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#include <stdlib.h>
#include <vector>
#include <fstream>
#ifdef _OPENMP
#include <omp.h>
#endif
using namespace std;
#include "libnormaliz/libnormaliz.h"
#include "libnormaliz/cone.h"
#include "libnormaliz/vector_operations.h"
#include "libnormaliz/cone_property.h"
#include "libnormaliz/integer.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(size_t i=0;i<jump_cands.size();++i){
test_polytope[test_polytope.size()-1]=jump_cands[i];
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(size_t i=0;i<supp_hyps_moved.size();++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(size_t i=0;i<supp_hyps_moved.size();++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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