[Rcpp-devel] RcppEigen: Avoiding accessing elements with coeff(i, j) in sparse matrix

[Søren Højsgaard]

Dear all, 
I have a large sparse adjacency matrix X for an undirected graph. For a subset 'idx' of the vertices I want to find out if the subgraph defined by this subset is complete (i.e. has edges between all variables). So in R, one would check if X[idx,idx] has only ones outside the diagonal, but this is slow and I want to do it with Rcpp. Here is one attempt where I simply add up the elements above (or below) the diagonal, and to access the elements of X I use coeff which is relatively slow (because X is a sparse matrix).

#include <RcppEigen.h>
typedef Eigen::MappedSparseMatrix<double> MSpMat;
typedef Eigen::SparseVector<double> SpVec;
typedef SpVec::InnerIterator InIter;

//[[Rcpp::export]]
double foo (MSpMat X, Eigen::VectorXi idx){
  SpVec sidx = idx.sparseView();
  double out=0;
  int i2, j2;
  for (InIter i_(sidx); i_; ++i_){
    i2 = i_.index(); 
    for (InIter j_(sidx); j_; ++j_){
      j2 = j_.index(); 
      if (i2>j2)
	out += X.coeff( i2, j2);
    }
  }
  return out;
}

/*** R
library(Matrix)
M1 <- new("dgCMatrix"
    , i = c(1L, 2L, 3L, 0L, 2L, 3L, 0L, 1L, 3L, 0L, 1L, 2L, 4L, 5L, 3L, 5L, 3L, 4L)
    , p = c(0L, 3L, 6L, 9L, 14L, 16L, 18L)
    , Dim = c(6L, 6L)
    , Dimnames = list(c("a", "b", "c", "d", "e", "f"), c("a", "b", "c", "d", "e", "f"))
    , x = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
    , factors = list()
)
M1 

foo(M1, c(2,3,4))

*/
Can anyone see a better way of doing this? 

I was thinking about whether the sparse matrix iterators could be a solution, but I can't a hold on it. I was also thinking about using sparse matrices in RcppArmadillo, but I guess the problem (speed) is the same (haven't tried!).

Any advice will be greatly appreciated.
Cheers
Søren