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#include <vector>
#include <iostream>
#include <cassert>
#include "prettyprint.hpp"
//#include <boost/numeric/ublas/symmetric.hpp>
class binomial_coeff_table {
std::vector<std::vector<int> > B;
int n_max, k_max;
public:
binomial_coeff_table(int n, int k) {
n_max = n;
k_max = k;
B.resize(n + 1);
for( int i = 0; i <= n; i++ ) {
B[i].resize(k + 1);
for ( int j = 0; j <= std::min(i, k); j++ )
{
if (j == 0 || j == i)
B[i][j] = 1;
else
B[i][j] = B[i-1][j-1] + B[i-1][j];
}
}
}
int operator()(int n, int k) const {
// std::cout << "B(" << n << "," << k << ")\n";
return B[n][k];
}
};
template<typename OutputIterator>
OutputIterator get_simplex_vertices( int idx, int dim, int n, const binomial_coeff_table& binomial_coeff, OutputIterator out )
{
--n;
for( int k = dim + 1; k > 0; --k ) {
while( binomial_coeff( n , k ) > idx ) {
--n;
}
*out++ = n;
idx -= binomial_coeff( n , k );
}
return out;
}
template <typename DistanceMatrix>
class rips_filtration_comparator {
private:
std::vector<int> vertices;
const binomial_coeff_table& binomial_coeff;
public:
const DistanceMatrix& dist;
const int dim;
rips_filtration_comparator(const DistanceMatrix& _dist, const int _dim, const binomial_coeff_table& _binomial_coeff): dist(_dist), dim(_dim), vertices(_dim + 1),
binomial_coeff(_binomial_coeff) {};
bool operator()(const int a, const int b)
{
assert(a < binomial_coeff(dist.size(), dim + 1));
assert(b < binomial_coeff(dist.size(), dim + 1));
decltype(dist(0,0)) a_diam = 0, b_diam = 0;
//vertices.clear(); //std::back_inserter(vertices)
get_simplex_vertices(a, dim, dist.size(), binomial_coeff, vertices.begin() );
for (int i = 0; i <= dim; ++i)
for (int j = i + 1; j <= dim; ++j) {
auto d = dist(vertices[i], vertices[j]);
a_diam = std::max(a_diam, dist(vertices[i], vertices[j]));
// std::cout << " i = " << i << " j = " << j << " d = " << d << std::endl;
// std::cout << " a_vertices[i] = " << vertices[i] << " a_vertices[j] = " << vertices[j] << std::endl;
// std::cout << " a_diam = " << a_diam << std::endl;
}
// std::cout << "a_diam = " << a_diam << std::endl;
//vertices.clear(); //std::back_inserter(vertices)
get_simplex_vertices(b, dim, dist.size(), binomial_coeff, vertices.begin() );
for (int i = 0; i <= dim; ++i)
for (int j = i + 1; j <= dim; ++j) {
b_diam = std::max(b_diam, dist(vertices[i], vertices[j]));
if (a_diam < b_diam)
return true;
}
// std::cout << "b_diam = " << b_diam << std::endl;
return (a_diam == b_diam && a <= b);
}
};
template<typename OutputIterator>
void get_simplex_coboundary( int idx, int dim, int n, const binomial_coeff_table& binomial_coeff, OutputIterator coboundary )
{
--n;
int modified_idx = idx;
for( int k = dim + 1; k >= 0 && n >= 0; --k ) {
while( binomial_coeff( n , k ) > idx ) {
// std::cout << "binomial_coeff(" << n << ", " << k << ") = " << binomial_coeff( n , k ) << " > " << idx << std::endl;
*coboundary++ = modified_idx + binomial_coeff( n , k + 1 );
if (n==0) break;
--n;
}
idx -= binomial_coeff( n , k );
modified_idx -= binomial_coeff( n , k );
modified_idx += binomial_coeff( n , k + 1 );
--n;
}
return;
}
class distance_matrix {
public:
typedef double value_type;
std::vector<std::vector<double> > distances;
double operator()(const int a, const int b) const {
return distances[a][b];
}
size_t size() const {
return distances.size();
}
};
int main() {
distance_matrix dist;
dist.distances = {
{0,1,2,3},
{1,0,1,2},
{2,1,0,1},
{3,2,1,0}
};
dist.distances = {
{0,1,1,1,1},
{1,0,1,1,1},
{1,1,0,1,1},
{1,1,1,0,1},
{1,1,1,1,0}
};
binomial_coeff_table binomial_coeff(dist.size(), 4);
std::cout << dist (0,1) << std::endl;
rips_filtration_comparator<distance_matrix> comp1(dist, 1, binomial_coeff);
rips_filtration_comparator<distance_matrix> comp2(dist, 2, binomial_coeff);
std::cout << (comp1(0,1) ? "0<1" : "0>=1") << std::endl;
std::cout << (comp1(1,0) ? "1<0" : "1>=0") << std::endl;
std::cout << (comp1(0,2) ? "0<2" : "0>=2") << std::endl;
std::cout << (comp1(1,2) ? "1<2" : "1>=2") << std::endl;
std::vector<int> edges = {0,1,2,3,4,5};
std::sort(edges.begin(), edges.end(), comp1);
std::cout << "sorted edges: " << edges << std::endl;
std::vector<int> triangles = {0,1,2,3};
std::sort(triangles.begin(), triangles.end(), comp2);
std::cout << "sorted triangles: " << triangles << std::endl;
int dim = 1;
int simplex_index = 2;
std::vector<int> vertices;
get_simplex_vertices( simplex_index, dim, dist.size(), binomial_coeff, std::back_inserter(vertices) );
std::cout << "coboundary of simplex " << vertices << ":" << std::endl;
std::vector<int> coboundary;
get_simplex_coboundary( simplex_index, dim, dist.size(), binomial_coeff, std::back_inserter(coboundary) );
for (int coboundary_simplex_index: coboundary) {
std::vector<int> vertices;
get_simplex_vertices( coboundary_simplex_index, dim + 1, dist.size(), binomial_coeff, std::back_inserter(vertices) );
std::cout << " " << vertices << std::endl;
}
}
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