void incomplete_qr(int m, int n, const int *Acolstart, const int *Arowindex, const double *Avalue,
double Qdroptol,
const int *Rcolstart, const int *Rrowindex, double *Rvalue, double *Rdiag)
{
// column storage for intermediate Q
std::vector<StaticSparseVector> Q(n);
// for each column of Q, how many more times it will be used in making R
// (once this gets decremented to zero, we can free the column)
std::vector<int> dependency_count(n,0);
for(int i=0; i<n; ++i){
for(int a=Rcolstart[i]; a<Rcolstart[i+1]; ++a){
int j=Rrowindex[a];
if(j<i) ++dependency_count[j];
}
}
// construct R a column at a time
for(int i=0; i<n; ++i){
DynamicSparseVector q;
copy_column(Acolstart[i], Acolstart[i+1], Arowindex, Avalue, q);
for(int a=Rcolstart[i]; a<Rcolstart[i+1]; ++a){
int j=Rrowindex[a];
if(j<i){
Rvalue[a]=dot_product(Q[j], q);
add_to_vector(-Rvalue[a], Q[j], q);
--dependency_count[j];
if(dependency_count[j]==0) Q[j].clear();
}else // j>i
Rvalue[a]=0; // ideally structure of R is upper triangular, so this waste of space won't happen
}
Rdiag[i]=vector_norm(q);
copy_large_entries(q, Qdroptol*Rdiag[i], Q[i]);
normalize(Q[i]);
}
}
constexpr auto is_independent(TSystemSignature ss)
{
return mp::bool_v<(dependency_count(ss) == 0)>;
}
