/usr/include/polymake/topaz/next/Filtration.h is in libpolymake-dev-common 3.2r2-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 | #ifndef POLYMAKE_TOPAZ_FILTRATION_H
#define POLYMAKE_TOPAZ_FILTRATION_H
#include "polymake/Array.h"
#include "polymake/Matrix.h"
#include "polymake/Set.h"
#include "polymake/SparseVector.h"
#include "polymake/graph/Lattice.h"
#include "polymake/graph/Decoration.h"
#include "polymake/internal/matrix_methods.h"
namespace polymake { namespace topaz {
//dimension and index are needed to find the corresponding boundary via the given matrices.
struct Cell{
int deg,dim,idx;
Cell(){
deg=dim=idx=0;
}
Cell(int deg_in, int dim_in, int idx_in){
deg = deg_in;
dim = dim_in;
idx = idx_in;
}
bool operator!= (const Cell & other) const{
return deg!=other.deg || dim!=other.dim || idx!=other.idx;
}
//for testing.
friend std::ostream & operator<<(std::ostream & os, const Cell & c){
os << "(" << c.deg << "," << c.dim << "," << c.idx << ")";
return os;
}
};
template<typename MatrixType>
class Filtration{
typedef typename MatrixType::value_type Coeff;
typedef typename MatrixType::persistent_nonsymmetric_type MatNS;
public:
Array<Cell> C; //after object initialization, this array is always sorted as required by the persistent homology algorithm.
Array<MatrixType> bd_matrix; //boundary matrices by dimension. idx of the cells corresponds to the row in the corresponding matrix
Array<Array<int> > ind; //keep track of indices to implement proper bd function
Filtration() : C(), bd_matrix(), ind(){ }
Filtration(Array<Cell> & C_in, const Array<MatrixType> & bd_in, bool sorted=false) : C(C_in), bd_matrix(bd_in), ind(bd_in.size()){
if(sorted) update_indices();
else sort();
}
Filtration(const graph::Lattice<graph::lattice::BasicDecoration> & HD, Array<int> degs) : C(HD.nodes()-2), //-2 for empty set and dummy
bd_matrix(HD.rank()) {
int dim = HD.rank()-1;
const auto vertex_set = HD.nodes_of_rank(1); // nodes of dim 0
int n_bd = vertex_set.size(); //number of vertices
bd_matrix[0] = ones_matrix<Coeff>(n_bd,1);
Map<int,int> reindex_map; // map index in hasse diagram to index in boundary matrix.
int count_index = 0;
for(int i : vertex_set) {
C[i-1] = Cell(degs[i-1],0,count_index);
reindex_map[i] = count_index;
++count_index;
}
//compute boundary matrices for d>0:
for(int d=1; d<dim; d++){
const auto d_set = HD.nodes_of_rank(d+1);
int n = d_set.size();//number of d-simplices
MatrixType bd(n,n_bd);
n_bd = n;
Map<int,int> new_reindex_map;
///////////////////////
int r = 0; //row index
for(int f : d_set){ //iterate d-simplices
auto face = HD.face(f);
new_reindex_map[f] = r; //fill in index map for next iteration
C[f-1] = Cell(degs[f-1],d,r);//put indices into cell array
for(int sf : HD.in_adjacent_nodes(f)){ //iterate d-1-simplices
auto subface = HD.face(sf);
int i = 0; //find index of the vertex missing in current subface
for(auto f_it = entire(face), sf_it = entire(subface);
(*f_it)==(*sf_it) && !sf_it.at_end(); ++f_it, ++sf_it)
++i;
bd(r,reindex_map[sf]) = i%2 ? Coeff(1) : -Coeff(1);
}
++r;
}
///////////////////////////
/*
int r=0; //row index;
for (auto f=entire(d_set); !f.at_end(); ++f){//iterate over d-faces
new_reindex_map[*f] = r;
Coeff sgn = Coeff(1);
C[*f-1] = Cell(degs[*f-1],d,r);//put indices into cell array
for (auto subf=HD.in_adjacent_nodes(*f).begin(); !subf.at_end(); ++subf){//iterate over their boundary
bd[r][reindex_map[*subf]]=sgn;
sgn = -sgn;
}
r++;
}
*/
bd_matrix[d] = bd;
reindex_map = new_reindex_map;
}
sort();
}
//keeps track of ind matrix for easy access of boundaries
void update_indices(){
ind.resize(bd_matrix.size());
for(auto i = ensure(ind,(pm::cons<pm::end_sensitive, pm::indexed>*)0).begin(); !i.at_end(); ++i)
(*i).resize(bd_matrix[i.index()].rows());
for (auto c=ensure(C, (pm::cons<pm::end_sensitive, pm::indexed>*)0).begin(); !c.at_end(); ++c) {
ind[(*c).dim][(*c).idx] = c.index();
}
}
public:
int n_cells() const{
return C.size();
}
int n_frames() const{
return C[n_cells()-1].deg; //TODO this only works with sorted array...
}
int dim() const{
return bd_matrix.size()-1;
}
typedef SparseVector<Coeff> Chain;
Chain bd(int i) const{
Cell cell = C[i];
int d = cell.dim;
Chain c(C.size());
if(d==0) return c; //points have empty boundary
Chain b = bd_matrix[d].row(cell.idx);
for (auto e = entire(b); !e.at_end(); ++e) {
c[ind[d-1][e.index()]] = *e;
}
return c;
}
// sort cells by degree first and dimension second, as required by persistent homology algo.
private:
struct cellComparator {
bool operator()(const Cell& c1, const Cell& c2) {
if (c1.deg < c2.deg) return true;
if (c1.deg == c2.deg){
if(c1.dim < c2.dim) return true;
if(c1.dim == c2.dim) return c1.idx < c2.idx; // idx gets sorted lex to allow equality checking
}
return false;
}
};
void sort(){
std::sort(C.begin(), C.end(), cellComparator());
update_indices();//TODO do this while sorting?
}
public:
const Cell operator[](int i) const{
return C[i];
}
const MatrixType boundary_matrix(int d){
return bd_matrix[d];
}
const Array<Cell> cells() const{
return C;
}
//returns d-bd matrix of t-th frame TODO accept non-sorted filtrations?
pm::MatrixMinor<MatrixType&, const Set<int>&, const Set<int>& > boundary_matrix(int d, int t){
if(t>n_frames()) throw std::runtime_error("Filtration: input exceeds number of frames");
if(d>dim()) throw std::runtime_error("Filtration: input exceeds filtration dimension");
MatrixType B = bd_matrix[d];
Set<int> frame; //indices of d-simplices present in this frame
Set<int> frame_bd; //indices of d-1-simplices present
for(auto i = ensure(ind[d],(pm::cons<pm::end_sensitive, pm::indexed>*)0).begin(); !i.at_end(); ++i){
if(C[*i].deg <= t) frame += i.index();
}
if(d>0){
for(auto i = ensure(ind[d-1],(pm::cons<pm::end_sensitive, pm::indexed>*)0).begin(); !i.at_end(); ++i){
if(C[*i].deg <= t) frame_bd += i.index();
}
}else frame_bd = sequence(0,B.cols());
return B.minor(frame,frame_bd);
}
pm::ensure_features<Array<Cell>, pm::cons<pm::end_sensitive, pm::indexed> >::const_iterator get_iter() const{
return ensure(C, (pm::cons<pm::end_sensitive, pm::indexed>*)0).begin();
}
//for testing.
friend std::ostream & operator<<(std::ostream & os, const Filtration & c){
for(int i=0; i<c.n_cells(); ++i) os << c[i] << ",";
return os;
}
template<typename MatrixType2>
bool operator==(const Filtration<MatrixType2> & other) const{
return bd_matrix == other.bd_matrix && C == other.C;
}
template <typename> friend struct pm::spec_object_traits;
};
}}
namespace pm{
template <>
struct spec_object_traits< Serialized< polymake::topaz::Cell > > :
spec_object_traits<is_composite> {
typedef polymake::topaz::Cell masquerade_for;
typedef cons<int,cons<int,int> > elements;
template <typename Me, typename Visitor>
static void visit_elements(Me& me, Visitor& v)
{
v << me.deg << me.dim << me.idx;
}
};
template <typename MatrixType>
struct spec_object_traits< Serialized< polymake::topaz::Filtration<MatrixType> > > :
spec_object_traits<is_composite> {
typedef polymake::topaz::Filtration<MatrixType> masquerade_for;
typedef cons<Array<polymake::topaz::Cell>, Array<MatrixType> > elements;
template <typename Me, typename Visitor>
static void visit_elements(Me& me, Visitor& v) //for data_load
{
v << me.C << me.bd_matrix;
me.update_indices();
}
template <typename Visitor>
static void visit_elements(const pm::Serialized<masquerade_for>& me, Visitor& v) //for data_save
{
v << me.C << me.bd_matrix;
}
};
}
#endif
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