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example_one_skeleton_rips_from_correlation_matrix.cpp
#include <gudhi/Rips_complex.h>
#include <gudhi/Simplex_tree.h>
#include <gudhi/distance_functions.h>
#include <iostream>
#include <string>
#include <vector>
#include <limits> // for std::numeric_limits
int main() {
// Type definitions
using Simplex_tree = Gudhi::Simplex_tree<>;
using Filtration_value = Simplex_tree::Filtration_value;
using Rips_complex = Gudhi::rips_complex::Rips_complex<Filtration_value>;
using Distance_matrix = std::vector<std::vector<Filtration_value>>;
// User defined correlation matrix is:
// |1 0.06 0.23 0.01 0.89|
// |0.06 1 0.74 0.01 0.61|
// |0.23 0.74 1 0.72 0.03|
// |0.01 0.01 0.72 1 0.7 |
// |0.89 0.61 0.03 0.7 1 |
Distance_matrix correlations;
correlations.push_back({});
correlations.push_back({0.06});
correlations.push_back({0.23, 0.74});
correlations.push_back({0.01, 0.01, 0.72});
correlations.push_back({0.89, 0.61, 0.03, 0.7});
// ----------------------------------------------------------------------------
// Convert correlation matrix to a distance matrix:
// ----------------------------------------------------------------------------
double threshold = 0;
for (size_t i = 0; i != correlations.size(); ++i) {
for (size_t j = 0; j != correlations[i].size(); ++j) {
// Here we check if our data comes from corelation matrix.
if ((correlations[i][j] < -1) || (correlations[i][j] > 1)) {
std::cerr << "The input matrix is not a correlation matrix. The program will now terminate.\n";
throw "The input matrix is not a correlation matrix. The program will now terminate.\n";
}
correlations[i][j] = 1 - correlations[i][j];
// Here we make sure that we will get the threshold value equal to maximal
// distance in the matrix.
if (correlations[i][j] > threshold) threshold = correlations[i][j];
}
}
//-----------------------------------------------------------------------------
// Now the correlation matrix is a distance matrix and can be processed further.
//-----------------------------------------------------------------------------
Distance_matrix distances = correlations;
Rips_complex rips_complex_from_points(distances, threshold);
Simplex_tree stree;
rips_complex_from_points.create_complex(stree, 1);
// ----------------------------------------------------------------------------
// Display information about the one skeleton Rips complex. Note that
// the filtration displayed here comes from the distance matrix computed
// above, which is 1 - initial correlation matrix. Only this way, we obtain
// a complex with filtration. If a correlation matrix is used instead, we would
// have a reverse filtration (i.e. filtration of boundary of each simplex S
// is greater or equal to the filtration of S).
// ----------------------------------------------------------------------------
std::clog << "Rips complex is of dimension " << stree.dimension() << " - " << stree.num_simplices() << " simplices - "
<< stree.num_vertices() << " vertices." << std::endl;
std::clog << "Iterator on Rips complex simplices in the filtration order, with [filtration value]:" << std::endl;
for (auto f_simplex : stree.filtration_simplex_range()) {
std::clog << " ( ";
for (auto vertex : stree.simplex_vertex_range(f_simplex)) {
std::clog << vertex << " ";
}
std::clog << ") -> "
<< "[" << stree.filtration(f_simplex) << "] ";
std::clog << std::endl;
}
return 0;
}
Gudhi::Simplex_tree
Simplex Tree data structure for representing simplicial complexes.
Definition Simplex_tree.h:98
Gudhi::Simplex_tree< Gudhi::Simplex_tree_options_fast_persistence >::Filtration_value
Options::Filtration_value Filtration_value
Definition Simplex_tree.h:105
Gudhi::Simplex_tree::simplex_vertex_range
Simplex_vertex_range simplex_vertex_range(Simplex_handle sh) const
Returns a range over the vertices of a simplex.
Definition Simplex_tree.h:369
Gudhi::Simplex_tree::filtration
static Filtration_value filtration(Simplex_handle sh)
Returns the filtration value of a simplex.
Definition Simplex_tree.h:727
Gudhi::Simplex_tree::filtration_simplex_range
Filtration_simplex_range const & filtration_simplex_range(Indexing_tag=Indexing_tag()) const
Returns a range over the simplices of the simplicial complex, in the order of the filtration.
Definition Simplex_tree.h:358
Gudhi::Simplex_tree::num_vertices
size_t num_vertices() const
Returns the number of vertices in the complex.
Definition Simplex_tree.h:778
Gudhi::Simplex_tree::num_simplices
size_t num_simplices() const
Returns the number of simplices in the simplex_tree.
Definition Simplex_tree.h:791
Gudhi::rips_complex::Rips_complex
Rips complex data structure.
Definition Rips_complex.h:45
Gudhi::rips_complex::Rips_complex::create_complex
void create_complex(SimplicialComplexForRips &complex, int dim_max)
Initializes the simplicial complex from the Rips graph and expands it until a given maximal dimension...
Definition Rips_complex.h:104
distance_functions.h
Global distance functions.