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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: Square-Root Factor of a Positive-Definite 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 pdFactor {nlme}"><tr><td>pdFactor {nlme}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Square-Root Factor of a Positive-Definite Matrix</h2> <h3>Description</h3> <p>A square-root factor of the positive-definite matrix represented by <code>object</code> is obtained. Letting <i>S</i> denote a positive-definite matrix, a square-root factor of <i>S</i> is any square matrix <i>L</i> such that <i>S = L'L</i>. This function extracts <i>L</i>. </p> <h3>Usage</h3> <pre> pdFactor(object) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>object</code></td> <td> <p>an object inheriting from class <code>pdMat</code>, representing a positive definite matrix, which must have been initialized (i.e. <code>length(coef(object)) > 0</code>).</p> </td></tr> </table> <h3>Value</h3> <p>a vector with a square-root factor of the positive-definite matrix associated with <code>object</code> stacked column-wise. </p> <h3>Note</h3> <p>This function is used intensively in optimization algorithms and its value is returned as a vector for efficiency reasons. The <code>pdMatrix</code> function can be used to obtain square-root factors in matrix form. </p> <h3>Author(s)</h3> <p>José Pinheiro and Douglas Bates <a href="mailto:bates@stat.wisc.edu">bates@stat.wisc.edu</a></p> <h3>References</h3> <p>Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer. </p> <h3>See Also</h3> <p><code><a href="pdMatrix.html">pdMatrix</a></code></p> <h3>Examples</h3> <pre> pd1 <- pdCompSymm(4 * diag(3) + 1) pdFactor(pd1) </pre> <hr /><div style="text-align: center;">[Package <em>nlme</em> version 3.1-139 <a href="00Index.html">Index</a>]</div> </body></html>