp"
#include "vector.hpp"
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;
}
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;
return s_new;
}
Euclidean act(const Euclidean& x) const {
Vector<T, D> tnew = r * x.t + t;
Matrix<T, D> rnew = r * x.r;
Euclidean pnew(tnew, rnew);
return pnew;
}
Euclidean inverse() const {
Vector<T, D> tnew = -r.transpose() * t;
Matrix<T, D> rnew = r.transpose();
Euclidean pnew(tnew, rnew);
return pnew;
}
};
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;
}
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;
}
};
|
