[This article was first published on Rcpp Gallery, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Two posts showed how to compute eigenvalues using Armadillo and using Eigen. As we also looked at using the
GNU GSL, this post will show how to conpute eigenvalues using GSL.

As mentioned in the previous GSL post, we instantiate C language pointers suitable for GSL (here the matrix `M`). Those must be freed manually, as shown before the `return` statement.

```// [[Rcpp::depends(RcppGSL)]]

#include <RcppGSL.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_eigen.h>

// [[Rcpp::export]]
Rcpp::NumericVector getEigenValues(Rcpp::NumericMatrix sM) {

RcppGSL::matrix<double> M(sM); 	// create gsl data structures from SEXP
int k = M.ncol();

RcppGSL::vector<double> ev(k);  	// instead of gsl_vector_alloc(k);
gsl_eigen_symm_workspace *w = gsl_eigen_symm_alloc(k);
gsl_eigen_symm (M, ev, w);
gsl_eigen_symm_free (w);

// we need to invoke wrap() here to help the compiler, but at least we save a loop
// we also need to create a new Rcpp object as the RcppGSL one needs to be free'd.
Rcpp::NumericVector res(Rcpp::wrap(ev));

M.free();               		// important: GSL wrappers use C structure
ev.free();

return res;				// return results vector
}
```

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)

 14.2100  2.4099  1.6856  0.3319
```

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

```eigen(Z)

\$values
 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
``` 