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
|
/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author(s): Siargey Kachanovich
*
* Copyright (C) 2015 Inria
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#ifndef WITNESS_COMPLEX_H_
#define WITNESS_COMPLEX_H_
#include <gudhi/Active_witness/Active_witness.h>
#include <gudhi/Witness_complex/all_faces_in.h>
#include <utility>
#include <vector>
#include <list>
#include <limits>
namespace Gudhi {
namespace witness_complex {
/**
* \private
* \class Witness_complex
* \brief Constructs (weak) witness complex for a given table of nearest landmarks with respect to witnesses.
* \ingroup witness_complex
*
* \tparam Nearest_landmark_table_ needs to be a range of a range of pairs of nearest landmarks and distances.
* The class Nearest_landmark_table_::value_type must be a copiable range.
* The range of pairs must admit a member type 'iterator'. The dereference type
* of the pair range iterator needs to be 'std::pair<std::size_t, double>'.
*/
template< class Nearest_landmark_table_ >
class Witness_complex {
private:
typedef typename Nearest_landmark_table_::value_type Nearest_landmark_range;
typedef std::size_t Witness_id;
typedef std::size_t Landmark_id;
typedef std::pair<Landmark_id, double> Id_distance_pair;
typedef Active_witness<Id_distance_pair, Nearest_landmark_range> ActiveWitness;
typedef std::list< ActiveWitness > ActiveWitnessList;
typedef std::vector< Landmark_id > typeVectorVertex;
typedef std::vector<Nearest_landmark_range> Nearest_landmark_table_internal;
typedef Landmark_id Vertex_handle;
protected:
Nearest_landmark_table_internal nearest_landmark_table_;
public:
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/* @name Constructor
*/
//@{
Witness_complex() {
}
/**
* \brief Initializes member variables before constructing simplicial complex.
* \details Records nearest landmark table.
* @param[in] nearest_landmark_table needs to be a range (one entry per witness)
* of sorted ranges of pairs of nearest landmarks and distances.
* The class Nearest_landmark_table_::value_type must be a copiable range.
* The range of pairs must admit a member type 'iterator'. The dereference type
* of the pair range iterator needs to be 'std::pair<std::size_t, double>'
* where the first element is the index of the landmark, and the second its
* (squared) distance to the witness.
*/
Witness_complex(Nearest_landmark_table_ const & nearest_landmark_table)
: nearest_landmark_table_(std::begin(nearest_landmark_table), std::end(nearest_landmark_table)) {
}
/** \brief Outputs the (weak) witness complex of relaxation 'max_alpha_square'
* in a simplicial complex data structure.
* \details The function returns true if the construction is successful and false otherwise.
* @param[out] complex Simplicial complex data structure compatible which is a model of
* SimplicialComplexForWitness concept.
* @param[in] max_alpha_square Maximal squared relaxation parameter.
* @param[in] limit_dimension Represents the maximal dimension of the simplicial complex
* (default value = no limit).
*/
template < typename SimplicialComplexForWitness >
bool create_complex(SimplicialComplexForWitness& complex,
double max_alpha_square,
std::size_t limit_dimension = std::numeric_limits<std::size_t>::max()) const {
if (complex.num_vertices() > 0) {
std::cerr << "Witness complex cannot create complex - complex is not empty.\n";
return false;
}
if (max_alpha_square < 0) {
std::cerr << "Witness complex cannot create complex - squared relaxation parameter must be non-negative.\n";
return false;
}
ActiveWitnessList active_witnesses;
Landmark_id k = 0; /* current dimension in iterative construction */
for (auto&& w : nearest_landmark_table_)
active_witnesses.emplace_back(w);
while (!active_witnesses.empty() && k <= limit_dimension) {
typename ActiveWitnessList::iterator aw_it = active_witnesses.begin();
std::vector<Landmark_id> simplex;
simplex.reserve(k+1);
while (aw_it != active_witnesses.end()) {
bool ok = add_all_faces_of_dimension(k,
max_alpha_square,
std::numeric_limits<double>::infinity(),
aw_it->begin(),
simplex,
complex,
aw_it->end());
assert(simplex.empty());
if (!ok)
active_witnesses.erase(aw_it++); // First increase the iterator and then erase the previous element
else
aw_it++;
}
k++;
}
return true;
}
//@}
private:
/* \brief Adds recursively all the faces of a certain dimension dim witnessed by the same witness.
* Iterator is needed to know until how far we can take landmarks to form simplexes.
* simplex is the prefix of the simplexes to insert.
* The output value indicates if the witness rests active or not.
*/
template < typename SimplicialComplexForWitness >
bool add_all_faces_of_dimension(int dim,
double alpha2,
double norelax_dist2,
typename ActiveWitness::iterator curr_l,
std::vector<Landmark_id>& simplex,
SimplicialComplexForWitness& sc,
typename ActiveWitness::iterator end) const {
if (curr_l == end)
return false;
bool will_be_active = false;
typename ActiveWitness::iterator l_it = curr_l;
if (dim > 0) {
for (; l_it != end && l_it->second - alpha2 <= norelax_dist2; ++l_it) {
simplex.push_back(l_it->first);
if (sc.find(simplex) != sc.null_simplex()) {
typename ActiveWitness::iterator next_it = l_it;
will_be_active = add_all_faces_of_dimension(dim-1,
alpha2,
norelax_dist2,
++next_it,
simplex,
sc,
end) || will_be_active;
}
assert(!simplex.empty());
simplex.pop_back();
// If norelax_dist is infinity, change to first omitted distance
if (l_it->second <= norelax_dist2)
norelax_dist2 = l_it->second;
}
} else if (dim == 0) {
for (; l_it != end && l_it->second - alpha2 <= norelax_dist2; ++l_it) {
simplex.push_back(l_it->first);
double filtration_value = 0;
// if norelax_dist is infinite, relaxation is 0.
if (l_it->second > norelax_dist2)
filtration_value = l_it->second - norelax_dist2;
if (all_faces_in(simplex, &filtration_value, sc)) {
will_be_active = true;
sc.insert_simplex(simplex, filtration_value);
}
assert(!simplex.empty());
simplex.pop_back();
// If norelax_dist is infinity, change to first omitted distance
if (l_it->second < norelax_dist2)
norelax_dist2 = l_it->second;
}
}
return will_be_active;
}
};
} // namespace witness_complex
} // namespace Gudhi
#endif // WITNESS_COMPLEX_H_
|
