new post on Eigen for eigenvalues

Author: eddelbuettel

_posts/2013-01-11-eigen-eigenvalues.md

@@ -0,0 +1,77 @@
+---
+title: Using Eigen for eigenvalues
+author: Dirk Eddelbuettel
+license: GPL (>= 2)
+tags: eigen matrix
+summary: This example shows how to compute eigenvalues using Eigen
+layout: post
+src: 2013-01-11-eigen-eigenvalues.cpp
+---
+
+[A previous post](../armadillo-eigenvalues) showed how to compute 
+eigenvalues using the [Armadillo](http://arma.sf.net) library via RcppArmadillo.
+
+Here, we do the same using [Eigen](http://eigen.tuxfamily.org) 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<MatrixXd> M) {
+    SelfAdjointEigenSolver<MatrixXd> es(M);
+    return es.eigenvalues();
+}
+{% endhighlight %}
+
+
+We can illustrate this easily via a random sample matrix.
+
+{% highlight r %}
+set.seed(42)
+X <- matrix(rnorm(4*4), 4, 4)
+Z <- X %*% t(X)
+
+getEigenValues(Z)
+{% endhighlight %}
+
+
+
+<pre class="output">
+[1]  0.3319  1.6856  2.4099 14.2100
+</pre>
+
+
+In comparison, R gets the same results (in reverse order) and also returns the eigenvectors.
+
+{% highlight r %}
+eigen(Z)
+{% endhighlight %}
+
+
+
+<pre class="output">
+$values
+[1] 14.2100  2.4099  1.6856  0.3319
+
+$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
+</pre>
+
+
+Eigen has other _a lot_ of other decompositions, see [its documentation](http://eigen.tuxfamily.org/) 
+for more details.

src/2013-01-11-eigen-eigenvalues.cpp

@@ -0,0 +1,56 @@
+// -*- mode: C++; c-indent-level: 4; c-basic-offset: 4; indent-tabs-mode: nil; -*-
+/**
+ * @title Using Eigen for eigenvalues
+ * @author Dirk Eddelbuettel
+ * @license GPL (>= 2)
+ * @tags eigen matrix
+ * @summary This example shows how to compute eigenvalues using Eigen
+ *
+
+ * [A previous post](../armadillo-eigenvalues) showed how to compute 
+ * eigenvalues using the [Armadillo](http://arma.sf.net) library via RcppArmadillo.
+ *
+ * Here, we do the same using [Eigen](http://eigen.tuxfamily.org) 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.
+ */
+
+/*** R
+set.seed(42)
+X <- matrix(rnorm(4*4), 4, 4)
+Z <- X %*% t(X)
+
+getEigenValues(Z)
+*/
+
+/**
+ * In comparison, R gets the same results (in reverse order) and also returns the eigenvectors.
+ */
+
+/*** R
+eigen(Z)
+*/
+
+/** 
+ * Eigen has other _a lot_ of other decompositions, see [its documentation](http://eigen.tuxfamily.org/) 
+ * for more details.
+ */