MappedSparseMatrix in RcppEigen

Question

I want to use conjugate gradient algorithm implemented in RcppEigen package for solving large sparse matrices.

Since I am new to Rcpp and C++, I just started with the d

Answer 1

You need to use your Eigen::MappedSparseMatrix type in the Eigen::ConjugateGradient function. Try the following code:

#include <RcppEigen.h>

typedef Eigen::MappedSparseMatrix< double > mappedSparseMatrix ;
typedef Eigen::Map< Eigen::VectorXd > mappedVector ;

// [[Rcpp::depends(RcppEigen)]]
// [[Rcpp::export]]
Eigen::VectorXd cgSparse(
    const mappedSparseMatrix A,
    const mappedVector b
) {
    Eigen::ConjugateGradient< mappedSparseMatrix, Eigen::Lower > cg( A ) ;
    return cg.solve( b ) ;
}

Comparing with R's solve() function:

B <- matrix( c( 1, 2, 0, 2, 5, 0, 0, 0, 3  ), 3, 3, TRUE )
b <- c( 5, 1, 7 )
B %*% solve( B, b )
       [,1]
[1,]    5
[2,]    1
[3,]    7

B %*% cgSparse( as( B, 'dgCMatrix' ), b )
     [,1]
[1,]    5
[2,]    1
[3,]    7