# Using Eigen for eigenvalues

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A previous post showed how to compute eigenvalues using the Armadillo library via RcppArmadillo.

Here, we do the same using Eigen and the RcppEigen package.

#include <RcppEigen.h> // [[Rcpp::depends(RcppEigen)]] using Eigen::Map; // 'maps' rather than copies using Eigen::MatrixXd; // variable size matrix, double precision using Eigen::VectorXd; // variable size vector, double precision using Eigen::SelfAdjointEigenSolver; // one of the eigenvalue solvers // [[Rcpp::export]] VectorXd getEigenValues(Map<MatrixXd> M) { SelfAdjointEigenSolver<MatrixXd> es(M); return es.eigenvalues(); }

We can illustrate this easily via a random sample matrix.

set.seed(42) X <- matrix(rnorm(4*4), 4, 4) Z <- X %*% t(X) getEigenValues(Z) [1] 0.3319 1.6856 2.4099 14.2100

In comparison, R gets the same results (in reverse order) and also returns the eigenvectors.

eigen(Z) $values [1] 14.2100 2.4099 1.6856 0.3319 $vectors [,1] [,2] [,3] [,4] [1,] 0.69988 -0.55799 0.4458 -0.00627 [2,] -0.06833 -0.08433 0.0157 0.99397 [3,] 0.44100 -0.15334 -0.8838 0.03127 [4,] 0.55769 0.81118 0.1413 0.10493

Eigen has other *a lot* of other decompositions, see its documentation for more details.

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