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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: Finding stable orthogonal re-parameterization of the square...</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 gam.reparam {mgcv}"><tr><td>gam.reparam {mgcv}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Finding stable orthogonal re-parameterization of the square root penalty.</h2> <h3>Description</h3> <p>INTERNAL function for finding an orthogonal re-parameterization which avoids "dominant machine zero leakage" between components of the square root penalty. </p> <h3>Usage</h3> <pre> gam.reparam(rS, lsp, deriv) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>rS</code></td> <td> <p>list of the square root penalties: last entry is root of fixed penalty, if <code>fixed.penalty==TRUE</code> (i.e. <code>length(rS)>length(sp)</code>). The assumption here is that <code>rS[[i]]</code> are in a null space of total penalty already; see e.g. <code>totalPenaltySpace</code> and <code>mini.roots</code>.</p> </td></tr> <tr valign="top"><td><code>lsp</code></td> <td> <p>vector of log smoothing parameters.</p> </td></tr> <tr valign="top"><td><code>deriv</code></td> <td> <p>if <code>deriv==1</code> also the first derivative of the log-determinant of the penalty matrix is returned, if <code>deriv>1</code> also the second derivative is returned.</p> </td></tr> </table> <h3>Value</h3> <p>A list containing </p> <ul> <li><p><code>S</code>: the total penalty matrix similarity transformed for stability. </p> </li> <li><p><code>rS</code>: the component square roots, transformed in the same way. </p> </li> <li><p><code>Qs</code>: the orthogonal transformation matrix <code>S = t(Qs)%*%S0%*%Qs</code>, where <code>S0</code> is the untransformed total penalty implied by <code>sp</code> and <code>rS</code> on input. </p> </li> <li><p><code>det</code>: log|S|. </p> </li> <li><p><code>det1</code>: dlog|S|/dlog(sp) if <code>deriv >0</code>. </p> </li> <li><p><code>det2</code>: hessian of log|S| wrt log(sp) if <code>deriv>1</code>. </p> </li></ul> <h3>Author(s)</h3> <p>Simon N. Wood <simon.wood@r-project.org>. </p> <hr /><div style="text-align: center;">[Package <em>mgcv</em> version 1.8-28 <a href="00Index.html">Index</a>]</div> </body></html>