RcppEigen LLT resulted in a vector of NaN - eigen

Question

I am trying the below RcppEigen function to solve a linear model. It compiled with no error but when I am applying it in R, it gave a vector of NaN values. I tried similar script with C++ without R and it worked perfectly. Any suggestions?
// [[Rcpp::depends(RcppEigen)]]
// [[Rcpp::plugins("cpp11")]]
#include <RcppEigen.h>
#include <Rcpp.h>
#include <Eigen/Dense>
using namespace std;
using namespace Eigen;
using namespace Rcpp;
// [[Rcpp::export]]
SEXP LLtSolve(const MatrixXd A, const MatrixXd b) {
LLT<MatrixXd> llt;
llt.compute(A);
return Rcpp::wrap(llt.solve(b));
}
An example R code:
library(Rcpp)
sourceCpp("Functions.cpp") # contains the previous LLtSolve function
n=1000
A=matrix(rnorm(n*n),nrow=n,ncol=n)
b=matrix(rnorm(n),nrow=n,ncol=1)
xxx=Sys.time()
f=LLtSolve(A,b)
Sys.time()-xxx
f[1:4]

Answer 1

Your code works if you reduce n. For example:
> set.seed(42)
> n=500
> A=matrix(rnorm(n*n),nrow=n,ncol=n)
> b=matrix(rnorm(n),nrow=n,ncol=1)
> f=LLtSolve(A,b)
> min(f)
[1] -1.40086e+300
> max(f)
[1] 1.757129e+300
However, the minimum and maximum values are already quite extreme. When you increase the problem size further, you will reach the point where the result is no longer representable as a double:
> .Machine$double.xmax
[1] 1.797693e+308
> .Machine$double.xmin
[1] 2.225074e-308
This is not the case for a sparse matrix, e.g.:
// [[Rcpp::depends(RcppEigen)]]
#include <RcppEigen.h>
#include <Eigen/SparseLU>
using namespace Eigen;
// [[Rcpp::export]]
MatrixXd SparseSolve(const SparseMatrix<double>& A, const MatrixXd& b) {
SparseLU<SparseMatrix<double> > solver;
solver.compute(A);
if(solver.info()!=Success) {
Rcpp::stop("decomposition failed");
}
MatrixXd x = solver.solve(b);
if(solver.info()!=Success) {
Rcpp::stop("solving failed");
}
return x;
}
/*** R
set.seed(42)
n <- 10000
A <- Matrix::rsparsematrix(n, n, density = 0.2)
b <- matrix(rnorm(n), nrow = n, ncol = 1)
system.time(f <- SparseSolve(A,b))
f[1:4]
*/
Result:
> set.seed(42)
> n <- 10000
> A <- Matrix::rsparsematrix(n, n, density = 0.2)
> b <- matrix(rnorm(n), nrow = n, ncol = 1)
> system.time(f <- SparseSolve(A,b))
user system elapsed
80.640 0.524 81.163
> f[1:4]
[1] -1.5994258 -0.6987579 1.3042338 0.1084376