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#pragma once
#include <array>
#include <list>
#include <vector>
#include "matrix.hpp"
#include "vector.hpp"
template <int D> void one_sequences(std::list<std::array<double, D>>& sequences, unsigned level) {
if (level > 0) {
unsigned new_level = level - 1;
unsigned old_length = sequences.size();
for (std::array<double, D>& sequence : sequences) {
std::array<double, D> new_sequence = sequence;
new_sequence[new_level] = -1;
sequences.push_front(new_sequence);
}
one_sequences<D>(sequences, new_level);
}
}
template <class U, int D> std::vector<Vector<U, D>> torus_vecs(U L) {
std::vector<Vector<U, D>> vecs;
std::array<double, D> ini_sequence;
ini_sequence.fill(1);
std::list<std::array<double, D>> sequences;
sequences.push_back(ini_sequence);
one_sequences<D>(sequences, D);
sequences.pop_front(); // don't want the identity matrix!
for (std::array<double, D> sequence : sequences) {
Vector<U, D> v;
for (unsigned i = 0; i < D; i++) {
if (sequence[i] == 1) {
v(i) = 0;
} else {
v(i) = L / 2;
}
}
vecs.push_back(v);
}
return vecs;
}
template <class U, int D> std::vector<Matrix<U, D>> torus_mats() {
std::vector<Matrix<U, D>> mats;
std::array<double, D> ini_sequence;
ini_sequence.fill(1);
std::list<std::array<double, D>> sequences;
sequences.push_back(ini_sequence);
one_sequences<D>(sequences, D);
sequences.pop_back(); // don't want the identity matrix!
for (std::array<double, D> sequence : sequences) {
Matrix<U, D> m;
for (unsigned i = 0; i < D; i++) {
for (unsigned j = 0; j < D; j++) {
if (i == j) {
m(i, j) = sequence[i];
} else {
m(i, j) = 0;
}
}
}
mats.push_back(m);
}
for (unsigned i = 0; i < D; i++) {
for (unsigned j = 0; j < D; j++) {
if (i != j) {
Matrix<U, D> m;
for (unsigned k = 0; k < D; k++) {
for (unsigned l = 0; l < D; l++) {
if ((k == i && l == j) || (k == j && l == i)) {
if (i < j) {
m(k, l) = 1;
} else {
m(k, l) = -1;
}
} else {
m(k, l) = 0;
}
}
}
mats.push_back(m);
}
}
}
return mats;
}
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