Rcpp submat from a big sparse matrix - r

Question

I am trying to multiply a vec by a subset of a very big sparse matrix (as the script followed), but it fails to complier when using sourceCpp, it reports error: no matching function for call to ‘arma::SpMat<double>::submat(arma::uvec&, arma::uvec&), it would be much appreciate if someone could do me a favour.
#include <RcppArmadillo.h>
// [[Rcpp::plugins(cpp11)]]
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::export]]
double myf(sp_mat X, vec g, uvec xi){
double u = g(xi).t() * X.submat(xi, xi) * g(xi);
return u;
}

Answer 1

So, as #RalfStubner mentioned, the matrix access for sparse matrices is continuous only. That said, the access approach taken is symmetric for the actual sparse matrix since the same index is being used. So, in this case, it makes sense to revert back to a standard element accessor of (x,y). As a result, the summation reduction can be done with a single loop.
#include <RcppArmadillo.h>
// [[Rcpp::plugins(cpp11)]]
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::export]]
double submat_multiply(const arma::sp_mat& X,
const arma::vec& g, const arma::uvec& xi){
// Add an assertion
if(X.n_rows != g.n_elem) {
Rcpp::stop("Mismatched row and column dimensions of X (%s) and g (%s).",
X.n_rows, g.n_elem);
}
// Reduction
double summed = 0;
for (unsigned int i = 0; i < xi.n_elem; ++i) {
// Retrieve indexing element
arma::uword index_at_i = xi(i);
// Add components together
summed += g(index_at_i) * X(index_at_i, index_at_i) * g(index_at_i);
}
// Return result
return summed;
}
Another approach, but potentially more costly, would be to extract out the diagonal of the sparse matrix and convert it to a dense vector. From there apply an element-wise multiplication and summation.
#include <RcppArmadillo.h>
// [[Rcpp::plugins(cpp11)]]
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::export]]
double submat_multiply_v2(const arma::sp_mat& X,
const arma::vec& g, const arma::uvec& xi){
// Add an assertion
if(X.n_rows != g.n_elem) {
Rcpp::stop("Mismatched row and column dimensions of X (%s) and g (%s).",
X.n_rows, g.n_elem);
}
// Copy sparse diagonal to dense vector
arma::vec x_diag(X.diag());
// Obtain the subset
arma::vec g_sub = g.elem(xi);
// Perform element-wise multiplication and then sum.
double summed = arma::sum(g_sub % x_diag.elem(xi) % g_sub);
// Return result
return summed;
}
Test code:
# Sparse matrix
library(Matrix)
i <- c(1,4:8,10); j <- c(2, 9, 6:10); x <- 7 * (1:7)
X <- sparseMatrix(i, j, x = x)
X
# 10 x 10 sparse Matrix of class "dgCMatrix"
#
# [1,] . 7 . . . . . . . .
# [2,] . . . . . . . . . .
# [3,] . . . . . . . . . .
# [4,] . . . . . . . . 14 .
# [5,] . . . . . 21 . . . .
# [6,] . . . . . . 28 . . .
# [7,] . . . . . . . 35 . .
# [8,] . . . . . . . . 42 .
# [9,] . . . . . . . . . .
# [10,] . . . . . . . . . 49
# Vector
g <- 1:10
# Indices
xi <- c(0, 3, 4, 9)
# Above function
submat_multiply(X, g, xi)
# [1] 4900
submat_multiply_v2(X, g, xi)
# [1] 4900