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#include <cstdlib>
#include <vector>
#include <fstream>
#include <ctime>
#ifdef _OPENMP
#include <omp.h>
#endif
using namespace std;
#include "libnormaliz/libnormaliz.h"
using namespace libnormaliz;
typedef long long Integer;
Cone<Integer> rand_simplex(size_t dim, long bound) {
vector<vector<Integer> > vertices(dim + 1, vector<Integer>(dim));
while (true) { // an eternal loop ...
for (size_t i = 0; i <= dim; ++i) {
for (size_t j = 0; j < dim; ++j)
vertices[i][j] = rand() % (bound + 1);
}
Cone<Integer> Simplex(Type::polytope, vertices);
// we must check the rank and normality
if (Simplex.getRank() == dim + 1 && Simplex.isDeg1HilbertBasis())
return Simplex;
}
vector<vector<Integer> > dummy_gen(1, vector<Integer>(1, 1)); // to make the compiler happy
return Cone<Integer>(Type::cone, dummy_gen);
}
bool exists_jump_over(Cone<Integer>& Polytope, const vector<vector<Integer> >& jump_cands) {
vector<vector<Integer> > test_polytope = Polytope.getExtremeRays();
test_polytope.resize(test_polytope.size() + 1);
for (const auto& jump_cand : jump_cands) {
test_polytope[test_polytope.size() - 1] = jump_cand;
Cone<Integer> TestCone(Type::cone, test_polytope);
if (TestCone.getNrDeg1Elements() != Polytope.getNrDeg1Elements() + 1)
continue;
if (TestCone.isDeg1HilbertBasis())
return true;
}
return false;
}
vector<Integer> lattice_widths(Cone<Integer>& Polytope) {
if (!Polytope.isDeg1ExtremeRays()) {
cerr << "Cone in lattice_widths is not defined by lattice polytope" << endl;
exit(1);
}
vector<Integer> widths(Polytope.getNrExtremeRays());
for (size_t i = 0; i < Polytope.getNrSupportHyperplanes(); ++i) {
widths[i] = 0;
for (size_t j = 0; j < Polytope.getNrExtremeRays(); ++j) {
// v_scalar_product is a useful function from vector_operations.h
Integer test = v_scalar_product(Polytope.getSupportHyperplanes()[i], Polytope.getExtremeRays()[j]);
if (test > widths[i])
widths[i] = test;
}
}
return widths;
}
int main(int argc, char* argv[]) {
time_t ticks;
srand(time(&ticks));
cout << "Seed " << ticks << endl; // we may want to reproduce the run
size_t polytope_dim = 4;
size_t cone_dim = polytope_dim + 1;
long bound = 6;
vector<Integer> grading(cone_dim, 0); // at some points we need the explicit grading
grading[polytope_dim] = 1;
size_t nr_simplex = 0; // for the progress report
while (true) {
#ifdef _OPENMP
omp_set_num_threads(1);
#endif
Cone<Integer> Candidate = rand_simplex(polytope_dim, bound);
nr_simplex++;
if (nr_simplex % 1000 == 0)
cout << "simplex " << nr_simplex << endl;
vector<vector<Integer> > supp_hyps_moved = Candidate.getSupportHyperplanes();
for (auto& i : supp_hyps_moved)
i[polytope_dim] += 1;
Cone<Integer> Candidate1(Type::inequalities, supp_hyps_moved, Type::grading, to_matrix(grading));
if (Candidate1.getNrDeg1Elements() > Candidate.getNrDeg1Elements())
continue; // there exists a point of height 1
cout << "No ht 1 jump"
<< " #latt " << Candidate.getNrDeg1Elements() << endl;
// move the hyperplanes further outward
for (auto& i : supp_hyps_moved)
i[polytope_dim] += polytope_dim;
Cone<Integer> Candidate2(Type::inequalities, supp_hyps_moved, Type::grading, to_matrix(grading));
cout << "Testing " << Candidate2.getNrDeg1Elements() << " jump candidates" << endl;
// including the lattice points in P
if (exists_jump_over(Candidate, Candidate2.getDeg1Elements()))
continue;
cout << "No ht <= 1+dim jump" << endl;
vector<Integer> widths = lattice_widths(Candidate);
for (size_t i = 0; i < supp_hyps_moved.size(); ++i)
supp_hyps_moved[i][polytope_dim] += -polytope_dim + (widths[i]) * (polytope_dim - 2);
vector<vector<mpz_class> > mpz_supp_hyps;
convert(mpz_supp_hyps, supp_hyps_moved);
vector<mpz_class> mpz_grading = convertTo<vector<mpz_class> >(grading);
#ifdef _OPENMP
omp_set_num_threads(4);
#endif
Cone<mpz_class> Candidate3(Type::inequalities, mpz_supp_hyps, Type::grading, to_matrix(mpz_grading));
Candidate3.compute(ConeProperty::Deg1Elements, ConeProperty::Approximate);
vector<vector<Integer> > jumps_cand; // for conversion from mpz_class
convert(jumps_cand, Candidate3.getDeg1Elements());
cout << "Testing " << jumps_cand.size() << " jump candidates" << endl;
if (exists_jump_over(Candidate, jumps_cand))
continue;
cout << "Maximal simplex found" << endl;
cout << "Vertices" << endl;
Candidate.getExtremeRaysMatrix().pretty_print(cout);
cout << "Number of lattice points = " << Candidate.getNrDeg1Elements();
cout << " Multiplicity = " << Candidate.getMultiplicity() << endl;
} // end while
} // end main
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