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#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);
}
}
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;
}
};
Orthogonal walsh(unsigned k) {
if (k == 0) {
return Orthogonal(1);
} else {
Orthogonal s = walsh(k - 1);
Orthogonal t = Orthogonal(2 * s.size());
for (unsigned i = 0; i < s.size(); i++) {
for (unsigned j = 0; j < s.size(); j++) {
double sij = s(i, j);
t(i, j) = sij;
t(s.size() + i, j) = sij;
t(i, s.size() + j) = sij;
t(s.size() + i, s.size() + j) = -sij;
}
}
return t;
}
}
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);
}
}
}
};
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