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#ifndef WOLFF_MODELS_ORTHOGONAL_H
#define WOLFF_MODELS_ORTHOGONAL_H
#include <random>
#include <cmath>
#include "../system.hpp"
#include "vector.hpp"
namespace wolff {
#include "../types.h"
template <q_t q, class T>
class orthogonal_t : public std::array<std::array<T, q>, q> {
public :
bool is_reflection;
orthogonal_t() : is_reflection(false) {
for (q_t i = 0; i < q; i++) {
(*this)[i].fill(0);
(*this)[i][i] = (T)1;
}
}
vector_t<q, T> act(const vector_t <q, T>& v) const {
vector_t <q, T> v_rot;
v_rot.fill(0);
if (is_reflection) {
double prod = 0;
for (q_t i = 0; i < q; i++) {
prod += v[i] * (*this)[0][i];
}
for (q_t i = 0; i < q; i++) {
v_rot[i] = v[i] - 2 * prod * (*this)[0][i];
}
} else {
for (q_t i = 0; i < q; i++) {
for (q_t j = 0; j < q; j++) {
v_rot[i] += (*this)[i][j] * v[j];
}
}
}
return v_rot;
}
orthogonal_t<q, T> act(const orthogonal_t <q, T>& m) const {
orthogonal_t <q, T> m_rot;
m_rot.is_reflection = false;
if (is_reflection) {
for (q_t i = 0; i < q; i++) {
double akOki = 0;
for (q_t k = 0; k < q; k++) {
akOki += (*this)[0][k] * m[k][i];
}
for (q_t j = 0; j < q; j++) {
m_rot[j][i] = m[j][i] - 2 * akOki * (*this)[0][j];
}
}
} else {
for (q_t i = 0; i < q; i++) {
m_rot[i].fill(0);
for (q_t j = 0; j < q; j++) {
for (q_t k = 0; k < q; k++) {
m_rot[i][j] += (*this)[i][j] * m[j][k];
}
}
}
}
return m_rot;
}
vector_t <q, T> act_inverse(const vector_t <q, T>& v) const {
if (is_reflection) {
return this->act(v); // reflections are their own inverse
} else {
vector_t <q, T> v_rot;
v_rot.fill(0);
for (q_t i = 0; i < q; i++) {
for (q_t j = 0; j < q; j++) {
v_rot[i] += (*this)[j][i] * v[j];
}
}
return v_rot;
}
}
vector_t <q, T> act_inverse(const orthogonal_t <q, T>& m) const {
if (is_reflection) {
return this->act(m); // reflections are their own inverse
} else {
orthogonal_t <q, T> m_rot;
m_rot.is_reflection = false;
for (q_t i = 0; i < q; i++) {
m_rot[i].fill(0);
for (q_t j = 0; j < q; j++) {
for (q_t k = 0; k < q; k++) {
m_rot[i][j] += (*this)[j][i] * m[j][k];
}
}
}
return m_rot;
}
}
};
template <q_t q>
orthogonal_t <q, double> generate_rotation_uniform (std::mt19937& r, const system<orthogonal_t<q, double>, vector_t<q, double>>&, v_t) {
std::normal_distribution<double> dist(0.0,1.0);
orthogonal_t <q, double> ptr;
ptr.is_reflection = true;
double v2 = 0;
for (q_t i = 0; i < q; i++) {
ptr[0][i] = dist(r);
v2 += ptr[0][i] * ptr[0][i];
}
double mag_v = sqrt(v2);
for (q_t i = 0; i < q; i++) {
ptr[0][i] /= mag_v;
}
return ptr;
}
template <q_t q>
orthogonal_t <q, double> generate_rotation_perturbation (std::mt19937& r, const system<orthogonal_t<q, double>, vector_t<q, double>>& S, v_t i0, double epsilon, unsigned int n) {
std::normal_distribution<double> dist(0.0,1.0);
orthogonal_t <q, double> m;
m.is_reflection = true;
vector_t <q, double> v;
if (n > 1) {
std::uniform_int_distribution<unsigned int> udist(0, n);
unsigned int rotation = udist(r);
double cosr = cos(2 * M_PI * rotation / (double)n / 2.0);
double sinr = sin(2 * M_PI * rotation / (double)n / 2.0);
v[0] = S.s[i0][0] * cosr - S.s[i0][1] * sinr;
v[1] = S.s[i0][1] * cosr + S.s[i0][0] * sinr;
for (q_t i = 2; i < q; i++) {
v[i] = S.s[i0][i];
}
} else {
v = S.s[i0];
}
double m_dot_v = 0;
for (q_t i = 0; i < q; i++) {
m[0][i] = dist(r); // create a random vector
m_dot_v += m[0][i] * v[i];
}
double v2 = 0;
for (q_t i = 0; i < q; i++) {
m[0][i] = m[0][i] - m_dot_v * v[i]; // find the component orthogonal to v
v2 += pow(m[0][i], 2);
}
double mag_v = sqrt(v2);
for (q_t i = 0; i < q; i++) {
m[0][i] /= mag_v; // normalize
}
v2 = 0;
double factor = epsilon * dist(r);
for (q_t i = 0; i < q; i++) {
m[0][i] += factor * v[i]; // perturb orthogonal vector in original direction
v2 += pow(m[0][i], 2);
}
mag_v = sqrt(v2);
for (q_t i = 0; i < q; i++) {
m[0][i] /= mag_v; // normalize
}
return m;
}
}
#endif
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