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/* 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): Marc Glisse
*
* Copyright (C) 2015 INRIA Saclay - Ile-de-France (France)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <gudhi/Simplex_tree.h>
#include <gudhi/Persistent_cohomology.h>
#include <iostream>
#include <vector>
#include <cstdint> // for std::uint8_t
/* We could perfectly well use the default Simplex_tree<> (which uses
* Simplex_tree_options_full_featured), the following simply demonstrates
* how to save on storage by not storing a filtration value. */
struct MyOptions : Gudhi::Simplex_tree_options_full_featured {
// Implicitly use 0 as filtration value for all simplices
static const bool store_filtration = false;
// The persistence algorithm needs this
static const bool store_key = true;
// I have few vertices
typedef short Vertex_handle;
// Maximum number of simplices to compute persistence is 2^8 - 1 = 255. One is reserved for null_key
typedef std::uint8_t Simplex_key;
};
using ST = Gudhi::Simplex_tree<MyOptions>;
using Field_Zp = Gudhi::persistent_cohomology::Field_Zp;
using Persistent_cohomology = Gudhi::persistent_cohomology::Persistent_cohomology<ST, Field_Zp>;
int main() {
ST st;
/* Complex to build. */
/* 1 3 */
/* o---o */
/* /X\ / */
/* o---o o */
/* 2 0 4 */
const short triangle012[] = {0, 1, 2};
const short edge03[] = {0, 3};
const short edge13[] = {1, 3};
const short vertex4[] = {4};
st.insert_simplex_and_subfaces(triangle012);
st.insert_simplex_and_subfaces(edge03);
st.insert_simplex(edge13);
st.insert_simplex(vertex4);
// Sort the simplices in the order of the filtration
st.initialize_filtration();
// Class for homology computation
Persistent_cohomology pcoh(st);
// Initialize the coefficient field Z/2Z for homology
pcoh.init_coefficients(2);
// Compute the persistence diagram of the complex
pcoh.compute_persistent_cohomology();
// Print the result. The format is, on each line: 2 dim 0 inf
// where 2 represents the field, dim the dimension of the feature.
// 2 0 0 inf
// 2 0 0 inf
// 2 1 0 inf
// means that in Z/2Z-homology, the Betti numbers are b0=2 and b1=1.
pcoh.output_diagram();
// Print the Betti numbers are b0=2 and b1=1.
std::cout << std::endl;
std::cout << "The Betti numbers are : ";
for (int i = 0; i < st.dimension(); i++)
std::cout << "b" << i << " = " << pcoh.betti_number(i) << " ; ";
std::cout << std::endl;
}
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