Persistent_cohomology/plain_homology.cpp

/* 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. */

// 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;

};

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);

// FIXME: Remove this line

st.set_dimension(2);

// 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;

}

GUDHI Version 2.0.0 - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. | Generated on Wed Apr 19 2017 22:26:16 for GUDHI by 1.8.11 |