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#include <iostream>
#include <string>
#include <algorithm>
#include <utility> // std::pair, std::make_pair
#include <cmath> // float comparison
#include <limits>
#define BOOST_TEST_DYN_LINK
#define BOOST_TEST_MODULE "betti_numbers"
#include <boost/test/unit_test.hpp>
#include <gudhi/Simplex_tree.h>
#include <gudhi/Persistent_cohomology.h>
struct MiniSTOptions : 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;
};
using Mini_simplex_tree = Gudhi::Simplex_tree<MiniSTOptions>;
using Mini_st_persistence =
Gudhi::persistent_cohomology::Persistent_cohomology<Mini_simplex_tree, Gudhi::persistent_cohomology::Field_Zp>;
/*
* Compare two intervals by dimension, then by length.
*/
template<class Simplicial_complex>
struct cmp_intervals_by_dim_then_length {
explicit cmp_intervals_by_dim_then_length(Simplicial_complex * sc)
: sc_(sc) { }
template<typename Persistent_interval>
bool operator()(const Persistent_interval & p1, const Persistent_interval & p2) {
if (sc_->dimension(get < 0 > (p1)) == sc_->dimension(get < 0 > (p2)))
return (sc_->filtration(get < 1 > (p1)) - sc_->filtration(get < 0 > (p1))
> sc_->filtration(get < 1 > (p2)) - sc_->filtration(get < 0 > (p2)));
else
return (sc_->dimension(get < 0 > (p1)) > sc_->dimension(get < 0 > (p2)));
}
Simplicial_complex* sc_;
};
BOOST_AUTO_TEST_CASE( plain_homology_betti_numbers )
{
Mini_simplex_tree st;
/* Complex to build. */
/* 1 4 */
/* o---o */
/* /3\ / */
/* o---o o */
/* 2 0 5 */
const short tetra0123[] = {0, 1, 2, 3};
const short edge04[] = {0, 4};
const short edge14[] = {1, 4};
const short vertex5[] = {5};
st.insert_simplex_and_subfaces(tetra0123);
st.insert_simplex_and_subfaces(edge04);
st.insert_simplex(edge14);
st.insert_simplex(vertex5);
// Sort the simplices in the order of the filtration
st.initialize_filtration();
// Class for homology computation
Mini_st_persistence pcoh(st);
// Initialize the coefficient field Z/3Z for homology
pcoh.init_coefficients(3);
// 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.
std::clog << "BETTI NUMBERS" << std::endl;
BOOST_CHECK(pcoh.betti_number(0) == 2);
BOOST_CHECK(pcoh.betti_number(1) == 1);
BOOST_CHECK(pcoh.betti_number(2) == 0);
std::vector<int> bns = pcoh.betti_numbers();
BOOST_CHECK(bns.size() == 3);
BOOST_CHECK(bns[0] == 2);
BOOST_CHECK(bns[1] == 1);
BOOST_CHECK(bns[2] == 0);
std::clog << "GET PERSISTENT PAIRS" << std::endl;
// Custom sort and output persistence
cmp_intervals_by_dim_then_length<Mini_simplex_tree> cmp(&st);
auto persistent_pairs = pcoh.get_persistent_pairs();
std::sort(std::begin(persistent_pairs), std::end(persistent_pairs), cmp);
BOOST_CHECK(persistent_pairs.size() == 3);
// persistent_pairs[0] = 2 1 0 inf
BOOST_CHECK(st.dimension(get<0>(persistent_pairs[0])) == 1);
BOOST_CHECK(st.filtration(get<0>(persistent_pairs[0])) == 0);
BOOST_CHECK(get<1>(persistent_pairs[0]) == st.null_simplex());
// persistent_pairs[1] = 2 0 0 inf
BOOST_CHECK(st.dimension(get<0>(persistent_pairs[1])) == 0);
BOOST_CHECK(st.filtration(get<0>(persistent_pairs[1])) == 0);
BOOST_CHECK(get<1>(persistent_pairs[1]) == st.null_simplex());
// persistent_pairs[2] = 2 0 0 inf
BOOST_CHECK(st.dimension(get<0>(persistent_pairs[2])) == 0);
BOOST_CHECK(st.filtration(get<0>(persistent_pairs[2])) == 0);
BOOST_CHECK(get<1>(persistent_pairs[2]) == st.null_simplex());
std::clog << "INTERVALS IN DIMENSION" << std::endl;
auto intervals_in_dimension_0 = pcoh.intervals_in_dimension(0);
std::clog << "intervals_in_dimension_0.size() = " << intervals_in_dimension_0.size() << std::endl;
for (std::size_t i = 0; i < intervals_in_dimension_0.size(); i++)
std::clog << "intervals_in_dimension_0[" << i << "] = [" << intervals_in_dimension_0[i].first << "," <<
intervals_in_dimension_0[i].second << "]" << std::endl;
BOOST_CHECK(intervals_in_dimension_0.size() == 2);
BOOST_CHECK(intervals_in_dimension_0[0].first == 0);
BOOST_CHECK(intervals_in_dimension_0[0].second == std::numeric_limits<Mini_simplex_tree::Filtration_value>::infinity());
BOOST_CHECK(intervals_in_dimension_0[1].first == 0);
BOOST_CHECK(intervals_in_dimension_0[1].second == std::numeric_limits<Mini_simplex_tree::Filtration_value>::infinity());
auto intervals_in_dimension_1 = pcoh.intervals_in_dimension(1);
std::clog << "intervals_in_dimension_1.size() = " << intervals_in_dimension_1.size() << std::endl;
for (std::size_t i = 0; i < intervals_in_dimension_1.size(); i++)
std::clog << "intervals_in_dimension_1[" << i << "] = [" << intervals_in_dimension_1[i].first << "," <<
intervals_in_dimension_1[i].second << "]" << std::endl;
BOOST_CHECK(intervals_in_dimension_1.size() == 1);
BOOST_CHECK(intervals_in_dimension_1[0].first == 0);
BOOST_CHECK(intervals_in_dimension_1[0].second == std::numeric_limits<Mini_simplex_tree::Filtration_value>::infinity());
auto intervals_in_dimension_2 = pcoh.intervals_in_dimension(2);
std::clog << "intervals_in_dimension_2.size() = " << intervals_in_dimension_2.size() << std::endl;
BOOST_CHECK(intervals_in_dimension_2.size() == 0);
}
using Simplex_tree = Gudhi::Simplex_tree<>;
using St_persistence =
Gudhi::persistent_cohomology::Persistent_cohomology<Simplex_tree, Gudhi::persistent_cohomology::Field_Zp>;
BOOST_AUTO_TEST_CASE( betti_numbers )
{
Simplex_tree st;
/* Complex to build. */
/* 1 4 */
/* o---o */
/* /3\ / */
/* o---o o */
/* 2 0 5 */
const short tetra0123[] = {0, 1, 2, 3};
const short edge04[] = {0, 4};
const short edge14[] = {1, 4};
const short vertex5[] = {5};
st.insert_simplex_and_subfaces(tetra0123, 4.0);
st.insert_simplex_and_subfaces(edge04, 2.0);
st.insert_simplex(edge14, 2.0);
st.insert_simplex(vertex5, 1.0);
// Sort the simplices in the order of the filtration
st.initialize_filtration();
// Class for homology computation
St_persistence pcoh(st);
// Initialize the coefficient field Z/3Z for homology
pcoh.init_coefficients(3);
// Compute the persistence diagram of the complex
pcoh.compute_persistent_cohomology();
// Check the Betti numbers are b0=2, b1=1 and b2=0.
BOOST_CHECK(pcoh.betti_number(0) == 2);
BOOST_CHECK(pcoh.betti_number(1) == 1);
BOOST_CHECK(pcoh.betti_number(2) == 0);
// Check the Betti numbers are b0=2, b1=1 and b2=0.
std::vector<int> bns = pcoh.betti_numbers();
BOOST_CHECK(bns.size() == 3);
BOOST_CHECK(bns[0] == 2);
BOOST_CHECK(bns[1] == 1);
BOOST_CHECK(bns[2] == 0);
// Check the persistent Betti numbers in [4., 10.] are b0=2, b1=1 and b2=0.
BOOST_CHECK(pcoh.persistent_betti_number(0, 4., 10.) == 2);
BOOST_CHECK(pcoh.persistent_betti_number(1, 4., 10.) == 1);
BOOST_CHECK(pcoh.persistent_betti_number(2, 4., 10.) == 0);
// Check the persistent Betti numbers in [2., 100.] are b0=2, b1=0 and b2=0.
BOOST_CHECK(pcoh.persistent_betti_number(0, 2., 100.) == 2);
BOOST_CHECK(pcoh.persistent_betti_number(1, 2., 100.) == 0);
BOOST_CHECK(pcoh.persistent_betti_number(2, 2., 100.) == 0);
// Check the persistent Betti numbers in [1., 1000.] are b0=1, b1=0 and b2=0.
BOOST_CHECK(pcoh.persistent_betti_number(0, 1., 1000.) == 1);
BOOST_CHECK(pcoh.persistent_betti_number(1, 1., 1000.) == 0);
BOOST_CHECK(pcoh.persistent_betti_number(2, 1., 1000.) == 0);
// Check the persistent Betti numbers in [.9, 1000.] are b0=0, b1=0 and b2=0.
BOOST_CHECK(pcoh.persistent_betti_number(0, .9, 1000.) == 0);
BOOST_CHECK(pcoh.persistent_betti_number(1, .9, 1000.) == 0);
BOOST_CHECK(pcoh.persistent_betti_number(2, .9, 1000.) == 0);
// Check the persistent Betti numbers in [4.1, 10000.] are b0=2, b1=1 and b2=0.
bns = pcoh.persistent_betti_numbers(4.1, 10000.);
BOOST_CHECK(bns[0] == 2);
BOOST_CHECK(bns[1] == 1);
BOOST_CHECK(bns[2] == 0);
// Check the persistent Betti numbers in [2.1, 100000.] are b0=2, b1=0 and b2=0.
bns = pcoh.persistent_betti_numbers(2.1, 100000.);
BOOST_CHECK(bns[0] == 2);
BOOST_CHECK(bns[1] == 0);
BOOST_CHECK(bns[2] == 0);
// Check the persistent Betti numbers in [1.1, 1000000.] are b0=1, b1=0 and b2=0.
bns = pcoh.persistent_betti_numbers(1.1, 1000000.);
BOOST_CHECK(bns[0] == 1);
BOOST_CHECK(bns[1] == 0);
BOOST_CHECK(bns[2] == 0);
// Check the persistent Betti numbers in [.1, 10000000.] are b0=0, b1=0 and b2=0.
bns = pcoh.persistent_betti_numbers(.1, 10000000.);
BOOST_CHECK(bns[0] == 0);
BOOST_CHECK(bns[1] == 0);
BOOST_CHECK(bns[2] == 0);
// Custom sort and output persistence
cmp_intervals_by_dim_then_length<Simplex_tree> cmp(&st);
auto persistent_pairs = pcoh.get_persistent_pairs();
std::sort(std::begin(persistent_pairs), std::end(persistent_pairs), cmp);
BOOST_CHECK(persistent_pairs.size() == 3);
// persistent_pairs[0] = 2 1 4 inf
BOOST_CHECK(st.dimension(get<0>(persistent_pairs[0])) == 1);
BOOST_CHECK(st.filtration(get<0>(persistent_pairs[0])) == 4);
BOOST_CHECK(get<1>(persistent_pairs[0]) == st.null_simplex());
// persistent_pairs[1] = 2 0 2 inf
BOOST_CHECK(st.dimension(get<0>(persistent_pairs[1])) == 0);
BOOST_CHECK(st.filtration(get<0>(persistent_pairs[1])) == 2);
BOOST_CHECK(get<1>(persistent_pairs[1]) == st.null_simplex());
// persistent_pairs[2] = 2 0 1 inf
BOOST_CHECK(st.dimension(get<0>(persistent_pairs[2])) == 0);
BOOST_CHECK(st.filtration(get<0>(persistent_pairs[2])) == 1);
BOOST_CHECK(get<1>(persistent_pairs[2]) == st.null_simplex());
std::clog << "INTERVALS IN DIMENSION" << std::endl;
auto intervals_in_dimension_0 = pcoh.intervals_in_dimension(0);
std::clog << "intervals_in_dimension_0.size() = " << intervals_in_dimension_0.size() << std::endl;
for (std::size_t i = 0; i < intervals_in_dimension_0.size(); i++)
std::clog << "intervals_in_dimension_0[" << i << "] = [" << intervals_in_dimension_0[i].first << "," <<
intervals_in_dimension_0[i].second << "]" << std::endl;
BOOST_CHECK(intervals_in_dimension_0.size() == 2);
BOOST_CHECK(intervals_in_dimension_0[0].first == 2);
BOOST_CHECK(intervals_in_dimension_0[0].second == std::numeric_limits<Mini_simplex_tree::Filtration_value>::infinity());
BOOST_CHECK(intervals_in_dimension_0[1].first == 1);
BOOST_CHECK(intervals_in_dimension_0[1].second == std::numeric_limits<Mini_simplex_tree::Filtration_value>::infinity());
auto intervals_in_dimension_1 = pcoh.intervals_in_dimension(1);
std::clog << "intervals_in_dimension_1.size() = " << intervals_in_dimension_1.size() << std::endl;
for (std::size_t i = 0; i < intervals_in_dimension_1.size(); i++)
std::clog << "intervals_in_dimension_1[" << i << "] = [" << intervals_in_dimension_1[i].first << "," <<
intervals_in_dimension_1[i].second << "]" << std::endl;
BOOST_CHECK(intervals_in_dimension_1.size() == 1);
BOOST_CHECK(intervals_in_dimension_1[0].first == 4);
BOOST_CHECK(intervals_in_dimension_1[0].second == std::numeric_limits<Mini_simplex_tree::Filtration_value>::infinity());
auto intervals_in_dimension_2 = pcoh.intervals_in_dimension(2);
std::clog << "intervals_in_dimension_2.size() = " << intervals_in_dimension_2.size() << std::endl;
BOOST_CHECK(intervals_in_dimension_2.size() == 0);
std::clog << "EMPTY COMPLEX" << std::endl;
Simplex_tree empty;
empty.initialize_filtration();
St_persistence pcoh_empty(empty, false);
pcoh_empty.init_coefficients(2);
pcoh_empty.compute_persistent_cohomology();
BOOST_CHECK(pcoh_empty.betti_numbers().size() == 0);
BOOST_CHECK(pcoh_empty.persistent_betti_numbers(0,1).size() == 0);
}
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