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
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
#pragma once
#include "randutils/randutils.hpp"
#include <vector>
inline double Ei(double x) { return -fabs(x); }
class Orthogonal {
private:
unsigned d;
std::vector<double> m;
public:
Orthogonal(unsigned size) : m(size * size) {
d = size;
for (unsigned i = 0; i < size; i++) {
m[size * i + i] = sqrt(size);
}
}
Orthogonal(const std::vector<double>& x) : m(x) {
d = sqrt(x.size());
}
unsigned size() const { return d; }
double& operator()(unsigned i, unsigned j) { return m[d * i + j]; }
const double& operator()(unsigned i, unsigned j) const { return m[d * i + j]; }
double energy() const {
double E = 0;
for (unsigned i = 0; i < this->size(); i++) {
for (unsigned j = 0; j < this->size(); j++) {
E += Ei(this->operator()(i, j));
}
}
return E;
}
};
class Givens {
private:
Orthogonal& m;
bool transpose;
unsigned axis_1;
unsigned axis_2;
double Δθ;
std::vector<double> rows;
public:
Givens(Orthogonal& m, bool t, unsigned a1, unsigned a2, double θ0, randutils::mt19937_rng& rng)
: m(m), rows(2 * m.size()) {
transpose = t;
axis_1 = a1;
axis_2 = a2;
Δθ = rng.uniform(-θ0, θ0);
}
Givens(Orthogonal& m, double θ0, randutils::mt19937_rng& rng) : m(m), rows(2 * m.size()) {
Δθ = rng.uniform(-θ0, θ0);
unsigned axis1axis2 = rng.uniform((unsigned)0, m.size() * (m.size() - 1) - 1);
axis_1 = axis1axis2 / (m.size() - 1);
axis_2 = axis1axis2 % (m.size() - 1);
transpose = axis_2 >= axis_1;
if (transpose) {
axis_2++;
}
}
double tryRotation() {
double ΔE = 0;
double c = cos(Δθ);
double s = sin(Δθ);
for (unsigned i = 0; i < m.size(); i++) {
double m1i, m2i, m1i_new, m2i_new;
if (transpose) {
m1i = m(i, axis_1);
m2i = m(i, axis_2);
} else {
m1i = m(axis_1, i);
m2i = m(axis_2, i);
}
ΔE -= Ei(m1i) + Ei(m2i);
m1i_new = c * m1i + s * m2i;
m2i_new = c * m2i - s * m1i;
ΔE += Ei(m1i_new) + Ei(m2i_new);
rows[i] = m1i_new;
rows[m.size() + i] = m2i_new;
}
return ΔE;
}
void acceptRotation() const {
for (unsigned i = 0; i < m.size(); i++) {
if (transpose) {
m(i, axis_1) = rows[i];
m(i, axis_2) = rows[m.size() + i];
} else {
m(axis_1, i) = rows[i];
m(axis_2, i) = rows[m.size() + i];
}
}
}
};
class Measurement {
public:
virtual void after_step(bool, const Givens&, double, double, double, const Orthogonal&){};
virtual void after_sweep(double, double, const Orthogonal&){};
};
typedef enum {
none,
up,
down
} color;
class MCMC {
private:
Measurement& A;
double θ0;
public:
randutils::mt19937_rng rng;
double β;
double E;
Orthogonal M;
MCMC(unsigned n, double β0, Measurement& A) : A(A), M(n), β(β0) {
θ0 = M_PI;
E = M.energy();
}
bool step(Givens& g, bool dry = false) {
double ΔE = g.tryRotation();
bool accepted = ΔE < 0 || exp(-β * ΔE) > rng.uniform((double)0.0, 1.0);
if (accepted) {
E += ΔE;
g.acceptRotation();
}
if (!dry) {
A.after_step(accepted, g, θ0, E, ΔE, M);
}
return accepted;
}
double sweep(bool dry = false) {
unsigned total = 0;
unsigned accepted = 0;
for (unsigned i = 0; i < M.size() - 1; i++) {
for (unsigned j = i + 1; j < M.size(); j++) {
Givens g1(M, false, i, j, θ0, rng);
Givens g2(M, true, i, j, θ0, rng);
if (this->step(g1, dry))
accepted++;
if (this->step(g2, dry))
accepted++;
total += 2;
}
}
return (double)accepted / (double)total;
}
void tune(unsigned N, double ε) {
for (unsigned i = 0; i < N; i++) {
double ratio_accepted = this->sweep(true);
if (ratio_accepted > 0.5) {
θ0 *= 1 + ε;
} else {
θ0 /= 1 + ε;
}
}
}
void run(unsigned N, bool dry = false) {
for (unsigned i = 0; i < N; i++) {
this->sweep(dry);
if (!dry) {
A.after_sweep(θ0, E, M);
}
}
}
};
|
