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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: Find rank of upper triangular matrix</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 Rrank {mgcv}"><tr><td>Rrank {mgcv}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Find rank of upper triangular matrix</h2> <h3>Description</h3> <p>Finds rank of upper triangular matrix R, by estimating condition number of upper <code>rank</code> by <code>rank</code> block, and reducing <code>rank</code> until this is acceptably low. Assumes R has been computed by a method that uses pivoting, usually pivoted QR or Choleski. </p> <h3>Usage</h3> <pre> Rrank(R,tol=.Machine$double.eps^.9) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>R</code></td> <td> <p>An upper triangular matrix, obtained by pivoted QR or pivoted Choleski.</p> </td></tr> <tr valign="top"><td><code>tol</code></td> <td> <p>the tolerance to use for judging rank.</p> </td></tr> </table> <h3>Details</h3> <p> The method is based on Cline et al. (1979) as described in Golub and van Loan (1996). </p> <h3>Author(s)</h3> <p> Simon N. Wood <a href="mailto:simon.wood@r-project.org">simon.wood@r-project.org</a></p> <h3>References</h3> <p>Cline, A.K., C.B. Moler, G.W. Stewart and J.H. Wilkinson (1979) An estimate for the condition number of a matrix. SIAM J. Num. Anal. 16, 368-375 </p> <p>Golub, G.H, and C.F. van Loan (1996) Matrix Computations 3rd ed. Johns Hopkins University Press, Baltimore. </p> <h3>Examples</h3> <pre> set.seed(0) n <- 10;p <- 5 X <- matrix(runif(n*(p-1)),n,p) qrx <- qr(X,LAPACK=TRUE) Rrank(qr.R(qrx)) </pre> <hr /><div style="text-align: center;">[Package <em>mgcv</em> version 1.8-28 <a href="00Index.html">Index</a>]</div> </body></html>