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Diffstat (limited to 'trunk/src/Simplex_tree/test/simplex_tree_unit_test.cpp')
-rw-r--r-- | trunk/src/Simplex_tree/test/simplex_tree_unit_test.cpp | 1138 |
1 files changed, 1138 insertions, 0 deletions
diff --git a/trunk/src/Simplex_tree/test/simplex_tree_unit_test.cpp b/trunk/src/Simplex_tree/test/simplex_tree_unit_test.cpp new file mode 100644 index 00000000..17ddc605 --- /dev/null +++ b/trunk/src/Simplex_tree/test/simplex_tree_unit_test.cpp @@ -0,0 +1,1138 @@ +#include <iostream> +#include <fstream> +#include <string> +#include <algorithm> +#include <utility> // std::pair, std::make_pair +#include <cmath> // float comparison +#include <limits> +#include <functional> // greater + +#define BOOST_TEST_DYN_LINK +#define BOOST_TEST_MODULE "simplex_tree" +#include <boost/test/unit_test.hpp> +#include <boost/mpl/list.hpp> + +// ^ +// /!\ Nothing else from Simplex_tree shall be included to test includes are well defined. +#include "gudhi/Simplex_tree.h" + +using namespace Gudhi; + +typedef boost::mpl::list<Simplex_tree<>, Simplex_tree<Simplex_tree_options_fast_persistence>> list_of_tested_variants; + + +template<class typeST> +void test_empty_simplex_tree(typeST& tst) { + typedef typename typeST::Vertex_handle Vertex_handle; + const Vertex_handle DEFAULT_VERTEX_VALUE = Vertex_handle(- 1); + BOOST_CHECK(tst.null_vertex() == DEFAULT_VERTEX_VALUE); + BOOST_CHECK(tst.num_vertices() == (size_t) 0); + BOOST_CHECK(tst.num_simplices() == (size_t) 0); + typename typeST::Siblings* STRoot = tst.root(); + BOOST_CHECK(STRoot != nullptr); + BOOST_CHECK(STRoot->oncles() == nullptr); + BOOST_CHECK(STRoot->parent() == DEFAULT_VERTEX_VALUE); + BOOST_CHECK(tst.dimension() == -1); +} + +template<class typeST> +void test_iterators_on_empty_simplex_tree(typeST& tst) { + std::cout << "Iterator on vertices: " << std::endl; + for (auto vertex : tst.complex_vertex_range()) { + std::cout << "vertice:" << vertex << std::endl; + BOOST_CHECK(false); // shall be empty + } + std::cout << "Iterator on simplices: " << std::endl; + for (auto simplex : tst.complex_simplex_range()) { + BOOST_CHECK(simplex != simplex); // shall be empty - to remove warning of non-used simplex + } + + std::cout + << "Iterator on Simplices in the filtration, with [filtration value]:" + << std::endl; + for (auto f_simplex : tst.filtration_simplex_range()) { + BOOST_CHECK(false); // shall be empty + std::cout << "test_iterators_on_empty_simplex_tree - filtration=" + << tst.filtration(f_simplex) << std::endl; + } +} + +BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_when_empty, typeST, list_of_tested_variants) { + typedef std::pair<typename typeST::Simplex_handle, bool> typePairSimplexBool; + typedef std::vector<typename typeST::Vertex_handle> typeVectorVertex; + + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST OF DEFAULT CONSTRUCTOR" << std::endl; + typeST st; + + test_empty_simplex_tree(st); + + test_iterators_on_empty_simplex_tree(st); + // TEST OF EMPTY INSERTION + std::cout << "TEST OF EMPTY INSERTION" << std::endl; + typeVectorVertex simplexVectorEmpty; + BOOST_CHECK(simplexVectorEmpty.empty() == true); + typePairSimplexBool returnEmptyValue = st.insert_simplex(simplexVectorEmpty, 0.0); + BOOST_CHECK(returnEmptyValue.first == typename typeST::Simplex_handle(nullptr)); + BOOST_CHECK(returnEmptyValue.second == true); + + test_empty_simplex_tree(st); + + test_iterators_on_empty_simplex_tree(st); +} + +bool AreAlmostTheSame(float a, float b) { + return std::fabs(a - b) < std::numeric_limits<float>::epsilon(); +} + +BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_from_file, typeST, list_of_tested_variants) { + // TEST OF INSERTION + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST OF SIMPLEX TREE FROM A FILE" << std::endl; + typeST st; + + std::string inputFile("simplex_tree_for_unit_test.txt"); + std::ifstream simplex_tree_stream(inputFile.c_str()); + simplex_tree_stream >> st; + + // Display the Simplex_tree + std::cout << "The complex contains " << st.num_simplices() << " simplices" << std::endl; + std::cout << " - dimension " << st.dimension() << std::endl; + + // Check + BOOST_CHECK(st.num_simplices() == 143353); + BOOST_CHECK(st.dimension() == 3); + + int previous_size = 0; + for (auto f_simplex : st.filtration_simplex_range()) { + // Size of simplex + int size = 0; + for (auto vertex : st.simplex_vertex_range(f_simplex)) { + // Remove warning + (void) vertex; + size++; + } + BOOST_CHECK(AreAlmostTheSame(st.filtration(f_simplex), (0.1 * size))); // Specific test: filtration = 0.1 * simplex_size + BOOST_CHECK(previous_size <= size); // Check list is sorted (because of sorted filtrations in simplex_tree.txt) + previous_size = size; + } + simplex_tree_stream.close(); +} + +template<class typeST, class typeSimplex> +void test_simplex_tree_contains(typeST& simplexTree, typeSimplex& simplex, int pos) { + auto f_simplex = simplexTree.filtration_simplex_range().begin() + pos; + + std::cout << "test_simplex_tree_contains - filtration=" << simplexTree.filtration(*f_simplex) << "||" << simplex.second << std::endl; + BOOST_CHECK(AreAlmostTheSame(simplexTree.filtration(*f_simplex), simplex.second)); + + int simplexIndex = simplex.first.size() - 1; + std::sort(simplex.first.begin(), simplex.first.end()); // if the simplex wasn't sorted, the next test could fail + for (auto vertex : simplexTree.simplex_vertex_range(*f_simplex)) { + std::cout << "test_simplex_tree_contains - vertex=" << vertex << "||" << simplex.first.at(simplexIndex) << std::endl; + BOOST_CHECK(vertex == simplex.first.at(simplexIndex)); + BOOST_CHECK(simplexIndex >= 0); + simplexIndex--; + } +} + +template<class typeST, class typePairSimplexBool> +void test_simplex_tree_insert_returns_true(const typePairSimplexBool& returnValue) { + BOOST_CHECK(returnValue.second == true); + // Simplex_handle = boost::container::flat_map< typeST::Vertex_handle, Node >::iterator + typename typeST::Simplex_handle shReturned = returnValue.first; + BOOST_CHECK(shReturned != typename typeST::Simplex_handle(nullptr)); +} + +// Global variables +int dim_max = -1; + +template<class typeST, class Filtration_value> +void set_and_test_simplex_tree_dim_fil(typeST& simplexTree, int vectorSize, const Filtration_value& fil) { + if (vectorSize > dim_max + 1) { + dim_max = vectorSize - 1; + simplexTree.set_dimension(dim_max); + std::cout << " set_and_test_simplex_tree_dim_fil - dim_max=" << dim_max + << std::endl; + } + + BOOST_CHECK(simplexTree.dimension() == dim_max); + + // Another way to count simplices: + size_t num_simp = 0; + for (auto f_simplex : simplexTree.complex_simplex_range()) { + // Remove warning + (void) f_simplex; + num_simp++; + } + + BOOST_CHECK(simplexTree.num_simplices() == num_simp); +} + +BOOST_AUTO_TEST_CASE_TEMPLATE(simplex_tree_insertion, typeST, list_of_tested_variants) { + typedef typename typeST::Filtration_value Filtration_value; + typedef std::pair<typename typeST::Simplex_handle, bool> typePairSimplexBool; + typedef std::vector<typename typeST::Vertex_handle> typeVectorVertex; + typedef std::pair<typeVectorVertex, Filtration_value> typeSimplex; + const Filtration_value FIRST_FILTRATION_VALUE = 0.1; + const Filtration_value SECOND_FILTRATION_VALUE = 0.2; + const Filtration_value THIRD_FILTRATION_VALUE = 0.3; + const Filtration_value FOURTH_FILTRATION_VALUE = 0.4; + // reset since we run the test several times + dim_max = -1; + + // TEST OF INSERTION + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST OF INSERTION" << std::endl; + typeST st; + + // ++ FIRST + std::cout << " - INSERT 0" << std::endl; + typeVectorVertex firstSimplexVector{0}; + BOOST_CHECK(firstSimplexVector.size() == 1); + typeSimplex firstSimplex = std::make_pair(firstSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE)); + typePairSimplexBool returnValue = st.insert_simplex(firstSimplex.first, firstSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, firstSimplexVector.size(), firstSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 1); + + // ++ SECOND + std::cout << " - INSERT 1" << std::endl; + typeVectorVertex secondSimplexVector{1}; + BOOST_CHECK(secondSimplexVector.size() == 1); + typeSimplex secondSimplex = std::make_pair(secondSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE)); + returnValue = st.insert_simplex(secondSimplex.first, secondSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, secondSimplexVector.size(), secondSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 2); + + // ++ THIRD + std::cout << " - INSERT (0,1)" << std::endl; + typeVectorVertex thirdSimplexVector{0, 1}; + BOOST_CHECK(thirdSimplexVector.size() == 2); + typeSimplex thirdSimplex = std::make_pair(thirdSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE)); + returnValue = st.insert_simplex(thirdSimplex.first, thirdSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, thirdSimplexVector.size(), thirdSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 2); // Not incremented !! + + // ++ FOURTH + std::cout << " - INSERT 2" << std::endl; + typeVectorVertex fourthSimplexVector{2}; + BOOST_CHECK(fourthSimplexVector.size() == 1); + typeSimplex fourthSimplex = std::make_pair(fourthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE)); + returnValue = st.insert_simplex(fourthSimplex.first, fourthSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, fourthSimplexVector.size(), fourthSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 3); + + // ++ FIFTH + std::cout << " - INSERT (2,0)" << std::endl; + typeVectorVertex fifthSimplexVector{2, 0}; + BOOST_CHECK(fifthSimplexVector.size() == 2); + typeSimplex fifthSimplex = std::make_pair(fifthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE)); + returnValue = st.insert_simplex(fifthSimplex.first, fifthSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, fifthSimplexVector.size(), fifthSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 3); // Not incremented !! + + // ++ SIXTH + std::cout << " - INSERT (2,1)" << std::endl; + typeVectorVertex sixthSimplexVector{2, 1}; + BOOST_CHECK(sixthSimplexVector.size() == 2); + typeSimplex sixthSimplex = std::make_pair(sixthSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE)); + returnValue = st.insert_simplex(sixthSimplex.first, sixthSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, sixthSimplexVector.size(), sixthSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 3); // Not incremented !! + + // ++ SEVENTH + std::cout << " - INSERT (2,1,0)" << std::endl; + typeVectorVertex seventhSimplexVector{2, 1, 0}; + BOOST_CHECK(seventhSimplexVector.size() == 3); + typeSimplex seventhSimplex = std::make_pair(seventhSimplexVector, Filtration_value(THIRD_FILTRATION_VALUE)); + returnValue = st.insert_simplex(seventhSimplex.first, seventhSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, seventhSimplexVector.size(), seventhSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 3); // Not incremented !! + + // ++ EIGHTH + std::cout << " - INSERT 3" << std::endl; + typeVectorVertex eighthSimplexVector{3}; + BOOST_CHECK(eighthSimplexVector.size() == 1); + typeSimplex eighthSimplex = std::make_pair(eighthSimplexVector, Filtration_value(FIRST_FILTRATION_VALUE)); + returnValue = st.insert_simplex(eighthSimplex.first, eighthSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, eighthSimplexVector.size(), eighthSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 4); + + // ++ NINETH + std::cout << " - INSERT (3,0)" << std::endl; + typeVectorVertex ninethSimplexVector{3, 0}; + BOOST_CHECK(ninethSimplexVector.size() == 2); + typeSimplex ninethSimplex = std::make_pair(ninethSimplexVector, Filtration_value(SECOND_FILTRATION_VALUE)); + returnValue = st.insert_simplex(ninethSimplex.first, ninethSimplex.second); + + test_simplex_tree_insert_returns_true<typeST>(returnValue); + set_and_test_simplex_tree_dim_fil(st, ninethSimplexVector.size(), ninethSimplex.second); + BOOST_CHECK(st.num_vertices() == (size_t) 4); // Not incremented !! + + // ++ TENTH + std::cout << " - INSERT 0 (already inserted)" << std::endl; + typeVectorVertex tenthSimplexVector{0}; + BOOST_CHECK(tenthSimplexVector.size() == 1); + // With a different filtration value + typeSimplex tenthSimplex = std::make_pair(tenthSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE)); + returnValue = st.insert_simplex(tenthSimplex.first, tenthSimplex.second); + + BOOST_CHECK(returnValue.second == false); + // Simplex_handle = boost::container::flat_map< typeST::Vertex_handle, Node >::iterator + typename typeST::Simplex_handle shReturned = returnValue.first; + BOOST_CHECK(shReturned == typename typeST::Simplex_handle(nullptr)); + BOOST_CHECK(st.num_vertices() == (size_t) 4); // Not incremented !! + BOOST_CHECK(st.dimension() == dim_max); + + // ++ ELEVENTH + std::cout << " - INSERT (2,1,0) (already inserted)" << std::endl; + typeVectorVertex eleventhSimplexVector{2, 1, 0}; + BOOST_CHECK(eleventhSimplexVector.size() == 3); + typeSimplex eleventhSimplex = std::make_pair(eleventhSimplexVector, Filtration_value(FOURTH_FILTRATION_VALUE)); + returnValue = st.insert_simplex(eleventhSimplex.first, eleventhSimplex.second); + + BOOST_CHECK(returnValue.second == false); + // Simplex_handle = boost::container::flat_map< typeST::Vertex_handle, Node >::iterator + shReturned = returnValue.first; + BOOST_CHECK(shReturned == typename typeST::Simplex_handle(nullptr)); + BOOST_CHECK(st.num_vertices() == (size_t) 4); // Not incremented !! + BOOST_CHECK(st.dimension() == dim_max); + + /* Inserted simplex: */ + /* 1 */ + /* o */ + /* /X\ */ + /* o---o---o */ + /* 2 0 3 */ + + // [0.1] 0 + // [0.1] 1 + // [0.1] 2 + // [0.1] 3 + // [0.2] 1 0 + // [0.2] 2 0 + // [0.2] 2 1 + // [0.2] 3 0 + // [0.3] 2 1 0 + // !! Be careful, simplex are sorted by filtration value on insertion !! + std::cout << "simplex_tree_insertion - first - 0" << std::endl; + test_simplex_tree_contains(st, firstSimplex, 0); // (0) -> 0 + std::cout << "simplex_tree_insertion - second - 1" << std::endl; + test_simplex_tree_contains(st, secondSimplex, 1); // (1) -> 1 + std::cout << "simplex_tree_insertion - third - 4" << std::endl; + test_simplex_tree_contains(st, thirdSimplex, 4); // (0,1) -> 4 + std::cout << "simplex_tree_insertion - fourth - 2" << std::endl; + test_simplex_tree_contains(st, fourthSimplex, 2); // (2) -> 2 + std::cout << "simplex_tree_insertion - fifth - 5" << std::endl; + test_simplex_tree_contains(st, fifthSimplex, 5); // (2,0) -> 5 + std::cout << "simplex_tree_insertion - sixth - 6" << std::endl; + test_simplex_tree_contains(st, sixthSimplex, 6); //(2,1) -> 6 + std::cout << "simplex_tree_insertion - seventh - 8" << std::endl; + test_simplex_tree_contains(st, seventhSimplex, 8); // (2,1,0) -> 8 + std::cout << "simplex_tree_insertion - eighth - 3" << std::endl; + test_simplex_tree_contains(st, eighthSimplex, 3); // (3) -> 3 + std::cout << "simplex_tree_insertion - nineth - 7" << std::endl; + test_simplex_tree_contains(st, ninethSimplex, 7); // (3,0) -> 7 + + // Display the Simplex_tree - Can not be done in the middle of 2 inserts + std::cout << "The complex contains " << st.num_simplices() << " simplices" << std::endl; + std::cout << " - dimension " << st.dimension() << std::endl; + std::cout << std::endl << std::endl << "Iterator on Simplices in the filtration, with [filtration value]:" << std::endl; + for (auto f_simplex : st.filtration_simplex_range()) { + std::cout << " " << "[" << st.filtration(f_simplex) << "] "; + for (auto vertex : st.simplex_vertex_range(f_simplex)) { + std::cout << (int) vertex << " "; + } + std::cout << std::endl; + } + +} + +BOOST_AUTO_TEST_CASE_TEMPLATE(NSimplexAndSubfaces_tree_insertion, typeST, list_of_tested_variants) { + typedef std::pair<typename typeST::Simplex_handle, bool> typePairSimplexBool; + typedef std::vector<typename typeST::Vertex_handle> typeVectorVertex; + typedef std::pair<typeVectorVertex, typename typeST::Filtration_value> typeSimplex; + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST OF RECURSIVE INSERTION" << std::endl; + typeST st; + typePairSimplexBool returnValue; + int position = 0; + + // ++ FIRST + std::cout << " - INSERT (2,1,0)" << std::endl; + typeVectorVertex SimplexVector1{2, 1, 0}; + BOOST_CHECK(SimplexVector1.size() == 3); + returnValue = st.insert_simplex_and_subfaces(SimplexVector1); + + BOOST_CHECK(st.num_vertices() == (size_t) 3); // +3 (2, 1 and 0 are not existing) + + // Check it is well inserted + BOOST_CHECK(true == returnValue.second); + position = 0; + std::sort(SimplexVector1.begin(), SimplexVector1.end(), std::greater<typename typeST::Vertex_handle>()); + for (auto vertex : st.simplex_vertex_range(returnValue.first)) { + // Check returned Simplex_handle + std::cout << "vertex = " << vertex << " | vector[" << position << "] = " << SimplexVector1[position] << std::endl; + BOOST_CHECK(vertex == SimplexVector1[position]); + position++; + } + + // ++ SECOND + std::cout << " - INSERT 3" << std::endl; + typeVectorVertex SimplexVector2{3}; + BOOST_CHECK(SimplexVector2.size() == 1); + returnValue = st.insert_simplex_and_subfaces(SimplexVector2); + + BOOST_CHECK(st.num_vertices() == (size_t) 4); // +1 (3 is not existing) + + // Check it is well inserted + BOOST_CHECK(true == returnValue.second); + position = 0; + std::sort(SimplexVector2.begin(), SimplexVector2.end(), std::greater<typename typeST::Vertex_handle>()); + for (auto vertex : st.simplex_vertex_range(returnValue.first)) { + // Check returned Simplex_handle + std::cout << "vertex = " << vertex << " | vector[" << position << "] = " << SimplexVector2[position] << std::endl; + BOOST_CHECK(vertex == SimplexVector2[position]); + position++; + } + + // ++ THIRD + std::cout << " - INSERT (0,3)" << std::endl; + typeVectorVertex SimplexVector3{3, 0}; + BOOST_CHECK(SimplexVector3.size() == 2); + returnValue = st.insert_simplex_and_subfaces(SimplexVector3); + + BOOST_CHECK(st.num_vertices() == (size_t) 4); // Not incremented (all are existing) + + // Check it is well inserted + BOOST_CHECK(true == returnValue.second); + position = 0; + std::sort(SimplexVector3.begin(), SimplexVector3.end(), std::greater<typename typeST::Vertex_handle>()); + for (auto vertex : st.simplex_vertex_range(returnValue.first)) { + // Check returned Simplex_handle + std::cout << "vertex = " << vertex << " | vector[" << position << "] = " << SimplexVector3[position] << std::endl; + BOOST_CHECK(vertex == SimplexVector3[position]); + position++; + } + + // ++ FOURTH + std::cout << " - INSERT (1,0) (already inserted)" << std::endl; + typeVectorVertex SimplexVector4{1, 0}; + BOOST_CHECK(SimplexVector4.size() == 2); + returnValue = st.insert_simplex_and_subfaces(SimplexVector4); + + BOOST_CHECK(st.num_vertices() == (size_t) 4); // Not incremented (all are existing) + + // Check it was not inserted (already there from {2,1,0} insertion) + BOOST_CHECK(false == returnValue.second); + + // ++ FIFTH + std::cout << " - INSERT (3,4,5)" << std::endl; + typeVectorVertex SimplexVector5{3, 4, 5}; + BOOST_CHECK(SimplexVector5.size() == 3); + returnValue = st.insert_simplex_and_subfaces(SimplexVector5); + + BOOST_CHECK(st.num_vertices() == (size_t) 6); + + // Check it is well inserted + BOOST_CHECK(true == returnValue.second); + position = 0; + std::sort(SimplexVector5.begin(), SimplexVector5.end(), std::greater<typename typeST::Vertex_handle>()); + for (auto vertex : st.simplex_vertex_range(returnValue.first)) { + // Check returned Simplex_handle + std::cout << "vertex = " << vertex << " | vector[" << position << "] = " << SimplexVector5[position] << std::endl; + BOOST_CHECK(vertex == SimplexVector5[position]); + position++; + } + + // ++ SIXTH + std::cout << " - INSERT (0,1,6,7)" << std::endl; + typeVectorVertex SimplexVector6{0, 1, 6, 7}; + BOOST_CHECK(SimplexVector6.size() == 4); + returnValue = st.insert_simplex_and_subfaces(SimplexVector6); + + BOOST_CHECK(st.num_vertices() == (size_t) 8); // +2 (6 and 7 are not existing - 0 and 1 are already existing) + + // Check it is well inserted + BOOST_CHECK(true == returnValue.second); + position = 0; + std::sort(SimplexVector6.begin(), SimplexVector6.end(), std::greater<typename typeST::Vertex_handle>()); + for (auto vertex : st.simplex_vertex_range(returnValue.first)) { + // Check returned Simplex_handle + std::cout << "vertex = " << vertex << " | vector[" << position << "] = " << SimplexVector6[position] << std::endl; + BOOST_CHECK(vertex == SimplexVector6[position]); + position++; + } + + /* Inserted simplex: */ + /* 1 6 */ + /* o---o */ + /* /X\7/ */ + /* o---o---o---o */ + /* 2 0 3\X/4 */ + /* o */ + /* 5 */ + /* */ + /* In other words: */ + /* A facet [2,1,0] */ + /* An edge [0,3] */ + /* A facet [3,4,5] */ + /* A cell [0,1,6,7] */ + + typeSimplex simplexPair1 = std::make_pair(SimplexVector1, 0.0); + typeSimplex simplexPair2 = std::make_pair(SimplexVector2, 0.0); + typeSimplex simplexPair3 = std::make_pair(SimplexVector3, 0.0); + typeSimplex simplexPair4 = std::make_pair(SimplexVector4, 0.0); + typeSimplex simplexPair5 = std::make_pair(SimplexVector5, 0.0); + typeSimplex simplexPair6 = std::make_pair(SimplexVector6, 0.0); + test_simplex_tree_contains(st, simplexPair1, 6); // (2,1,0) is in position 6 + test_simplex_tree_contains(st, simplexPair2, 7); // (3) is in position 7 + test_simplex_tree_contains(st, simplexPair3, 8); // (3,0) is in position 8 + test_simplex_tree_contains(st, simplexPair4, 2); // (1,0) is in position 2 + test_simplex_tree_contains(st, simplexPair5, 14); // (3,4,5) is in position 14 + test_simplex_tree_contains(st, simplexPair6, 26); // (7,6,1,0) is in position 26 + + // ------------------------------------------------------------------------------------------------------------------ + // Find in the simplex_tree + // ------------------------------------------------------------------------------------------------------------------ + typeVectorVertex simpleSimplexVector{1}; + typename typeST::Simplex_handle simplexFound = st.find(simpleSimplexVector); + std::cout << "**************IS THE SIMPLEX {1} IN THE SIMPLEX TREE ?\n"; + if (simplexFound != st.null_simplex()) + std::cout << "***+ YES IT IS!\n"; + else + std::cout << "***- NO IT ISN'T\n"; + // Check it is found + BOOST_CHECK(simplexFound != st.null_simplex()); + + typeVectorVertex unknownSimplexVector{15}; + simplexFound = st.find(unknownSimplexVector); + std::cout << "**************IS THE SIMPLEX {15} IN THE SIMPLEX TREE ?\n"; + if (simplexFound != st.null_simplex()) + std::cout << "***+ YES IT IS!\n"; + else + std::cout << "***- NO IT ISN'T\n"; + // Check it is NOT found + BOOST_CHECK(simplexFound == st.null_simplex()); + + simplexFound = st.find(SimplexVector6); + std::cout << "**************IS THE SIMPLEX {0,1,6,7} IN THE SIMPLEX TREE ?\n"; + if (simplexFound != st.null_simplex()) + std::cout << "***+ YES IT IS!\n"; + else + std::cout << "***- NO IT ISN'T\n"; + // Check it is found + BOOST_CHECK(simplexFound != st.null_simplex()); + + typeVectorVertex otherSimplexVector{1, 15}; + simplexFound = st.find(otherSimplexVector); + std::cout << "**************IS THE SIMPLEX {15,1} IN THE SIMPLEX TREE ?\n"; + if (simplexFound != st.null_simplex()) + std::cout << "***+ YES IT IS!\n"; + else + std::cout << "***- NO IT ISN'T\n"; + // Check it is NOT found + BOOST_CHECK(simplexFound == st.null_simplex()); + + typeVectorVertex invSimplexVector{1, 2, 0}; + simplexFound = st.find(invSimplexVector); + std::cout << "**************IS THE SIMPLEX {1,2,0} IN THE SIMPLEX TREE ?\n"; + if (simplexFound != st.null_simplex()) + std::cout << "***+ YES IT IS!\n"; + else + std::cout << "***- NO IT ISN'T\n"; + // Check it is found + BOOST_CHECK(simplexFound != st.null_simplex()); + + // Display the Simplex_tree - Can not be done in the middle of 2 inserts + std::cout << "The complex contains " << st.num_simplices() << " simplices" << std::endl; + std::cout << " - dimension " << st.dimension() << std::endl; + std::cout << std::endl << std::endl << "Iterator on Simplices in the filtration, with [filtration value]:" << std::endl; + for (auto f_simplex : st.filtration_simplex_range()) { + std::cout << " " << "[" << st.filtration(f_simplex) << "] "; + for (auto vertex : st.simplex_vertex_range(f_simplex)) { + std::cout << (int) vertex << " "; + } + std::cout << std::endl; + } +} + +template<class typeST, class Vertex_handle> +void test_cofaces(typeST& st, const std::vector<Vertex_handle>& expected, int dim, const std::vector<typename typeST::Simplex_handle>& res) { + typename typeST::Cofaces_simplex_range cofaces; + if (dim == 0) + cofaces = st.star_simplex_range(st.find(expected)); + else + cofaces = st.cofaces_simplex_range(st.find(expected), dim); + for (auto simplex = cofaces.begin(); simplex != cofaces.end(); ++simplex) { + typename typeST::Simplex_vertex_range rg = st.simplex_vertex_range(*simplex); + for (auto vertex = rg.begin(); vertex != rg.end(); ++vertex) { + std::cout << "(" << *vertex << ")"; + } + std::cout << std::endl; + BOOST_CHECK(std::find(res.begin(), res.end(), *simplex) != res.end()); + } +} + +BOOST_AUTO_TEST_CASE_TEMPLATE(coface_on_simplex_tree, typeST, list_of_tested_variants) { + typedef std::vector<typename typeST::Vertex_handle> typeVectorVertex; + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST COFACE ALGORITHM" << std::endl; + typeST st; + + typeVectorVertex SimplexVector{2, 1, 0}; + st.insert_simplex_and_subfaces(SimplexVector); + + SimplexVector = {3, 0}; + st.insert_simplex_and_subfaces(SimplexVector); + + SimplexVector = {3, 4, 5}; + st.insert_simplex_and_subfaces(SimplexVector); + + SimplexVector = {0, 1, 6, 7}; + st.insert_simplex_and_subfaces(SimplexVector); + + /* Inserted simplex: */ + /* 1 6 */ + /* o---o */ + /* /X\7/ */ + /* o---o---o---o */ + /* 2 0 3\X/4 */ + /* o */ + /* 5 */ + + // FIXME + st.set_dimension(3); + + std::vector<typename typeST::Vertex_handle> simplex_result; + std::vector<typename typeST::Simplex_handle> result; + std::cout << "First test - Star of (3):" << std::endl; + + simplex_result = {3}; + result.push_back(st.find(simplex_result)); + + simplex_result = {3, 0}; + result.push_back(st.find(simplex_result)); + + simplex_result = {4, 3}; + result.push_back(st.find(simplex_result)); + + simplex_result = {5, 4, 3}; + result.push_back(st.find(simplex_result)); + + simplex_result = {5, 3}; + result.push_back(st.find(simplex_result)); + simplex_result.clear(); + + std::vector<typename typeST::Vertex_handle> vertex = {3}; + test_cofaces(st, vertex, 0, result); + vertex.clear(); + result.clear(); + + vertex.push_back(1); + vertex.push_back(7); + std::cout << "Second test - Star of (1,7): " << std::endl; + + simplex_result = {7, 1}; + result.push_back(st.find(simplex_result)); + + simplex_result = {7, 6, 1, 0}; + result.push_back(st.find(simplex_result)); + + simplex_result = {7, 1, 0}; + result.push_back(st.find(simplex_result)); + + simplex_result = {7, 6, 1}; + result.push_back(st.find(simplex_result)); + + test_cofaces(st, vertex, 0, result); + result.clear(); + + std::cout << "Third test - 2-dimension Cofaces of simplex(1,7) : " << std::endl; + + simplex_result = {7, 1, 0}; + result.push_back(st.find(simplex_result)); + + simplex_result = {7, 6, 1}; + result.push_back(st.find(simplex_result)); + + test_cofaces(st, vertex, 1, result); + result.clear(); + + std::cout << "Cofaces with a codimension too high (codimension + vetices > tree.dimension) :" << std::endl; + test_cofaces(st, vertex, 5, result); + + //std::cout << "Cofaces with an empty codimension" << std::endl; + //test_cofaces(st, vertex, -1, result); + // std::cout << "Cofaces in an empty simplex tree" << std::endl; + // typeST empty_tree; + // test_cofaces(empty_tree, vertex, 1, result); + //std::cout << "Cofaces of an empty simplex" << std::endl; + //vertex.clear(); + // test_cofaces(st, vertex, 1, result); + +} + +BOOST_AUTO_TEST_CASE_TEMPLATE(copy_move_on_simplex_tree, typeST, list_of_tested_variants) { + typedef std::vector<typename typeST::Vertex_handle> typeVectorVertex; + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST COPY MOVE CONSTRUCTORS" << std::endl; + typeST st; + + typeVectorVertex SimplexVector{2, 1, 0}; + st.insert_simplex_and_subfaces(SimplexVector); + + SimplexVector = {3, 0}; + st.insert_simplex_and_subfaces(SimplexVector); + + SimplexVector = {3, 4, 5}; + st.insert_simplex_and_subfaces(SimplexVector); + + SimplexVector = {0, 1, 6, 7}; + st.insert_simplex_and_subfaces(SimplexVector); + + /* Inserted simplex: */ + /* 1 6 */ + /* o---o */ + /* /X\7/ */ + /* o---o---o---o */ + /* 2 0 3\X/4 */ + /* o */ + /* 5 */ + + // FIXME + st.set_dimension(3); + + std::cout << "Printing st - address = " << &st << std::endl; + + // Copy constructor + typeST st_copy = st; + std::cout << "Printing a copy of st - address = " << &st_copy << std::endl; + + // Check the data are the same + BOOST_CHECK(st == st_copy); + // Check there is a new simplex tree reference + BOOST_CHECK(&st != &st_copy); + + // Move constructor + typeST st_move = std::move(st); + std::cout << "Printing a move of st - address = " << &st_move << std::endl; + + // Check the data are the same + BOOST_CHECK(st_move == st_copy); + // Check there is a new simplex tree reference + BOOST_CHECK(&st_move != &st_copy); + BOOST_CHECK(&st_move != &st); + + typeST st_empty; + // Check st has been emptied by the move + BOOST_CHECK(st == st_empty); + BOOST_CHECK(st.dimension() == -1); + BOOST_CHECK(st.num_simplices() == 0); + BOOST_CHECK(st.num_vertices() == (size_t)0); + + std::cout << "Printing st once again- address = " << &st << std::endl; +} + +template<class typeST> +void test_simplex_is_vertex(typeST& st, typename typeST::Simplex_handle sh, typename typeST::Vertex_handle v) { + BOOST_CHECK(st.dimension(sh) == 0); + auto&& r = st.simplex_vertex_range(sh); + auto i = std::begin(r); + BOOST_CHECK(*i == v); + BOOST_CHECK(++i == std::end(r)); +} + +BOOST_AUTO_TEST_CASE(non_contiguous) { + typedef Simplex_tree<> typeST; + typedef typeST::Simplex_handle Simplex_handle; + std::cout << "********************************************************************" << std::endl; + std::cout << "TEST NON-CONTIGUOUS VERTICES" << std::endl; + typeST st; + typeST::Vertex_handle e[] = {3,-7}; + std::cout << "Insert" << std::endl; + st.insert_simplex_and_subfaces(e); + BOOST_CHECK(st.num_vertices() == 2); + BOOST_CHECK(st.num_simplices() == 3); + std::cout << "Find" << std::endl; + Simplex_handle sh = st.find(e); + BOOST_CHECK(sh != st.null_simplex()); + std::cout << "Endpoints" << std::endl; + auto p = st.endpoints(sh); + test_simplex_is_vertex(st, p.first, 3); + test_simplex_is_vertex(st, p.second, -7); + std::cout << "Boundary" << std::endl; + auto&& b = st.boundary_simplex_range(sh); + auto i = std::begin(b); + test_simplex_is_vertex(st, *i, -7); + test_simplex_is_vertex(st, *++i, 3); + BOOST_CHECK(++i == std::end(b)); +} + +BOOST_AUTO_TEST_CASE(make_filtration_non_decreasing) { + std::cout << "********************************************************************" << std::endl; + std::cout << "MAKE FILTRATION NON DECREASING" << std::endl; + typedef Simplex_tree<> typeST; + typeST st; + + st.insert_simplex_and_subfaces({2, 1, 0}, 2.0); + st.insert_simplex_and_subfaces({3, 0}, 2.0); + st.insert_simplex_and_subfaces({3, 4, 5}, 2.0); + + /* Inserted simplex: */ + /* 1 */ + /* o */ + /* /X\ */ + /* o---o---o---o */ + /* 2 0 3\X/4 */ + /* o */ + /* 5 */ + + std::cout << "Check default insertion ensures the filtration values are non decreasing" << std::endl; + BOOST_CHECK(!st.make_filtration_non_decreasing()); + + // Because of non decreasing property of simplex tree, { 0 } , { 1 } and { 0, 1 } are going to be set from value 2.0 + // to 1.0 + st.insert_simplex_and_subfaces({0, 1, 6, 7}, 1.0); + + // Inserted simplex: + // 1 6 + // o---o + // /X\7/ + // o---o---o---o + // 2 0 3\X/4 + // o + // 5 + + std::cout << "Check default second insertion ensures the filtration values are non decreasing" << std::endl; + BOOST_CHECK(!st.make_filtration_non_decreasing()); + + // Copy original simplex tree + typeST st_copy = st; + + // Modify specific values for st to become like st_copy thanks to make_filtration_non_decreasing + st.assign_filtration(st.find({0,1,6,7}), 0.8); + st.assign_filtration(st.find({0,1,6}), 0.9); + st.assign_filtration(st.find({0,6}), 0.6); + st.assign_filtration(st.find({3,4,5}), 1.2); + st.assign_filtration(st.find({3,4}), 1.1); + st.assign_filtration(st.find({4,5}), 1.99); + + std::cout << "Check the simplex_tree is rolled back in case of decreasing filtration values" << std::endl; + BOOST_CHECK(st.make_filtration_non_decreasing()); + BOOST_CHECK(st == st_copy); + + // Other simplex tree + typeST st_other; + st_other.insert_simplex_and_subfaces({2, 1, 0}, 3.0); // This one is different from st + st_other.insert_simplex_and_subfaces({3, 0}, 2.0); + st_other.insert_simplex_and_subfaces({3, 4, 5}, 2.0); + st_other.insert_simplex_and_subfaces({0, 1, 6, 7}, 1.0); + + // Modify specific values for st to become like st_other thanks to make_filtration_non_decreasing + st.assign_filtration(st.find({2}), 3.0); + // By modifying just the simplex {2} + // {0,1,2}, {1,2} and {0,2} will be modified + + std::cout << "Check the simplex_tree is repaired in case of decreasing filtration values" << std::endl; + BOOST_CHECK(st.make_filtration_non_decreasing()); + BOOST_CHECK(st == st_other); + + // Modify specific values for st still to be non-decreasing + st.assign_filtration(st.find({0,1,2}), 10.0); + st.assign_filtration(st.find({0,2}), 9.0); + st.assign_filtration(st.find({0,1,6,7}), 50.0); + st.assign_filtration(st.find({0,1,6}), 49.0); + st.assign_filtration(st.find({0,1,7}), 48.0); + // Other copy simplex tree + typeST st_other_copy = st; + + std::cout << "Check the simplex_tree is not modified in case of non-decreasing filtration values" << std::endl; + BOOST_CHECK(!st.make_filtration_non_decreasing()); + BOOST_CHECK(st == st_other_copy); + +} + +struct MyOptions : Simplex_tree_options_full_featured { + // Not doing persistence, so we don't need those + static const bool store_key = false; + static const bool store_filtration = false; + // I have few vertices + typedef short Vertex_handle; +}; + +BOOST_AUTO_TEST_CASE(remove_maximal_simplex) { + std::cout << "********************************************************************" << std::endl; + std::cout << "REMOVE MAXIMAL SIMPLEX" << std::endl; + + + typedef Simplex_tree<MyOptions> miniST; + miniST st; + + // FIXME + st.set_dimension(3); + + st.insert_simplex_and_subfaces({0, 1, 6, 7}); + st.insert_simplex_and_subfaces({3, 4, 5}); + + // Constructs a copy at this state for further test purpose + miniST st_pruned = st; + + st.insert_simplex_and_subfaces({3, 0}); + st.insert_simplex_and_subfaces({2, 1, 0}); + + // Constructs a copy at this state for further test purpose + miniST st_complete = st; + // st_complete and st: + // 1 6 + // o---o + // /X\7/ + // o---o---o---o + // 2 0 3\X/4 + // o + // 5 + // st_pruned: + // 1 6 + // o---o + // \7/ + // o o---o + // 0 3\X/4 + // o + // 5 + +#ifdef GUDHI_DEBUG + std::cout << "Check exception throw in debug mode" << std::endl; + // throw excpt because sh has children + BOOST_CHECK_THROW (st.remove_maximal_simplex(st.find({0, 1, 6})), std::invalid_argument); + BOOST_CHECK_THROW (st.remove_maximal_simplex(st.find({3})), std::invalid_argument); + BOOST_CHECK(st == st_complete); +#endif + + st.remove_maximal_simplex(st.find({0, 2})); + st.remove_maximal_simplex(st.find({0, 1, 2})); + st.remove_maximal_simplex(st.find({1, 2})); + st.remove_maximal_simplex(st.find({2})); + st.remove_maximal_simplex(st.find({0, 3})); + + BOOST_CHECK(st == st_pruned); + // Remove all, but as the simplex tree is not storing filtration, there is no modification + st.prune_above_filtration(0.0); + BOOST_CHECK(st == st_pruned); + + miniST st_wo_seven; + // FIXME + st_wo_seven.set_dimension(3); + + st_wo_seven.insert_simplex_and_subfaces({0, 1, 6}); + st_wo_seven.insert_simplex_and_subfaces({3, 4, 5}); + // st_wo_seven: + // 1 6 + // o---o + // \X/ + // o o---o + // 0 3\X/4 + // o + // 5 + + // Remove all 7 to test the both remove_maximal_simplex cases (when _members is empty or not) + st.remove_maximal_simplex(st.find({0, 1, 6, 7})); + st.remove_maximal_simplex(st.find({0, 1, 7})); + st.remove_maximal_simplex(st.find({0, 6, 7})); + st.remove_maximal_simplex(st.find({0, 7})); + st.remove_maximal_simplex(st.find({1, 6, 7})); + st.remove_maximal_simplex(st.find({1, 7})); + st.remove_maximal_simplex(st.find({6, 7})); + st.remove_maximal_simplex(st.find({7})); + + BOOST_CHECK(st == st_wo_seven); +} + +BOOST_AUTO_TEST_CASE(prune_above_filtration) { + std::cout << "********************************************************************" << std::endl; + std::cout << "PRUNE ABOVE FILTRATION" << std::endl; + typedef Simplex_tree<> typeST; + typeST st; + + // FIXME + st.set_dimension(3); + + st.insert_simplex_and_subfaces({0, 1, 6, 7}, 1.0); + st.insert_simplex_and_subfaces({3, 4, 5}, 2.0); + + // Constructs a copy at this state for further test purpose + typeST st_pruned = st; + st_pruned.initialize_filtration(); // reset + + st.insert_simplex_and_subfaces({3, 0}, 3.0); + st.insert_simplex_and_subfaces({2, 1, 0}, 4.0); + + // Constructs a copy at this state for further test purpose + typeST st_complete = st; + // st_complete and st: + // 1 6 + // o---o + // /X\7/ + // o---o---o---o + // 2 0 3\X/4 + // o + // 5 + // st_pruned: + // 1 6 + // o---o + // \7/ + // o o---o + // 0 3\X/4 + // o + // 5 + + bool simplex_is_changed = false; + // Check the no action cases + // greater than initial filtration value + simplex_is_changed = st.prune_above_filtration(10.0); + if (simplex_is_changed) + st.initialize_filtration(); + BOOST_CHECK(st == st_complete); + BOOST_CHECK(!simplex_is_changed); + // equal to initial filtration value + simplex_is_changed = st.prune_above_filtration(6.0); + if (simplex_is_changed) + st.initialize_filtration(); + BOOST_CHECK(st == st_complete); + BOOST_CHECK(!simplex_is_changed); + // lower than initial filtration value, but still greater than the maximum filtration value + simplex_is_changed = st.prune_above_filtration(5.0); + if (simplex_is_changed) + st.initialize_filtration(); + BOOST_CHECK(st == st_complete); + BOOST_CHECK(!simplex_is_changed); + + // Display the Simplex_tree + std::cout << "The complex contains " << st.num_simplices() << " simplices"; + std::cout << " - dimension " << st.dimension() << std::endl; + std::cout << "Iterator on Simplices in the filtration, with [filtration value]:" << std::endl; + for (auto f_simplex : st.filtration_simplex_range()) { + std::cout << " " << "[" << st.filtration(f_simplex) << "] "; + for (auto vertex : st.simplex_vertex_range(f_simplex)) { + std::cout << (int) vertex << " "; + } + std::cout << std::endl; + } + + // Check the pruned cases + simplex_is_changed = st.prune_above_filtration(2.5); + if (simplex_is_changed) + st.initialize_filtration(); + BOOST_CHECK(st == st_pruned); + BOOST_CHECK(simplex_is_changed); + + // Display the Simplex_tree + std::cout << "The complex pruned at 2.5 contains " << st.num_simplices() << " simplices"; + std::cout << " - dimension " << st.dimension() << std::endl; + + simplex_is_changed = st.prune_above_filtration(2.0); + if (simplex_is_changed) + st.initialize_filtration(); + + std::cout << "The complex pruned at 2.0 contains " << st.num_simplices() << " simplices"; + std::cout << " - dimension " << st.dimension() << std::endl; + + BOOST_CHECK(st == st_pruned); + BOOST_CHECK(!simplex_is_changed); + + typeST st_empty; + // FIXME + st_empty.set_dimension(3); + simplex_is_changed = st.prune_above_filtration(0.0); + if (simplex_is_changed) + st.initialize_filtration(); + + // Display the Simplex_tree + std::cout << "The complex pruned at 0.0 contains " << st.num_simplices() << " simplices"; + std::cout << " - dimension " << st.dimension() << std::endl; + + BOOST_CHECK(st == st_empty); + BOOST_CHECK(simplex_is_changed); + + // Test case to the limit + simplex_is_changed = st.prune_above_filtration(-1.0); + if (simplex_is_changed) + st.initialize_filtration(); + BOOST_CHECK(st == st_empty); + BOOST_CHECK(!simplex_is_changed); +} + +BOOST_AUTO_TEST_CASE(mini_prune_above_filtration) { + std::cout << "********************************************************************" << std::endl; + std::cout << "MINI PRUNE ABOVE FILTRATION" << std::endl; + typedef Simplex_tree<MyOptions> typeST; + typeST st; + + // FIXME + st.set_dimension(3); + + st.insert_simplex_and_subfaces({0, 1, 6, 7}); + st.insert_simplex_and_subfaces({3, 4, 5}); + st.insert_simplex_and_subfaces({3, 0}); + st.insert_simplex_and_subfaces({2, 1, 0}); + + // st: + // 1 6 + // o---o + // /X\7/ + // o---o---o---o + // 2 0 3\X/4 + // o + // 5 + + st.initialize_filtration(); + + // Display the Simplex_tree + std::cout << "The complex contains " << st.num_simplices() << " simplices" << std::endl; + BOOST_CHECK(st.num_simplices() == 27); + + // Test case to the limit - With these options, there is no filtration, which means filtration is 0 + bool simplex_is_changed = st.prune_above_filtration(1.0); + if (simplex_is_changed) + st.initialize_filtration(); + // Display the Simplex_tree + std::cout << "The complex pruned at 1.0 contains " << st.num_simplices() << " simplices" << std::endl; + BOOST_CHECK(!simplex_is_changed); + BOOST_CHECK(st.num_simplices() == 27); + + simplex_is_changed = st.prune_above_filtration(0.0); + if (simplex_is_changed) + st.initialize_filtration(); + // Display the Simplex_tree + std::cout << "The complex pruned at 0.0 contains " << st.num_simplices() << " simplices" << std::endl; + BOOST_CHECK(!simplex_is_changed); + BOOST_CHECK(st.num_simplices() == 27); + + // Test case to the limit + simplex_is_changed = st.prune_above_filtration(-1.0); + if (simplex_is_changed) + st.initialize_filtration(); + // Display the Simplex_tree + std::cout << "The complex pruned at -1.0 contains " << st.num_simplices() << " simplices" << std::endl; + BOOST_CHECK(simplex_is_changed); + BOOST_CHECK(st.num_simplices() == 0); + + // Display the Simplex_tree + std::cout << "The complex contains " << st.num_simplices() << " simplices" << std::endl; + +} |