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+/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ * Author(s): Marc Glisse
+ *
+ * Copyright (C) 2015 Inria
+ *
+ * Modification(s):
+ * - YYYY/MM Author: Description of the modification
+ */
+
+#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 5 */
+ /* o---o---o */
+ /* / \ / */
+ /* o---o o */
+ /* 2 0 4 */
+
+ const short edge01[] = {0, 1};
+ const short edge02[] = {0, 2};
+ const short edge12[] = {1, 2};
+ const short edge03[] = {0, 3};
+ const short edge13[] = {1, 3};
+ const short edge35[] = {3, 5};
+ const short vertex4[] = {4};
+ st.insert_simplex_and_subfaces(edge01);
+ st.insert_simplex_and_subfaces(edge02);
+ st.insert_simplex_and_subfaces(edge12);
+ st.insert_simplex_and_subfaces(edge03);
+ st.insert_simplex(edge13);
+ st.insert_simplex_and_subfaces(edge35);
+ st.insert_simplex(vertex4);
+
+ // Sort the simplices in the order of the filtration
+ st.initialize_filtration();
+
+ // Class for homology computation
+ // By default, since the complex has dimension 1, only 0-dimensional homology would be computed.
+ // Here we also want persistent homology to be computed for the maximal dimension in the complex (persistence_dim_max = true)
+ Persistent_cohomology pcoh(st, true);
+
+ // 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
+ // 2 1 0 inf
+ // means that in Z/2Z-homology, the Betti numbers are b0=2 and b1=2.
+ pcoh.output_diagram();
+
+ // Print the Betti numbers are b0=2 and b1=2.
+ std::cout << std::endl;
+ std::cout << "The Betti numbers are : ";
+ for (int i = 0; i < 3; i++)
+ std::cout << "b" << i << " = " << pcoh.betti_number(i) << " ; ";
+ std::cout << std::endl;
+}