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namespace md {
/**
*
* @param values vector of length n
* @return [a_1,...,a_n] such that
* 1) values[a_1] <= values[a_2] <= ... <= values[a_n]
* 2) a_1,...,a_n is a permutation of 1,..,n
*/
template<class T>
IndexVec get_sorted_indices(const std::vector<T>& values)
{
IndexVec result(values.size());
std::iota(result.begin(), result.end(), 0);
std::sort(result.begin(), result.end(),
[&values](size_t a, size_t b) { return values[a] < values[b]; });
return result;
}
// helper function to initialize const member positions_ in ModulePresentation
template<class Real>
PointVec<Real> concat_gen_and_rel_positions(const PointVec<Real>& generators,
const typename ModulePresentation<Real>::RelVec& relations)
{
std::unordered_set<Point<Real>> ps(generators.begin(), generators.end());
for(const auto& rel : relations) {
ps.insert(rel.position_);
}
return PointVec<Real>(ps.begin(), ps.end());
}
template<class Real>
void ModulePresentation<Real>::init_boundaries()
{
max_x_ = -std::numeric_limits<Real>::max();
max_y_ = -std::numeric_limits<Real>::max();
min_x_ = std::numeric_limits<Real>::max();
min_y_ = std::numeric_limits<Real>::max();
for(const auto& gen : positions_) {
min_x_ = std::min(gen.x, min_x_);
min_y_ = std::min(gen.y, min_y_);
max_x_ = std::max(gen.x, max_x_);
max_y_ = std::max(gen.y, max_y_);
}
bounding_box_ = Box<Real>(Point<Real>(min_x_, min_y_), Point<Real>(max_x_, max_y_));
}
template<class Real>
ModulePresentation<Real>::ModulePresentation(const PointVec<Real>& _generators, const RelVec& _relations) :
generators_(_generators),
relations_(_relations)
{
positions_ = concat_gen_and_rel_positions(generators_, relations_);
init_boundaries();
}
template<class Real>
void ModulePresentation<Real>::translate(Real a)
{
for(auto& g : generators_) {
g.translate(a);
}
for(auto& r : relations_) {
r.position_.translate(a);
}
positions_ = concat_gen_and_rel_positions(generators_, relations_);
init_boundaries();
}
/**
*
* @param slice line on which generators are projected
* @param sorted_indices [a_1,...,a_n] s.t. wpush(generator[a_1]) <= wpush(generator[a_2]) <= ..
* @param projections sorted weighted pushes of generators
*/
template<class Real>
void ModulePresentation<Real>::project_generators(const DualPoint<Real>& slice,
IndexVec& sorted_indices, RealVec& projections) const
{
size_t num_gens = generators_.size();
RealVec gen_values;
gen_values.reserve(num_gens);
for(const auto& pos : generators_) {
gen_values.push_back(slice.weighted_push(pos));
}
sorted_indices = get_sorted_indices(gen_values);
projections.clear();
projections.reserve(num_gens);
for(auto i : sorted_indices) {
projections.push_back(gen_values[i]);
}
}
template<class Real>
void ModulePresentation<Real>::project_relations(const DualPoint<Real>& slice, IndexVec& sorted_rel_indices,
RealVec& projections) const
{
size_t num_rels = relations_.size();
RealVec rel_values;
rel_values.reserve(num_rels);
for(const auto& rel : relations_) {
rel_values.push_back(slice.weighted_push(rel.position_));
}
sorted_rel_indices = get_sorted_indices(rel_values);
projections.clear();
projections.reserve(num_rels);
for(auto i : sorted_rel_indices) {
projections.push_back(rel_values[i]);
}
}
template<class Real>
void ModulePresentation<Real>::get_slice_projection_matrix(const DualPoint<Real>& slice,
phat::boundary_matrix<>& phat_matrix,
RealVec& gen_projections, RealVec& rel_projections) const
{
IndexVec sorted_gen_indices, sorted_rel_indices;
project_generators(slice, sorted_gen_indices, gen_projections);
project_relations(slice, sorted_rel_indices, rel_projections);
phat_matrix.set_num_cols(relations_.size());
for(Index i = 0; i < (Index) relations_.size(); i++) {
IndexVec current_relation = relations_[sorted_rel_indices[i]].components_;
for(auto& j : current_relation) {
j = sorted_gen_indices[j];
}
std::sort(current_relation.begin(), current_relation.end());
// modules do not have dimension, set all to 0
phat_matrix.set_dim(i, 0);
phat_matrix.set_col(i, current_relation);
}
}
template<class Real>
Diagram<Real> ModulePresentation<Real>::weighted_slice_diagram(const DualPoint<Real>& slice) const
{
RealVec gen_projections, rel_projections;
phat::boundary_matrix<> phat_matrix;
get_slice_projection_matrix(slice, phat_matrix, gen_projections, rel_projections);
phat::persistence_pairs phat_persistence_pairs;
phat::compute_persistence_pairs<phat::standard_reduction>(phat_persistence_pairs, phat_matrix, true);
Diagram<Real> dgm;
constexpr Real real_inf = std::numeric_limits<Real>::infinity();
for(Index i = 0; i < (Index) phat_persistence_pairs.get_num_pairs(); i++) {
std::pair<phat::index, phat::index> new_pair = phat_persistence_pairs.get_pair(i);
bool is_finite_pair = new_pair.second != phat::k_infinity_index;
Real birth = gen_projections.at(new_pair.first);
Real death = is_finite_pair ? rel_projections.at(new_pair.second) : real_inf;
if (birth != death) {
dgm.emplace_back(birth, death);
}
}
return dgm;
}
template<class Real>
PointVec<Real> ModulePresentation<Real>::positions() const
{
return positions_;
}
template<class Real>
Box<Real> ModulePresentation<Real>::bounding_box() const
{
return bounding_box_;
}
} // namespace md
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