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 dense matrices.

    // [[Rcpp::depends(RcppEigen)]]
    #include <Rcpp.h>
    #include <RcppEigen.h>
    #include <Eigen/IterativeLinearSolvers>
    using Eigen::SparseMatrix;
    using Eigen::MappedSparseMatrix;
    using Eigen::Map;
    using Eigen::MatrixXd;
    using Eigen::VectorXd;
    using Rcpp::as;
    using Eigen::ConjugateGradient;
    typedef Eigen::MappedSparseMatrix<double> MSpMat;

    // [[Rcpp::export]]
    VectorXd getEigenValues(SEXP As, SEXP bs) {
    const Map<MatrixXd> A(as<Map<MatrixXd> > (As));
    const Map<VectorXd> b(as<Map<VectorXd> > (bs));
    ConjugateGradient<MatrixXd> cg;
    cg.compute(A);
    VectorXd x=cg.solve(b);
    return x;
    }

This works as expected. Therefore, I thought to extend this to suit to sparse matrices.

   // [[Rcpp::depends(RcppEigen)]]
   #include <Rcpp.h>
   #include <RcppEigen.h>
   #include <Eigen/IterativeLinearSolvers>
   using Eigen::SparseMatrix;
   using Eigen::MappedSparseMatrix;
   using Eigen::Map;
   using Eigen::MatrixXd;
   using Eigen::VectorXd;
   using Rcpp::as;
   using Eigen::ConjugateGradient;
   typedef Eigen::MappedSparseMatrix<double> MSpMat;

   // [[Rcpp::export]]
   VectorXd getEigenValues(SEXP As, SEXP bs) {
   const MSpMat A = as<MSpMat>(As);
   const Map<VectorXd> b(as<Map<VectorXd> > (bs));
   ConjugateGradient<SparseMatrix<double> > cg;
   cg.compute(A);
   VectorXd x=cg.solve(b);
   return x;
   }

However, this tends to give really strange results. The code in itself is also not giving any errors. Hope someone could help me to correct this error.

Thanks.

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