EVOLUTION-MANAGER
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Albers' example Matrix with "Difficult" Eigen Factorization</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for CAex {Matrix}"><tr><td>CAex {Matrix}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Albers' example Matrix with "Difficult" Eigen Factorization</h2> <h3>Description</h3> <p>An example of a sparse matrix for which <code><a href="../../base/html/eigen.html">eigen</a>()</code> seemed to be difficult, an unscaled version of this has been posted to the web, accompanying an E-mail to R-help (<a href="https://stat.ethz.ch/mailman/listinfo/r-help">https://stat.ethz.ch/mailman/listinfo/r-help</a>), by Casper J Albers, Open University, UK. </p> <h3>Usage</h3> <pre>data(CAex)</pre> <h3>Format</h3> <p>This is a <i>72 * 72</i> symmetric matrix with 216 non-zero entries in five bands, stored as sparse matrix of class <code><a href="dgCMatrix-class.html">dgCMatrix</a></code>. </p> <h3>Details</h3> <p>Historical note (2006-03-30): In earlier versions of <span style="font-family: Courier New, Courier; color: #666666;"><b>R</b></span>, <code><a href="../../base/html/eigen.html">eigen</a>(CAex)</code> fell into an infinite loop whereas <code><a href="../../base/html/eigen.html">eigen</a>(CAex, EISPACK=TRUE)</code> had been okay. </p> <h3>Examples</h3> <pre> data(CAex) str(CAex) # of class "dgCMatrix" image(CAex)# -> it's a simple band matrix with 5 bands ## and the eigen values are basically 1 (42 times) and 0 (30 x): zapsmall(ev <- eigen(CAex, only.values=TRUE)$values) ## i.e., the matrix is symmetric, hence sCA <- as(CAex, "symmetricMatrix") ## and stopifnot(class(sCA) == "dsCMatrix", as(sCA, "matrix") == as(CAex, "matrix")) </pre> <hr /><div style="text-align: center;">[Package <em>Matrix</em> version 1.2-17 <a href="00Index.html">Index</a>]</div> </body></html>