2013-01-11-eigen-eigenvalues.md

title	author	license	tags	summary	layout	src
Using Eigen for eigenvalues	Dirk Eddelbuettel	GPL (>= 2)	eigen matrix	This example shows how to compute eigenvalues using Eigen	post	2013-01-11-eigen-eigenvalues.cpp

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.

{% highlight cpp %} #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 M) { SelfAdjointEigenSolver es(M); return es.eigenvalues(); } {% endhighlight %}

We can illustrate this easily via a random sample matrix.

{% highlight r %} set.seed(42) X <- matrix(rnorm(44), 4, 4) Z <- X %% t(X)

getEigenValues(Z) {% endhighlight %}

[1]  0.3319  1.6856  2.4099 14.2100

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

{% highlight r %} eigen(Z) {% endhighlight %}

$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.